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https://vimeo.com/channels/aeexpressions | 1,537,604,476,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267158205.30/warc/CC-MAIN-20180922064457-20180922084857-00112.warc.gz | 649,083,855 | 22,688 | 1. A simple expression to make a wheel spin in relation to the horizontal position.
If you have a Null object called "wheel controller" to animate the X position, the expression on your wheel layer would look like this:
circ = (width*(scale[0]/100)) * 3.1416;
360/circ *thisComp.layer("wheel controller").transform.position[0];
Note: The wheel should be a child of "wheel controller"
2. Basic Wiggle that can be applied to the position, scale, opacity ....
the code is built as Wiggle(A,B)
A= Frequency(x times per secondes)
B= Amplitude in pixel
as here for example applied on the position
wiggle(5,25)
3. Inertial Bounce
can be put on the scale, position ... and creates this bounce as when a ball hit the ground
n = 0;
if (numKeys > 0){
n = nearestKey(time).index;
if (key(n).time > time){
n--;
}
}
if (n == 0){
t = 0;
}else{
t = time - key(n).time;
}
if (n > 0){
v = velocityAtTime(key(n).time - thisComp.frameDuration/15);
amp = .05;
freq = 4;
decay = 8;
value + v*amp*Math.sin(freq*t*2*Math.PI)/Math.exp(decay*t);
}else{
value;
}
Watch Out for some reason, the enter (=go to next line) are replaced by ? sign that is not understood by AE, so be sure to delete the ? mark to have the expression working
otherwise here is the a version without enter
n = 0;if (numKeys > 0){n = nearestKey(time).index;if (key(n).time > time){n--;}}if (n == 0){t = 0;}else{t = time - key(n).time;}if (n > 0){v = velocityAtTime(key(n).time - thisComp.frameDuration/15);amp = .05;freq = 4;decay = 8;value + v*amp*Math.sin(freq*t*2*Math.PI)/Math.exp(decay*t);}else{value;}
4. Add twice the effect "Slider Control", call one "freq" and the other "amount"
When you add the wiggle expressions, connect the amount to "amount" and the frequency to the other one:
wiggle(effect("freq")("Slider"), effect("amount")("Slider"))
Now you can keyframe the sliders and start and stop and manipulate the wiggle.
5. It is applied to the OPACITY of the layer. It picks a random number for the opacity value the layer only some of the time, based on whether another random number ("probability") is less than or equal to 1. You can change the likelyhood of a random opacity being selected by changing the value of "probability."
The rest of the time the opacity is set to the value of "opacity_normal" which is set to 100 by default.
This concept be easily adaptable to other times when you only want something to happen some of the time by using the if...else operators. For example - you could apply something similar to the position or rotation of a layer and it would hop around some of the time.
//applyTo: opacity
// HIGHER values for probability make a random opacity LESS likely.
// A value of 1 will always create a random opacity, a value of 2 will
// create a random opacity 50% of the time, value of 4 will be 25%, etc.
probability = 6;
// "opacity_normal" is the value set for opacity when the a random opacity is NOT chosen.
opacity_normal = 100;
x = random(probability);
if (x);
# After Effects Expressions Library
Coline Brun-Naujalis
A library of After Effects expressions to make animation easier. If you have any expression you would like to see in the channel, drop me a mail and I should do something about it.
#### Shout Box
Heads up: the shoutbox will be retiring soon. It’s tired of working, and can’t wait to relax. You can still send a message to the channel owner, though!
Channels are a simple, beautiful way to showcase and watch videos. Browse more Channels. | 909 | 3,477 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2018-39 | latest | en | 0.755854 |
http://fastfix.my/?exam=video/how-to-create-and-read-scatter-plots/ | 1,610,732,029,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703495936.3/warc/CC-MAIN-20210115164417-20210115194417-00321.warc.gz | 38,074,079 | 30,963 | ### Lean Six Sigma Green Belt
Course
Time
9 hours 53 minutes
Difficulty
Intermediate
CEU/CPE
10
### Video Transcription
00:00
Hi, guys. Welcome back. I'm Katherine MacGyver, and this is lean six Sigma Green Belt, and we're going to pick up where we left off on regression analysis.
00:09
So what we're gonna do today is we're gonna have an introduction to scatter plots were gonna understand how to create them and understand how to read them.
00:18
The first step in regression analysis is creating a scatter plot. This will give you a two fold one. It will allow you to read the relationship between the data visually
00:33
and to You'll be able to then do your regression analysis,
00:38
which will formulaic Lee give you that relationship. So
00:44
a scatter plot
00:46
is an X Y graph. You have two measurements. You always have your X and your Y variables. And from that you will be able to create a single point on a Cartesian system. Remember that from middle school
01:06
that will give you a measurement of that data element.
01:10
So
01:11
as you read scatter plots, a upward slant to the right is a positive relationship. A downward slant to the right, so we're gonna read from left to right is a negative relationship.
01:29
We will notice from the okay, Cuba data.
01:32
Um, that you are more likely to receive messages if you are measured as more attractive. Eso there is our relationship. Your dependent variable is going to be your Why access in the OK, Cupid's case. It is the number of messages received
01:53
01:55
is your X axis. And in case of OK, cupid is going to be measured. Attractiveness. So as you are measured as more attractive, you are going to receive more messages.
02:10
If this were a negative relationship as you are measured as more attractive, you will receive less messages.
02:20
Um, this is important for us to know both directions of the relationship because remember, our independent variables are the variables we can change. Our dependent variables are the ones that were looking to change or our process outputs.
02:34
So independent variable. How maney work orders dependent variable. How long does it take us to complete those work orders? So when we're creating a scatter plot in Excel, remember that
02:46
we like excel because almost everybody has it in excel. You're going to want to capture your two data sets as columns eso the the two data sets that we're looking at here is the year our presidents were born and the year they were elected.
03:05
So two columns that you're going to select both of them.
03:07
You're going to click insert graph and you're going to insert a scatter plot. It is going to give you a graph like we are looking at right now. And what I can tell you by looking at this is that there is a pretty good relationship from the year that the president was born and the year that they were elected, we could
03:28
determine that if you were,
03:30
you were probably not gonna be elected before you were born. So we see no negative relationships. And honestly, if we look at it, the data is pretty tightly clustered. Which tells us that there is pretty. There's a lot of consistency between those relationship, So this is a really nice scatter plot to review
03:49
because it's very clear we're looking at a positive
03:52
or a strongly positive result between our presidents, year of birth and the year they were elected.
04:00
So
04:01
today we did an overview of our scatter plots. You know that your dependent is your y variable. Your independent is your ex variable and two created an excel. It's Azizi is click, click, Click. So you're going to go ahead and capture your data, Create your scatter plot, and you're gonna take a visual sniff test and see.
04:21
Yeah, presidents are probably not going to be elected to office before they're born, So a positive relationship makes sense.
04:30
Our next module, we're gonna go into more in depth. We're gonna actually do our correlation analysis, so I will see you guys there.
### Lean Six Sigma Green Belt
This Six Sigma Green Belt course teaches students how and where to apply the Six Sigma process improvement methodologies. Upon completing the course, students will have the skills and knowledge to pass the Six Sigma Green Belt certification exam.
### Instructed By
Kathryn McIver
Lead Instructor at Evidence-Based Management Association
Instructor | 1,013 | 4,389 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2021-04 | latest | en | 0.966693 |
https://www.ohare-airport.org/how-do-you-find-the-prevalence-of-a-confidence-interval/ | 1,680,003,432,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296948858.7/warc/CC-MAIN-20230328104523-20230328134523-00201.warc.gz | 992,027,272 | 8,977 | ## How do you find the prevalence of a confidence interval?
To calculate the confidence interval, we must find p′, q′. p′ = 0.842 is the sample proportion; this is the point estimate of the population proportion. Since the requested confidence level is CL = 0.95, then α = 1 – CL = 1 – 0.95 = 0.05 ( α 2 ) ( α 2 ) = 0.025.
How do you calculate the prevalence ratio?
For example, if 80 out of 100 exposed subjects have a particular disease and 50 out of 100 non-exposed subjects have the disease, then the odds ratio (OR) is (80/20)/(50/50) = 4. However, the prevalence ratio (PR) is (80/100)/(50/100) = 1.6.
How do you calculate a 95% confidence interval for a ratio?
SD[ln(IR)] = (1/2 + 1/8)^0.5 = 0.7912 Finally, we can calculate the 95% limits of the rate ratio: =exp[ln(0.1097) ± 1.96(0.7912)] = 0.0233, 0.5172 Therefore the rate ratio and its 95% confidence interval is: 0.11 (0.02 to 0.52).
### What does RR 95% CI mean?
Relative risk is calculated in prospective studies Relative risk with 95% confidence interval is the inferential statistic used in prospective cohort and randomized controlled trials. With relative risk, the width of the confidence interval is the inference related to the precision of the treatment effect.
Why prevalence is a ratio?
The prevalence of a health outcome is simply the proportion of individuals with the health outcome in a population. The PR is similar to a RR when the outcome occurs over a short period of time. For example, one would calculate a prevalence ratio for an acute outbreak of tuberculosis in a prison population.
Is prevalence expressed as a ratio?
In science, prevalence describes a proportion (typically expressed as a percentage). For example, the prevalence of obesity among American adults in 2001 was estimated by the U. S. Centers for Disease Control (CDC) at approximately 20.9%.
#### What is odds ratio and confidence interval?
An odds ratio is a measure of association between the presence or absence of two properties. The value of the odds ratio tells you how much more likely someone under 25 might be to make a claim, for example, and the associated confidence interval indicates the degree of uncertainty associated with that ratio.
What is rate vs ratio?
A ratio is a comparison of two numbers. A ratio can be written using a colon, 3:5 , or as a fraction 35 . A rate , by contrast, is a comparison of two quantities which can have different units. For example 5 miles per 3 hours is a rate, as is 34 dollars per square foot.
What does an odds ratio of 2.5 mean?
If odds ratio is 2.5, then there is a 2.5 times higher likelihood of having the outcome compared to the comparison group. Here the odds ratio would be 0.80. The odds ratio also shows the strength of the association between the variable and the outcome.
## How do you know if odds ratio is statistically significant?
If the p-value is equal to or less than a predetermined cutoff (usually 0.05, or a 5 in 100 probability that the finding is due to chance alone), the association is said to be statistically significant. If it is greater than the predetermined cutoff, the association is said to be not statistically significant.
How do you find the prevalence of a confidence interval? To calculate the confidence interval, we must find p′, q′. p′ = 0.842 is the sample proportion; this is the point estimate of the population proportion. Since the requested confidence level is CL = 0.95, then α = 1 – CL = 1 – 0.95… | 846 | 3,473 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.46875 | 4 | CC-MAIN-2023-14 | latest | en | 0.904238 |
https://www.physicsforums.com/threads/questions-on-metric-spaces.995969/ | 1,685,683,915,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224648322.84/warc/CC-MAIN-20230602040003-20230602070003-00262.warc.gz | 1,030,261,395 | 16,814 | Questions on metric spaces
• I
• trees and plants
trees and plants
Hello. The questions i make here in this thread are basically about like explanations of topics on metric spaces. We know about compactness, completeness, connectedness, separatedness, total boundedness of metric spaces. I know that continuity of the real line means that it has no gaps. What could we say about the properties of the metric spaces i described above in the spirit of the description of the continuity of the real line? I am not talking about the definition which is an abstraction, i am talking about the application of the definition like above in the real line. Thank you.
Answers and Replies
The connected and compact subset of the real numbers can be characterised as follows:
Connected subset of the real line = interval
Compact set = closed + bounded subset (Heine Borel theorem).
What is your definition of "separated metric space" or what do you mean when talking about separatedness?
The connected and compact subset of the real numbers can be characterised as follows:
Connected subset of the real line = interval
Compact set = closed + bounded subset (Heine Borel theorem).
What is your definition of "separated metric space" or what do you mean when talking about separatedness?
Thank you. I am sorry i made mistakes. The correct are separable and separability not what i wrote. What about completeness( if i remember correctly it is about sequences, cauchy sequences, convergence)
Last edited by a moderator:
Thank you. I am sorry i made mistakes. The correct are separable and separability not what i wrote. What about completeness( if i remember correctly it is about sequences, cauchy sequences, convergence)
Every subset of the reals is separable. A subset of the reals is complete if and only it is closed.
I have another question but is a little off topic I think. Is C which is the set of complex numbers equipped with the metric that is related to the norm, d(x,y)=llx-yll2=√((x1-x0)2+(y1-y2)2), where x=(x1,x2), y=(y1,y2) a metric space? Is it separable? Is it complete if and only if it is closed? Excuse me if these questions have as answer no.
I have another question but is a little off topic I think. Is C which is the set of complex numbers equipped with the metric that is related to the norm, d(x,y)=llx-yll2=√((x1-x0)2+(y1-y2)2), where x=(x1,x2), y=(y1,y2) a metric space? Is it separable? Is it complete if and only if it is closed? Excuse me if these questions have as answer no.
Yes, it is a metric space. It is separable. Can you think of a countable dense subset? Hint: Use density of ##\Bbb{Q}## in ##\Bbb{R}##. It is definitely complete, because ##\mathbb{R}## is complete. Asking that it is closed makes little sense because every topological space is automatically closed in itself.
Yes, it is a metric space. It is separable. Can you think of a countable dense subset? Hint: Use density of ##\Bbb{Q}## in ##\Bbb{R}##. It is definitely complete, because ##\mathbb{R}## is complete. Asking that it is closed makes little sense because every topological space is automatically closed in itself.
Thank you, perhaps the answer is that ℚ2 is dense in ℝ2? and because ℝ2 is homeomorphic to ℂ then ℚ2 is dense in ℂ?
member 587159
Thank you, perhaps the answer is that ℚ2 is dense in ℝ2? and because ℝ2 is homeomorphic to ℂ then ℚ2 is dense in ℂ?
Yes, that's exactly it!
Yes, that's exactly it!
Oh, i answered it correctly.
member 587159 | 855 | 3,472 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.796875 | 4 | CC-MAIN-2023-23 | latest | en | 0.920863 |
https://ktane.timwi.de/HTML/Epic%20Shapes.html | 1,696,129,370,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510734.55/warc/CC-MAIN-20231001005750-20231001035750-00590.warc.gz | 390,984,633 | 2,297 | ## On the Subject of Epic Shapes
Geometry but Cooler.
• The module has 3 buttons, each with a number.
• Each button must be clicked a certain number of times.
• The display contains two figures.
• The button order is from left to right.
• After clicking the buttons the correct number of times, submit it to disarm the module.
In the manual, you will have to use X, Y, Z, etc. and replace them with numbers that will be used to solve the module.
Red Background If the bigger shape is a star, then x = 3. Otherwise, if the bigger shape is a square, then x = 1. Otherwise, if the bigger shape is a pentagon, then x = 6. Otherwise, x = 2. Blue Background If the bigger shape is a star, then x = 2. Otherwise, if the bigger shape is a square, then x = 5. Otherwise, if the bigger shape is a pentagon, then x = 4. Otherwise, x = 1. Green Background If the bigger shape is a star, then x = 1. Otherwise, if the bigger shape is a square, then x = 3. Otherwise, if the bigger shape is a pentagon, then x = 2. Otherwise, x = 6. Other Background If the bigger shape is a star, then x = 4. Otherwise, if the bigger shape is a square, then x = 2. Otherwise, if the bigger shape is a pentagon, then x = 1. Otherwise, x = 3.
When the X value is assigned, go to “Small Figure Types.”
## Small Figure Types
• Recognize the smaller shape and assign the Y value based on it.
• Keep in mind that shapes can be rotated and filled inside.
• If the smaller figure is a square and it’s not filled in, then y = 2.
• Otherwise, if the smaller figure is a pentagon, it is rotated normally and it is filled in, then y = 5.
• Otherwise, if the smaller figure is a star and it is filled in, then y = 1.
• Otherwise, if the smaller figure is a square and it is filled in, then y = 4.
• Otherwise, y = 6.
When the Y value is assigned, go to “Buttons.”
## Buttons
• Use the numbers on the buttons to assign the Z value.
• Get the first button number and assign it as A.
• Get the second button number and assign it as B.
• If A is greater than B, then perform A-B. Otherwise, perform B-A.
• Assign the resulting number from the previous calculation as D.
• Get the third button number and assign it as C.
• The Z value will be equal to D+C.
Now add the X, Y, and Z values together, and the result of the calculation will be assigned as W.
When the W value is assigned, go to the last step, “Defusing.”
## Defusing
• After getting all your information, locate the rule that applies first and follow the given instructions from it.
If W is between 0 and 8, thenClick the first button A times, after thatClick the second button B times, after thatClick the third button C times. Otherwise, if W is between 9 and 16, thenClick the first button 6 times, after thatClick the second button 3 times, after thatClick the third button A times. Otherwise, if W is between 17 and 25 and there are 2 or more batteries on the bomb, thenClick the first button C times, after thatClick the second button B times, after thatClick the third button C times. Otherwise, if none of the above applies, thenClick the first button C times, after thatClick the second button once, after thatClick the third button A times.
When each button has been clicked the correct number of times, press the “SUBMIT” button to disarm the module. | 831 | 3,293 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.46875 | 3 | CC-MAIN-2023-40 | latest | en | 0.840749 |
https://www.slideserve.com/sumana/reinforcement-learning | 1,516,561,738,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084890823.81/warc/CC-MAIN-20180121175418-20180121195418-00585.warc.gz | 974,561,357 | 17,777 | Reinforcement Learning
1 / 33
# Reinforcement Learning - PowerPoint PPT Presentation
Reinforcement Learning. Basic idea: Receive feedback in the form of rewards Agent’s utility is defined by the reward function Must learn to act so as to maximize expected rewards. This slide deck courtesy of Dan Klein at UC Berkeley. Grid World. The agent lives in a grid
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
## PowerPoint Slideshow about 'Reinforcement Learning' - sumana
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Presentation Transcript
Reinforcement Learning
• Basic idea:
• Receive feedback in the form of rewards
• Agent’s utility is defined by the reward function
• Must learn to act so as to maximize expected rewards
This slide deck courtesy of Dan Klein at UC Berkeley
Grid World
• The agent lives in a grid
• Walls block the agent’s path
• The agent’s actions do not always go as planned:
• 80% of the time, the action North takes the agent North (if there is no wall there)
• 10% of the time, North takes the agent West; 10% East
• If there is a wall in the direction the agent would have been taken, the agent stays put
• Small “living” reward each step
• Big rewards come at the end
• Goal: maximize sum of rewards*
Markov Decision Processes
• An MDP is defined by:
• A set of states s S
• A set of actions a A
• A transition function T(s,a,s’)
• Prob that a from s leads to s’
• i.e., P(s’ | s,a)
• Also called the model
• A reward function R(s, a, s’)
• Sometimes just R(s) or R(s’)
• A start state (or distribution)
• Maybe a terminal state
• MDPs are a family of non-deterministic search problems
• Reinforcement learning: MDPs where we don’t know the transition or reward functions
• Andrey Markov (1856-1922)
• “Markov” generally means that given the present state, the future and the past are independent
• For Markov decision processes, “Markov” means:
Solving MDPs
• In deterministic single-agent search problems, want an optimal plan, or sequence of actions, from start to a goal
• In an MDP, we want an optimal policy *: S → A
• A policy gives an action for each state
• An optimal policy maximizes expected utility if followed
• Defines a reflex agent
Optimal policy when R(s, a, s’) = -0.03 for all non-terminals s
Example Optimal Policies
R(s) = -0.01
R(s) = -0.03
R(s) = -0.4
R(s) = -2.0
Example: High-Low
• Three card types: 2, 3, 4
• Infinite deck, twice as many 2’s
• After each card, you say “high” or “low”
• New card is flipped
• If you’re right, you win the points shown on the new card
• Ties are no-ops
• If you’re wrong, game ends
• Differences from expectimax:
• #1: get rewards as you go
• #2: you might play forever!
3
4
2
2
High-Low as an MDP
• States: 2, 3, 4, done
• Actions: High, Low
• Model: T(s, a, s’):
• P(s’=4 | 4, Low) = 1/4
• P(s’=3 | 4, Low) = 1/4
• P(s’=2 | 4, Low) = 1/2
• P(s’=done | 4, Low) = 0
• P(s’=4 | 4, High) = 1/4
• P(s’=3 | 4, High) = 0
• P(s’=2 | 4, High) = 0
• P(s’=done | 4, High) = 3/4
• Rewards: R(s, a, s’):
• Number shown on s’ if s s’
• 0 otherwise
• Start: 3
3
4
2
2
High
Low
3
3
, High
, Low
T = 0.25, R = 3
T = 0, R = 4
T = 0.25, R = 0
T = 0.5, R = 2
3
2
4
High
Low
High
Low
Low
High
Example: High-Low
3
MDP Search Trees
• Each MDP state gives an expectimax-like search tree
s is a state
s
a
(s, a) is a q-state
s, a
(s,a,s’) called a transition
T(s,a,s’) = P(s’|s,a)
R(s,a,s’)
s,a,s’
s’
Utilities of Sequences
• In order to formalize optimality of a policy, need to understand utilities of sequences of rewards
• Typically consider stationary preferences:
• Theorem: only two ways to define stationary utilities
• Discounted utility:
Infinite Utilities?!
• Problem: infinite state sequences have infinite rewards
• Solutions:
• Finite horizon:
• Terminate episodes after a fixed T steps (e.g. life)
• Gives nonstationary policies ( depends on time left)
• Absorbing state: guarantee that for every policy, a terminal state will eventually be reached (like “done” for High-Low)
• Discounting: for 0 < < 1
• Smaller means smaller “horizon” – shorter term focus
Discounting
• Typically discount rewards by < 1 each time step
• Sooner rewards have higher utility than later rewards
• Also helps the algorithms converge
s
a
s, a
s,a,s’
s’
Recap: Defining MDPs
• Markov decision processes:
• States S
• Start state s0
• Actions A
• Transitions P(s’|s,a) (or T(s,a,s’))
• Rewards R(s,a,s’) (and discount )
• MDP quantities so far:
• Policy = Choice of action for each state
• Utility (or return) = sum of discounted rewards
s
a
s, a
s,a,s’
s’
Optimal Utilities
• Fundamental operation: compute the values (optimal expectimax utilities) of states s
• Why? Optimal values define optimal policies!
• Define the value of a state s:
V*(s) = expected utility starting in s and acting optimally
• Define the value of a q-state (s,a):
Q*(s,a) = expected utility starting in s, taking action a and thereafter acting optimally
• Define the optimal policy:
*(s) = optimal action from state s
s
a
s, a
s,a,s’
s’
The Bellman Equations
• Definition of “optimal utility” leads to a simple one-step lookahead relationship amongst optimal utility values:
Optimal rewards = maximize over first action and then follow optimal policy
• Formally:
s
a
s, a
s,a,s’
s’
Solving MDPs
• We want to find the optimal policy*
• Proposal 1: modified expectimax search, starting from each state s:
Why Not Search Trees?
• Why not solve with expectimax?
• Problems:
• This tree is usually infinite (why?)
• Same states appear over and over (why?)
• We would search once per state (why?)
• Idea: Value iteration
• Compute optimal values for all states all at once using successive approximations
• Will be a bottom-up dynamic program similar in cost to memoization
• Do all planning offline, no replanning needed!
Value Estimates
• Calculate estimates Vk*(s)
• Not the optimal value of s!
• The optimal value considering only next k time steps (k rewards)
• As k , it approaches the optimal value
• Why:
• If discounting, distant rewards become negligible
• If terminal states reachable from everywhere, fraction of episodes not ending becomes negligible
• Otherwise, can get infinite expected utility and then this approach actually won’t work
Value Iteration
• Idea:
• Start with V0*(s) = 0, which we know is right (why?)
• Given Vi*, calculate the values for all states for depth i+1:
• This is called a value update or Bellman update
• Repeat until convergence
• Theorem: will converge to unique optimal values
• Basic idea: approximations get refined towards optimal values
• Policy may converge long before values do
Example: =0.9, living reward=0, noise=0.2
max happens for a=right, other actions not shown
Example: Value Iteration
V2
V3
• Information propagates outward from terminal states and eventually all states have correct value estimates
Convergence*
• Define the max-norm:
• Theorem: For any two approximations U and V
• I.e. any distinct approximations must get closer to each other, so, in particular, any approximation must get closer to the true U and value iteration converges to a unique, stable, optimal solution
• Theorem:
• I.e. once the change in our approximation is small, it must also be close to correct
MDP Search Trees
• Each MDP state gives an expectimax-like search tree
s is a state
s
a
(s, a) is a q-state
s, a
(s,a,s’) called a transition
T(s,a,s’) = P(s’|s,a)
R(s,a,s’)
s,a,s’
s’
Practice: Computing Actions
• Which action should we chose from state s:
• Given optimal values V?
• Given optimal q-values Q?
• Lesson: actions are easier to select from Q’s!
Utilities for Fixed Policies
• Another basic operation: compute the utility of a state s under a fix (general non-optimal) policy
• Define the utility of a state s, under a fixed policy :
V(s) = expected total discounted rewards (return) starting in s and following
• Recursive relation (one-step look-ahead / Bellman equation):
s
(s)
s, (s)
s, (s),s’
s’
Policy Evaluation
• How do we calculate the V’s for a fixed policy?
• Idea one: modify Bellman updates
• Idea two: it’s just a linear system, solve with Matlab (or whatever)
Policy Iteration
• Problem with value iteration:
• Considering all actions each iteration is slow: takes |A| times longer than policy evaluation
• But policy doesn’t change each iteration, time wasted
• Alternative to value iteration:
• Step 1: Policy evaluation: calculate utilities for a fixed policy (not optimal utilities!) until convergence (fast)
• Step 2: Policy improvement: update policy using one-step lookahead with resulting converged (but not optimal!) utilities (slow but infrequent)
• Repeat steps until policy converges
• This is policy iteration
• It’s still optimal!
• Can converge faster under some conditions
Policy Iteration
• Policy evaluation: with fixed current policy , find values with simplified Bellman updates:
• Iterate until values converge
• Policy improvement: with fixed utilities, find the best action according to one-step look-ahead
Comparison
• In value iteration:
• Every pass (or “backup”) updates both utilities (explicitly, based on current utilities) and policy (possibly implicitly, based on current policy)
• In policy iteration:
• Several passes to update utilities with frozen policy
• Occasional passes to update policies
• Hybrid approaches (asynchronous policy iteration):
• Any sequences of partial updates to either policy entries or utilities will converge if every state is visited infinitely often
Reinforcement Learning
• Reinforcement learning:
• Still have an MDP:
• A set of states s S
• A set of actions (per state) A
• A model T(s,a,s’)
• A reward function R(s,a,s’)
• Still looking for a policy (s)
• New twist: don’t know T or R
• I.e. don’t know which states are good or what the actions do
• Must actually try actions and states out to learn
[DEMO]
Example: Animal Learning
• RL studied experimentally for more than 60 years in psychology
• Rewards: food, pain, hunger, drugs, etc.
• Mechanisms and sophistication debated
• Example: foraging
• Bees learn near-optimal foraging plan in field of artificial flowers with controlled nectar supplies
• Bees have a direct neural connection from nectar intake measurement to motor planning area
Example: Backgammon
• Reward only for win / loss in terminal states, zero otherwise
• TD-Gammon learns a function approximation to V(s) using a neural network
• Combined with depth 3 search, one of the top 3 players in the world
• You could imagine training Pacman this way…
• … but it’s tricky! (It’s also P3) | 3,010 | 11,088 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2018-05 | latest | en | 0.868831 |
https://www.unitconverters.net/density/gram-cubic-meter-to-milligram-cubic-meter.htm | 1,653,632,054,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662636717.74/warc/CC-MAIN-20220527050925-20220527080925-00210.warc.gz | 1,214,627,753 | 3,151 | Home / Density Conversion / Convert Gram/cubic Meter to Milligram/cubic Meter
# Convert Gram/cubic Meter to Milligram/cubic Meter
Please provide values below to convert gram/cubic meter [g/m^3] to milligram/cubic meter, or vice versa.
From: gram/cubic meter To: milligram/cubic meter
### Gram/cubic Meter to Milligram/cubic Meter Conversion Table
Gram/cubic Meter [g/m^3]Milligram/cubic Meter
0.01 g/m^310 milligram/cubic meter
0.1 g/m^3100 milligram/cubic meter
1 g/m^31000 milligram/cubic meter
2 g/m^32000 milligram/cubic meter
3 g/m^33000 milligram/cubic meter
5 g/m^35000 milligram/cubic meter
10 g/m^310000 milligram/cubic meter
20 g/m^320000 milligram/cubic meter
50 g/m^350000 milligram/cubic meter
100 g/m^3100000 milligram/cubic meter
1000 g/m^31000000 milligram/cubic meter
### How to Convert Gram/cubic Meter to Milligram/cubic Meter
1 g/m^3 = 1000 milligram/cubic meter
1 milligram/cubic meter = 0.001 g/m^3
Example: convert 15 g/m^3 to milligram/cubic meter:
15 g/m^3 = 15 × 1000 milligram/cubic meter = 15000 milligram/cubic meter | 328 | 1,054 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2022-21 | latest | en | 0.304964 |
http://www.wired.com/wiredscience/2013/05/how-do-you-model-orbital-motion-in-a-game/ | 1,387,644,330,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1387345776257/warc/CC-MAIN-20131218054936-00089-ip-10-33-133-15.ec2.internal.warc.gz | 887,405,346 | 29,338 | How Do You Model Orbital Motion In a Game?
Screen capture from the iPhone game, Space Agency
I completely blame Dan Fullerton (@aplusphysics). He said it would be cool to use this Kerbal Space Program in physics. Here are his details on this idea. The Kerbal Space Program is a space simulator that runs on your computer. It looks really cool, but I didn’t play with it. Instead I wanted to see if they had something like this for phones. Yup, they do. It’s called Space Agency – iTunes link.
Although it’s a fun game, I had problems with it at first because it doesn’t follow real world physics. I don’t mean that I didn’t like the game. I mean I had a problem – I couldn’t do one of the levels. In one mission, you have to dock with another object in orbit. For your own spacecraft, you can turn and thrust. This means you can use the rocket thrust to push your spacecraft either tangent to your orbital path or perpendicular.
Composite screen capture from Space Agency
Here is the problem. When you thrust tangent to the orbital path, your spacecraft moves faster but stays at the same orbital radius. When you thrust perpendicular to the path, your spacecraft changes its orbital radius, but not the speed. Although this makes navigation in orbit a bit simpler, it isn’t what I expected.
Orbital Physics 101
Let’s say I have an object in orbit around the Earth. There are two, well maybe three important ideas.
Gravity. The gravitational force is an interaction between objects with mass. The farther away the objects get, the lower in magnitude the gravitational force becomes. I can model the magnitude of the gravitational forces as:
In this model, G is the gravitational constant. M and m are the masses of the two objects (I will let the Earth’s mass be M) and r is the distance between the centers of the objects (if you assume they are spherically symmetric).
The next thing to know is the momentum principle. It says:
Or, the total vector force on an object is equation to the time-rate of change of its vector momentum. Basically, forces change the momentum of an object. In this case, we can say that the vector momentum is the product of mass and vector velocity.
The last thing is the change in momentum for an object moving in a circle (like a circular orbit). If it is moving with a constant speed in a circle, the magnitude of the change in vector momentum would be:
R is the radius of the circle. If you like to look at this in terms of the speed of the object, v is the magnitude of the velocity. Or maybe you prefer to look at the angular velocity – ω. Either way gives you the same thing.
Back to the spacecraft. Let’s look at this capsule in orbit (circular orbit). There is only one force on the object, the gravitational force.
Putting all this stuff together into the momentum principle, I get:
If you want to be at a particular circular orbit radius (R), you have to go a certain speed (v). That’s it. If you increase your speed while in a circular orbit, you will not be at the same circular orbital distance.
Gravity in Space Agency
Clearly, the game Space Agency doesn’t use the same model of gravity that the real world uses. Big point here: that is OK. It’s a game. If this used realistic gravity, a rendezvous in orbit with another spacecraft would likely be super difficult.
Even though it’s not “real” gravity, I would still like an idea about the gravitational parameters in this game. Let me look at an orbiting space craft and get an estimate for M (the planet mass) and G the gravitational constant. That way, I can reproduce the same situation. From the same view of the game above, it is pretty simple to get an estimate of the speed. Let me call the radius of the planet, a value of 1 rp (for radius of planet). Now, I can use Air Server and Tracker Video to get a plot of the angular position of the spacecraft.
This puts the angular velocity at 0.267 radians/second at an orbital distance of about 2.75 rp. This would give a magnitude of velocity at around 0.73 rp/s. Using this, I can solve for GM for this particular planet (I assume it’s not Earth).
If you want to check, you can show yourself that GM should indeed have units of distance cubed per second squared. Anyway, I will use this value for GM even though it doesn’t work. It doesn’t work because I can have another object with the same angular orbit speed but at a different radius. Perhaps there is a gravitational model for this game that would work, but I will save that for later.
What about the thrust? I’m glad you asked. In the video example above, I can find the angular velocity both before and after I turn on the thrusters in the direction of motion of the space craft. If I also look at the time the that the thruster is on, I can get the angular acceleration during this time. Before the rockets were fired, I had an angular speed of 0.259 rad/s and after it was 0.282 rad/s. The rocket burn time was 1.87 seconds. From this I can get both the angular acceleration (α) and the tangental acceleration (at).
I will use that rocket acceleration for both tangential and perpendicular rocket thrusts. They might not be the same though – you could check this as a homework assignment.
Modeling Space Agency Orbits
Really, this is the fun part. Here I will use VPython to calculate both the gravitational force and rocket thrust on a space craft. I will use the standard numerical recipe to determine the spacecraft motion. Breaking the motion into small time steps, during each step I will dot the following:
• Calculate the gravitational force (and rocket force if needed).
• Use this force to find the new momentum after a short time interval.
• Use the momentum to update the position.
• Update the time and repeat.
When building things like this – the first step is to get an orbital motion without rockets. Then I can add the rocket thrust once I am sure the other stuff is working correctly.
Here is an example from that program (and here is the python program if you want it). In this case, a spacecraft starts off in a circular orbit. At t = 5 seconds, it fires the rocket in the direction of motion until t = 10 seconds. The red line shows the motion of an object that did not have a rocket (just for comparison).
You can see that this does not keep the spacecraft in a circular orbit. What if I fire the rocket perpendicular to the direction of motion? Here is a plot of that trajectory (no movie, just a picture).
Output from VPython
This doesn’t move the spacecraft to a higher orbit. It does change things though.
Ok, back to my main point. Space Agency is a cool game – but it doesn’t use real physics. If it did use real physics, how would you get two objects to meet in orbit? It wouldn’t be so easy, would it? Really, I think this is the game that I am going to make. I will call it Realistic Orbital Rendezvous.
Rhett Allain is an Associate Professor of Physics at Southeastern Louisiana University. He enjoys teaching and talking about physics. Sometimes he takes things apart and can't put them back together. | 1,545 | 7,076 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2013-48 | longest | en | 0.941942 |
https://physics.stackexchange.com/questions/571040/why-do-rotating-bodies-have-friction-between-when-the-surface-is-accelerating | 1,719,030,078,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862249.29/warc/CC-MAIN-20240622014659-20240622044659-00714.warc.gz | 402,366,454 | 43,263 | # Why do rotating bodies have friction between when the surface is accelerating?
For a body rolling with a constant velocity, there is no friction between the surface and lowermost point of the body, as there is no relative velocity between the body and the ground when it is rolling and no slipping. But if the body is accelerating with the help of another body or something, then the frictional force appears. Why is this happening? As here too, there is no relative motion between the surface and the lowermost point. I know that we need friction to create torque and so no slipping occurs. I want to know what is the difference between the two cases I mentioned. What is going on at the lowermost point of contact?
• There can certainly be friction even when there is constant speed. Such as in skiing. Gravity just balances out this friction in such case. Commented Aug 3, 2020 at 17:07
• a real body never touches a surface with just with one point. Commented Aug 3, 2020 at 17:25
• do you mean rolling contact? Commented Aug 3, 2020 at 17:31
You appear to be missing the concept of static friction and thinking only of kinetic friction.
Kinetic friction is the friction between two objects in relative motion, also called slipping. This friction force has a magnitude $$F_{kinetic}=\mu_k N$$ where $$N$$ is the magnitude of the normal force and $$\mu_k$$ is the coefficient of kinetic friction. The direction of this force is in the direction to oppose slipping.
The other type of friction is called static friction and it is a force that occurs between two objects that are not currently slipping. This force is interesting because it’s magnitude is an inequality $$F_{static} \le \mu_s N$$. Because it is an inequality it may take any value less than or equal to the maximum. Subject to that constraint, the static friction assumes whatever magnitude and direction is necessary to prevent slipping.
Note that usually $$\mu_s \gt \mu_k$$ so you can actually have larger friction forces without slipping than with slipping. This is the principle behind anti lock brakes on cars.
The friction force that you say “appears” is static friction, and it is whatever force is needed to prevent slipping.
• Up vote for pointing out to the OP that the difficulty is not understanding the difference between static and kinetic friction. Commented Aug 3, 2020 at 21:45
Your statements do seem to apply to a rolling object. If there is acceleration, the friction provides the torque required for the corresponding angular acceleration.
Possibly...
Static friction only acts when not only there is no relative motion between surfaces but also there is no met force acting on the body so in case of rolling with constant speed with no net external force, friction does act and in case of rolling with acceleration there is a net force so static friction acts.
Kinetic friction never acts in case of pure rolling as there is no relative slipping.
Static friction is a force that keeps an object at rest. It must be overcome to start moving the object. Once an object is in motion, it experiences kinetic friction. If a small amount of force is applied to an object, the static friction has an equal magnitude in the opposite direction.
In the case of rolling with constant speed, static friction is the friction that keeps the wheel rolling without slipping. The corresponding force on the contact point between the wheel and the surface on which the wheel rolls is directed backward, giving the wheel a forward motion. This force increases if the wheel accelerates (or changes from pointing backward to pointing forward when decelerating). If the acceleration reaches a certain value, the static friction changes into kinetic friction. The point of contact ain't stationary wrt the surface anymore and the wheel stars slipping. In that case, the force due to the kinetic friction gripping on the point of contact also points backward but this time, because of the energy released between the rotating wheel and the surface (think of the Formula 1 racing cars at the start: the cars are surrounded by smoke caused by this slipping) the kinetic friction is less efficient in accelerating the wheel (or decelerating it).
• Nothing is correct in your answer.(reason for -1) Commented Aug 15, 2020 at 14:12
• @Kartikey Alright than!! Thanks, woman! Commented Aug 15, 2020 at 18:04
• There is no static friction in pure rolling if speed remains constant!! You say friction is directed backwards, then why don't it produce a torque and increase it's angular velocity? The wheel is moving forward but friction is directed backwards, then why don't the linear velocity decrease, and the wheel comes to Rest. Just Think. Note-Talk only about case of perfectly riding bodies. Commented Aug 15, 2020 at 18:14
• "The corresponding force on the contact point between the wheel and the surface on which the wheel rolls is directed backward, giving the wheel a forward motion." How came up to that? A backward force can be produce a forward motion in any case. Commented Aug 15, 2020 at 18:21
• @Kartikey Just start thinking a bit! Commented Aug 15, 2020 at 18:24 | 1,101 | 5,155 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.9375 | 4 | CC-MAIN-2024-26 | latest | en | 0.952364 |
https://latitudenews.com/en/did-you-hear-about-math-worksheet-answer.html | 1,701,250,942,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100057.69/warc/CC-MAIN-20231129073519-20231129103519-00565.warc.gz | 425,299,483 | 7,375 | # Did You Hear About Math Worksheet Answer
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Web this worksheet will explain about “did you hear about.” all about mathematics. Math worksheet page 31 (with answer key) ”. It is a math sheet created to practice polynomials that has degree two. 4/28/2022 wiki user ∙ 11y ago study now see answers (2). | 517 | 2,136 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2023-50 | latest | en | 0.919223 |
http://www.numbersaplenty.com/18486 | 1,566,173,492,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027314353.10/warc/CC-MAIN-20190818231019-20190819013019-00456.warc.gz | 302,705,828 | 3,519 | Search a number
18486 = 2321379
BaseRepresentation
bin100100000110110
3221100200
410200312
51042421
6221330
7104616
oct44066
927320
1018486
1112986
12a846
138550
146a46
155726
hex4836
18486 has 24 divisors (see below), whose sum is σ = 43680. Its totient is φ = 5616.
The previous prime is 18481. The next prime is 18493. The reversal of 18486 is 68481.
18486 is a modest number, since divided by 486 gives 18 as remainder.
It is a Curzon number.
It is a nialpdrome in base 13.
It is a congruent number.
It is not an unprimeable number, because it can be changed into a prime (18481) by changing a digit.
It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 195 + ... + 273.
It is an arithmetic number, because the mean of its divisors is an integer number (1820).
218486 is an apocalyptic number.
It is a practical number, because each smaller number is the sum of distinct divisors of 18486, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (21840).
18486 is an abundant number, since it is smaller than the sum of its proper divisors (25194).
It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.
18486 is a wasteful number, since it uses less digits than its factorization.
18486 is an evil number, because the sum of its binary digits is even.
The sum of its prime factors is 100 (or 97 counting only the distinct ones).
The product of its digits is 1536, while the sum is 27.
The square root of 18486 is about 135.9632303235. The cubic root of 18486 is about 26.4411891470.
The spelling of 18486 in words is "eighteen thousand, four hundred eighty-six". | 485 | 1,714 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.234375 | 3 | CC-MAIN-2019-35 | latest | en | 0.910876 |
https://web2.0calc.com/questions/please-help-very-confusing | 1,591,168,850,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347432237.67/warc/CC-MAIN-20200603050448-20200603080448-00179.warc.gz | 590,682,438 | 6,092 | +0
0
160
2
Consider the function g(x)=3, find g(2).
Jan 30, 2019
#1
+111328
+2
Yep...confusing !!!
Note that g(x) = 3 can be considered as the line y = 3
So....note that any x value on this line will have the associated y value of 3
So.....for example.....the points (-1, 3) (0, 3) (1, 3) ( 2, 3) (3, 3) etc. are all on the line
So g(2) is really the point (2, 3)
So g(2) = 3
Hope that makes some sense !!!
Jan 30, 2019
#2
+111328
+2
Another way to see this is to write g(x) in a slightly different manner....
g(x) = 3x^0
So
g(2) =
3 (2)^0 =
3 ..... !!!
Jan 30, 2019 | 254 | 609 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.6875 | 4 | CC-MAIN-2020-24 | longest | en | 0.635347 |
https://forum.lazarus.freepascal.org/index.php/topic,52852.msg390555/topicseen.html | 1,611,652,223,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610704799711.94/warc/CC-MAIN-20210126073722-20210126103722-00386.warc.gz | 347,169,022 | 11,945 | Bookstore
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Author Topic: [SOLVED] Dynamic array - when to use DArray += [value]; (Read 617 times)
egsuh
• Hero Member
• Posts: 575
[SOLVED] Dynamic array - when to use DArray += [value];
« on: January 13, 2021, 05:09:59 am »
Hi,
What can I do in the following case?
Code: Pascal [Select][+][-]
1. var
2. EList: array of integer;
3. i: integer;
4. begin
5. // ......
6. EList += [i]; // Compiler says "Dynamic Array of LongInt" + "Set of Byte" is not overloaded.
7. end;
8.
« Last Edit: January 14, 2021, 04:05:03 am by egsuh »
lucamar
• Hero Member
• Posts: 3455
Re: Dynamic array - when to use DArray += [value];
« Reply #1 on: January 13, 2021, 05:44:12 am »
The compiler, logically enough, thinks that you're trying to add a dynamic array and a set (as deduced from the construct: [i]) and she doesn't know how to do that.
What you should write instead depends on what you want to do with such exotic sintax: if, as seems logical, you want to append the integer as the last element of the array, do something like:
Code: Pascal [Select][+][-]
1. var
2. EList: array of integer;
3. i, Last: integer;
4. begin
5. // ......
6. Last := Length(EList);
7. SetLength(EList, Last+1)
8. EList[Last] := i;
9. end;
If you really wish I guess you could overload the + operator to do that:
Code: Pascal [Select][+][-]
1. { COMPLETELY UNTESTED!!!
2. Might need some (re)work ...}
3. type
4. TIntArray = array of Integer;
5.
6. operator + (a: TIntArray; i: integer): TIntArray;
7. begin
8. Result := a;
9. SetLength(Result, Length(a)+1);
10. Result[High(Result)] := i;
11. end;
12.
13. {...}
14. { now you should be able to do ...}
15. var
16. EList: array of integer;
17. i: integer;
18. begin
19. // ......
20. EList += i;
21. end;
though I wouldn't recommend it. IMHO, it looks really ... outrê
If what you want to do is some other thing, please explain with a little more detail ...
« Last Edit: January 13, 2021, 05:47:20 am by lucamar »
Turbo Pascal 3 CP/M - Amstrad PCW 8256 (512 KB !!!)
Lazarus/FPC 2.0.8/3.0.4 & 2.0.10/3.2.0 - 32/64 bits on:
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PascalDragon
• Hero Member
• Posts: 2622
• Compiler Developer
Re: Dynamic array - when to use DArray += [value];
« Reply #2 on: January 13, 2021, 08:47:48 am »
What can I do in the following case?
• make sure that you're using 3.2.0 or newer
As the builtin +-operator for arrays disables custom operator overloads the modeswitch is disabled by default except in mode Delphi (where it can be disabled with {\$modeswitch arrayoperators-}).
lucamar
• Hero Member
• Posts: 3455
Re: Dynamic array - when to use DArray += [value];
« Reply #3 on: January 13, 2021, 03:35:17 pm »
• make sure that you're using 3.2.0 or newer
Oops! I forgot again the "new" creator for dynamic arrays, which would make the compiler interpret "[i]" as a new array and allow it to be "added" to other dyn. arrays ...
Please, disregard my previous post (though I still think that sintax is ugly )
Turbo Pascal 3 CP/M - Amstrad PCW 8256 (512 KB !!!)
Lazarus/FPC 2.0.8/3.0.4 & 2.0.10/3.2.0 - 32/64 bits on:
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egsuh
• Hero Member
• Posts: 575
Re: Dynamic array - when to use DArray += [value];
« Reply #4 on: January 14, 2021, 04:04:45 am »
Quote
Oh yes... In mode Delphi, I didn't need this. Thank you.
PascalDragon
• Hero Member
• Posts: 2622
• Compiler Developer
Re: Dynamic array - when to use DArray += [value];
« Reply #5 on: January 14, 2021, 09:06:31 am »
Please, disregard my previous post (though I still think that sintax is ugly )
Why? Arrays have been used like this inside code for decades with open array parameters.
If you mean the +=, then I agree however.
lucamar
• Hero Member
• Posts: 3455
Re: Dynamic array - when to use DArray += [value];
« Reply #6 on: January 14, 2021, 10:50:28 am »
If you mean the +=, then I agree however.
I meant the combination of both: the "+=" makes the single-element array, alone there by itself, look confusing and out of place; it's not inmediately discernible what that means.
Of course, that might be just I looking at a little (or never, in my case) used construction and other people find it quite normal
Turbo Pascal 3 CP/M - Amstrad PCW 8256 (512 KB !!!)
Lazarus/FPC 2.0.8/3.0.4 & 2.0.10/3.2.0 - 32/64 bits on:
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PascalDragon
• Hero Member
• Posts: 2622
• Compiler Developer
Re: [SOLVED] Dynamic array - when to use DArray += [value];
« Reply #7 on: January 14, 2021, 03:12:24 pm »
In (Object) Pascal, if you have [ ... ] on the right side as a separate element (not a property index), it's either a set or an array. And += adds that set or array to the left hand side. Don't know what should be confusing or out of place here. | 1,579 | 4,934 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2021-04 | latest | en | 0.758893 |
https://byjus.com/question-answer/if-pth-qth-and-rth-term-of-an-ap-are-a-b-c-respectively-then/ | 1,638,619,933,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362969.51/warc/CC-MAIN-20211204094103-20211204124103-00426.warc.gz | 223,396,448 | 19,902 | Question
# If pth, qth and rth term of an AP are a, b, c respectively, then show that (a-b)r+(b-c)p+(c-a)q=0
Solution
## Let A = first term of the AP. and Let d = common difference of the AP Now a = A+(p-1).d.......(1) b = A+(q-1).d.......(2) c = A+(r-1).d........(3) Subtracting 2nd from 1st , 3rd from 2nd and 1st from 3rd we get a-b = (p-q).d......(4) b-c = (q-r).d........(5) c-a = (r-p).d.......(6) multiply 4,5,6 by c,a,b respectively we have c.(a-b) = c.(p-q).d......(4) a.(b-c) = a.(q-r).d........(5) b.(c-a) = b.(r-p).d.......(6) a(q-r).d+b(r-p).d+c(p-q).d = 0(a(q-r)+b(r-p)+c(p-q)).d = 0 Now since d is common difference it should be non zero Hence a(q-r)+b(r-p)+c(p-q)= 0
Suggest corrections | 296 | 708 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.1875 | 4 | CC-MAIN-2021-49 | latest | en | 0.801719 |
https://confit.atlas.jp/guide/event/zisin2019/subject/S09-09/withdrawlist?cryptoId= | 1,719,125,546,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862464.38/warc/CC-MAIN-20240623064523-20240623094523-00881.warc.gz | 154,263,574 | 7,094 | # Presentation information
Room B
General session » S09. Statistical seismology and underlying physical processes
# [S09]AM-2
Mon. Sep 16, 2019 10:45 AM - 12:00 PM ROOM B (Symposium Hall, International Science Innovation Building)
chairperson:Kazuyoshi Nanjo(University of Shizuoka), Kohei Nagata(MRI)
11:45 AM - 12:00 PM
# [S09-09] Variation of activity of felt aftershocks: An application of the modified Omori formula to aftershocks of the 2019 off Yamagata earthquake
Dependence of activity of felt aftershocks (K value) with epicentral distance has been studied by fitting the modified Omori formula (Utsu, 1961) to the aftershock sequences of the off Southern Yamagata Prefecture earthquake of June 18, 2019 observed at eight seismological stations in Yamagata and Niigata prefectures. The aftershocks used in the analysis are limited to those whose epicenters are located off the coast of Yamagata prefecture or Kaetsu area of Niigata prefecture. The fitting of the modified Omori formula is made to the time sequences of aftershocks with seismic intensities greater than one at each of the eight stations. The aftershocks with seismic intensities greater than one are called felt aftershocks in the present study. Because the data set of aftershocks located by JMA is used, the fitting of the formula is also made to all the located felt aftershocks. The interval of two hours is adopted after several trial fitting of the formula to the data. Three intervals are obtained from the origin time of the main shock 22:22 of June 18 to 4:22 of the next day. The values of p=1.3 and K=20 are derived from fitting the formula to the data set of all the located felt aftershocks. The value of c=0.1 is assumed. The values of p=1.3 and c=0.1 are fixed and K value is determined from the aftershocks felt at each of eight stations. The results are summarized in Figures 1 and 2. Figure 1 shows the numbers of felt aftershocks at three time intervals for each of eight stations, the best fitting formula and the K value for each station. Result from the all the located felt aftershocks are also shown in Figure1. In Figure 2, the values of K obtained for eight stations are plotted as a function of epicentral distance. The K value plotted at epicenter (0 km) is obtained from the data set of all the located felt aftershocks. Figure 2 may show the decrease of the value of K with increasing epicentral distance. | 593 | 2,419 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2024-26 | latest | en | 0.941107 |
http://math.stackexchange.com/questions/255118/five-true-or-false-questions-on-abstract-algebra | 1,469,478,329,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257824345.69/warc/CC-MAIN-20160723071024-00085-ip-10-185-27-174.ec2.internal.warc.gz | 155,057,593 | 17,305 | # Five true or false questions on abstract algebra
Which of the following statements are true:
1. every countable group G has only countably many distinct subgroups.
2. any automorphism of the group $\mathbb{Q}$ under addition is of the form $x→qx$ for some $q\in\mathbb{Q}$
3. all non-trivial proper subgroups of $(\mathbb{R},+)$ are cyclic.
4. every infinite abelian group has at least one element of infinite order.
5. there is an element of order $51$ in the multiplicative group $(\mathbb{Z}/103\mathbb{Z})^*$
My thoughts:
1. true as union of uncountable number of countable set is uncountable
2. true as any homomorphism must be one of those form
3. false as $(\mathbb{Q},+)$ is not cyclic.
4. false example circle group.
5. true by Fermat's little theorem.
Are my guesses correct?
-
5 is true, but I don't think Fermat is involved. 4 is false, but I don't know what the circle group is --- if its the group of rotations of the circle, it certainly has elements of infinite order. – Gerry Myerson Dec 10 '12 at 3:56
Your justification of (1) is weird, to say the least: what has that to do with the question asked?. (2) This is no mathematical justification at all. (3) Good. (4) Not good, as the circle group has lots of elements of infinite order. You can take the Prufer group, though. (5) Well, yes...but you can't apply Cauchy's Theorem directly as $\,51\,$ is not a prime – DonAntonio Dec 10 '12 at 4:22
(1) Let $G$ be the direct sum of copies of $\Bbb Z/2\Bbb Z$ indexed by $\Bbb N$. $G$ is countably infinite, but each subset $A\subseteq\Bbb N$ generates a distinct subgroup $G_A=\{x\in G:x_n=0\text{ for all }n\in\Bbb N\setminus A\}$ of $G$, and $\Bbb N$ has uncountably many subsets.
(4) The statement is indeed false; the group $G$ above is an infinite Abelian group in which every non-zero element has order $2$. However, the circle group is not a counterexample: $e^{i\theta}$ has infinite order iff $\frac{\theta}{2\pi}$ is irrational, so the circle group has uncountably many elements of infinite order and only countably many of finite order.
-
does Q/Z provide a counterexample for (4)? – jim Dec 10 '12 at 10:58
@jim: Yes: $n\left(\frac{m}n+\Bbb Z\right)=0+\Bbb Z$. – Brian M. Scott Dec 10 '12 at 11:00
For part 5, note that $$|(\mathbb{Z}/103\mathbb{Z})^*| = \phi(103) = 102$$ and since $(\mathbb{Z}/103\mathbb{Z})^*$ is an abelian group we know that there exists a subgroup for every divisor of $102$. Hence we know that there exists some subgroup, $H$, such that $|H| = 51$. Now if you know that $(\mathbb{Z}/103\mathbb{Z})^*$ is actually cyclic, and since each subgroup of a cyclic group is also cyclic, there exists some $a \in (\mathbb{Z}/103\mathbb{Z})^*$ such that $\langle a \rangle = H$. Thus $|H| = |\langle a \rangle | = |a| = 51$.
-
## protected by user26857Dec 2 '15 at 22:35
Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count). | 909 | 3,045 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2016-30 | latest | en | 0.909101 |
https://lcrawfords-manymansions.com/divination/quick-answer-what-can-we-predict-using-the-least-squares-method.html | 1,643,204,248,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320304954.18/warc/CC-MAIN-20220126131707-20220126161707-00313.warc.gz | 412,685,519 | 18,946 | # Quick Answer: What can we predict using the least squares method?
Contents
## What does the least squares regression line predict?
A regression line (LSRL – Least Squares Regression Line) is a straight line that describes how a response variable y changes as an explanatory variable x changes. The line is a mathematical model used to predict the value of y for a given x.
## Can Least Square be used to predict unknown value?
In the least squares method the unknown parameters are estimated by minimizing the sum of the squared deviations between the data and the model. … As a result, nonlinear least squares regression could be used to fit this model, but linear least squares cannot be used.
## What are the advantages of least square method?
The advantages of this method are: Non-linear least squares software may be available in many statistical software packages that do not support maximum likelihood estimates. It can be applied more generally than maximum likelihood.
## What does the least squares method do exactly?
The least-squares method is a statistical procedure to find the best fit for a set of data points by minimizing the sum of the offsets or residuals of points from the plotted curve. Least squares regression is used to predict the behavior of dependent variables.
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## What does an R 2 value of 1 mean?
R2 is a statistic that will give some information about the goodness of fit of a model. In regression, the R2 coefficient of determination is a statistical measure of how well the regression predictions approximate the real data points. An R2 of 1 indicates that the regression predictions perfectly fit the data.
## What is least square method in time series?
Least Square is the method for finding the best fit of a set of data points. It minimizes the sum of the residuals of points from the plotted curve. It gives the trend line of best fit to a time series data. This method is most widely used in time series analysis.
## Why are least squares not absolute?
One of reasons is that the absolute value is not differentiable. As mentioned by others, the least-squares problem is much easier to solve. But there’s another important reason: assuming IID Gaussian noise, the least-squares solution is the Maximum-Likelihood estimate.
## Why least square method is better than high low method?
Accuracy. One of the greatest benefits of the least-squares regression method is relative accuracy compared to the scattergraph and high-low methods. The scattergraph method of cost estimation is wildly subjective due to the requirement of the manager to draw the best visual fit line through the cost information.
## What are best fit lines?
Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points. … A straight line will result from a simple linear regression analysis of two or more independent variables.
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## What is an important disadvantage of sum of squares?
Limitations of Using the Sum of Squares
An analyst may have to work with years of data to know with a higher certainty how high or low the variability of an asset is. As more data points are added to the set, the sum of squares becomes larger as the values will be more spread out. | 670 | 3,399 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.796875 | 4 | CC-MAIN-2022-05 | latest | en | 0.885309 |
http://profilersports.screenstepslive.com/s/builder/m/557/l/61754-calculations-greater-than-and-less-than-and-nested-if-calculations-for-use-with-gps-fields-and-hr-fields | 1,611,297,411,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703529128.47/warc/CC-MAIN-20210122051338-20210122081338-00044.warc.gz | 81,800,731 | 21,888 | System Development, Software Updates, Quick Guides and Builder Training InformationBuilder Site Help Documentation Calculations and Table CalculationsCalculations: Greater than and less than, and Nested If calculations (for use with GPS fields and HR fields)
# Calculations: Greater than and less than, and Nested If calculations (for use with GPS fields and HR fields)
## How to set up the greater than and lesser than calcs.
Note: All of these will return "Answer" as I've set them up. The first number in the brackets is the query field and the second number is the limit we are interested in
Abbreviations
gt = greater than
gteq = greater than or equal to
lt = less than
lteq = less than or equal to
## Examples of different equations used to calculate Time and Distance parameters in a GPS analysis Event Form
All of the Equations are listed here to ensure you can quickly copy and use them in your own Time Series Forms.
FIELD NAME FIELD TYPE CALCULATION -OUTCOME/REASON
Drill time Calculation (End time Start time)/60/1000 -To give you time of each drill in minutes
Start Distance Table Calculation , Aggregate: minifpositive if(gteq(GPS.time,Start time), GPS.distance,-1)
-Distance at start of drill
End Distance Table Calculation, Aggregate: maxifpositive if(lteq(GPS.time,End time), GPS.distance,-1) -Distance at end of drill
Drill Distance Calculation safe( End Distance - Start Distance) -Distance for the drill
Drill Workrate Calculation safe( Drill Distance/Drill time) -Workrate for the drill
Max Speed (Drill) Table Calculation Aggregate: maxifpositive if(gteq(GPS.time,Start time), if(lteq(GPS.time,End time), GPS.speed,-1),-1) -Max speed reached in this drill
Distance < X Table Calculation, Aggregate: sumifpositive safe(if(gteq(GPS.time,Start time), if(lteq(GPS.time,End time), if(lteq(GPS.speed,X),GPS.distance.delta,-1),-1),-1))
-Distance covered at speeds lower than X km/h
Time <X Table Calculation Aggregate: sumifpositive (safe(if(gteq(GPS.time,Start time), if(lteq(GPS.time,End time), if(lteq(GPS.speed,X),GPS.time.delta,-1),-1),-1)))/1000/60
-Time spent at speeds lower than X km/h
Distance X to Y Table Calculation Aggregate: sumifpositive safe(if(gteq(GPS.time,Start time), if(lteq(GPS.time,End time), if(gt(GPS.speed,X), if(lteq(GPS.speed,Y),GPS.distance.delta,-1),-1),-1),-1))
-Distance covered between speeds of X and Y km/h. use this formula for all other speed zones
Time X to Y Table Calculation, Aggregate: sumifpositive (safe(if(gteq(GPS.time,Start time), if(lteq(GPS.time,End time), if(gt(GPS.speed,X), if(lteq(GPS.speed,Y),GPS.time.delta,-1),-1),-1),-1)))/1000/60
-Time spent between speeds of X and Y km/hr. use this formula for all other speed zones
Distance < 50% MRS Table Calculation Aggregate: sumifpositive safe(if(gteq(GPS.time,Start time), if(lteq(GPS.time,End time), if(lteq(GPS.speed,(0.5 * Max Sprint Speed)),GPS.distance.delta,-1),-1),-1))
-Distance covered at speeds less than 50% of the athletes individual Maximal Sprint Speed. Use the same formula for TIME just replace GPS.distance.delta with GPS.time.delta.
Distance 50 to 75 %MRS Table Calculation, Aggregate: sumifpositive safe(if(gteq(GPS.time,Start time), if(lteq(GPS.time,End time), if(gt(GPS.speed,(0.5*Max Sprint Speed)), if(lteq(GPS.speed,(0.75*Max Sprint Speed)),GPS.distance.delta,-1),-1),-1),-1))
-Distance covered at speeds between 50 and 75% of MRS. Use this formula for any other relative speed zones. Use the same formula for TIME just replace GPS.distance.delta with GPS.time.delta.
Distance > 75%MRS Table Calculation, Aggregate: sumifpositive safe(if(gteq(GPS.time,Start time), if(lteq(GPS.time,End time), if(gt(GPS.speed,(0.75* Max Sprint Speed)),GPS.distance.delta,-1),-1),-1))
-Distance covered at speeds greater than 75% of MRS.
TIME use the same formula for TIME just replace GPS.distance.delta with GPS.time.delta.
## Translating one of the nested IF statements. What they mean.
AGG: sumifpositive
Formula: safe(if(gteq(GPS.time,Start time), if(lteq(GPS.time,End time), if(gt(GPS.speed,X), if(lteq(GPS.speed,Y),GPS.distance.delta,-1),-1),-1),-1))
What this means
If the time in this row in the raw upload file is greater than or equal to the start time of this drill, AND less than or equal to the end time of this drill, AND if the speed is greater than x km/h, AND the speed is less than Y km/h, THEN give me the distance delta value. If any rows in the file don’t meet all four IF statements then give them a -1 value. This is a table calculation, so go to the next row and do it all again. And keep doing it until you have looked at every row in the file. You will end up with some rows which met all four criteria and some that didn’t. Because I selected the aggregate to be SUMIFPOSITIVE I want you to take all those values that meet the IF statements and add them together to give me the total distance for this drill. SAFE means if all of this ends up giving me a number show me that number, if not, show me a zero, but just don’t give me a blank (because blanks cannot be used in calculations).
The above table of formulas is only concerned with time, distance and speed variables. The same formulas can be used (slightly modify them to reference the columns you want) to perform HR calculations such as average HR in this drill, Max HR in this Drill, etc. if your GPS units export accelerometer data you can also use the same logic to create calculations to provide summary values of acceleration data.
NOTE: the more fields you want the longer this table will be and it will not display nicely in the application.
## Examples of Summary Calculation for the a whole session (e.g. total distance and total time)
Once you have filtered and processed the raw file in a Table you can add in summary calculations for the session. Examples of these are outlined here:
FIELD NAME FIELD TYPE CALCULATION
Total Distance Table Calculation Aggregate: SUM Drill Distance
Total Time Table Calculation Aggregate: SUM Drill Time
Max Speed Table Calculation Aggregate: MAX Max Speed (Drill)
Total Distance < X Table Calculation Aggregate: SUM Distance <X
Total Distance X to Y Table Calculation Aggregate: SUM Distance X to Y
Total Time <X Table Calculation Aggregate: SUM Time <X
Total Time X to Y Table Calculation Aggregate: SUM Time X to Y
Total Distance 50 to 75%MRS Table Calculation Aggregate: SUM Distance 50 to 75%MRS
Total Time 50 to 75% MRS Table Calculation Aggregate: SUM Time 50 to 75% MRS
Repeat as necessary for all absolute and relative speed zones.
If you are collecting HR, data as well you can include additional fields for the HR analysis. | 1,778 | 7,254 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2021-04 | latest | en | 0.629871 |
http://www.solutioninn.com/the-following-partial-excel-add-in-megastat-regression-output | 1,505,861,037,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818686043.16/warc/CC-MAIN-20170919221032-20170920001032-00148.warc.gz | 572,773,517 | 7,767 | # Question: The following partial Excel add in MegaStat regression output
The following partial Excel add- in ( MegaStat) regression output for the service time data relates to predicting service times for 1, 2, 3, 4, 5, 6, and 7 copiers.
a. Report (as shown on the computer output) a point estimate of and a 95 percent confidence interval for the mean time to service four copiers.
b. Report (as shown on the computer output) a point prediction of and a 95 percent prediction interval for the time to service four copiers on a single call.
c. For this case: n = 11, b0 = 11.4641, b1 = 24.6022, and s 4.615. Using this information and a distance value (called Leverage on the add-in output), hand calculate (within rounding) the confidence interval of part a and the prediction interval of part b.
d. If we examine the service time data, we see that there was at least one call on which Accu-Copiers serviced each of 1, 2, 3, 4, 5, 6, and 7 copiers. The 95 percent confidence intervals for the mean service times on these calls might be used to schedule future service calls. To understand this, note that a person making service calls will (in, say, a year or more) make a very large number of service calls. Some of the person’s individual service times will be below, and some will be above, the corresponding mean service times. However, because the very large number of individual service times will average out to the mean service times, it seems fair to both the efficiency of the company and to the person making service calls to schedule service calls by using estimates of the mean service times. Therefore, suppose we wish to schedule a call to service five copiers. Examining the computer output, we see that a 95 percent confidence interval for the mean time to service five copiers is [130.753, 138.197]. Because the mean time might be 138.197 minutes, it would seem fair to allow 138 minutes to make the service call. Now suppose we wish to schedule a call to service four copiers. Determine how many minutes to allow for the service call.
Sales0
Views46 | 491 | 2,071 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.390625 | 3 | CC-MAIN-2017-39 | latest | en | 0.893255 |
http://www.jiskha.com/display.cgi?id=1266544453 | 1,495,961,726,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463609610.87/warc/CC-MAIN-20170528082102-20170528102102-00086.warc.gz | 686,978,808 | 3,561 | # physics
posted by on .
A block of mass 4.0 kg is put on top of a block of mass M = 6.0 kg. To cause the top block to slip on the bottom one, while the bottom one is held fixed, a horizontal force of at least 19 N must be applied to the top block. The assembly of blocks is now placed on a horizontal, frictionless table.
a.) Find the magnitude of the maximum horizontal force F that can be applied to the lower block so that the blocks will move together.
b.) Find the magnitude of the resulting acceleration of the blocks.
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Post a New Question | 151 | 661 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2017-22 | latest | en | 0.862436 |
http://www.lawnsite.com/threads/mowing-times.2480/ | 1,481,179,653,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698542414.34/warc/CC-MAIN-20161202170902-00116-ip-10-31-129-80.ec2.internal.warc.gz | 562,664,912 | 35,902 | # mowing times
Discussion in 'Lawn Mowing' started by Jason, Jan 1, 2000.
1. ### JasonLawnSite Senior Memberfrom Michigan (Lennon)Posts: 256
Was curious if anybody had a simple formula to figure mowing times? It would be nice to be able to plug in some numbers to come up with a rough estimate of time to mow.<br> For example a formula that takes into account deck size(52", speed traveled (5mph), and area (43,560 sq/ft).<br>I'd want the formula to be simple, I know there are lot's of variables that affect your actual mowing times, like obstacles, grass condition, type of grass, lenght of grass etc...<br> Basically I want to figure out a obstacle free, square 1 acre plot, with no trimming times added. Also no loading and unloading equimpent times, no time for slowing down and turning around. Just a straight time for mowing 1 acre at 5 mph with a 52" deck. <br> If anybody has a simple formula I'd appreciate it. Thanks. Happy New Year !
2. ### Eric ELMHusband, Father, Friend, Angelfrom Chicago, IL USAPosts: 4,831
Jason, I just put a program in Excel to come up with the numbers. If you want the Excel file, email me and I'll send it to you. Here is the forumula if you want to put it in your self. (deck size divided by 12) times (MPH times 5280)divided by 43560 gives you the amount of acres you will mow in an hour. If you have a 52 inch deck and overlap 2 inches, just put in 50 inches for deck size. I could also put this in the Works spreadsheet if some wanted that file. For speed, just put in an average speed too. If you are mowing at 10 MPH, you probably average 7 or 8 MPH, taking in to consideration that you are making turns and objects in the way. It's been many years since I took math, but this should be right. If I'm wrong guys, let me know.<p>----------<br>Eric@ELM<br>http://pages.prodigy.net/eric.erickson/index.html
3. ### green1thumbLawnSite Memberfrom GAPosts: 7
Jason, production times and formulars are nessary tools for an estimating system. After you chose a system be sure to customize it for your company. Just because you have a mower that should cut twenty five thousand square feet per hour does not mean it will. Your rate may be more or less<p>----------<br>Walter Lewis<br>
4. ### Nilsson AssociatesLawnSite Memberfrom ConnecticutPosts: 243
Mowing times, almost any work time you could think of is found in the Labor Time Data Handbook at nilsson associates link at www.turfquip.com <br>Nilsson.Assoc@Snet.Net
5. ### RogerLawnSite Fanaticfrom McMurray, PAPosts: 5,927
I have written a program for developing mowing rates (sq ft/hr; acre/hr). Variables are mower width, overlap, speed, and efficiency. For efficiency, I mean the percent of time mowing grass, and NOT moving around obstacles, turning, emptying bags, etc.<p>I have graphs I generated I keep in my notebook, available when making an estimate. 100% means ALWAYS cutting! Several months ago, somebody on this Forum asked a similar question, so I created charts for him, and e-mailed them to him. <p>E-mail me if interested, and I'll be happy to send them along. Give me a range of mow widths, range of overlaps, range of speed.<p>However, in the past year or two, I've been able to use my experience to estimate the time required to mow a lawn. Yes, I can get sq ft, but there are too many other factors that are important in the residential yards I see here. The most difficult issue for a new lawn is the extra time required for bagging, when one does not know the growth rate of the grass and fertilization pattern. The estimate usually have to be made before the season starts, so the grass is dormant at that time.<p>I find that after I settle on a pattern for a lawn, the time required (for those of 1:00 to 2:00 hrs) never varies more than 2-3 minutes per mowing. I keep a stop watch running for every job. If the time varies more than that, I have to ask "why?"
6. ### HOMERLawnSite Gold Memberfrom Alabama the BeautifulPosts: 3,183
WHEN YOU DO THE ESTIMATES FOR MOWING TIME, HOW DO YOU FACTOR IN THE TIME FOR EDGEING, TRIMMING, BLOWING, PULLING A WEED OR TWO, AND TALKING TO THE CUSTOMER WHEN HE COMES OUT, BORED TO DEATH WITH NOTHING BETTER TO DO THAN KEEP YOU FROM HEADING TO YOUR NEXT YARD. THE FORMULA IDEA WOULD, IN MY OPINION, WORK FOR A GOLF COURSE OR BALL FIELD, BUT FOR A RESIDENTIAL LAWN I THINK A MORE PRACTICAL APPROACH WOULD BE TO FIND OUT WHAT LAWNS ARE GOING FOR IN YOUR AREA AND GUESSTIMATE THE LENGTH OF TIME IT WILL TAKE YOU TO DO ALLLLLLLLLLLL OF THE WORK FROM START TO FINISH. IF YOU HAVE DONE A FEW LAWNS YOU SHOULD HAVE A GOOD IDEA OF THE LENGTH OF TIME IT WILL TAKE. AS FOR ME, RESIDENTIAL MOWING TIME IS THE FASTEST OF ALL THE OPERATIONS (THANKS TO MY FLATLANDER AND CITY SLICKER)CLEAN UP TIME TAKES ALMOST AS LONG IF DONE PROPERLY. I REALIZE YOU SHOULD DO THE MATH BUT THE BOTTOM LINE IS IF YOU GET HUNG UP ON MOWING TIME ONLY TO FIGURE A JOB, YOU MIGHT COME OUT A LOSER. THE CUSTOMER YOU ARE TRYING TO GET MAY HAVE ALREADY HAD A SERVICE BEFORE AND WILL PROBABLY GO \$5.00 MORE A CUT BECAUSE YOU ASSURE THEM YOU WILL DO A BETTER JOB, BUT THEY ARE NOT STUPID AND COULD CARE LESS HOW MANY SQ.FT YOU ARE MOWING. THEY DO KNOW WHAT THE ARE WILLING TO PAY AND IF YOU CAN DO IT FOR THAT THEN YOU MAY GET THE JOB, IF YOU CAN'T UNFORTUNATELY THERE IS ALWAYS SOMEBODY THAT WILL DO IT CHEAPER. GET AN IDEA OF HOW MUCH YOU NEED TO MAKE AN HOUR AND BID BASED ON THIS INFO. YOU WILL LOSE SOME AND WIN ON THE OTHERS, DEPENDING ON CONDITIONS. AN AVERAGE RESIDENTIAL SHOULD TAKE 25 TO 30 MINUTES, NO LONGER THAN 45. THIS IS AN AVERAGE SIZED LOT NOT A LARGE ONE. WITH THE RIGHT EQUIPMENT EVEN A LARGE FLAT LOT WILL GET YOU MORE PER CUT BUT THEY DON'T KNOW YOU HAVE A MOWER THAT WILL MOW IT IN 15 MINUTES..........TILL YOU GET THERE! THIS ISN'T INTENDED TO DISCOUNT THE FORMULA METHOD, BUT THERE IS SO MUCH MORE TO CONSIDER THAN JUST THE MOWING TIME.
7. ### RogerLawnSite Fanaticfrom McMurray, PAPosts: 5,927
Homer,<br>You are right - mowing time is only a portion of the total time required to do a job. That is why I rely on my experience for time estimates, and not primarily on mowing rates. Other activities vary so much from job to job, as you point out. However, when starting out in the business, using some mowing rate for estimates is the best place to start. Soon, one learns which jobs are profitable, and which ones are loosers. Experience will help to discern those loosers in the future.<p>In our area, my average residential lawn takes at least one hour, most 1:30. But, I'm more interested in being sure I get paid on my time basis, not how many I can get mowed per day. If I'm not competative because I'm having to charge too much for each job, then I have a problem. However, this has not been a problem. I have more customers who have offered to pay me more per mow than I expect, than customers who I have asked more to do the job. <br>
8. ### HOMERLawnSite Gold Memberfrom Alabama the BeautifulPosts: 3,183
HI ROGER, I GUESS THE PROBLEM I HAD WITH THE FORMULA METHOD WOULD BE IF YOU CALCULATED EVERYTHING USING A MURRAY MOWER TRAVELING 3.5 MPH CUTTING A 38" SWATH ETC. ETC. ETC. YOU MIGHT COME UP WITH A TIME THAT IS EXTREMELY HIGH AND BASED ON YOUR PRICE PER SQ.FT, YOUR QUOTE MAY BE \$20.00 HIGHER THAN THE CUSTOMERS HAVE BEEN USED TO PAYING. IF YOU TOOK A ZTR WITH A TRAVEL SPEED MUCH HIGHER USING THE SAME \$ FIGURE YOU COULD DO IT MUCH CHEAPER. BUT..............YOU HAVE A HIGHER PRICED MOWER TO PAY FOR AS WELL. IN OTHER WORDS YOU WOULD PENALIZE THE CUSTOMER BECAUSE YOU HAD SLOW EQUIPMENT. I HOPE I WORDED THIS CORRECTLY. I WOULDN'T WANT ANYBODY LOSING JOBS BECAUSE THEY HAD A FALSE SENSE OF WHAT PEOPLE ARE REALLY GETTING PAID FOR SOME OF THESE YARDS. WHEN I STARTED WITH MY 40" TRACTOR IT WOULD TAKE ME 2.0 HRS TO MOW SOME OF MY YARDS. I STILL HAVE THE YARDS I STARTED WITH 5 YEARS AGO, HAVEN'T RAISED THE PRICE ON THEM, BUT CAN NOW MOW THEM IN 20 MINUTES. I HAD TO TAKE WHAT THE GOING RATE WAS AT THE TIME( IT AIN'T CHANGED MUCH EITHER) KNOWING I WANTED TO MAKE MORE AND THINKING I WAS GETTING WAXED, BUT IT WAS ONLY ME AND THE ONE MOWER I WAS HAVING TO PAY FOR. IT WAS A SIDE BUSINESS TOO AND IF I MADE ENOUGH TO PAY THE PAYMENT AND THE GAS I WAS ACTUALLY HAPPY. THE LONGER YOUR IN IT THE MORE YOU WILL PICK UP AND THE FASTER YOU WILL HAVE TO GET TO KEEP UP. YOU GOTTA CHANGE WITH THE TIMES OR STAY SMALL. CHANGE MEANS SPENDING \$\$\$\$\$\$\$\$\$\$\$\$\$\$ TO BE COMPETITIVE. I KNOW YOU HAVE TO START SOMEWHERE AND IT MIGHT WORK FINE, THESE ARE ONLY MY OPINIONS BASED ON MY EXPERIENCE. THANKS<br>
9. ### Eric ELMHusband, Father, Friend, Angelfrom Chicago, IL USAPosts: 4,831
It seems like what Jason wanted was a way to figure out how much a mower could cut in an hour on an open lot. The program I made in Excel could also be used to compare if you have two guys mowing with 48 inch decks and walking behind them at 3 MPH or having one guy mowing with a 60 inch deck at 10 MPH, to find out the 1 mower a foot wider will do twice as much. Anyway, this program you just put in your cutting width (deck width minus overlap) and what you think your average speed is and it calculates how many acres. Very simple, fill in the blanks and it works.<p>----------<br>Eric@ELM<br>http://pages.prodigy.net/eric.erickson/index.html | 2,532 | 9,323 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2016-50 | latest | en | 0.937327 |
http://www.chegg.com/homework-help/questions-and-answers/single-conservative-forcef-x-bx-aacts-477-kg-particle-x-meters-b-455-n-m-anda-457-n-partic-q814126 | 1,371,649,301,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368708789647/warc/CC-MAIN-20130516125309-00093-ip-10-60-113-184.ec2.internal.warc.gz | 376,790,010 | 8,121 | ## Conservative Forces
A single conservative force
F(x)=bx+a
acts on a 4.77 kg particle, where x is in meters, b=4.55 N/m anda=4.57 N. As the particle moves along the x axis from x=1.57m tox=6.6m, calculate the work done by this force in Joules.
I don't have any idea how to start this one any help is muchappreciated. | 98 | 322 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.71875 | 3 | CC-MAIN-2013-20 | latest | en | 0.904285 |
https://www.convertunits.com/from/acre+foot+%5BUS+survey%5D/to/pint | 1,656,545,026,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103645173.39/warc/CC-MAIN-20220629211420-20220630001420-00112.warc.gz | 767,564,189 | 12,973 | ## ››Convert acre foot [US survey] to pint [US, liquid]
acre foot [US survey] pint
Did you mean to convert acre foot acre foot [US survey] to pint [US, liquid] pint [US, dry] pint [UK]
How many acre foot [US survey] in 1 pint? The answer is 3.8360818377789E-7.
We assume you are converting between acre foot [US survey] and pint [US, liquid].
You can view more details on each measurement unit:
acre foot [US survey] or pint
The SI derived unit for volume is the cubic meter.
1 cubic meter is equal to 0.00081070848625322 acre foot [US survey], or 2113.3764099325 pint.
Note that rounding errors may occur, so always check the results.
Use this page to learn how to convert between acre feet and pints.
Type in your own numbers in the form to convert the units!
## ››Quick conversion chart of acre foot [US survey] to pint
1 acre foot [US survey] to pint = 2606826.55451 pint
2 acre foot [US survey] to pint = 5213653.10902 pint
3 acre foot [US survey] to pint = 7820479.66353 pint
4 acre foot [US survey] to pint = 10427306.21804 pint
5 acre foot [US survey] to pint = 13034132.77256 pint
6 acre foot [US survey] to pint = 15640959.32707 pint
7 acre foot [US survey] to pint = 18247785.88158 pint
8 acre foot [US survey] to pint = 20854612.43609 pint
9 acre foot [US survey] to pint = 23461438.9906 pint
10 acre foot [US survey] to pint = 26068265.54511 pint
## ››Want other units?
You can do the reverse unit conversion from pint to acre foot [US survey], or enter any two units below:
## Enter two units to convert
From: To:
## ››Metric conversions and more
ConvertUnits.com provides an online conversion calculator for all types of measurement units. You can find metric conversion tables for SI units, as well as English units, currency, and other data. Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types. Examples include mm, inch, 100 kg, US fluid ounce, 6'3", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more! | 568 | 2,033 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.984375 | 3 | CC-MAIN-2022-27 | latest | en | 0.729399 |
https://fr.mathworks.com/matlabcentral/cody/problems/2010-wrap-a-vector-but-insert-nan-s-at-the-wrap-positions/solutions/357229 | 1,580,294,331,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579251796127.92/warc/CC-MAIN-20200129102701-20200129132701-00508.warc.gz | 459,316,127 | 16,006 | Cody
# Problem 2010. Wrap a vector, but insert NaN's at the wrap-positions.
Solution 357229
Submitted on 21 Nov 2013 by Thomas Vanaret
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
%% x = 1:20; m = 3; y = wrapnan(x,m); y_correct = [1 2 nan 0 1 2 nan 0 1 2 nan 0 1 2 nan 0 1 2 nan 0 1 2 nan 0 1 2]; assert(isequaln(y,y_correct)) filetext = fileread('wrapnan.m'); assert(isempty(strfind(filetext, 'regexp')),'regexp* command is forbidden'); assert(isempty(strfind(filetext, 'eval')),'eval* command is forbidden'); assert(isempty(strfind(filetext, 'inline')),'inline command is forbidden');
ans = Columns 1 through 16 1 2 NaN 0 1 2 NaN 0 1 2 NaN 0 1 2 NaN 0 Columns 17 through 26 1 2 NaN 0 1 2 NaN 0 1 2
2 Pass
%% x = [1 50 95 105 195 205 190 310 290 250 201 10]; m = 100; y = wrapnan(x,m); y_correct = [1 50 95 nan 5 95 nan 5 nan 90 nan 10 nan 90 50 1 nan 10]; assert(isequaln(y,y_correct))
ans = Columns 1 through 16 1 50 95 NaN 5 95 NaN 5 NaN 90 NaN 10 NaN 90 50 1 Columns 17 through 18 NaN 10
3 Pass
%% x = [0.25 0.45 0.80 0.90 1.25 0.60 0.10 0.20 1.70 1.60 1.50 1.80 1.40 0.10]; m = 0.5; y = wrapnan(x,m); y_correct = [0.25 0.45 NaN 0.30 0.40 NaN 0.25 NaN 0.10 NaN 0.10 0.20 NaN 0.20 0.10 0.00 0.30 NaN 0.40 NaN 0.10]; assert(isequaln(roundn(y,2),roundn(y_correct,2)))
ans = Columns 1 through 10 0.2500 0.4500 NaN 0.3000 0.4000 NaN 0.2500 NaN 0.1000 NaN Columns 11 through 20 0.1000 0.2000 NaN 0.2000 0.1000 0 0.3000 NaN 0.4000 NaN Column 21 0.1000 | 670 | 1,584 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.328125 | 3 | CC-MAIN-2020-05 | latest | en | 0.2649 |
https://physics.stackexchange.com/questions/138979/instantaneous-axis-of-rotation-and-rolling-cone-motion | 1,660,567,294,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572174.8/warc/CC-MAIN-20220815115129-20220815145129-00692.warc.gz | 408,547,511 | 68,159 | Instantaneous axis of rotation and rolling cone motion
Suppose a cone is purely rolling (no slipping) around a fixed axis. Elaborately, it is revolving around a fixed axis perpendicular to the ground and passing through its vertex and also rotating, and the vertex is stationary.
Now the instantaneous axis of rotation (IAR) of the cone is the 'line' that is touching the ground right? So how do you find the velocity of any other point using that? I mean, in the rolling wheel, you multiply the angular velocity by the distance from the IAR to get the velocity. Is it the same here?
If it is, then consider the center of base of the cone. If the height of cone is $$h$$ then its distance from the IAR is clearly $$h\sin x$$ where $$x$$ is the cone's half apex angle. So its velocity should be $$ah\sin x$$, where $$a$$ is the angular velocity with which the cone is rotating. Is this right?
Now we can also analyse the cone's motion by considering it in two parts: rotation + revolution, right? So again considering the center of base of the cone, it has no velocity by virtue of rotation (since the cone is rotating about an axis through the center), right? And by virtue of it rotating in a circle (of radius $$h\cos x$$) around the axis passing through its vertex, it has velocity $$bh\cos x$$ , where $$b$$ is the angular velocity with which the cone is revolving.
Now these two must be same, so we get $$b=a \tan x$$.
But Wikipedia states here that the ratio is $$\sin x$$.
And at the same time, this video (which I found in the external links section of the Wikipedia page) states that $$a=b\cot x$$ which is same as what I got.
I'm really confused. Is everything that I did right? If not please correct me. Thank you.
How to find velocity of any point on the cone? There ought to be two approaches , one using IAR and another by considering motion as rotation + revolution but I'm not able to do it.
• The wikipedia article describes a cone rolling on a cone. You apparently are trying to describe a cone rolling on a plane. Oct 6, 2014 at 11:45
• @DavidHammen Yes but it also says " In the special case of a cone rolling on a flat surface, this ratio becomes sin alpha, where alpha is the cone's half apex angle" Oct 6, 2014 at 11:59
• Well, (thought experiment) how is the instantaneous linear velocity of the center of the cone's base different from the velocity of the center of a rolling disk? Solve that and convert into angular velocity about the vertex of the cone, maybe. Oct 6, 2014 at 13:15
• @CarlWitthoft Oh , so the cone's base is like a rolling disk but it is touching the ground at an angle. If that angle is theta then I'd guess linear velocity of center to be um $w*r*sin(theta)$, is that right? edit: Now I'm thinking it's just $w*r$, hmm. Oct 6, 2014 at 18:10
• @AGoogler See my revised answer. I believe I've found my mistake: I divided $\cos$ by $\sin$ and somehow got $\tan$, whereas it should of course have been $\cot$! Now the answer makes a great deal more sense. The computation is exactly as you say: the instantaneous axis is along the contact plane and you multiply $h\sin\alpha$ by the instantaneous angular speed. Oct 12, 2014 at 4:39
Let the cone lie on the $\hat{X}\wedge \hat{Y}$ plane (z=0) and let the $z$ axis pierce this plane at the cone's apex. If the cone's half angle is $\alpha$, then its axis of symmetry as a function of time is defined by the vector
$$A(t)=\cos\alpha \left(\cos(\omega_0\,t) \hat{X} + \sin(\omega_0\,t) \hat{Y}\right)+\sin\alpha \hat{Z}$$
where $\omega_0 = 2\pi/\tau$ and $\tau$ is time it takes the cone to make exactly one circuit on the $\hat{X}\wedge \hat{Y}$ plane. Thus the cone's axis of symmetry rotates with angular velocity $\omega_0\,\hat{Z}$. I define my directions and symbols below:
If the cone doesn't slip, this means that the rotation about the axis $A(t)$ has an angular velocity $- \omega_0 A(t)/\sin\alpha$. Sketch the cone near the apex to see this: at a distance $R$ along the edge (defined by the vector $\cos(\omega_0\,t) \hat{X} + \sin(\omega_0\,t) \hat{Y}$) in the $\hat{X}\wedge \hat{Y}$ plane where the cone meets the plane, the tip of this edge moves at speed $v_e=\omega_0\,R$. The circular cone cross section (orthogonal to the cone's axis of rotational symmetry) through this point is like a wheel of radius $r=R\,\sin\alpha$ cambered inwards at angle $\alpha$. This "wheel" must spin at angular velocity $-\omega_0\,R\,A(t)/r$ so that its rim's velocity is $-v_e=-\omega_0\,R$ to offset the velocity $v_e=\omega_0\,R$ of the edge at this point and keep the point of the wheel in contact with the ground stationary.
We add these two angular velocities to get:
$$\Omega(t) = \omega_0\left(\hat{Z} - \frac{A(t)}{\sin\alpha}\right)=-\omega_0 \,\cot\alpha\,\left(\cos(\omega_0\,t) \hat{X} + \sin(\omega_0\,t) \hat{Y}\right)$$
which, as you correctly guessed, is always along the line where the cone meets the plane.
The instantaneous speed of a point on the cone's axis of symmetry a distance $h$ from the base is $|\Omega|\,h\,\sin\alpha = \omega_0\,h\,\cot\alpha\,\sin\alpha = \omega_0 \,h\,\cos\alpha$ ($|\Omega|$ times as you say, the orthogonal distance $h\,\sin\alpha$ of the point from the instantaneous axis of rotation.
Note that we get the same answer by simply working this speed out for an angular velocity $\omega_0\,\hat{Z}$, which is valid because the axis of the cone has no velocity owing to the rotation in the direction $A(t)$. The point on the cone's axis of symmetry is a distance $h\,\cos\alpha$ from the $\hat{Z}$ axis. Thus the speed is, as before, $\omega_0\,h\,\cos\alpha$.
• Hi , thanks for the answer. Your notation and way of solving the problem was a bit new for me but I'm trying to understand. A few questions: Oct 10, 2014 at 9:49
• 1. the final angular velocity is wtanx along the contact line. So if i wanted to find velocity of any point on the cone , would i just multiply wtanx by the perpendicular distance of that point from the line? 2. If so then velocity of centre of base of cone would be hsinxwtanx where h is height. But it should be hcosxw since hcosx is distance from z axis and centre has no velocity due to rotation of cone. Please help,I'm confused. Oct 10, 2014 at 9:57
• @AGoogler Let me come back to this: am a little busy at the moment: can see your problem and there must be a difference between our notations somewhere. Oct 10, 2014 at 10:34
• @AGoogler Still haven't forgotten about you. I'll be mulling over your question over the weekend - sometimes I do a great deal of slow thinking whilst watching my children play, and I'll take your problem with me. Oct 11, 2014 at 0:47
• Thanks , your help is really appreciated. Meanwhile can you suggest a good physics book for me ? (mostly classical mechanics , rotational mechanics with an emphasis on problem solving) Oct 11, 2014 at 7:15 | 1,866 | 6,864 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 11, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.21875 | 4 | CC-MAIN-2022-33 | longest | en | 0.946873 |
https://support.nag.com/numeric/nl/nagdoc_latest/examples/source/f08fqfe.f90.html | 1,708,578,841,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947473690.28/warc/CC-MAIN-20240222030017-20240222060017-00329.warc.gz | 581,375,777 | 2,612 | NAG Library Manual, Mark 29.3
``` Program f08fqfe
! F08FQF Example Program Text
! Mark 29.3 Release. NAG Copyright 2023.
! .. Use Statements ..
Use nag_library, Only: nag_wp, x04daf, zheevd, zscal
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Integer, Parameter :: nin = 5, nout = 6
! .. Local Scalars ..
Integer :: i, ifail, info, k, lda, liwork, &
lrwork, lwork, n
Character (1) :: job, uplo
! .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: a(:,:), work(:)
Real (Kind=nag_wp), Allocatable :: rwork(:), w(:)
Integer, Allocatable :: iwork(:)
! .. Intrinsic Procedures ..
Intrinsic :: abs, cmplx, conjg, maxloc
! .. Executable Statements ..
Write (nout,*) 'F08FQF Example Program Results'
! Skip heading in data file
lda = n
liwork = 5*n + 3
lrwork = 2*n*n + 5*n + 1
lwork = n*(n+2)
Allocate (a(lda,n),work(lwork),rwork(lrwork),w(n),iwork(liwork))
! Read A from data file
If (uplo=='U') Then
Else If (uplo=='L') Then
End If
! Calculate all the eigenvalues and eigenvectors of A
! The NAG name equivalent of zheevd is f08fqf
Call zheevd(job,uplo,n,a,lda,w,work,lwork,rwork,lrwork,iwork,liwork, &
info)
Write (nout,*)
If (info>0) Then
Write (nout,*) 'Failure to converge.'
Else
! Print eigenvalues and eigenvectors
Write (nout,*) 'Eigenvalues'
Do i = 1, n
Write (nout,99999) i, w(i)
End Do
Write (nout,*)
Flush (nout)
! Normalize the eigenvectors so that the element of largest absolute
! value is real.
Do i = 1, n
rwork(1:n) = abs(a(1:n,i))
k = maxloc(rwork(1:n),1)
Call zscal(n,conjg(a(k,i))/cmplx(abs(a(k,i)),kind=nag_wp),a(1,i),1)
End Do
! ifail: behaviour on error exit
! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04daf('General',' ',n,n,a,lda,'Eigenvectors',ifail)
End If
99999 Format (3X,I5,5X,2F8.4)
End Program f08fqfe
``` | 662 | 1,996 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2024-10 | latest | en | 0.548437 |
https://uesigns.com/qa/quick-answer-what-math-should-a-3-year-old-know.html | 1,611,766,772,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610704828358.86/warc/CC-MAIN-20210127152334-20210127182334-00614.warc.gz | 584,381,802 | 9,131 | # Quick Answer: What Math Should A 3 Year Old Know?
## When should kids count to 10?
Between the ages of two and four, children’s ability to understand the actual concept of numbers and counting improves dramatically.
Most children are counting up to ten, or even beyond, by age four.
Skips in counting (1, 2, 3, 6…), however, are not uncommon even through kindergarten..
## Can most 2 year olds count to 10?
Though every child is different, most toddlers will be able to count to 10 by the time they are two-years-old. At this point in time they are probably repeating them mostly by memory and have yet to understand what they actually mean. This concept is known as “rote” counting.
## How high should a 4 year old be able to count to?
The average 4-year-old can count up to ten, although he may not get the numbers in the right order every time.
## What is normal behavior for a 3 year old?
During this year your child really starts to understand that her body, mind and emotions are her own. She knows the difference between feeling happy, sad, afraid or angry. Your child also shows fear of imaginary things, cares about how others act and shows affection for familiar people.
## Should a 3 year old be able to write their name?
It’s exciting when your child’s scribbles begin to look more like real letters. Some threes even start writing their name, or a few letters of it. But writing is one of those developmental milestones that varies greatly from child to child. Don’t stress out if your child isn’t even interested in writing.
## Can a 3 year old add and subtract?
By 2-years-old, many like 35-plus piece puzzles, memorize favorite books, and know the entire alphabet. By 3-years-old, they talk constantly, skip count, count backwards, and do simple adding and subtracting because they enjoy it.
## How many letters should a 3 year old know?
About 20 percent of children can recognize a few letters by age 3, often the letter that starts his or her own first name as well as other letters contained within the name. You may also notice that some of your child’s scribbles are starting to look like letters, especially the first letter of his or her name.
## What age should a child recognize letters and numbers?
A: Most children learn to recognize letters between ages 3 and 4. Typically, children will recognize the letters in their name first. By age 5, most kindergarteners begin to make sound-letter associations, such as knowing that “book” starts with the letter B.
## What should a 3 year old know educationally?
3- to 4-Year-Old Development: Cognitive MilestonesCorrectly name familiar colors.Understand the idea of same and different, start comparing sizes.Pretend and fantasize more creatively.Follow three-part commands.Remember parts of a story.Understand time better (for example, morning, afternoon, night)More items…•
## Why do toddlers wake at 3am?
Both too much and too little daytime sleep can spell problems at night. If you think your toddler might be overtired, try an earlier bedtime and make sure she’s napping enough during the day. If you think she’s waking at night because she’s napping too much, try shortening her nap.
## What number should a 5 year old count to?
Most 5-year-olds can recognize numbers up to ten and write them. Older 5-year-olds may be able to count to 100 and read numbers up to 20. A 5-year-old’s knowledge of relative quantities is also advancing. If you ask whether six is more or less than three, your child will probably know the answer.
## When should a child be able to count to 20?
Five-year-olds are transitioning into elementary school mathematics. At this age, a child can often count up to twenty and beyond, and they’ll start to apply this knowledge every week at school.
## How do I know if my 3 year old is gifted?
12 signs of a gifted childQuick learning. According to Louis, a telltale sign that a child is exceptionally bright for their age is how quickly they learn. … Big vocabulary. … Lots of curiosity. … Eagerness to learn. … Early reading. … Talent for puzzles or patterns. … Exceptional creativity. … Advanced reasoning skills.More items…•
## What math should a 4 year old know?
4 Years: As your kids enter preschool, their grasp of number skills will likely show another leap forward. During this year, your kids will learn more simple addition and subtraction problems (like 2+2 or 4-3) with the help of a visual aid, and be able to recognize and name one-digit numbers when they see them.
## What math skills should a 5 year old have?
Age five is an exciting year for developing math skills. School-aged children focus on addition and subtraction at first, and then eventually reach multiplication (in the form of skip counting) and division (in the form of equal shares).
## At what age should child know colors?
Generally, children learn to identify colours by 18 months. They can name different colours by the age of 2.5-3 years. However, sometimes it can be frustrating for parents as teaching colours is not as easy as other activities, say like teaching numbers.
## Should a 3 year old know the alphabet?
By age 3: Kids may recognize about half the letters in the alphabet and start to connect letters to their sounds. (Like s makes the /s/ sound.) By age 4: Kids often know all the letters of the alphabet and their correct order.
## What age should a child learn addition?
When teaching basic math skills such as addition, move at a comfortable pace for your student, ensuring that they have mastered number basics and can count to at least ten. Most children are ready to add by age 5 but may be able to understand these concepts at an earlier age.
## What should a 3 year old write?
Large Writing Implements A three-year-old with typical development should be able to hold and color with a regular crayon, marker, or pencil, but a younger child may benefit from a larger crayon with a more stable base. The larger design makes it easier for the toddler to hold and start to draw on paper.
## Is my toddler gifted checklist?
They are intended to serve as a checklist of the abilities revealed by many gifted children. Did your child walk and talk earlier than most other children of his age and gender? Did she show a comparatively early interest in words? Does he have an exceptionally large vocabulary for his age?
## At what age should a child count to 3?
By age 2, a child can count to two (“one, two”), and by 3, he can count to three, but if he can make it all the way up to 10, he’s probably reciting from rote memory. Kids this age don’t yet actually understand, and can’t identify, the quantities they’re naming. | 1,477 | 6,665 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2021-04 | latest | en | 0.970714 |
http://mathhelpforum.com/differential-geometry/177362-analytic-functions.html | 1,480,760,421,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698540915.89/warc/CC-MAIN-20161202170900-00495-ip-10-31-129-80.ec2.internal.warc.gz | 172,367,264 | 11,132 | 1. ## Analytic functions
The question
Let z = x + iy, with x and y real
If $f(z) = x^3 + iy^3$, find the value of the derivative of f at every point z where the derivative exists. Where is f analytic?
My attempt:
I used Cauchy Riemann sums as follows,
$u_x = 3x^2$
$u_y = 0$
$v_x = 0$
$v_y = 3y^2$
The equations hold when $3x^2 = 3y^2$. This equals |x| = |y| which are intersecting lines through the origin of the x-y plane. So, the function has a derivative on these intersecting lines. If my understanding of analyticity is correct, this function is analytic nowhere since there's no epsilon neighbourhood where the function is differentiable.
My issue is, how do I find the value of the derivative? Do I use the definition of a derivative, or is there an easy way to find it using my result above?
Thanks.
2. Originally Posted by Glitch
The question
If my understanding of analyticity is correct, this function is analytic nowhere since there's no epsilon neighbourhood where the function is differentiable.
Right, according to the definition of analytic function, $f$ must be complex differentiable on a region $R\subset\mathbb{C}$ .
3. Just restrict h to real values when applying the limit definition of the derivative. Since you know that f is differentiable at |x|=|y|, then the real-restricted limit must be equal to the complex limit. We end up getting
$f'(x+iy)=u_x(x,y)+iv_x(x,y)$.
By the way, the reason we know f is differentiable on those lines is because all the first-order partial derivatives (1) satisfy the Cauchy-Riemann equations; and (2) are continuous. You mentioned (1) but don't forget that (2) is also required.
4. Thanks guys. So should I be using the definition of the derivative, or is there a faster way to compute it using the partial derivatives?
5. Well it's generally true that $f'(x+iy)=u_x(x,y)+iv_x(x,y)$. So if all you need to do is compute it, then your task is easy. But if you need to prove it, then the definition of the derivative will have to do, unless you have a theorem at your disposal.
6. Thank you again. That saves me a lot of time! | 539 | 2,099 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.640625 | 4 | CC-MAIN-2016-50 | longest | en | 0.917094 |
https://m.hanspub.org/journal/paper/30769 | 1,611,719,738,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610704820894.84/warc/CC-MAIN-20210127024104-20210127054104-00535.warc.gz | 424,522,298 | 13,995 | 手动变速器换挡操作机构频响分析
# 手动变速器换挡操作机构频响分析Frequency Response Analysis of Manual Transmission Shifting Operation Mechanism
Abstract: Aiming at the problem that the secondary impact caused by shifting of a domestic vehicle manual transmission affects the quality of shifting operation of users, the performance of the external con-trol mechanism of gearbox was studied and its structural dynamic response performance was opti-mized to reduce the secondary impact of shifting. By creating the finite element model of the exter-nal control mechanism of the manual transmission and using NASTRAN analysis tool, the frequency response analysis and demonstration are carried out based on the calculation with theoretical deri-vation of mode and frequency response. The experimental results show that the simulation results are accurate and reliable. Finally, the factors that affected the secondary impact were discussed from the system damping coefficient and the stiffness of the cable bracket. The results show that increasing the damping of the shift system, increasing the stiffness of the shift cable bracket and reducing the stiffness of the shift cable joint were beneficial to reducing the secondary impact of the shift.
1. 引言
2. 换挡机构分析
2.1. 换挡机构工作原理
Figure 1. Shift out operating mechanism
2.2. 换挡机构模态
$\left[M\right]\left\{\stackrel{¨}{x}\right\}+\left[C\right]\left\{\stackrel{˙}{x}\right\}+\left[K\right]\left\{x\right\}=\left\{f\right\}$ (1)
$\left[H\left(s\right)\right]=\frac{\left\{X\left(s\right)\right\}}{\left\{F\left(s\right)\right\}}={\left[Z\left(s\right)\right]}^{-1}=\frac{1}{{s}^{2}\left[M\right]+s\left[C\right]+\left[K\right]}$ (2)
2.3. 换挡机构频响分析理论
$m\stackrel{¨}{x}+c\stackrel{˙}{x}+kx={P}_{0}\mathrm{sin}\omega t$ (3)
$x=B\mathrm{sin}\left(\omega t-\varphi \right)$ (4)
$H\left(\omega \right)=\frac{x\left(w\right)}{P\left(w\right)}=\frac{1}{k-m{\omega }^{2}+ic\omega }$ (5)
$A\left(\omega \right)=\frac{\frac{1}{{\omega }_{n}^{2}}}{\sqrt{{\left[1-{\left(\frac{\omega }{{\omega }_{n}}\right)}^{2}\right]}^{2}+{\left[2\xi \frac{\omega }{{\omega }_{n}}\right]}^{2}}}$ (6)
Figure 2. Amplitude frequency diagram
3. 有限元模型的建立
Figure 3. Fem model of external control system
Table 1. Material name and parameter list
Figure 4. Select the location of the test points
Table 2. Comparative analysis of free modal simulation and experimental results
4. 频率响应分析
Figure 5. The position where dynamic loads are applied
4.1. 系统阻尼系数对振动响应的影响
(a) (b)(c)
Figure 6. Response of corresponding position under different damping coefficients. (a) End of the rod; (b) Balancing weight; (c) Shift stay
4.2. 拉索支架刚度对振动响应的影响
(a) (b) (c)
Figure 7. Response of the corresponding position under different stiffness of the cable supports. (a) End of the rod; (b) Balancing weight; (c) Shift stay
5. 结论
1) 在合适的范围内尽量增加整个系统的阻尼，有利于减小二次冲击的峰值。可考虑在拉索支架安装座处添加阻尼橡胶垫。
2) 增加换挡拉索支架的刚度，有利于减小产生的低频成分的二次冲击的峰值，同时提高产生共振的固有频率。可考虑适当增加拉索支架的厚度；改变拉索支架加强筋的结构，以增大刚度。
3) 适当减小换挡拉索接头刚度，有利于增大变形，吸收更多的二次冲击能量。可考虑对换挡拉索接头橡胶进行镂空设计。
NOTES
*通讯作者。
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[10] 周志强, 孙宝群, 汪韶杰, 周友. 某手动变速器仿真分析与优化研究[J]. 农业装备与车辆工程, 2019, 57(3): 49-52.
[11] 傅志方, 华宏星. 模态分析理论与应用[M]. 上海: 上海交通大学出版社, 2000: 50-86.
[12] 杨景义, 王信义. 试验模态分析[M]. 北京: 北京理工大学出版社, 1990: 117-158.
Top | 1,654 | 3,826 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 28, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2021-04 | latest | en | 0.745734 |
https://www.r-bloggers.com/importance-sampling-with-infinite-variance/ | 1,556,286,032,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578806528.96/warc/CC-MAIN-20190426133444-20190426155444-00086.warc.gz | 782,474,256 | 18,036 | # importance sampling with infinite variance
November 12, 2015
By
(This article was first published on Xi'an's Og » R, and kindly contributed to R-bloggers)
“In this article it is shown that in a fairly general setting, a sample of size approximately exp(D(μ|ν)) is necessary and sufficient for accurate estimation by importance sampling.”
Sourav Chatterjee and Persi Diaconis arXived yesterday an exciting paper where they study the proper sample size in an importance sampling setting with no variance. That’s right, with no variance. They give as a starting toy example the use of an Exp(1) proposal for an Exp(1/2) target, where the importance ratio exp(x/2)/2 has no ξ order moment (for ξ≥2). So the infinity in the variance is somehow borderline in this example, which may explain why the estimator could be considered to “work”. However, I disagree with the statement “that a sample size a few thousand suffices” for the estimator of the mean to be close to the true value, that is, 2. For instance, the picture I drew above is the superposition of 250 sequences of importance sampling estimators across 10⁵ iterations: several sequences show huge jumps, even for a large number of iterations, which are characteristic of infinite variance estimates. Thus, while the expected distance to the true value can be closely evaluated via the Kullback-Leibler divergence between the target and the proposal (which by the way is infinite when using a Normal as proposal and a Cauchy as target), there are realisations of the simulation path that can remain far from the true value and this for an arbitrary number of simulations. (I even wonder if, for a given simulation path, waiting long enough should not lead to those unbounded jumps.) The first result is frequentist, while the second is conditional, i.e., can occur for the single path we have just simulated… As I taught in class this very morning, I thus remain wary about using an infinite variance estimator. (And not only in connection with the harmonic mean quagmire. As shown below by the more extreme case of simulating an Exp(1) proposal for an Exp(1/10) target, where the mean is completely outside the range of estimates.) Wary, then, even though I find the enclosed result about the existence of a cut-off sample size associated with this L¹ measure quite astounding.
“…the traditional approach of testing for convergence using the estimated variance of the importance sampling estimate has a flaw: for any given tolerance level ε, there is high probability that the test declares convergence at or before a sample size that depends only on ε and not on the two distributions f and g. This is absurd, since convergence may take arbitrarily long, depending on the problem”
The second part of the paper starts from the remark that the empirical variance estimate is a poor choice of convergence criterion. Especially when the theoretical variance does not exist. As put by Art Owen in his importance sampling notes, “Badly skewed weights could give a badly estimated mean along with a bad variance estimate that masks the problem”. The authors suggest to consider instead a sort of inverse effective sample size derived from the importance weights and given by max ω[t] / ∑ ω[t], which should be small enough. However, replicating the above Exp(1) versus Exp(1/10) example, the (selected) picture below shows that this criterion may signal that all is fine just before storm hits!
The effective sample size has exactly the same issue in that a much lower value of the criterion may just be lurking around the corner. Which makes it hard to trust it at face value.
R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more... | 841 | 3,951 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2019-18 | latest | en | 0.929443 |
https://wiki.cdot.senecacollege.ca/w/index.php?title=J.Y.S&oldid=46914&printable=yes | 1,571,264,387,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986670928.29/warc/CC-MAIN-20191016213112-20191017000612-00293.warc.gz | 757,049,223 | 7,141 | # J.Y.S
Jump to: navigation, search
This page is to efficiently manage DBS301 Group assignments together !
## Member List
First Name Last Name wiki id Learn e-mail Phone
YuJin Jeong yujin.jeong yjeong 647 - 832 - 6771
Saad
James
Dale
# Assignment 1
## Due Date
Thursday, October 21st, 4:00pm Printout submission only( SELECT Statements + ALL outputs)
## Solution
### 1.
YuJin
```SELECT employee_id, RPAD(CONCAT(CONCAT(last_name, ', '),first_name), 25) "Full Name", job_id,
TO_CHAR(TRUNC(hire_date, 'MONTH'), 'fmMonth Ddspth "in the year" YYYY') "Start Date"
FROM employees
WHERE TO_CHAR(hire_date, 'Mon') IN ('May', 'Nov')
ORDER BY hire_date DESC;
```
Saad
James
Dale
### 2.
YuJin
```SELECT 'Employee named ' || first_name || ' ' || last_name || ' who is '|| job_id || \
' will have a new salary of \$' || salary*1.15 "Happy Employees"
FROM employees
WHERE salary BETWEEN 5000 AND 12000
AND job_id IN ('IT_PROG', 'ST_CLERK')
ORDER BY salary;
```
Saad
James
Dale
### 3.
YuJin
```SELECT last_name, salary, job_id,
NVL(TO_CHAR(manager_id), 'No Manager') "Manager #",
TO_CHAR(salary*12, '\$999,999') "Total Income"
FROM employees
WHERE (job_id LIKE 'MK%' OR NVL(manager_id, 0) = 0)
AND salary*(1 + NVL(commission_pct,0)) + 1000 > 10000
ORDER BY salary;
```
Saad
James
Dale
YuJin
Saad
James
Dale
YuJin
Saad
James
Dale
YuJin
Saad
James
Dale | 466 | 1,424 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2019-43 | latest | en | 0.640672 |
http://www.numbersaplenty.com/18793 | 1,590,734,850,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347402457.55/warc/CC-MAIN-20200529054758-20200529084758-00407.warc.gz | 191,123,944 | 3,401 | Search a number
18793 is a prime number
BaseRepresentation
bin100100101101001
3221210001
410211221
51100133
6223001
7105535
oct44551
927701
1018793
1113135
12aa61
138728
146bc5
15587d
hex4969
18793 has 2 divisors, whose sum is σ = 18794. Its totient is φ = 18792.
The previous prime is 18787. The next prime is 18797. The reversal of 18793 is 39781.
It can be divided in two parts, 187 and 93, that multiplied together give a triangular number (17391 = T186).
18793 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.
It is a strong prime.
It can be written as a sum of positive squares in only one way, i.e., 17424 + 1369 = 132^2 + 37^2 .
It is a cyclic number.
It is not a de Polignac number, because 18793 - 213 = 10601 is a prime.
It is a nialpdrome in base 12.
It is not a weakly prime, because it can be changed into another prime (18797) by changing a digit.
It is a pernicious number, because its binary representation contains a prime number (7) of ones.
It is a polite number, since it can be written as a sum of consecutive naturals, namely, 9396 + 9397.
It is an arithmetic number, because the mean of its divisors is an integer number (9397).
218793 is an apocalyptic number.
It is an amenable number.
18793 is a deficient number, since it is larger than the sum of its proper divisors (1).
18793 is an equidigital number, since it uses as much as digits as its factorization.
18793 is an odious number, because the sum of its binary digits is odd.
The product of its digits is 1512, while the sum is 28.
The square root of 18793 is about 137.0875632579. The cubic root of 18793 is about 26.5867573105.
The spelling of 18793 in words is "eighteen thousand, seven hundred ninety-three". | 513 | 1,784 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2020-24 | latest | en | 0.906643 |
http://mathhelpforum.com/calculus/109669-stationary-points-easy-wrong.html | 1,527,310,794,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794867309.73/warc/CC-MAIN-20180526033945-20180526053945-00072.warc.gz | 183,265,559 | 10,515 | # Thread: Stationary Points - easy or wrong?
1. ## Stationary Points - easy or wrong?
I have to find and classify the stationary points of
$\displaystyle f(x,y)=2x^3-2y^3-3ax^2+3by^2+100$
$\displaystyle a,b \in \Re$
So:
$\displaystyle f_x=6x^2-6ax=0 \Rightarrow 6x^2=6ax \Rightarrow x=a$
$\displaystyle f_y=-6y^2+6by=0+ \Rightarrow-6y^2+6by=0 \Rightarrow y=b$
$\displaystyle f_{xx}=12x-6a$
$\displaystyle f_{yy}=-12y+6b$
$\displaystyle f_{xx}(a,b)=12a-6a=6a$
$\displaystyle f_{yy}(a,b)=-12b+6b=-6b$
$\displaystyle \triangle(a,b)=-36ab$
Have I done this right? How would I classify this?
2. Hello, billym!
I will assume that $\displaystyle a\text{ and }b$ are positive.
Find and classify the stationary points of:
. . $\displaystyle f(x,y)=2x^3-2y^3-3ax^2+3by^2+100 \qquad a,b \in \Re^{{\color{red}+}}$
$\displaystyle f_x \:=\:6x^2 - 6ax \:=\:0 \quad\Rightarrow\quad 6x(x-a) \:=\:0 \quad\Rightarrow\quad x \:=\:0,a$
$\displaystyle f_y \:=\:-6y^2 + 6by \:=\:0 \quad\Rightarrow\quad 6y(b - y) \:=\:0 \quad\Rightarrow\quad y \:=\:0,b$
There are four stationary points to examine: .$\displaystyle (0,0), (a,b),(a,0),(0,b),$
We have: .$\displaystyle \begin{Bmatrix}f_{xx} &=& 12x - 6a \\ f_{yy} &=& -12y + 6b \\ f_{xy} &=& 0 \end{Bmatrix}$
Then: .$\displaystyle D \;=\;6(2x-a)\,(-6)(2y-b) - 0^2 \;=\;-36(2x-a)(2y-b)$
At $\displaystyle (0,0)\!:\;\;D \:=\:(-36)(-a)(-b) \:=\:-36$ . . . saddle point at $\displaystyle (0,0,100)$
At $\displaystyle (a,b)\!:\;\;D \:=\:(-36)(a)(b) \:=\:-36ab$ . . . saddle point at $\displaystyle (a,\:b,\:b^3-a^3+100)$
At $\displaystyle (a,0)\!:\;\;D \:=\:(-36)(a)(-b) \:=\:+36ab$ . . . extreme point
. . At $\displaystyle a,0)\!:\;\;f_{xx} \:=\:12a - 6a \:=\:+6a$ . . . minimum at $\displaystyle (a,\:0.\:100-a^3)$
At $\displaystyle (0,b)\!:\;\;D \:=\:(-36)(-a)(b) \:=\:+36ab$ . . . extreme point
. . At $\displaystyle (0,b)\!:\;\;f_{yy} \:=\:-12b + 6b \:=\:-6b$ . . . maximum at $\displaystyle (0,\:b,\:100 + b^3)$
3. Originally Posted by billym
I have to find and classify the stationary points of
$\displaystyle f(x,y)=2x^3-2y^3-3ax^2+3by^2+100$
$\displaystyle a,b \in \Re$
So:
$\displaystyle f_x=6x^2-6ax=0 \Rightarrow 6x^2=6ax \Rightarrow x=a$
$\displaystyle \color{red}Or\,\,x=0$
$\displaystyle f_y=-6y^2+6by=0+ \Rightarrow-6y^2+6by=0 \Rightarrow y=b$
$\displaystyle \color{red}Or\,\,y=0$
$\displaystyle f_{xx}=12x-6a$
$\displaystyle f_{yy}=-12y+6b$
$\displaystyle f_{xx}(a,b)=12a-6a=6a$
$\displaystyle f_{yy}(a,b)=-12b+6b=-6b$
$\displaystyle \triangle(a,b)=-36ab$
Have I done this right? How would I classify this?
Yes, it looks fiine (just check the cases in red above), and now (a,b) is a saddle point (also called sometimes stationary point) iff $\displaystyle ab>0$, so that the function's Hessian (the matrix whose determinant you denoted by $\displaystyle \Delta$) is indefinite (if you don't know these terms from linear algebra, which would be odd since you're studying multiariable calculus then just forget them...for now).
Tonio | 1,182 | 3,008 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.34375 | 4 | CC-MAIN-2018-22 | latest | en | 0.38082 |
http://thecooperschool.org/scoop/fractions-and-settlers/ | 1,553,356,022,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912202872.8/warc/CC-MAIN-20190323141433-20190323163433-00135.warc.gz | 209,985,401 | 19,915 | ## THE COOPER SCHOOL
### Fractions and Settlers March 29, 2018
Look Out For Birds!
It’s about that time of year where birds take over Grade Two. Our final culminating project starts just after break and kids are already squawking with excitement!!! We wrote some poems inspired by birds of the lowcountry this week and we encourage students to explore birds even more over Spring Break. Some great activities would be a bird walk/hike, a journal of birds you’ve seen on a trip or in the backyard, and even exploring with binoculars. Students can share their sightings on our first Morning Meeting upon return!
Half and Half
Can you believe our little guys are dividing and making fractions? This week we explored halves, fourths, thirds using grouping. We learned that if we could split a number into even groups, we form fractions based on the parts to whole ratio. As of now, we’ve been using even and odd numbers up to 20. Another one of our strategies is to draw an array of the total and then circle equal groups based on the denominator. Try asking your child a problem like, “If Sally has 8 apples, and her brother eats ¼ of them, how many did her brother eat?”
Charles Towne and Kiawah Natives
Grade Two wrapped up our social studies unit on the Charles Towne settlers this week. Yesterday we discussed the things that the Kiawahs taught the settlers about hunting and gathering and fishing in the lowcountry. We’ve been playing this clever game where students can earn the titles of the 8 proprietors of Charles Towne. These founders of our city were given this title and land in the Carolinas in exchange for loyalty to King Charles II. In order to demonstrate the political implications of their titles, Second Grade proprietors were able to line up first and choose other proprietors to serve with them. We even exiled King Charles at one point!!
Important Dates
Spring Break Begins March 30
School Resumes April 9
### Annual Fund Update
Thank you so much to all of you who have so generously donated to the Annual Fund. This year, to my delight, the Silent Auction raised more money than ever before. I wanted to take a moment to let you know exactly where your Silent Auction donation dollars are going…
SITEMAP | 485 | 2,304 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2019-13 | latest | en | 0.934365 |
https://powerof-numerology.com/what-are-expression-numbers/ | 1,721,794,283,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763518154.91/warc/CC-MAIN-20240724014956-20240724044956-00130.warc.gz | 394,513,125 | 9,345 | Numerology
# What Are Expression Numbers
## What Are Expression Numbers
An expression number is derived from your original name as registered in your birth certificate. Sometimes birth names are entered erroneously in birth certificates but if the errors are minor and are accepted as they are, then they can be used to determine the Expression numbers.
Suppose you were adopted or had a name change, you should use your original name to determine the expression number. In case you are unable to remember your original name after adoption, you should use the earliest name that you can remember however this method will not be as effective without your original name.
Expression numbers are single-digit outcomes between 1 and 9. The answers come from adding together the numbers assigned to each letter of your name. Your expression number should not be mistaken for your Life Path Number which is derived from your date of birth.
The alphabet has 26 letters each of which finds a spot under the range of 1 to 9. Letter I is the last in the sequence to fall under a single-digit number which is 9. That means letter J (which falls under number 10) will now fall under number 1 simply by adding 1+0 to get 1. This process is repeated for the rest of the letters in the alphabet to obtain single-digit numbers under which they fall.
## How To Obtain Your Expression Number
The easiest way to obtain your expression number is to use our Expression Number Calculator. Or read this section to calculate it on your own.
Most people have 3 official names, several others have much more. Regardless, you can determine your expression number by first placing each letter of your name under the relevant number.
Then sum up the total of each of your names separately, ensuring you reduce each double-digit to a single-digit number.
Finally, sum up the single digits from each of your names to find your special number.
123456789
ABCDEFGHI
JKLMNOPQR
STUVWXYZ
For example, if the name is John Rayan the calculations will look like this:
John: 1 + 6 + 8 + 5 = 20 = 2 + 0 = 2
Rayan: 9 + 1 + 7 + 1 + 5 = 23 = 2 + 3 = 5
Next, sum up 2 and 5 to get 7.
If you come across numbers 11, 22 or 33 do not reduce them further as these are Master Numbers.
Determining your expression number helps you to achieve your ultimate purpose in life by enhancing your understanding of yourself at a deeper level. Your talents, abilities, and shortcomings became much clearer as you became you. Before you were born, your name was determined by your parents and they intuitively picked your name to match your energy.
## What Your Expression Number Means
### Expression Number 1
You are the go-getter, always at the front line overseeing things and ensuring tasks are completed and achieved.
### Expression Number 2
You offer conflict resolution and prefer peace to anything. Often you relate well with most people and you experience great influence from other people.
### Expression Number 3
You are hyper and thrive in social gatherings but you are unable to commit to anything long enough to see it through.
### Expression Number 4
You are the no-nonsense type who takes on all tasks and introduces order in all places while anchoring everything with stability.
### Expression Number 5
You are the free spirit who earns secret admiral from others. Your adventurous nature seems to derail you from being in one place or committing to anything.
### Expression Number 6
You are the darling of many with a very likable character so people come to you for advice. This at times gets into your head and you turn bossy and controlling.
### Expression Number 7
You look out for yourself and dedicate a lot of time in searching for the truth. Your biggest interest is in the sciences.
### Expression Number 8
Your competitive nature is admirable but questionable because you hesitate to work with others or take orders.
### Expression Number 9
You are philanthropic and optimistic and make a very good teammate. Your ultimate goal would be to make the world a better place.
### Expression Number 11
The Master Numbers also have their meanings much deeper and stronger than those of the normal expression numbers.
The most notable ones for Number 11 are empathy, psychic gifts and ability to channel spiritual information.
### Expression Number 22
People with immense ability to bring significant change to the world fall under Number 22.
### Expression Number 33
Number 33 exudes spiritual ability and you are a great advocate for honesty and justice.
Luna is the editor in chief and an absolute numerology nut. She loves teaching numerology and helping clients with the power of numerology to live a fulfilling life. | 988 | 4,724 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2024-30 | latest | en | 0.925776 |
https://discuss.python.org/t/queue-simulation/9673 | 1,660,304,995,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571692.3/warc/CC-MAIN-20220812105810-20220812135810-00683.warc.gz | 222,227,491 | 5,044 | # Queue simulation
Hi, I’m currently working on my mini project to build a simulation of queue system in bank. The goals of this program is to be able to divide right amount of queue for each teller, so none teller has longer queue than other tellers.
Here is glimpse of my code:
``````queue_dict = {'Angel':[],
'Mellysa':[],
'David':[],
'Thom':[],
'Monica':[]
}
queue_no = 0
while True:
queue_no += 1
customer_name = input("Enter your name: ")
if customer_name == '':
break
#Find the teller that has lowest number of queue
lowest_queue = np.inf
for teller_name, customers_queue in queue_dict.items():
if len(customers_queue)<lowest_queue:
lowest_queue = len(customers_queue)
chosen_teller = teller_name
# Get the customer on the queue of the chosen teller
queue_dict[chosen_teller].append(customer_name)
print(f"{customer_name}, please go the teller {chosen_teller}")
print()
``````
My question is, from my code above, can someone help me If i want to create a code to select the very first and last customer?
You cannot, because you only keep the order by teller queue. If you want to have a global ordering, you have to keep it. Either as a “memory” of the arrival order(`arrivals.append(customer_name)`, where arrivals is a list) or as a marker of the arrival order on the teller queue, `queue_dict[chosen_teller].append((customer_name, arrival_no))`, where you keep a counter for arrivals.
Thank you in advance for your hand on my case. But I still can’t figure it out where and how should I write my code in order to achieve my goal. Can you please help me with that?
How can I help you with that? You know how to create a list and append to it, so the first solution I proposed should not be a problem. On the list I called `arrivals` the first entry is the first customer to arrive and the last one the last customer to arrive. | 448 | 1,847 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2022-33 | latest | en | 0.885269 |
https://www.answers.com/Q/How_many_cups_of_shortening_equal_one_pound | 1,571,387,006,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986679439.48/warc/CC-MAIN-20191018081630-20191018105130-00249.warc.gz | 757,006,534 | 40,276 | Shortening
# How many cups of shortening equal one pound?
###### 04/22/2013
1 cup of shortening weighs 7 oz. So if 16 oz. = l pound, its about 2 1/4 cups. The best way to convert is to multiply how many cups you need by 16 oz., then divide by 7. That will get you back to cups. | 86 | 280 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.578125 | 4 | CC-MAIN-2019-43 | latest | en | 0.898756 |
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# Math Grade 5 Module 2 Learning Target Assessment (BILINGUAL)
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I created this assessment as an alternative for the Grade 5 Module 2 EngageNY Common Core final assessment. This assessment is more comprehensive and student friendly.
Each section of the test presents the learning target and then problems to go with that target. I arranged the test in this fashion to be able to easily identify the areas in which students have excelled and fallen short. I will then use this information to target those skills that need to be further reinforced during my interventions.
The test is worth points and covers all learning targets within Module 2 including.
Mental Strategies for Multi-Digit Whole Number Multiplication
The Standard Algorithm for Multi-Digit Whole Number Multiplication
Decimal Multi-Digit Multiplication
Measurement Word Problems with Whole Number and Decimal Operation
Mental Strategies for Multi-Digit Whole Number Division
Partial Quotient and Multi-Digit Whole Number Division
Partial Quotient and Decimal Multi-Digit Division
Measurement Word Problems with Multi-Digit Division
This test could also be used as a review packet.
Furthermore, I have created an almost identical document to this one with different numbers that I used a study guide for students before the test.
Check out the STUDY GUIDE here:
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\$2.00 | 358 | 1,654 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2017-34 | latest | en | 0.862735 |
https://www.askiitians.com/forums/Trigonometry/23/24184/trigo-trigo.htm | 1,701,892,817,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100603.33/warc/CC-MAIN-20231206194439-20231206224439-00158.warc.gz | 731,971,139 | 43,836 | # prove thattanA + 2tan2A + 4tan4A + 8cot8A = cotA
420 Points
13 years ago
Solving from right
tan A + 2tan2A + 4tan4A + 8cot8A = tan A + 2tan2A + 4tan4A + 8/tan8A
= tan A + 2tan2A + 4tan4A + 8(1-tan24A)/2tan4A
= tan A + 2tan2A + [{4tan4A(tan4A)} + 4 (1-tan24A)]/tan4A
= tan A + 2tan2A + [4tan24A + 4 - tan24A]/tan4A
= tan A + 2tan2A + 4/tan4A
Proceeding as above, we will reach to
tan A + 2tan2A + 4tan4A + 8cot8A = 1/tanA = cotA
Hence proved.
All the best.
AKASH GOYAL
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509 Points
13 years ago
TANA + 2TAN2A + 4TAN4A + 8COT8A = COTA .........1
WE HAVE FORMULA , COTA-TANA=2COT2A
EQ 1 CAN BE WRITTEN AS
2TAN2A + 4TAN4A + 8COT8A = COTA-TANA
2TAN2A + 4TAN4A + 8COT8A = 2COT2A ( BY USING FORMULA )
4TAN4A + 8COT8A = 2COT2A - 2TAN2A
4TAN4A + 8COT8A =4COT4A (BY USING FORMULA)
8COT8A = 4COT4A - 4TAN4A
=8COT8A (BY USING FORMULA )
HENCE PROVED
Rishi Sharma
3 years ago
Dear Student,
Solving from right
tan A + 2tan2A + 4tan4A + 8cot8A
= tan A + 2tan2A + 4tan4A+ 8/tan8A
= tan A + 2tan2A + 4tan4A + 8(1-tan24A)/2tan4A
= tan A + 2tan2A + [{4tan4A(tan4A)} + 4 (1-tan24A)]/tan4A
= tan A + 2tan2A + [4tan24A + 4 - tan24A]/tan4A
= tan A + 2tan2A + 4/tan4A
Proceeding as above, we will reach to
tan A + 2tan2A + 4tan4A + 8cot8A = 1/tanA = cotA
Thanks and Regards | 741 | 1,639 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2023-50 | latest | en | 0.619907 |
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All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing...
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Seite 39
von Robert Simson - 1806 - 518 Seiten
Vollansicht - Über dieses Buch
## A Complete Treatise on Practical Land-surveying: In All Its Departments ...
Anthony Nesbit - 1847 - 426 Seiten
...accuracy of the previous work. Moreover, since the sum of all the interior angles of any polygon is equal to twice as many right angles as the figure has sides, lessened by four ; as the given figure has five sides, the sum of all its interior angles must be 2x5...
Vollansicht - Über dieses Buch
## Elementary Course of Geometry ...
Charles William Hackley - 1847 - 248 Seiten
...Hence it follows that the sum of all the inward angles of the polygon alone, A + B -f- C + D + E, is equal to twice as many right angles as the figure has sides, wanting the said four right angles. QED Corol. 1. In any quadrangle, the sum of all the four inward...
Vollansicht - Über dieses Buch
## The definitions, postulates, axioms, and enunciations of the propositions of ...
Euclides - 1848
...opposite angles ; and the three ulterior angles of every triangle are together equal to two right angles. COR. 1. All the interior angles of any rectilineal...twice as many right angles as the figure has sides. COB. 2. All the exterior angles of any rectilineal figure, made by producing the sides successively...
Vollansicht - Über dieses Buch
## The first three books of Euclid's Elements of geometry, with theorems and ...
Euclid, Thomas Tate - 1849 - 108 Seiten
...triangles ; that is (Cor. 2. i. 15.), together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal...twice as many right angles as the figure has sides. COR. 2. All the exterior angles of any rectilineal figuro, are together equal to four right angles....
Vollansicht - Über dieses Buch
## Elements of Geometry and Conic Sections
Elias Loomis - 1849 - 252 Seiten
...(Prop. XXVII., BI), that is, as there are sides of the polygon BCDEF. Also, the angles of the polygon, together with four right angles, are equal to twice as many right angles as the figure has sides (Prop. XXVIII., BI); hence all the angles of the triangles are equal to all the angles of the polygon,...
Vollansicht - Über dieses Buch
## Elements of Geometry and Trigonometry Translated from the French of A.M ...
Charles Davies - 1849 - 384 Seiten
...to two right angles, taken as many times, less two, as the polygon has sides (Prop. XXVI.); that is, equal to twice as many right angles as the figure has sides, wanting four right angles. Hence, the interior angles plus four right Let the sides of the polygon...
Vollansicht - Über dieses Buch
## Minutes of the Committee of Council on Education, with Appendices, Band 2
...thickness. GEOMETRY AND TRIGONOMETRY. (One Question is only to be answered in each Section.) Section I. 1. All the interior angles of any rectilineal figure,...twice as many right angles as the figure has sides. 2. If the square described upon one side of a triangle be equal to the sum of the squares described...
Vollansicht - Über dieses Buch
## Reports on Elementary schools
...ring. GEOMETRY AND TRIGONOMETRY. (One Question is only to be answered in each Section.) Section I. 1. All the interior angles of any rectilineal figure,...twice as many right angles as the figure has sides. 2. If the square described upon one side of a triangle be equal to the sum of the squares described...
Vollansicht - Über dieses Buch
## The Church of England quarterly review, Band 28
1850
...revelation could supersede the reasoning of the proposition that all the interior angles of any rectilinear figure, together with four right angles, are equal...twice as many right angles as the figure has sides : and the dictum is equally true, too, in moral science — only in any particular case to dogmatize...
Vollansicht - Über dieses Buch
## Elementary Geometry: With Applications in Mensuration
Charles Davies - 1850 - 236 Seiten
...triangles is equal to two right angles (Th. xvii) : hence, the sum of the angles of all the triangles is equal to twice as many right angles as the figure has sides. But the sum of all the angles about the point P is equal to four right angles (Th. ii. Cor. 3) ; and...
Vollansicht - Über dieses Buch | 1,142 | 4,656 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2022-33 | latest | en | 0.857171 |
https://www.joyprosperitycoaching.com/business-tips/how-to-determine-what-a-business-is-worth.html | 1,618,544,584,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038088471.40/warc/CC-MAIN-20210416012946-20210416042946-00449.warc.gz | 709,924,263 | 10,705 | # How to determine what a business is worth
## How do you value a small business?
Here are the main methods. Asset valuation . For a simple business asset valuation , add up the assets of a business and subtract the liabilities. Price earnings ratio. The price earnings ratio (P/E ratio) is the value of a business divided by its profits after tax. Which P/E ratio to use? Entry cost valuation .
## What is the rule of thumb for valuing a business?
The most commonly used rule of thumb is simply a percentage of the annual sales, or better yet, the last 12 months of sales/revenues. Another rule of thumb used in the Guide is a multiple of earnings. In small businesses , the multiple is used against what is termed Seller’s Discretionary Earnings (SDE).
## What are the 3 ways to value a company?
Valuation Methods When valuing a company as a going concern, there are three main valuation methods used by industry practitioners: (1) DCF analysis, (2) comparable company analysis, and (3) precedent transactions. Comparable company analysis. Precedent transactions analysis. Discounted Cash Flow (DCF)
## How much should I pay for a business?
Usually, 20 to 25 percent is considered adequate. This means that the buyer should pay between \$80,000 and \$100,000 for this business .
## How do you value a business with no assets?
Market-based business valuations calculate your business’s value by comparing it to similar businesses that have previously sold. This method applies well to a business with no assets , but comes with the challenge of identifying sufficiently comparable competitors (who would presumably also have no assets .)
## How do you value a business quickly?
Value = Earnings after tax × P/E ratio. Once you’ve decided on the appropriate P/E ratio to use, you multiply the business’s most recent profits after tax by this figure. For example, using a P/E ratio of 6 for a business with post-tax profits of £100,000 gives a business valuation of £600,000.
You might be interested: Which of the following is not a difference between a retail business and a service business?
## How do you value a business based on cash flow?
Business valuation is typically based on three major methods: the income approach, the asset approach and the market (comparable sales) approach. Among the income approaches is the discounted cash flow methodology calculating the net present value (‘NPV’) of future cash flows for an enterprise.
## What are the 5 methods of valuation?
There are five main methods used when conducting a property evaluation; the comparison, profits, residual, contractors and that of the investment. A property valuer can use one of more of these methods when calculating the market or rental value of a property.
## Which valuation method is best?
Discounted Cash Flow Analysis ( DCF ) In this respect, DCF is the most theoretically correct of all of the valuation methods because it is the most precise.
## What is enterprise value of a company?
Enterprise value (EV) is a measure of a company’s total value , often used as a more comprehensive alternative to equity market capitalization. Enterprise value includes in its calculation the market capitalization of a company but also short-term and long-term debt as well as any cash on the company’s balance sheet.
## Is it smart to buy a business?
If you buy an existing business , you’re bound to save some time in the early stages of business ownership. Crucial tasks such as looking for real estate, hiring employees, and researching equipment can take a lot of time.
## What documents should you request when buying a business?
At a minimum, we recommend you request and review the following: last two financial years accounts (Profit and Loss and Balance Sheets); current year financials; last four quarters of Business Activity Statements (BAS); last income tax return; and. listing of every asset the sale will include.
You might be interested: How to get a business loan from a bank
## What should I check before buying a business?
Before you buy a business , do some due diligence. Learn About the Business Finances. Inspect the Physical Assets. Read the Lease. Check the Business’s Legal Status. Get the Owner’s Guarantee. Hold Back Some of the Purchase Price. | 882 | 4,280 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2021-17 | latest | en | 0.939204 |
https://www.coursehero.com/file/p6h7vuf/and-each-quarter-December-31-March-31-and-June-30-through-June-30-2024-three/ | 1,582,471,722,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875145774.75/warc/CC-MAIN-20200223123852-20200223153852-00319.warc.gz | 683,927,432 | 74,134 | # And each quarter december 31 march 31 and june 30
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and each quarter December 31, March 31, and June 30) through June 30, 2024 (three-year lease term). The florist had the option to purchase the truck on September 29, 2023, for \$14,000 when it was expected to have a residual value of \$14,000. The estimated useful life of the truck is four years. Mid-South Auto Leasing's quarterly Interest rate for determining payments was 3% (approximately 12% annually). mpanies use stralght-line depreciation or amortization. Anything Grows' Incremental Interest rate is 12% Doints eBook Hint: A lease term ends for accounting purposes when
an option becomes exercisable if it's expected to be exercised (l.e., a BPO). (FV of \$1. PV of \$1, FVA of \$1, PVA of \$1, FVAD of \$1 and PVAD of \$1) (Use appropriate factor(s) from the tables provided.) Print References Required: 1. Calculate the amount of selling profit that Mid-South would recognize In this sales-type lease. (Be careful to note that, although payments occur on the last calendar day of each quarter, since the first payment was at the beginning of the lease, payments represent an annuity due.) 2. Prepare the appropriate entries for Anything Grows and Mid-South on September 30, 2021. 3. Prepare an amortization schedule(s) describing the pattern of Interest expense for Anything Grows
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Depdendent Variable
Number of equations to solve: 23456789
Equ. #1:
Equ. #2:
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Equ. #6:
Equ. #7:
Equ. #8:
Equ. #9:
Solve for:
Dependent Variable
Number of inequalities to solve: 23456789
Ineq. #1:
Ineq. #2:
Ineq. #3:
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• square roots in radical form calculator | 1,019 | 4,268 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2018-13 | latest | en | 0.947862 |
http://library.thinkquest.org/27930/forces.htm | 1,386,897,409,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1386164789076/warc/CC-MAIN-20131204134629-00074-ip-10-33-133-15.ec2.internal.warc.gz | 98,748,404 | 4,306 | ## Introduction
At the temperatures common to our world, four discrete forces govern the interactions of matter - gravity, electromagnetism, the weak nuclear force, and the strong nuclear force. Each force is carried by a separate "messenger particle" unique to it and still being researched. The strong force is by far the strongest of the forces, followed by the electromagnetic force, the weak force, and finally the extremely feeble gravitational force. Though these four forces govern every matter interaction, a theory that unites them all is still being sought. The most recent candidate is string theory, further discussed in Introduction to String Theory.
## Messenger Particles
There is a unique messenger particle associated with each of the four fundamental forces. These particles can be considered the "smallest amount" of each force than can exist in nature. Experiments have confirmed the existence of three of the four particles, but the graviton has yet to be discovered. Calculations show that it should be massless. The weak gauge bosons come in two separate varieties with different masses.
Force Particle Mass Gravitational Force Graviton 0 Electromagnetic Force Photon 0 Weak Nuclear Force Weak Gauge Bosons 86, 97 Strong Nuclear Force Gluon 0
## Gravity
Gravity, the weakest of the four forces, is about 10-36 times the strength of the strong force. This weakness is easily demonstrable - on a dry day, rub a comb across your shirt to give it static electricity, then hold it over a piece of paper on a desk. If you were successful, the piece of paper lifts off the desk. It takes an entire planet to keep the paper on the desk, but this force is easily overcome with everyday materials employing the electromagnetic force.
However, the range of gravity is unlimited - every object in the universe exerts a gravitational force on everything else. The effects of gravity depend on two things: the mass of two bodies and the distance between them. In more precise terms, the attractive force between any two bodies is directly proportional to the product of the masses and inversely proportional to the square of the distance between the bodies. The dominance of gravity on macroscopic scales is due not to any intrinsic strength but instead to its enormous range and constant attractive nature, especially as compared to the other forces. These properties of gravity have made it extremely difficult to incorporate gravity into modern theoretical frameworks.
The messenger particle of gravity is the graviton. It has not been experimentally verified, mainly because it is extremely hard to find the smallest denomination of the weakest force. Recent calculations show that it will likely be massless. Interestingly, all versions of modern string theory incorporate gravity (unlike previous quantum theories) and not only allow but require a particle with the properties of the graviton. Its discovery will likely represent a major victory for string theory, since previous quantum theories based on the model of point particles give illogical, infinite answers when gravity is incorporated.
## Electromagnetism
The electromagnetic force is actually second in effective strength only to the strong force, but it is listed out of order here because it, like gravity, is more familiar to most people. Its strength is less than 1% of that of the strong force, but it, like gravity, has infinite range. However, unlike gravity, the electromagnetism has both attractive and repulsive properties that can combine or cancel each other out. Whereas gravity is always attractive, electromagnetism comes in two charges: positive and negative. Two positive or two negative things will repel each other, but one positive and one negative attract each other. This can be neatly illustrated by magnets: two of the same "pole" will repel each other, but two opposite poles attract each other.
This is the principle that keeps atoms together: the positively charged nucleus and the negatively charged electrons attract each other. This is also the principle of atomic size: more electrons have greater repulsive force, so atoms with more electrons are larger because of the electrons' mutual repulsion. Similarly, atoms with larger nuclei and the same number of electrons are smaller overall because they exert a greater attractive force on the electrons.
The messenger particle of electromagnetism is the photon, a massless particle that logically (since light is a manifestation of electromagnetism) travels at the speed of light (299 792 458 m/s or 299 972 km/s).
## The Weak Nuclear Force
The weak nuclear force is one of the less familiar fundamental forces. It operates only on the extremely short distance scales found in an atomic nucleus. The weak force is responsible for radioactive decay. In actuality, it is stronger than electromagnetism, but its messenger particles (W and Z bosons) are so massive and sluggish that they do not faithfully transmit its intrinsic strength.
## The Strong Nuclear Force
The strong nuclear force is the other unfamiliar fundamental force. Like the weak force, its range is limited to subatomic distances. Its "duties" are keeping quarks together inside protons and neutrons, and keeping protons and neutrons inside atomic nuclei. Its messenger particle is the massless gluon, so named because it "glues" elementary particles together.
## If the Forces Were Different . . .
Just as questions arise about the reasons behind the properties of elementary particles, scientists wonder about the reasons behind the properties of the forces and their particles as well. For example, why are three of the messenger particles massless, and the fourth is one of the heaviest known particles? Similarly, why do the ranges and strengths of the forces differ so drastically? Yet it cannot be disputed that the universe would be strikingly different if the force properties were otherwise. The formation of stable nuclei depends on the ratio of the strong and electromagnetic forces - the protons in a nucleus repel each other, but the strong force overcomes this repulsion. A small change in their relative strengths could allow the electromagnetic force to overcome the strong force, and atoms could not exist. If electrons were any more massive, then electrons and protons would be disposed to bond and form neutrons, thus disrupting the formation of heavy elements. The strength of gravity is also important: if it were any stronger, stellar matter would bind more strongly and stars would use their nuclear fuel much faster, thus negating the possibility of the evolution of life. If gravity were any weaker, matter might not "clump together" to form larger structures, thereby preventing the formation of stars in the first place. The answer to the question of why the forces are the way they are may yet come with string theory.
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### Nananana
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https://www.mathworks.com/matlabcentral/cody/problems/42581-create-sequnce-1-4-9-16-25/solutions/725758 | 1,585,567,186,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585370496901.28/warc/CC-MAIN-20200330085157-20200330115157-00460.warc.gz | 1,052,320,716 | 15,667 | Cody
# Problem 42581. Create sequnce 1 4 9 16 25.........
Solution 725758
Submitted on 30 Aug 2015 by Binbin Qi
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
%% x = 25; y_correct = [1 4 9 16 25]; assert(isequal(prntseq(x),y_correct))
y = 1 4 9 16 25
2 Pass
%% x = 100; y_correct = [1 4 9 16 25 36 49 64 81 100]; assert(isequal(prntseq(x),y_correct))
y = 1 4 9 16 25 36 49 64 81 100
3 Pass
%% x = 9; y_correct = [1 4 9]; assert(isequal(prntseq(x),y_correct))
y = 1 4 9
4 Pass
%% x = 36; y_correct = [1 4 9 16 25 36]; assert(isequal(prntseq(x),y_correct))
y = 1 4 9 16 25 36 | 288 | 710 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2020-16 | latest | en | 0.465239 |
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# Does the curve (x - a)^2 + (y - b)^2 = 16
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Does the curve (x - a)^2 + (y - b)^2 = 16 [#permalink] 29 Mar 2008, 11:22
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Does the curve $$(x - a)^2 + (y - b)^2 = 16$$ intersect the $$Y$$ axis?
1. $$a^2 + b^2 > 16$$
2. $$a = |b| + 5$$
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Re: DS: Curve [#permalink] 29 Mar 2008, 13:09
Expert's post
B
$$(x - a)^2 + (y - b)^2 = 16$$ is a circle with center at (a,b) and radius of 4.
1. $$a^2 + b^2 > 16$$ presents a plane with a hole at the center of coordinates. So, we can choose (a,b) at Y-axis and far away Y- axis. Insufficient.
2. $$a = |b| + 5$$ presents a semi-plane with a>=5. Therefore, any circle with the center at the semi-pane and radius 4 will not intersect Y-axis. Sufficient.
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Re: DS: Curve [#permalink] 29 Mar 2008, 15:32
I don't understand those plane explanations, Walker. If this is a GMAT problem, there has to be an easier explanations.
I paraphrase the question to ask is a in [-4,4], meaning it intersects the Y-axis, or is it not? a is the distance of moving left or right on the X-axis and since we know the radius is 4, a can tell us if the circle intersects the Y-axis.
1. Not sufficient because a can be a number in the interval and outside of it as well.
2. Sufficient because it says a > 5 and that means, a is outside the interval and therefore cannot intersect the Y-axis.
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Re: DS: Curve [#permalink] 29 Mar 2008, 20:13
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Maybe you are right. I like drawing, because it is fastest way for me
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Re: DS: Curve [#permalink] 08 May 2008, 22:24
I found question this sort of tough!! Are such complex problems expected in the real GMAT aor is my coordinate Geo weak?
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Re: DS: Curve [#permalink] 08 May 2008, 22:41
Neelesh likes Manhattan Math!
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Re: DS: Curve [#permalink] 10 May 2008, 07:40
walker wrote:
B
$$(x - a)^2 + (y - b)^2 = 16$$ is a circle with center at (a,b) and radius of 4.
1. $$a^2 + b^2 > 16$$ presents a plane with a hole at the center of coordinates. So, we can choose (a,b) at Y-axis and far away Y- axis. Insufficient.
2. $$a = |b| + 5$$ presents a semi-plane with a>=5. Therefore, any circle with the center at the semi-pane and radius 4 will not intersect Y-axis. Sufficient.
Walker or anyone: if you could explain how to draw these equations on a plane, it would be very helpful.
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Re: DS: Curve [#permalink] 10 May 2008, 10:29
How do you know it is a circle with radius 4 just by seeing the equation and not looking at 1 or 2?
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Re: DS: Curve [#permalink] 10 May 2008, 22:13
Expert's post
RyanDe680 wrote:
How do you know it is a circle with radius 4 just by seeing the equation and not looking at 1 or 2?
$$(x - a)^2 + (y - b)^2 = r^2$$ - is a general equation for a circle with center (a,b) and radius of r. So, r=4
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Re: DS: Curve [#permalink] 10 May 2008, 22:13
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Display posts from previous: Sort by | 1,935 | 5,785 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.796875 | 4 | CC-MAIN-2015-18 | longest | en | 0.799341 |
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An aid solution can make it much easier for you to manage your C-Minimal Theory course. On top of that, you can discover more regarding on your own and help you be successful. Discover the best tutoring service and you will have the ability to take your research study skills to the next level. | 2,546 | 12,678 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2021-25 | latest | en | 0.977071 |
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#### Daniel's 70 Weeks were fulfilled in 70 AD!
If we count 2 0 5 4 digits after the first 3 1 4
we land on digit # 2 3 6 8
3 .(1 4 . . . .3 1 4. . . .)(. . . . .2 0 5
Scott Yesterday, 01:49 PM
#### 9 1 1
First occurrence of 8 6 and 1 5 6,
3 . 1 4 . . . . .(8 6 . . . .1590 + 6 6 6. . . . . 1 5 6)
First occurrence of 1 5 6 and
Scott Yesterday, 11:35 AM
#### Daniel's 70 Weeks were fulfilled in 70 AD!
"May Fourteenth Two Thousand Eighteen" = 2 4 2 4
The English gematria sum of Israel's 70th anniversary date
when
Scott 11-30-2020, 11:13 AM
#### 9 1 1
First occurrence of 1947 and 2018,
(1 9 4 7 . . . . . . .2018. . . . . . . 2 0 1 8)
Using English gematria,
Scott 11-30-2020, 12:52 AM
#### 9 1 1
First occurrence of 1 3 1 8,
(3 . 1 4 . . . . . .3 7 2 7 + 1 5 9 0 positions. . . . . . . 1 3 1 8)
Counting 6 6
Scott 11-28-2020, 09:32 PM
#### 9 1 1
declaring not only the year, but even the blessed day and hour,
Scott 11-27-2020, 01:31 PM
#### Daniel's 70 Weeks were fulfilled in 70 AD!
Correction, its the 2nd (not first) occurrence of 1949 completing at digit # 1918.
We have completed 6 0 2 1 years from Adam so far.
Scott 11-26-2020, 07:21 AM
#### 9 1 1
I looked for my birth date thats coming up, 0 1/0 1/2 0 2 1, and it
doesn't make its first occurrence until well over 141 million digits,
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# A train starting from a railway station and moving with uniform acceleration attains a speed of $40km{{h}^{-1}}$ in 10 minutes. Find its acceleration in the units of $m{{s}^{-2}}$.\begin{align} & \text{A}\text{. }4 \\ & \text{B}\text{. }0.067 \\ & \text{C}\text{. }0.0185 \\ & \text{D}\text{. }1.11 \\ \end{align}
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Hint: As the train starts from rest, we will take its initial velocity to be zero. We know 1 hour contains 3600 seconds and 1 kilometer has 1000 meters, so we will convert the given final speed of train from $km{{h}^{-1}}$ to $m{{s}^{-1}}$. We will also convert the given time of 10 minutes into seconds; using 1 minute has 60 seconds. Finally we will apply the first equation of uniformly accelerated motion i.e. $v=u+at$ to find the acceleration of the train in $m{{s}^{-2}}$.
Formula used: First equation of uniformly accelerated motion: $v=u+at$
We have, a train starting from a railway station and moving with uniform acceleration attains a speed of $40km{{h}^{-1}}$ in 10 minutes,
As the train is starting from the station, the initial velocity of the train will be zero.
Let, $u$ represents the initial velocity of the train,
So, $u=0$
Now, in 10 minutes, the train attains a speed of $40km{{h}^{-1}}$
As the required acceleration is in $m{{s}^{-2}},$
We will convert the given time from minutes to seconds,
And, given speed from $km{{h}^{-1}}$ to $m{{s}^{-1}}$
We know that in a minute there are 60 seconds,
So, 1 minute is equal to 60 seconds
And, 10 minutes will be equal to: $10\times 60$ seconds
Or, 10 minutes will be equal to: 600 seconds
Now, we know that in 1 kilometer, there are a thousand meters, and in an hour there are 3600 seconds.
So, $1km=1000m$ and $1hour=3600\text{seconds}$
Or, $1km{{h}^{-1}}=\dfrac{1km}{1hour}$
Or, $1km{{h}^{-1}}=\dfrac{1000m}{3600\text{seconds}}$
Or, $1km{{h}^{-1}}=\dfrac{5}{18}m{{s}^{-1}}$
Thus, we have $1km{{h}^{-1}}=\dfrac{5}{18}m{{s}^{-1}}$
So, $40km{{h}^{-1}}$ will be equal to:
\begin{align} & 40km{{h}^{-1}}=40\times \dfrac{5}{18}m{{s}^{-1}} \\ & 40km{{h}^{-1}}=\dfrac{200}{18}m{{s}^{-1}} \\ & 40km{{h}^{-1}}=\dfrac{100}{9}m{{s}^{-1}} \\ \end{align}
Thus, the train attains a speed of $\dfrac{100}{9}m{{s}^{-1}}$ in 600 seconds.
Now, we know the first equation of uniformly accelerated motion is:
$v=u+at$
Where,
$v$ is the final velocity of the object
$u$ is the initial velocity of the object
$a$ is the uniform acceleration of the object
$t$ is the time taken by the object to reach velocity $v$ with uniform acceleration $a$
Now, for the train, we have
Initial velocity, $u=0$
Final velocity, $v=\dfrac{100}{9}m{{s}^{-1}}$
Time taken, $t=600\sec$
So, substituting the given values in the equation $v=u+at$
We have,
\begin{align} & \dfrac{100}{9}m{{s}^{-1}}=0+a\times 600\sec \\ & \dfrac{100}{9}m{{s}^{-1}}=a\times 600\sec \\ & a=\dfrac{\dfrac{100}{9}m{{s}^{-1}}}{600\sec } \\ & a=\dfrac{100}{9\times 600}m{{s}^{-2}} \\ & a=\dfrac{1}{54}m{{s}^{-2}} \\ & a=0.0185m{{s}^{-2}} \\ \end{align}
The acceleration of the train is $0.0185m{{s}^{-2}}$
So, the correct answer is “Option C”.
Note: For uniformly accelerated motion, we can apply any of the equations of motion in accordance with the terms given to us. While solving these types of numericals, every term should be taken in the SI units only to avoid any kind of calculation error. | 1,180 | 3,484 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 7, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5625 | 5 | CC-MAIN-2024-26 | latest | en | 0.797577 |
https://namanbhalla.in/understanding-the-cubic-root-of-3-explained-and/ | 1,716,559,551,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058719.70/warc/CC-MAIN-20240524121828-20240524151828-00765.warc.gz | 366,691,536 | 13,559 | What is the Cubic Root of 3 | Explained and Simplified
The concept of roots in mathematics is a fundamental one, and one of the most commonly encountered roots is the cubic root. The cubic root of a number is the value that, when raised to the power of three, gives the original number. In this article, we will explore the cubic root of 3 and explain it in a simplified manner.
When we talk about the cubic root of 3, we are essentially asking the question: “What number, when multiplied by itself three times, equals 3?” The answer to this question is approximately 1.4422. This means that 1.4422 raised to the power of three equals 3.
The cubic root of 3 can also be expressed as ∛3. The symbol ∛ is used to represent the cubic root in mathematical notation. It is important to note that the cubic root of 3 is an irrational number, meaning it cannot be expressed as a simple fraction or a finite decimal. Instead, it is a non-repeating and non-terminating decimal.
The concept of the cubic root has various applications in mathematics, physics, and engineering. For example, it is used in the calculation of volume, as the volume of a cube is equal to the length of one side raised to the power of three. Understanding the cubic root of 3 is essential for solving complex equations and problems in these fields.
In conclusion, the cubic root of 3 is a fundamental mathematical concept that represents the value that, when raised to the power of three, equals 3. It is an irrational number and is commonly denoted as ∛3. Understanding the cubic root is important for various applications in mathematics, physics, and engineering.
What is the Cubic Root of 3? Explained and Simplified
The cubic root of a number is the value that, when multiplied by itself three times, gives the original number. In other words, it is the value that, when raised to the power of 3, equals the original number.
READ MORE From GB to TB: Understanding the Conversion and Storage Capacity
The cubic root of 3 is a mathematical concept that allows us to find the value that, when cubed, gives us 3. It is denoted as ∛3 or 3^(1/3).
Calculating the cubic root of 3 can be done using various methods, including using a calculator or using mathematical formulas. One common method is to use the Newton-Raphson method, which is an iterative method for finding the roots of a function.
Another way to find the cubic root of 3 is to use a table of values. By looking at a table of values, we can find an approximate value for the cubic root of 3. For example, if we look at a table of values for the cube of numbers, we can see that 1 cubed is 1, 2 cubed is 8, and 3 cubed is 27. From this, we can estimate that the cubic root of 3 is between 1 and 2.
It is important to note that the cubic root of 3 is an irrational number, meaning it cannot be expressed as a simple fraction or a terminating or repeating decimal. It is a non-repeating, non-terminating decimal that goes on forever without a pattern.
In conclusion, the cubic root of 3 is a mathematical concept that represents the value that, when cubed, gives us 3. It is denoted as ∛3 or 3^(1/3). It can be calculated using various methods, such as the Newton-Raphson method or by using a table of values. However, it is an irrational number that cannot be expressed as a simple fraction or a terminating or repeating decimal.
Understanding the Concept of Cubic Root
The concept of cubic root is a mathematical operation that involves finding the number which, when multiplied by itself three times, gives a given number. In other words, it is the inverse operation of cubing a number.
For example, if we want to find the cubic root of 3, we are looking for a number that, when multiplied by itself three times, gives us 3. This number is denoted as ∛3.
The cubic root of 3 can be expressed as:
∛3 = 1.4422…
The cubic root of 3 is an irrational number, meaning it cannot be expressed as a simple fraction or a finite decimal. It is a never-ending, non-repeating decimal.
One way to approximate the value of the cubic root of 3 is by using a calculator or a mathematical software. However, it is important to note that this is only an approximation and not the exact value.
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Understanding the concept of cubic root is essential in various mathematical and scientific fields. It is used in solving equations, calculating volumes of cubes and other three-dimensional shapes, and in many other applications.
Here is a table showing the cubic root of some common numbers:
Number Cubic Root
1 1
8 2
27 3
64 4
125 5
By understanding the concept of cubic root, we can solve various mathematical problems and gain a deeper understanding of the relationship between numbers and their roots.
Definition and Explanation of Cubic Root
The cubic root is a mathematical operation that allows us to find the number that, when multiplied by itself three times, gives a specific value. In other words, it is the inverse operation of raising a number to the power of three.
For example, the cubic root of 3, denoted as ∛3, is the number that, when multiplied by itself three times, equals 3. In this case, the cubic root of 3 is approximately 1.4422.
The concept of the cubic root can be understood by considering the following equation: x^3 = 3. To find the value of x, we take the cubic root of both sides of the equation, resulting in x = ∛3.
The cubic root can be calculated using various methods, such as using a scientific calculator or by using mathematical formulas. It is important to note that not all numbers have exact cubic roots, and in such cases, we use approximations.
The cubic root is a fundamental concept in mathematics and has various applications in fields such as engineering, physics, and computer science. It is used to solve equations, calculate volumes of three-dimensional shapes, and model natural phenomena.
In summary, the cubic root is the inverse operation of raising a number to the power of three. It allows us to find the number that, when multiplied by itself three times, gives a specific value. The cubic root is an important mathematical concept with various applications in different fields.
Properties and Characteristics of Cubic Root
The cubic root is a mathematical operation that calculates the number which, when multiplied by itself three times, gives a given number. In the case of the cubic root of 3, it is the number that, when multiplied by itself three times, gives 3 as a result.
Here are some properties and characteristics of the cubic root:
• Unique Solution: Unlike square roots, which can have both positive and negative solutions, the cubic root has only one unique solution.
• Positive and Negative Cubic Roots: While the cubic root itself is always positive, it is important to note that a given number can have both positive and negative cubic roots. For example, the cubic root of 8 is 2, but it also has a negative cubic root of -2.
• Irreducible: The cubic root of a number cannot be further simplified into simpler terms. It is an irreducible expression.
• Non-integer Results: In most cases, the cubic root of a number will not result in an integer. It is often expressed as a decimal or a fraction.
• Approximation: When calculating the cubic root of a number, it is common to use approximation methods such as the Newton-Raphson method or the bisection method to find an approximate value.
• Relationship to Cube: The cubic root is closely related to the concept of a cube. Taking the cubic root of a number is equivalent to finding the side length of a cube with a given volume.
Understanding the properties and characteristics of the cubic root is essential in various mathematical and scientific fields, including algebra, calculus, and physics. It allows for the manipulation and analysis of numbers and equations involving cubic roots.
FAQ about topic Understanding the Cubic Root of 3: Explained and Simplified
What is the cubic root of 3?
The cubic root of 3 is the number that, when multiplied by itself three times, equals 3. It is approximately equal to 1.4422.
How do you calculate the cubic root of 3?
The cubic root of 3 can be calculated using a calculator or a mathematical formula. The formula is: cubic root of 3 = 3^(1/3). This can be simplified as 3^(1/3) = 3^(0.3333) = 1.4422.
What is the significance of the cubic root of 3?
The cubic root of 3 is a mathematical constant that is used in various calculations and equations. It is often used in geometry and engineering to calculate the volume of a cube or to find the side length of a cube when the volume is known.
Can the cubic root of 3 be expressed as a fraction?
No, the cubic root of 3 cannot be expressed as a fraction. It is an irrational number, which means it cannot be expressed as a ratio of two integers.
Are there any real-life applications of the cubic root of 3?
Yes, the cubic root of 3 has real-life applications in various fields. For example, it is used in computer graphics to calculate the scaling factor for 3D models. It is also used in physics and chemistry to solve equations involving cubic roots. | 2,044 | 9,194 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.6875 | 5 | CC-MAIN-2024-22 | latest | en | 0.939032 |
https://quant.stackexchange.com/questions/14776/how-to-combine-gaussian-marginals-with-gaussian-copula-to-obtain-multivariate-no | 1,713,206,066,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817014.15/warc/CC-MAIN-20240415174104-20240415204104-00441.warc.gz | 444,930,300 | 41,387 | # How to combine Gaussian marginals with Gaussian copula to obtain multivariate normals?
in the book "Numerical Methods and Optimization in Finance" I red the following: "Combining the Gaussian copula with Gaussian marginal gives a fancy way of expressing multivariate normals. However, the Gaussian copula can also be combined with other marginals, and Gaussian marginals can be linked via any copula”.
I would like to combine the Gaussian copula with Gaussian marginals, to obtain multivariate normals for my 7 asset classes. In addition, I would like to combine t-marginals with t-copula, to obtain a multivariate t-distribution. Does anyone know how to do this in MatLab?? I kinda struggle with this for quite some time!
This is how I approached the problem for the t marginals & t copula:
%% Define univariate process by t-distribution
for i = 1:nAssets
marginal{i} = fitdist(returns(:,i),'tlocationscale');
end
%% Copula calibration
for i = 1:nAssets
U(:,i) = marginal{i}.cdf(returns(:,i)); % transform margin to uniform
end
[rhoT, DoF] = copulafit('t', U, 'Method', 'ApproximateML');
%% Reverse transformation on each index
U = copularnd('t', rhoT, DoF, NumObs * NumSim);
for j = 1:nAssets
ExpReturns(:,:,j) = reshape(marginal{j}.icdf(U(:,j), DoF), NumObs, NumSim);
end
Does my approach make sense?? Any help is very much appreciated, especially on the MatLab code!!!
Best regards
• I am not sure what exactly you want to do with this code, do you want to simulate data from an estimated distribution? Sep 17, 2014 at 14:04
• Yes, you're absolutely right! After I've fitted the copula via copulafit, I simulate returns via copularnd and then reverse the transformation in the last step, since I don't want uniform margins. First, I'm not sure whether the tlocationScale fits a t-distribution. Second, I'm not sure whether I get a multivariate t-distribution with my approach. Lastly, I'm quite unsure whether the entire approach makes sense ... Sep 17, 2014 at 14:46
You can express the Normal distribution by Sklar's Theorem in terms of Gaussian Marginals and Gaussian Copula as follows:
$$F(x_1,...,x_n)=C(F(x_1),...,F(x_n))=C^{Gau}(N(x_1),...,N(x_n))$$
So the distribution equals the copula function with the respective inverse marginals as arguments.
You can aswell combine any types of Copula and (continuous) different Marginals to form new distributions by this formula:
$$F(x_1,...,x_n)=C(F(x_1),...,F(x_n))$$
So for Student-t-Copula:
$$F(x_1,...,x_n)=C_t(F_t(x_1),...,F_t(x_n))$$
Remark: You can also combine different types of marginals and copula, e.g. Gauss Copula with t-Marginals.
The MATLAB-function to generate Copula values can be found here:
Y = copulacdf('Gaussian',U,rho)
Y = copulacdf('t',U,rho,NU)
Just keep in mind that Gaussian marginals with Gaussian copula is nothing more than the multivariate Gaussian distribution (details e.g. here). For t-marginals with t-copula (with the same degree of freedom) you get the multivariate t-distribution.
Both multivariate distributions are characterized by their covariance matrix. The t-distribution has the additional parameter degrees of freedom and will thus produce tail dependence.
All in all you don't need the copula concept in these cases. The only benefit would be to use different degrees of freedom for the marginals and the copula in the t-distribution case.
• Thank you for your response. I do understand that I get a multivariate normal distribution by combining Gaussian marginals with Gaussian copulas. However, I struggle with implementing it MatLab. And I actually have to do it with copulas. In the other comment I laid down my approach, but I'm quite unsure whether this is right way to go ... Sep 17, 2014 at 8:48
• I see - you focus on the Matlab implementation and I rather tried to make clear the mathematics. In this case emcor is of more help I guess. Sep 17, 2014 at 8:58 | 990 | 3,906 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.1875 | 3 | CC-MAIN-2024-18 | longest | en | 0.863816 |
https://resources.wolframcloud.com/FunctionRepository/resources/PowerTriangulation/ | 1,701,924,444,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100632.0/warc/CC-MAIN-20231207022257-20231207052257-00564.warc.gz | 555,231,118 | 13,847 | Function Repository Resource:
# PowerTriangulation
Generate the power triangulation of a set of circles
Contributed by: Jan Mangaldan
ResourceFunction["PowerTriangulation"][{c1,c2,…}] gives a MeshRegion representing the power triangulation of the circles c1,c2, ….
## Details
The circles ci can be Circle or Disk objects.
Point objects are treated as circles with zero radius.
A power triangulation is also known as Laguerre triangulation or Laguerre–Delaunay triangulation; it generalizes the Delaunay triangulation.
A power triangulation can be considered as a weighted Delaunay triangulation of the circles' centers, with the radii of the circles as weights.
A power triangulation consists of triangles (in 2D) and n-dimensional simplices (in nD).
An nD power triangulation has simplex cells defined by n+1 circle centers, such that the circumsphere for the same n+1 points contains no other circle centers from the original circles ci.
ResourceFunction["PowerTriangulation"] takes the same options as MeshRegion.
## Examples
### Basic Examples (2)
Generate the power triangulation of a set of circles:
In[1]:=
Out[1]=
Show the power triangulation with the generating circles:
In[2]:=
Out[2]=
### Scope (2)
Create a power triangulation from a set of disks:
In[3]:=
Out[4]=
Basic properties:
In[5]:=
Out[5]=
Power triangulations are full dimensional:
In[6]:=
Out[6]=
Power triangulations are bounded:
In[7]:=
Out[7]=
Find its area and centroid:
In[8]:=
Out[8]=
Test for point membership or distance to the closest point in the region:
In[9]:=
Out[9]=
In[10]:=
Out[10]=
Generate the power triangulation of a mixture of Circle and Disk objects:
In[11]:=
Out[11]=
### Options (10)
#### MeshCellHighlight (2)
MeshCellHighlight allows you to specify highlighting for parts of a PowerTriangulation:
In[12]:=
Out[12]=
Individual cells can be highlighted using their cell index:
In[13]:=
Out[13]=
Or by the cell itself:
In[14]:=
Out[14]=
#### MeshCellLabel (2)
MeshCellLabel can be used to label parts of a PowerTriangulation:
In[15]:=
Out[15]=
Individual cells can be labeled using their cell index:
In[16]:=
Out[16]=
Or by the cell itself:
In[17]:=
Out[17]=
#### MeshCellMarker (2)
MeshCellMarker can be used to assign values to parts of a PowerTriangulation:
In[18]:=
Out[18]=
Use MeshCellLabel to show the markers:
In[19]:=
Out[19]=
#### MeshCellStyle (2)
MeshCellStyle allows you to specify styling for parts of a PowerTriangulation:
In[20]:=
Out[20]=
Individual cells can be highlighted using their cell index:
In[21]:=
Out[21]=
Or by the cell itself:
In[22]:=
Out[22]=
#### PlotTheme (2)
Use a theme with grid lines and a legend:
In[23]:=
Out[23]=
Use a theme to draw a wireframe:
In[24]:=
Out[24]=
### Properties and Relations (4)
The output of PowerTriangulation is always a full-dimensional MeshRegion:
In[25]:=
Out[25]=
In[26]:=
Out[26]=
The circumcircle for each triangle in a power triangulation contains no other circles' centers:
In[27]:=
Out[27]=
Find circumcircles for all triangles:
In[28]:=
Plot the circumcircles as disks:
In[29]:=
Out[29]=
The power triangulation of a set of circles all having the same radii is equivalent to the DelaunayMesh of the circles' centers:
In[30]:=
Out[30]=
The resource function PowerDiagram is the dual of PowerTriangulation:
In[31]:=
Out[32]=
## Version History
• 1.0.0 – 18 January 2021 | 935 | 3,467 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2023-50 | latest | en | 0.753656 |
http://encyclopedia2.thefreedictionary.com/prime+number | 1,539,691,662,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583510749.55/warc/CC-MAIN-20181016113811-20181016135311-00379.warc.gz | 109,381,640 | 14,696 | # prime number
Also found in: Dictionary, Thesaurus, Medical, Legal, Financial, Wikipedia.
## prime number:
see number theorynumber theory,
branch of mathematics concerned with the properties of the integers (the numbers 0, 1, −1, 2, −2, 3, −3, …). An important area in number theory is the analysis of prime numbers.
..... Click the link for more information.
.
## Prime Number
(or prime), a positive integer that is greater than 1 and has no divisors other than itself and 1. For example, 2,3,5,7,11, and 13 are prime numbers.
The concept of prime number is basic to the study of the divisibility of the natural numbers, or positive integers. Thus, according to the fundamental theorem of arithmetic, any positive integer greater than 1 either is a prime or can be factored into a product of primes in one and only one way, apart from the order of the factors.
As long ago as the ancient Greek mathematicians it was known that there are infinitely many prime numbers; a proof can be found in the ninth book of Euclid’s Elements. Problems of the divisibility of the natural numbers and, consequently, problems associated with prime numbers are of importance in the study of groups. In particular, the structure of a group with a finite number of elements is closely related to the way in which the number of elements, or order of the group, decomposes into prime factors. Problems of the divisibility of integral algebraic numbers are considered in the theory of algebraic numbers.
Since the concept of prime number proved to be insufficient for the construction of a theory of divisibility, the concept of ideal was developed. In 1837, P. G. L. Dirichlet showed that the arithmetic progression a + bx, where x = 1,2,… and a and b are relatively prime integėrs, contains infinitely many prime numbers.
An extremely difficult problem in number theory is the distribution of the primes among the natural numbers. This problem involves the study of the asymptotic behavior of the function π(ξ), which is the number of primes not greater than the positive number x. The first results in this direction were obtained by P. L. Chebyshev, who proved in 1850 that there exist two constants a and A such that
for all x2. In other words, π(x) increases as x/ln x. In 1896, J. Hadamard and C. J. de La Vallée Poussin made the next important step when they independently proved what is called the prime number theorem, which is a refinement of Chebyshev’s theorem. The prime number theorem states that the limit of the ratio of π(x) and x/ln x, as x becomes infinite, is 1.
Mathematicians have since devoted considerable effort toward refining the prime number theorem. The distribution of the prime numbers have been studied by means of both elementary methods and the methods of mathematical analysis. A particularly fruitful method is based on the identity
where the product is taken over all the primes ρ = 2,3, — This identity was introduced by L. Euler. It holds for all complex s whose real part is greater than 1. The identity is the basis for the study of the distribution of the prime numbers through the use of special functions called zeta functions ζ (s). For Re s > 1, the function is defined as the series
This function was used for real values of s by Chebyshev to study the distribution of the prime numbers. G. F. B. Riemann pointed out the importance of studying ζ(s) for complex values of 5. Riemann put forth the conjecture that all the roots of the equation ζ(s) = 0 in the right half plane have their real parts equal to ½. As of 1975, this conjecture had not been proved. Its proof would be an important step toward the solution of the problem of the distribution of the prime numbers. The distribution of the prime numbers is closely related to the Goldbach problem, the still unsolved problem of twin primes, and other problems in analytic number theory. The problem of twin primes is whether the number of prime numbers differing by 2, for example, 11 and 13, is finite or infinite. Tables of the prime numbers among the first 11,000,000 natural numbers show the existence of very large twin primes, for example, 10,006,427 and 10,006,429. This fact, however, does not prove that there are infinitely many such pairs. A number of primes outside the range of existing tables admit of a simple arithmetic expression. For example, it was shown in 1965 that 211,213 - 1 is a prime number; this number contains 3,376 digits.
### REFERENCES
Vinogradov, I. M. Osnovy teorii chisel, 8th ed. Moscow, 1972.
Hasse, H. Lektsii po teorii chisel. Moscow, 1953. (Translated from German.)
Ingham, A. E. Raspredelenie prostykh chisel. Moscow-Leningrad, 1936. (Translated from English.)
Prachar, K. Raspredelenie prostykh chisel. Moscow, 1967. (Translated from German.)
Trost, E. Prostye chisla. Moscow, 1959. (Translated from German.)
## prime number
[′prīm ′nəm·bər]
(mathematics)
A positive integer having no divisors except itself and the integer 1.
## prime number
an integer that cannot be factorized into other integers but is only divisible by itself or 1, such as 2, 3, 5, 7, and 11
## prime number
An integer greater than 1 that is not evenly divisible by any number other than itself, and, of course, 1. Prime numbers are considered a fundamental building block of numbers, especially number theory, a branch of mathematics.
The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Except for 2, all primes are odd numbers. As the numbers get higher, prime numbers tend to be found in pairs that are close together; for example, 29,669 and 29,671 are primes. The largest prime number thus far, which contains more than 65,000 digits, was discovered in 1986.
References in periodicals archive ?
Really big prime numbers don't have many practical uses yet, but cryptography algorithms based on prime numbers have been developed.
The machinery introduced above, the Euler phi-function and the prime number theorem, promises to make this possible.
Here I choose the large prime numbers p and q generating 40 and calculate the values of n, [phi] (n) and d according to the formula, as shown in Figure 5.
v] is the smallest odd prime number which is not smaller than [[mu].
For centuries, mathematicians have been playing with prime numbers.
This latest giant prime number was found as part of the Great Internet Mersenne Prime Search (GIMPS), a network that harnesses the spare power of 360,000 computers around the world to look for and calculate prime numbers.
This qualitative feature differs fundamentally from the prime number theorem for ordinary prime numbers where all roots contribute to the remainder term.
To design a fast primality test for finding a prime number is necessary and very important.
Children must learn, for example, that a prime number has exactly two factors.
Today's race looks more competitive, but it's still not in the Goodwood league and Prime Number has the potential to defy a 6lb penalty on a stiff course that will play to his strengths.
She described prime numbers as "like a fish" because she drew fish in two parts, a body and tail, similar to the two factors of a prime number.
At Tobin, students were busy picking up prime numbers by rapping the group's "Prime Number Rap" in unison as they clapped to a funky beat: "Now we likes to zap `em.
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Open / Close | 1,734 | 7,357 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2018-43 | latest | en | 0.937565 |
https://oeis.org/A102823 | 1,638,000,500,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964358153.33/warc/CC-MAIN-20211127073536-20211127103536-00478.warc.gz | 515,557,882 | 3,961 | The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A102823 "True already", base 10, start 0: a(n) is the least integer such that the sequence up to a(n-1) written in base 10 contains floor(a(n)/10) copies of the digit a(n) % 10, with a(0) = 0. 8
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 27, 28, 29, 30, 34, 35, 36, 37, 38, 39, 40, 45, 46, 47, 48, 49, 50, 56, 57, 58, 59, 60, 67, 68, 69, 70, 78, 79, 80, 89, 90, 100, 102, 103, 104, 105, 106, 107, 108, 109, 112, 113 (list; graph; refs; listen; history; text; internal format)
OFFSET 0,3 COMMENTS a(n) = A249626(n) for n <= 55. - Reinhard Zumkeller, Nov 03 2014 REFERENCES Inspired by discussion of "True so far" from Eric Angelini (A102357). LINKS EXAMPLE The first 11 values of the sequence written in decimal include 2 '1's and 1 '2', so the next value cannot be 11 (the count of '1's is not 1) but can be 12. CROSSREFS Cf. A102824-A102830, A102357. Cf. A249626. Sequence in context: A122260 A122254 A249626 * A179308 A247806 A333501 Adjacent sequences: A102820 A102821 A102822 * A102824 A102825 A102826 KEYWORD nonn,easy,base AUTHOR Hugo van der Sanden, Feb 26 2005 STATUS approved
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Last modified November 27 02:53 EST 2021. Contains 349344 sequences. (Running on oeis4.) | 607 | 1,649 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.265625 | 3 | CC-MAIN-2021-49 | latest | en | 0.756876 |
https://github.com/TheQuack45/MathToWords | 1,579,336,258,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250592394.9/warc/CC-MAIN-20200118081234-20200118105234-00277.warc.gz | 466,586,934 | 19,257 | # TheQuack45 / MathToWords
Simple program that takes an infix (algebraic) math expression and outputs the expression in words in an unambiguous format.
C#
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# MathToWords
This is a simple program that takes in an expression in algebraic (infix) notation and outputs it in a well-defined, English word format.
My word notation is essentially Polish notation/prefix notation in words. It will never be ambiguous, but it isn't all that easy for humans to keep track of. This program and format is mostly intended as a little toy project, but the format could theoretically be used for a more natural, but defined, way to speak mathematical expressions.
## Explanation
My word notation works much like prefix notation, so the operator is "placed" before its operand(s). For example, addition ("+") is written this way: "the sum of {a} and {b}". Prefix notation does get a bit hard to work with when you have a complicated expression, but the important thing to remember is that each operator has a fixed number of operands. So addition, for example, will always have two operands and thus will always be in the format described above. See the table below for the list of currently supported operations, and see below that for examples of the format in action.
Operator Text Format
a + b the sum of a and b
a - b the difference of a and b
a * b the product of a and b
a / b the quotient of a and b
a ^ b the result of a to the power of b
a % b the result of a modulus b
a ! the factorial of a
sin a the sine of a
cos a the cosine of a
tan a the tangent of a
csc a the cosecant of a
sec a the secant of a
cot a the cotangent of a
arcsin a the inverse sine of a
arccos a the inverse cosine of a
arctan a the inverse tangent of a
arccsc a the inverse cosecant of a
arcsec a the inverse secant of a
arccot a the inverse cotangent of a
## Examples
3+2 becomes:
``````the sum of three plus two
``````
27 * 5 - 5 becomes:
``````the difference of the product of twenty seven and five and five
``````
(24 * (9 + (6 * 76))) / 2 becomes:
``````the quotient of the product of twenty four and the sum of nine and the product of seventy six and two
``````
You can’t perform that action at this time. | 602 | 2,409 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2020-05 | latest | en | 0.878709 |
https://www.coursehero.com/file/5829904/174-pdfsam-math-54-differential-equation-solutions-odd/ | 1,513,427,394,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948587577.92/warc/CC-MAIN-20171216104016-20171216130016-00221.warc.gz | 716,039,726 | 74,633 | 174_pdfsam_math 54 differential equation solutions odd
# 174_pdfsam_math 54 differential equation solutions odd - t...
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Chapter 4 7. Solving the auxiliary equation, 2 r 2 +7 r 4=0 ,y ie lds r =1 / 2 , 4. Thus a general solution is given by u ( t )= c 1 e t/ 2 + c 2 e 4 t , where c 1 and c 2 are arbitrary constants. 9. The auxiliary equation for this problem is r 2 r 11 = 0, which has roots r = 1 ± 1+4 · 11 2 = 1 ± 3 5 2 . Thus, a general solution to the given equation is y ( t )= c 1 e (1+3 5) t/ 2 + c 2 e (1 3 5) t/ 2 . 11. Solving the auxiliary equation, 4 r 2 +20 r +25=(2 r +5) 2 = 0, we conclude that r = 5 / 2is its double root. Therefore, a general solution to the given diFerential equation is w ( t )= c 1 e 5 t/ 2 + c 2 te 5 t/ 2 . 13. The auxiliary equation for this problem is r 2 +2 r 8 = 0, which has roots r = 4 , 2. Thus, a general solution is given by y ( t )= c 1 e 4 t + c 2 e 2 t , where c 1 , c 2 are arbitrary constants. To satisfy the initial conditions, y (0) = 3, y 0 (0) =
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Unformatted text preview: ( t ) = โ 4 c 1 e โ 4 t + 2 c 2 e 2 t and solve the system y (0) = c 1 e โ 4 ยท + c 2 e 2 ยท = c 1 + c 2 = 3 , y (0) = โ 4 c 1 e โ 4 ยท + 2 c 2 e 2 ยท = โ 4 c 1 + 2 c 2 = โ 12 โ c 1 = 3 , c 2 = 0 . Therefore, the solution to the given initial value problem is y ( t ) = (3) e โ 4 t + (0) e 2 t = 3 e โ 4 t . 15. The auxiliary equation for this equation is r 2 + 2 r + 1 = ( r + 1) 2 = 0. We see that r = โ 1 is a repeated root. Thus, two linearly independent solutions are y 1 ( t ) = e โ t and y 2 ( t ) = te โ t . This means that a general solution is given by y ( t ) = c 1 e โ t + c 2 te โ t . 170...
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Ask a homework question - tutors are online | 745 | 1,892 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4 | 4 | CC-MAIN-2017-51 | latest | en | 0.800191 |
https://www.scribd.com/doc/277406874/all-form-medium1 | 1,544,867,680,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376826842.56/warc/CC-MAIN-20181215083318-20181215105318-00196.warc.gz | 1,024,433,655 | 30,587 | You are on page 1of 2
Name: __________________________
Score:
Exponents
(A) Rewrite in expanded form:
1)
(−12)ସ
= __________________________________________
3)
(−24)ଷ
= __________________________________________
2)
2ଽ
= __________________________________________
4)
7଼
= __________________________________________
(B) Rewrite in exponent form:
1)
18 × 18 × 18
= _______________
3)
23 × 23 × 23 × 23
= _______________
2)
(−3) × (−3) × (−3) × (−3) × (−3)
= _______________
4)
(−8) × (−8) × (−8) × (−8)
= _______________
(C) Rewrite in standard form:
1)
(−5)ସ
= _______________
3)
(−8)ଷ
= _______________
5)
(−10)ଷ
= _______________
7)
13ଶ
= _______________
9)
2
= _______________
2)
12ଶ
= _______________
4)
(−1)
= _______________
6)
9ଷ
= _______________
8)
(−14)ଶ
= _______________
10) 7ଷ
= _______________
Printable Math Worksheets @ www.mathworksheets4kids.com
Name: __________________________
Score:
(A) Rewrite in expanded form:
1)
(−12)ସ
= (−) × (−) × (−) × (−)
3)
(−24)ଷ
= (−) × (−) × (−)
2)
2ଽ
=××××××××
4)
7଼
=ૠ×ૠ×ૠ×ૠ×ૠ×ૠ×ૠ×ૠ
(B) Rewrite in exponent form:
1)
18 × 18 × 18
= ૡ
3)
23 × 23 × 23 × 23
=
2)
(−3) × (−3) × (−3) × (−3) × (−3)
= (−)
4)
(−8) × (−8) × (−8) × (−8)
= (−ૡ)
(C) Rewrite in standard form:
1)
(−5)ସ
=
3)
(−8)ଷ
= −
5)
(−10)ଷ
= −
7)
13ଶ
2)
12ଶ
=
4)
(−1)
= −
6)
9ଷ
= ૠૢ
8)
(−14)ଶ
= ૢ
= ૢ
2
10) 7ଷ
9)
=
=
Printable Math Worksheets @ www.mathworksheets4kids.com | 774 | 1,534 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.390625 | 3 | CC-MAIN-2018-51 | latest | en | 0.478276 |
https://www.xuebuyuan.com/3212063.html | 1,674,993,081,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499713.50/warc/CC-MAIN-20230129112153-20230129142153-00667.warc.gz | 1,070,905,452 | 11,078 | poj1688
2018年01月15日 ⁄ 综合 ⁄ 共 4764字 ⁄ 字号 评论关闭
【题意】
【输入】
【输出】
Sample Input
```2
4
100 100 20
100 135 20
135 100 20
135 135 20
1
10 10 40
```
Sample Output
```1
0
```
07年论文有讲（高逸涵《与圆有关的离散化方法》）
```program poj1688;
const
esp:extended=1e-8;
type
line=record
l,r:extended;
end;
node=record
x:extended;
incr:boolean;
end;
var
n,i,j,k,w,t,tot,all,total,o,ans,xx,oo,count:longint;
x,y,r:array [0..21] of longint;
event:array [0..601] of extended;
xl:array [0..61] of node;
temp:node;
ind:array [0..10001] of line;
own:array [0..10001] of longint;
sum:array [0..1] of longint;
dl:array [0..1,0..10001] of longint;
yes:array [0..10001] of boolean;
root,next,point:array [0..10001] of longint;
procedure swap_int (var a,b:longint);
var
i:longint;
begin
i:=a;
a:=b;
b:=i;
end;
procedure swap_dou (var a,b:extended);
var
i:extended;
begin
i:=a;
a:=b;
b:=i;
end;
procedure solve (i,j:longint);
var
left,right,t,mid,leftr,rightr:extended;
begin
t:=y[j]+(y[i]-y[j])*r[j]/(r[i]+r[j]);
left:=y[j]-r[j];
if y[i]-r[i]>left then left:=y[i]-r[i];
right:=t;
repeat
mid:=(left+right)/2;
leftr:=sqrt(sqr(r[j])-sqr(mid-y[j]));
rightr:=sqrt(sqr(r[i])-sqr(mid-y[i]));
if (x[j]+leftr<x[i]-rightr) or (x[j]-leftr>x[i]+rightr) then
left:=mid
else
right:=mid;
until abs(left-right)<1e-8;
inc(tot);
event[tot]:=left;
left:=t;
right:=y[j]+r[j];
if y[i]+r[i]<right then right:=y[i]+r[i];
repeat
mid:=(left+right)/2;
leftr:=sqrt(sqr(r[j])-sqr(mid-y[j]));
rightr:=sqrt(sqr(r[i])-sqr(mid-y[i]));
if (x[j]+leftr<x[i]-rightr) or (x[j]-leftr>x[i]+rightr) then
right:=mid
else
left:=mid;
until abs(left-right)<1e-8;
inc(tot);
event[tot]:=left;
end;
procedure qsort (s,e:longint);
var
i,j:longint;
k:extended;
begin
if s>=e then exit;
i:=s;
j:=e;
k:=event[(s+e) div 2];
while i<=j do
begin
while (i<=j)and(event[i]<k) do inc(i);
while (i<=j)and(event[j]>k) do dec(j);
if i>j then break;
swap_dou(event[i],event[j]);
inc(i);
dec(j);
end;
qsort(s,j);
qsort(i,e);
end;
procedure connect (s,e:longint);
begin
inc(oo);
point[oo]:=e;
next[oo]:=root[s];;
root[s]:=oo;
end;
procedure dfs (now:longint);
var
i:longint;
begin
yes[now]:=true;
i:=root[now];
while i<>0 do
begin
if not yes[point[i]] then
begin
own[point[i]]:=own[now];
if point[i]>=dl[o,1] then inc(count);
dfs(point[i]);
end;
i:=next[i];
end;
end;
procedure merge (now:longint);
var
i,j,k:longint;
a,b,t:extended;
begin
o:=1-o;
t:=event[now]-esp;
total:=0;
for i:=1 to n do
if sqr(y[i]-t)<sqr(r[i]) then
begin
inc(total);
xl[total].x:=x[i]-sqrt(sqr(r[i])-sqr(y[i]-t));
xl[total].incr:=true;
inc(total);
xl[total].x:=x[i]+sqrt(sqr(r[i])-sqr(y[i]-t));
xl[total].incr:=false;
end;
for i:=1 to total-1 do
for j:=i+1 to total do
if xl[i].x>xl[j].x then
begin
temp:=xl[i];
xl[i]:=xl[j];
xl[j]:=temp;
end;
k:=0;
w:=1;
for i:=1 to total do
if xl[i].incr then
begin
if k=0 then
begin
ind[dl[1-o,w]].r:=xl[i].x;
inc(w);
end;
inc(k);
end
else
begin
dec(k);
if k=0 then ind[dl[1-o,w]].l:=xl[i].x;
end;
t:=event[now]+esp;
total:=0;
for i:=1 to n do
if sqr(y[i]-t)<sqr(r[i]) then
begin
inc(total);
xl[total].x:=x[i]-sqrt(sqr(r[i])-sqr(y[i]-t));
xl[total].incr:=true;
inc(total);
xl[total].x:=x[i]+sqrt(sqr(r[i])-sqr(y[i]-t));
xl[total].incr:=false;
end;
for i:=1 to total-1 do
for j:=i+1 to total do
if xl[i].x>xl[j].x then
begin
temp:=xl[i];
xl[i]:=xl[j];
xl[j]:=temp;
end;
sum[o]:=1;
inc(all);
dl[o,1]:=all;
ind[all].l:=-1000000;
k:=0;
for i:=1 to total do
if xl[i].incr then
begin
if k=0 then ind[all].r:=xl[i].x;
inc(k);
end
else
begin
dec(k);
if k=0 then
begin
inc(all);
inc(sum[o]);
dl[o,sum[o]]:=all;
ind[all].l:=xl[i].x;
end;
end;
ind[all].r:=1000000;
for i:=1 to sum[o] do
yes[dl[o,i]]:=false;
for i:=1 to sum[1-o] do
yes[dl[1-o,i]]:=false;
for i:=1 to sum[1-o] do
root[dl[1-o,i]]:=0;
oo:=0;
for i:=1 to sum[1-o] do
for j:=1 to sum[1-o] do
if (i<>j)and(own[dl[1-o,i]]=own[dl[1-o,j]]) then
begin
connect(dl[1-o,i],dl[1-o,j]);
connect(dl[1-o,j],dl[1-o,i]);
end;
for i:=1 to sum[1-o] do
for j:=1 to sum[o] do
if not ((ind[dl[1-o,i]].l>ind[dl[o,j]].r)or(ind[dl[1-o,i]].r<ind[dl[o,j]].l)) then
begin
connect(dl[1-o,i],dl[o,j]);
connect(dl[o,j],dl[1-o,i]);
end;
for i:=1 to sum[1-o] do
if not yes[dl[1-o,i]] then
begin
count:=0;
dfs(dl[1-o,i]);
if count=0 then inc(ans);
end;
for i:=1 to sum[o] do
if not yes[dl[o,i]] then
begin
inc(xx);
own[dl[o,i]]:=xx;
end;
end;
begin
while t<>0 do
begin
fillchar(root,sizeof(root),false);
fillchar(next,sizeof(next),0);
for i:=1 to n do
for i:=1 to n-1 do
for j:=i+1 to n do
if x[i]-r[i]>x[j]-r[j] then
begin
swap_int(x[i],x[j]);
swap_int(y[i],y[j]);
swap_int(r[i],r[j]);
end;
tot:=0;
for i:=1 to n do
begin
inc(tot);
event[tot]:=y[i]-r[i];
inc(tot);
event[tot]:=y[i]+r[i];
end;
for i:=1 to n-1 do
for j:=i+1 to n do
if sqr(x[i]-x[j])+sqr(y[i]-y[j])<sqr(r[i]+r[j]) then
solve(i,j);
qsort(1,tot);
event[0]:=-10000000000;
o:=0;
sum[o]:=1;
all:=1;
ans:=0;
xx:=1;
dl[o,1]:=1;
own[1]:=1;
ind[1].l:=-1000000;
ind[1].r:=1000000;
for i:=1 to tot do
if event[i]-event[i-1]>esp then
merge(i);
writeln(ans);
dec(t);
end;
end.
```
【上篇】
【下篇】 | 2,111 | 4,984 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2023-06 | latest | en | 0.233227 |
https://metanumbers.com/796 | 1,718,365,771,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861546.27/warc/CC-MAIN-20240614110447-20240614140447-00469.warc.gz | 370,851,368 | 7,353 | # 796 (number)
796 is an even three-digits composite number following 795 and preceding 797. In scientific notation, it is written as 7.96 × 102. The sum of its digits is 22. It has a total of 3 prime factors and 6 positive divisors. There are 396 positive integers (up to 796) that are relatively prime to 796.
## Basic properties
• Is Prime? no
• Number parity even
• Number length 3
• Sum of Digits 22
• Digital Root 4
## Name
Name seven hundred ninety-six
## Notation
Scientific notation 7.96 × 102 796 × 100
## Prime Factorization of 796
Prime Factorization 22 × 199
Composite number
Distinct Factors Total Factors Radical ω 2 Total number of distinct prime factors Ω 3 Total number of prime factors rad 398 Product of the distinct prime numbers λ -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 796 is 22 × 199. Since it has a total of 3 prime factors, 796 is a composite number.
## Divisors of 796
1, 2, 4, 199, 398, 796
6 divisors
Even divisors 4 2 1 1
Total Divisors Sum of Divisors Aliquot Sum τ 6 Total number of the positive divisors of n σ 1400 Sum of all the positive divisors of n s 604 Sum of the proper positive divisors of n A 233.333 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G 28.2135 Returns the nth root of the product of n divisors H 3.41143 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 796 can be divided by 6 positive divisors (out of which 4 are even, and 2 are odd). The sum of these divisors (counting 796) is 1400, the average is 233.333.
## Other Arithmetic Functions (n = 796)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ 396 Total number of positive integers not greater than n that are coprime to n λ 198 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π ≈ 141 Total number of primes less than or equal to n r2 0 The number of ways n can be represented as the sum of 2 squares
There are 396 positive integers (less than 796) that are coprime with 796. And there are approximately 141 prime numbers less than or equal to 796.
## Divisibility of 796
m n mod m
2 0
3 1
4 0
5 1
6 4
7 5
8 4
9 4
The number 796 is divisible by 2 and 4.
## Classification of 796
• Deficient
### Expressible via specific sums
• Polite
• Non hypotenuse
## Base conversion 796
Base System Value
2 Binary 1100011100
3 Ternary 1002111
4 Quaternary 30130
5 Quinary 11141
6 Senary 3404
8 Octal 1434
10 Decimal 796
12 Duodecimal 564
20 Vigesimal 1jg
36 Base36 m4
## Basic calculations (n = 796)
### Multiplication
n×y
n×2 1592 2388 3184 3980
### Division
n÷y
n÷2 398 265.333 199 159.2
### Exponentiation
ny
n2 633616 504358336 401469235456 319569511422976
### Nth Root
y√n
2√n 28.2135 9.26768 5.31164 3.80349
## 796 as geometric shapes
### Circle
Diameter 1592 5001.42 1.99056e+06
### Sphere
Volume 2.11265e+09 7.96225e+06 5001.42
### Square
Length = n
Perimeter 3184 633616 1125.71
### Cube
Length = n
Surface area 3.8017e+06 5.04358e+08 1378.71
### Equilateral Triangle
Length = n
Perimeter 2388 274364 689.356
### Triangular Pyramid
Length = n
Surface area 1.09746e+06 5.94392e+07 649.931
## Cryptographic Hash Functions
md5 35cf8659cfcb13224cbd47863a34fc58 732c0a1fc174dbd3f549df2e96a5dae45900b9d0 724213d95916de041564e5d39c2373585dc15855743a42a5841d849b9f3716de 2931f6596ee108458703b5edf8a601518efb950cd73b959e3ab0e54236f823020d912f4b7fc8d6750fa28130249b41760c9cd1a9bbc2e0499f09728ce6fb91e8 7f9a74847137758b0df70a20c25a5b58a57a4165 | 1,320 | 3,839 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.734375 | 4 | CC-MAIN-2024-26 | latest | en | 0.843286 |
https://oeis.org/A207460 | 1,495,954,254,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463609605.31/warc/CC-MAIN-20170528062748-20170528082748-00333.warc.gz | 1,007,346,597 | 4,018 | This site is supported by donations to The OEIS Foundation.
The OEIS is looking to hire part-time people to help edit core sequences, upload scanned documents, process citations, fix broken links, etc. - Neil Sloane, njasloane@gmail.com
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A207460 Let a(1) = 4. For n > 1, a(n) is the least number greater than a(n-1) such that the Hamming distance D(a(n-1),a(n)) = 4. 0
4, 11, 16, 31, 35, 44, 49, 62, 70, 73, 82, 93, 97, 110, 112, 127, 143, 145, 158, 162, 173, 176, 191, 199, 200, 211, 220, 224, 239, 241, 254, 286, 290, 301, 304, 319, 327, 328, 339, 348, 352, 367, 369, 382, 398, 400, 415, 419 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,1 COMMENTS All terms are odious (A000069). LINKS CROSSREFS Cf. A000225, A205509, A205510, A205511, A205302, 205649, A205533, A122565, A206852, A206853, A206960, A207016, A207017. Sequence in context: A005224 A054870 A197567 * A107988 A038241 A248349 Adjacent sequences: A207457 A207458 A207459 * A207461 A207462 A207463 KEYWORD nonn,base AUTHOR Vladimir Shevelev, Feb 18 2012 STATUS approved
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Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc. | 489 | 1,387 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2017-22 | longest | en | 0.640091 |
https://www.latestinterviewquestions.com/network-theorems-multiple-choice-questions-answers | 1,561,517,583,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560628000044.37/warc/CC-MAIN-20190626013357-20190626035357-00065.warc.gz | 804,232,338 | 10,339 | # Network Theorems Multiple choice Questions & Answers
Posted On:February 5, 2019, Posted By: Latest Interview Questions, Views: 184, Rating :
## Best Network Theorems Objective Questions and Answers
Dear Readers, Welcome to Network Theorems Objective Questions and Answers have been designed specially to get you acquainted with the nature of questions you may encounter during your Job interview for the subject of Network Theorems Multiple choice Questions. These objective type Network Theorems Questions are very important for campus placement test and job interviews. As per my experience good interviewers hardly plan to ask any particular question during your Job interview and these model questions are asked in the online technical test and interview of many IT & Non IT Industries.
### 1. Kirchhoff's current law states that
(a) net current flow at the junction is positive
(b) Hebraic sum of the currents meeting at the junction is zero
(c) no curreht can leave the junction without some current entering it.
(d) total sum of currents meeting at the junction is zero
Ans: b
### 2. According to Kirchhoffs voltage law, the algebraic sum of all IR drops and e.m.fs. in any closed loop of a network is always
(a) negative
(b) positive
(c) determined by battery e.m.fs.
(d) zero
Ans: d
### 3. Kirchhoffs current law is applicable to only
(a) junction in a network
(b) closed loops in a network
(c) electric circuits
(d) electronic circuits
Ans: a
### 4. Kirchhoffs voltage law is related to
(a) junction currents
(b) battery e.m.fs.
(c) IR drops
(d) both (b) and (c)
(e) none of the above
Ans: d
### 5. Superposition theorem can be applied only to circuits having
(a) resistive elements
(b) passive elements
(c) non-linear elements
(d) linear bilateral elements
Ans: d
### 6. The concept on which Superposition theorem is based in
(a) reciprocity
(b) duality
(c) non-linearity
(d) linearity
Ans: d
### 7. Thevenin resistance Rth is found
(a) by removing voltage sources along with their internal resistances
(6) by short-circuiting the given two terminals
(c) between any two 'open' terminals
(d) between same open terminals as for Etk
Ans: d
### 8. An ideal voltage source should have
(a) large value of e.m.f.
(b) small value of e.m.f.
(c) zero source resistance
(d) infinite source resistance
Ans: c
### 9. For a voltage source
(a) terminal voltage is always lower than source e.m.f.
(b) terminal voltage cannot be higher than source e.m.f.
(c) the source e.m.f. and terminal voltage are equal
Ans: b
### 10. To determine the polarity of the voltage drop across a resistor, it is necessary to know
(a) value of current through the resistor
(b) direction of current through the resistor
(c) value of resistor
(d) e.m.fs. in the circuit
Ans: b
### 11. "Maximum power output is obtained from a network when the load resistance is equal to the output resistance of the network as seen from the terminals of the load". The above statement is associated with
(a) Millman's theorem
(b) Thevenin's theorem
(c) Superposition theorem
(d) Maximum power transfer theorem
Ans: d
### 12. "Any number of current sources in parallel may be replaced by a single current source whose current is the algebraic sum of individual source currents and source resistance is the parallel combination of individual source resistances".
The above statement is associated with
(a) Thevenin's theorem
(b) Millman's theorem
(c) Maximum power transfer theorem
(d) None of the above
Ans: b
### The above statement is associated with
(a) compensation theorem
(b) superposition theorem
(c) reciprocity theorem
(d) none of the above
Ans: c
### 14. Which of the following is non-linear circuit parameter ?
(a) Inductance
(b) Condenser
(c) Wire wound resistor
(d) Transistor
Ans: a
### 15. A capacitor is generally a
(a) bilateral and active component
(b) active, passive, linear and nonlinear component
(c) linear and bilateral component
(d) non-linear and active component
Ans: c
### 16. "In any network containing more than one sources of e.m.f. the current in any branch is the algebraic sum of a number of individual fictitious currents (the number being equal to the number of sources of e.m.f.), each of which is due to separate action of each source of e.m.f., taken in order, when the remaining sources of e.m.f. are replaced by conductors, the resistances of which are equal to the internal resistances of the respective sources".
The above statement is associated with
(a) Thevenin's theorem
(b) Norton's theorem
(c) Superposition theorem
(d) None of the above
Ans: c
### 17. Kirchhoff s law is applicable to
(a) passive networks only
(b) a.c. circuits only
(c) d.c. circuits only
(d) both a.c. as well d.c. circuits
Ans: d
### 18. Kirchhoff s law is not applicable to circuits with
(a) lumped parameters
(b) passive elements
(c) distributed parameters
(d) non-linear resistances
Ans: c
### 19. Kirchhoff s voltage law applies to circuits with
(a) nonlinear elements only
(b) linear elements only
(c) linear, non-linear, active and passive elements
(d) linear, non-linear, active, passive, time varying as wells as time-in-variant elements
Ans: d
(a) 6.66 Q
(b) 12 Q
(c) 18Q
(d) 20Q
Ans: a
### 21. For high efficiency of transfer of power, internal resistance of the source should be
(a) equal to the load resistance
(b) less than the load resistance
(c) more than the load resistance
(d) none of the above
Ans: b
(a) 100%
(b) 80%
(c) 75%
(d) 50%
Ans: d
(a) 10 Q
(6) 20 Q
(c) 30 Q
(d) 40 Q
Ans: c
### 24. For maximum transfer of power, inter¬nal resistance of the source should be
(b) less than the load resistance
(c) greater than the load resistance
(d) none of the above
Ans: a
### 25. If the energy is supplied from a source, whose resistance is 1 ohm, to a load of 100 ohms the source will be
(a) a voltage source
(b) a current source
(c) both of above
(d) none of the above
Ans: a
### 26. The circuit whose properties are same in either direction is known as
(a) unilateral circuit
(b) bilateral circuit
(c) irreversible circuit
(d) reversible circuit
Ans: b
### 27. In a series parallel circuit, any two resistances in the same current path must be in
(a) series with each other
(b) parallel with each other
(c) series with the voltage source.'
(d) parallel with the voltage source
Ans: a
### 28. The circuit has resistors, capacitors and semi-conductor diodes. The circuit will be known as
(a) non-linear circuit
(b) linear circuit
(c) bilateral circuit
(d) none of the above
Ans: a
### 29. A non-linear network does not satisfy
(a) superposition condition
(b) homogeneity condition
(c) both homogeneity as well as superposition condition
(d) homogeneity, superposition and associative condition
Ans: c
### 30. An ideal voltage source has
(a) zero internal resistance
(b) open circuit voltage equal to the voltage on full load
(c) terminal voltage in proportion to current
(d) terminal voltage in proportion to load
Ans: a
### 31. A network which contains one or more than one source of e.m.f. is known as
(a) linear network
(b) non-linear network
(c) passive network
(d) active network
Ans: c
### 32. The superposition theorem is applicable to
(a) linear, non-linear and time variant responses
(b) linear and non-linear resistors only
(c) linear responses only
(d) none of the above
Ans: c
### 33. Which of the following is not a nonlinear element ?
(a) Gas diode
(b) Heater coil
(c) Tunnel diode
(d) Electric arc
Ans:
### 34. Application of Norton's theorem to a circuit yields
(a) equivalent current source and impedance in series
(6) equivalent current source and impedance in parallel
(c) equivalent impedance
(d) equivalent current source
Ans: a
### 35. Millman's theorem yields
(a) equivalent resistance
(6) equivalent impedance
(c) equivalent voltage source
(d) equivalent voltage or current source
Ans: d
### 36. The superposition theorem is applicable to
(a) voltage only
(b) current "only
(c) both current and voltage
(d) current voltage and power
Ans: d
### 37. Between the branch voltages of a loop the Kirchhoff s voltage law imposes
(a) non-linear constraints
(b) linear constraints
(c) no constraints
(d) none of the above
Ans: b
### 38. A passive network is one which contains
(a) only variable resistances
(b) only some sources of e.m.f. in it
(c) only two sources of e.m.f. in it
(d) no source of e.m.f. in it
Ans: d
### 39. A terminal where three on more branches meet is known as
(a) node
(b) terminus
(c) combination
(d) anode
Ans: a
### 40. Which of the following is the passive element ?
(a) Capacitance
(b) Ideal current source
(c) Ideal voltage source
(d) All of the above
Ans: a
### 41. Which of the following is a bilateral element ?
(a) Constant current source
(b) Constant voltage source
(c) Capacitance
(d) None of the above
Ans: c
(a) branch
(b) loop
(c) circuit
(d) junction
Ans: b
### 43. A linear resistor having 0 < R < °o is a
(a) current controlled resistor
(6) voltage controlled resistor
(c) both current controlled and voltage controlled resistor
(d) none of the above
Ans: c
(a) R/6
(b) fi?
(c) 2R
(d) 4R
Ans: b
(a) RIG
(b) R/3
(c) 2R
(d) 3R
Ans: a
### 46. In Thevenin's theorem, to find Z
(a) all independent current sources are short circuited and independent voltage sources are open circuited
(b) all independent voltage sources are open circuited and all independent current sources are short circuited
(c) all independent voltage and current sources are short circuited
(d) all independent voltage sources are short circuited and all independent current sources are open circuited
Ans: d
Ans: a
### 48. The number of independent equations to solve a network is equal to
(a) the number of chords
(b) the number of branches
(c) sum of the number of branches and chords
(d) sum of number of branches, chords and nodes
Ans: a
### 49. The superposition theorem requires as many circuits to be solved as there are
(a) sources, nodes and meshes
(b) sources and nodes
(c) sources
(d) nodes
Ans: c
### 50. Choose the incorrect statement.
(a) A branch formed by the parallel connection of any resistor R and open circuit has the characteristic of an open circuit.
(b) A branch formed by the parallel connection of any resistor R and a short circuit has the characteristic of a short circuit.
(c) A branch formed by the series con¬nection of any resistor R and an open circuit has the characteristic of an open circuit.
(d) A branch formed by the series con¬nection of any resistor R and a short circuit has the characteristic of resistor R.
Ans: a | 2,848 | 10,947 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2019-26 | longest | en | 0.849969 |
https://www.coursehero.com/file/6630514/439-Physics-ProblemsTechnical-Physics/ | 1,529,525,180,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267863834.46/warc/CC-MAIN-20180620182802-20180620202802-00268.warc.gz | 795,759,265 | 148,710 | 439_Physics ProblemsTechnical Physics
# 439_Physics ProblemsTechnical Physics - Chapter 15 441...
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Chapter 15 441 Q15.16 Yes. An oscillator with damping can vibrate at resonance with amplitude that remains constant in time. Without damping, the amplitude would increase without limit at resonance. Q15.17 The phase constant must be π rad . Q15.18 Higher frequency. When it supports your weight, the center of the diving board flexes down less than the end does when it supports your weight. Thus the stiffness constant describing the center of the board is greater than the stiffness constant describing the end. And then f k m = F H G I K J 1 2 π is greater for you bouncing on the center of the board. Q15.19 The release of air from one side of the parachute can make the parachute turn in the opposite direction, causing it to release air from the opposite side. This behavior will result in a periodic driving force that can set the parachute into side-to-side oscillation. If the amplitude becomes large enough, the parachute will not supply the needed air resistance to slow the fall of the unfortunate skydiver.
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https://www.physicsforums.com/threads/degeneracy-of-the-energy-level.1005048/ | 1,675,686,341,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500339.37/warc/CC-MAIN-20230206113934-20230206143934-00206.warc.gz | 962,867,360 | 16,049 | # Degeneracy of the energy level
hidemi
Homework Statement:
The energy for one-dimensional particle-in-a-box is En = (n^2*h^2) / (8mL^2). For a particle in a three-dimensional cubic box (Lx=Ly =Lz), if an energy level has twice the energy of the ground state, what is the degeneracy of this energy level?
Relevant Equations:
En = (n^2*h^2) / (8mL^2)
En = [(nx/Lx)^2 + (ny/Ly)^2 + (nz/Lz)^2] *h^2 / (8mL^2)
Energy of the One-dimensional box:
ground state: En = (n^2*h^2) / (8mL^2), where n=1
twice the ground state: 2* En = 2 [(1^2*h^2) / (8mL^2)]
Energy of the Three-dimensional box:
En = (nx^2 + ny^2 + nz^2) *h^2 / (8mL^2) = 2 (1^2*h^2) / (8mL^2)
As stated, twice the ground state energy of one dimensional box is equal to that of the three -dimensional box. So, (nx^2 + ny^2 + nz^2) = 2, how would the degeneracy be 3? How should I continue?
Can someone help because I am confused, please? Thank you.
## Answers and Replies
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
As stated, twice the ground state energy of one dimensional box is equal to that of the three -dimensional box.
The problem statement doesn't in fact say this. It's referring to the ground state of the 3-d box.
BTW, what's up with the thread title?
hidemi
The problem statement doesn't in fact say this. It's referring to the ground state of the 3-d box.
If the energy level is twice the energy of the ground state in three dimensional cubic box, then the energy would be
2*[(nx^2 + ny^2 + nz^2) *h^2 / (8mL^2)]
= 2*[(1^2 + 1^2 + 1^2) *h^2 / (8mL^2)]
= 6*h^2 / (8mL^2)
Is this correct?
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
Yes.
hidemi
Yes.
The degeneracy would be a total of three because for the energy to be 6*h^2/(8mL^2), there are three possibilities: (2,1,1,), (1,2,1) and (1,1,2). Is it the correct reasoning?
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
Yes, that’s correct.
hidemi
Yes, that’s correct.
Thanks a lot! | 651 | 1,975 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.9375 | 4 | CC-MAIN-2023-06 | latest | en | 0.881787 |
https://www.stata.com/statalist/archive/2006-09/msg00492.html | 1,721,031,917,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514680.75/warc/CC-MAIN-20240715071424-20240715101424-00177.warc.gz | 909,623,834 | 4,303 | # Re: st: iv probit and endogenous binary variables
From Nishant Dass <[email protected]> To [email protected] Subject Re: st: iv probit and endogenous binary variables Date Wed, 13 Sep 2006 23:56:36 -0700 (PDT)
```Dear list-members,
I would like to add another question following Song Gao's
email.
What should one do if one also has an interaction term with
this endogenous binary variable on the RHS? (I realise
this has little to do with Stata and is simply an
econometrics question, so please excuse me for that.)
Thank you very much.
Regards,
Nishant
--- SONG GAO <[email protected]> wrote:
> Dear Statalisters,
>
> I understand that in a two step IVPROBIT, the first stage
> is OLS estimation.
>
> While my question is that I have binary endogenous
> variables in rhs
> which includes 3 choices. In order to fit ivprobit
> estimation, may I
> do the following regression?
>
> 1. In the first stage, run 3 linear probability
> regressions on the 3 choices;
> 2. Get the preditted probabilities of each of the
> choices;
> 3. Take the predictted probabilities as instruments in
> second stage
> ivprobit estimation.
>
> The above is my first question, my second question is
> that when I do
> IVREG and IVPROBIT, after I get the predictted values in
> the first
> stage, I found that people use two stata commands for
> second stage, if
> the predictted value is "zhat", the two commands in
> second stage are
> as followings:
>
> a. ivreg y x (z=zhat)
> b. reg y x zhat
>
> "a" is right.
>
> My thrid question is that if I have multiple endogenous
> regressors
> (both are binary varibles), I know this is very
> diffficult to solve,
> can I do it in the following way: Generate interaction
> terms of the
> two endogenous binary variables, thus, I have a series of
> dummies and
> take care of them following the traditional two step
> method.
>
> BTW, I am using STATA 9 SE.
>
> Thank you very much!
>
> Song
> *
> * For searches and help try:
> * http://www.stata.com/support/faqs/res/findit.html
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
>
__________________________________________________
Do You Yahoo!?
Tired of spam? Yahoo! Mail has the best spam protection around
http://mail.yahoo.com
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
``` | 686 | 2,453 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2024-30 | latest | en | 0.909539 |
https://forum.allaboutcircuits.com/threads/homework-help.47628/ | 1,545,131,270,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376829140.81/warc/CC-MAIN-20181218102019-20181218124019-00501.warc.gz | 600,882,048 | 16,636 | Homework Help
Discussion in 'Homework Help' started by Bill B, Dec 28, 2010.
1. Bill B Thread Starter Active Member
Nov 29, 2009
61
1
I have a homework problem I can't solve. This topic wasn't covered in class and the textbook offers no explanation, yet this problem is in the textbook! The problem is as follows:
Given a 100-Watt power source, what is the maximum allowable length for the following transmission media if a signal of 1 Watt is to be received?
a. 24-gauge twisted pair operating at 300kHz
b. 24-gauge twisted pair operating at 1MHz
c. 0.375" coaxial cable operating at 1MHz
d. 0.375" coaxial cable operating at 25MHz
e. optical fiber operating at its optimal frequency
So far I have determined that the total loss from 100W to 1W is 20dB. A twisted pair rated at 0-1MHz has an attenuation rate of .7dB/km @ 1kHz. I tried to manipuate the ratio and came up with 4.8 meters. I have no idea how to approach this problem. Any help would be appreciated.
Last edited: Dec 28, 2010
2. hgmjr Retired Moderator
Jan 28, 2005
9,030
218
This thread clearly belongs in the homework forum so I have relocated it there.
hgmjr
3. Bill B Thread Starter Active Member
Nov 29, 2009
61
1
Thanks. I should have known to put a thread titled Homework Help in the Homework Help forum. | 358 | 1,286 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2018-51 | latest | en | 0.946056 |
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# 5 Interpreting the appearance of sections
Most histological sections are two-dimensional slices, from a three-dimensional piece of tissue. Exactly what will be seen on the microscope slide depends on the plane of the section, i.e. the position of the microtome cut, in relation to the anatomical structures in the tissue. Most tissues are cut in a plane, which allows the underlying structure of that tissue to be seen and interpreted most easily. For example, sections of the intestine and skin are usually cut in transverse section, so that all layers of the tissue are visible. Positioning the tissue before embedding and knowing its orientation are therefore critically important, so that the sectioning is done in the correct plane. For biopsy specimens, there is no option for deciding the plane of the section, as the direction of the needle tract determines what tissue is available and how it is orientated. Pathologists expect to view sections in their best orientation as this then gives them the best opportunity of identifying abnormalities.
Many anatomical structures are not readily visible in thin, two-dimensional sections, simply because most of the structure is not present. In this case the three-dimensional structure needs to be interpreted from what can be seen. In order to give you some insight into this problem, take the three structures shown in Figure 10 and make simple sketches of how they would appear if sectioned in the planes indicated.
Figure 10 Understanding the plane of the section: make simple diagrams of the structures that would be seen if the following tissue or cell were sectioned in the planes indicated (A-C). Note that on the neuron, the thickness of the section is significant in relation to the thickness of the cell.
This exercise should make you appreciate that it is not just the orientation of the section but also the position (depth) into the tissue or tissue block that affects the appearance of the structures. For example, the blood vessel can appear as one or two structures, depending on the level of the section within the block. For this reason, it may be necessary to section a block at different levels to obtain suitable slides. (The initial cut-up of the tissue should have ensured that the lesion is within the block so it should not be necessary to hunt through the block to find it.)
Another problem in interpreting sections is that some structures (e.g. the neuron in Figure 10) are too big to be seen in a thin section - much of the cell and its overall architecture cannot be seen. One solution is to cut thicker sections.
## SAQ 7
List three considerations that might apply to the preparation and interpretation of thicker sections, which do not apply to regular 3µm sections. | 589 | 3,007 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2022-49 | latest | en | 0.94005 |
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# Find the equation of the plane passing through the point (-1, - 1, 2) and perpendicular to each of the following planes:2x + 3y - 3z = 2 and 5x - 4y + z = 6
Asked by Topperlearning User 2nd March 2015, 2:30 PM
The equation of the plane passing through the point (-1, -1, 2) is:
a(x + 1) + b(y + 1) + c (z - 2) = 0...(1)
Where a, b c are the direction ratios of the normal to the plane
It is given that the plane (1) is perpendicular to the planes.
2x +3y - 3z = 2 and 5x - 4y + z = 6
2a + 3b - 3c = 0...(2)
5a - 4b + c = 0...(3)
Solving equations (2) and (3), we have:
So the direction ratios of the normal to the required plane are multiples of 9, 17, and 23.
Thus, the equation of the required plane is:
Answered by Expert 2nd March 2015, 4:30 PM
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You have rated this answer /10 | 394 | 1,037 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2019-30 | latest | en | 0.898765 |
http://www.physicsforums.com/showthread.php?p=3868435 | 1,386,770,821,000,000,000 | text/html | crawl-data/CC-MAIN-2013-48/segments/1386164037376/warc/CC-MAIN-20131204133357-00015-ip-10-33-133-15.ec2.internal.warc.gz | 485,202,569 | 7,293 | # integral of x^2e^(-x^2)
by spaniks
Tags: integration, integration by parts
P: 6 1. The problem statement, all variables and given/known data Use the fact that the integral evaluated from -∞ to +∞ of e^(-x^2) is sqrt(∏) to evaluate the integral from -∞ to +∞ of x^2(e^(-x^2)). 2. Relevant equations 3. The attempt at a solution I tried using integration by parts and I came down to an indefinite integral of sqrt(∏)*x^2. I know the answer is sqrt(∏)/2 but I don't see how. Can someone tell me what im doing wrong please.
P: 272
Quote by spaniks 1. The problem statement, all variables and given/known data Use the fact that the integral evaluated from -∞ to +∞ of e^(-x^2) is sqrt(∏) to evaluate the integral from -∞ to +∞ of x^2(e^(-x^2)). 2. Relevant equations 3. The attempt at a solution I tried using integration by parts and I came down to an indefinite integral of sqrt(∏)*x^2. I know the answer is sqrt(∏)/2 but I don't see how. Can someone tell me what im doing wrong please.
That doesn't seem right. Try doing integration by parts by setting $u = x \text{ and } dv=xe^{-x^2}dx$.
P: 6 Thanks I got the answer using that method
Related Discussions General Physics 0 Classical Physics 0 Calculus & Beyond Homework 5 Calculus & Beyond Homework 5 Calculus & Beyond Homework 4 | 372 | 1,288 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2013-48 | longest | en | 0.906933 |
http://www.jiskha.com/display.cgi?id=1270749110 | 1,498,246,285,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320130.7/warc/CC-MAIN-20170623184505-20170623204505-00438.warc.gz | 562,508,022 | 3,595 | Chemistry
posted by on .
Determine the mass of gold that can be extracted if 25.0g of sodium cyanide is used.
4Au+8NaCN+O2--->4NaAu(CN)2+4NaOH
• Chemistry - ,
Convert 25.00 g NaCN to moles. moles = grams/molar mass.
Using the coefficients in the balanced equation, convert moles NaCN to moles Au.
Now convert moles Au to grams. g = moles x molar mass. | 113 | 357 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2017-26 | latest | en | 0.69614 |
http://math.stackexchange.com/questions/403345/differentiating-y-xe1-over-x/403349 | 1,469,484,459,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257824395.52/warc/CC-MAIN-20160723071024-00306-ip-10-185-27-174.ec2.internal.warc.gz | 158,042,624 | 17,167 | Differentiating $y= xe^{1\over x}$
Can someone please help me? I'm trying, but I really can't find the second derivative of $y= xe^{1/x}$. Thanks!
-
Your English was perfect, so I removed your apology for it ;) – Sharkos May 26 '13 at 23:41
By the product rule:
$$y'=x'e^{1/x}+x\left(e^{1/x}\right)'=e^{1/x}-\frac{1}{x}e^{1/x}$$
I used: $y=e^{f(x)}$, then $y'=f'(x)e^{f(x)}$. Then:
$$y''=-\frac{1}{x^2}e^{1/x}+\frac{1}{x^2}e^{1/x}+\frac{1}{x^3}e^{1/x}=\frac{1}{x^3}e^{1/x}$$
-
Thi is a hint to solve this kind of problem: you take the logarithm of the function and you have: $$\log y= \log(xe^{\frac{1}{x}})=\frac{1}{x}+\log x$$ so derive it: $$\frac{y'}{y}=-\frac{1}{x^2}+\frac{1}{x}$$ Thus $$y'=y(-\frac{1}{x^2}+\frac{1}{x})=-\frac{e^{\frac{1}{x}}}{x}+e^{\frac{1}{x}}$$
Deriving again with chain rule : $$y''=-\frac{e^{\frac{1}{x}}} {x^2}+ \frac{e^{\frac{1}{x}}}{x^2}+\frac{e^{\frac{1}{x}}}{x^3}= \frac{e^{\frac{1}{x}}}{x^3}$$
- | 426 | 940 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.25 | 4 | CC-MAIN-2016-30 | latest | en | 0.650423 |
http://mail-archives.apache.org/mod_mbox/impala-reviews/201707.mbox/%3Cgerrit.1500075819000.I37ad6232d7953bd75c18dc86e665b2b501a1ebe1@gerrit.cloudera.org%3E | 1,506,446,133,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818696653.69/warc/CC-MAIN-20170926160416-20170926180416-00202.warc.gz | 213,487,531 | 2,240 | # impala-reviews mailing list archives
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From "Taras Bobrovytsky (Code Review)" <ger...@cloudera.org>
Subject [Impala-ASF-CR] IMPALA-4939, IMPALA-4939: Decimal V2 multiplication
Date Fri, 14 Jul 2017 23:43:49 GMT
```Taras Bobrovytsky has uploaded a new change for review.
http://gerrit.cloudera.org:8080/7438
Change subject: IMPALA-4939, IMPALA-4939: Decimal V2 multiplication
......................................................................
IMPALA-4939, IMPALA-4939: Decimal V2 multiplication
Implement the new DECIMAL return type rules for multiply expressions,
active when query option DECIMAL_V2=1. The algorithm for determining
the type of the result of multiplication is described in the JIRA.
DECIMAL V1:
+-----------------------------------------------------------------------+
| typeof(cast('0.1' as decimal(38,38)) * cast('0.1' as decimal(38,38))) |
+-----------------------------------------------------------------------+
| DECIMAL(38,38) |
+-----------------------------------------------------------------------+
+-----------------------------------------------------------------------+
| typeof(cast('0.1' as decimal(38,15)) * cast('0.1' as decimal(38,15))) |
+-----------------------------------------------------------------------+
| DECIMAL(38,30) |
+-----------------------------------------------------------------------+
DECIMAL V2:
+-----------------------------------------------------------------------+
| typeof(cast('0.1' as decimal(38,38)) * cast('0.1' as decimal(38,38))) |
+-----------------------------------------------------------------------+
| DECIMAL(38,37) |
+-----------------------------------------------------------------------+
+-----------------------------------------------------------------------+
| typeof(cast('0.1' as decimal(38,15)) * cast('0.1' as decimal(38,15))) |
+-----------------------------------------------------------------------+
| DECIMAL(38,6) |
+-----------------------------------------------------------------------+
In this patch, we also fix the early multiplication overflow. We compute
an int256 intermediate value, which we then attempt to scale down and
round to int128.
---
M be/src/exprs/expr-test.cc
M be/src/runtime/decimal-value.inline.h
M be/src/util/bit-util.h
M be/src/util/decimal-util.h
M fe/src/main/java/org/apache/impala/analysis/TypesUtil.java
5 files changed, 385 insertions(+), 29 deletions(-)
git pull ssh://gerrit.cloudera.org:29418/Impala-ASF refs/changes/38/7438/1
--
To view, visit http://gerrit.cloudera.org:8080/7438
To unsubscribe, visit http://gerrit.cloudera.org:8080/settings
Gerrit-MessageType: newchange | 604 | 2,891 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2017-39 | latest | en | 0.457403 |
https://www.jiskha.com/display.cgi?id=1373225687 | 1,503,285,653,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886107487.10/warc/CC-MAIN-20170821022354-20170821042354-00213.warc.gz | 921,457,552 | 3,939 | # algebra 2
posted by .
The capacity of the gas tank in a car is 16.5 gallons. The car uses 10.5 gallons to travel 178.5 miles. After driving 85 more miles, only 1 gallon of gasoline remains in the tank. Which linear equation and graph model the amount of gas g left in the tank after driving m miles?
• algebra 2 -
178.5mi/10.5gal = 17 mi/gal
This is consistent with 85mi/5gal, so
g(m) = 16.5 - m/17
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More Similar Questions | 714 | 2,807 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2017-34 | latest | en | 0.936572 |
http://www.gradesaver.com/textbooks/math/prealgebra/prealgebra-7th-edition/chapter-9-test-page-693/28 | 1,524,367,133,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125945484.58/warc/CC-MAIN-20180422022057-20180422042057-00204.warc.gz | 431,457,924 | 13,712 | # Chapter 9 - Test: 28
8ft 4in
#### Work Step by Step
$2ft9in\times3=6ft27in=8ft4in$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 75 | 248 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2018-17 | latest | en | 0.811783 |
https://mathoverflow.net/questions/290407/understanding-koszul-duality-in-bgg-and-gelfand-manin | 1,721,592,496,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517768.40/warc/CC-MAIN-20240721182625-20240721212625-00816.warc.gz | 337,552,139 | 22,773 | # Understanding Koszul Duality in BGG and Gelfand, Manin
I'm trying to understand a particular point in the proof of Koszul duality between $D^b(\Lambda(V))$ and $D^b(S(V^*))$ as seen in "Algebraic Bundles over $\mathbb{P}^n$ and Problems of Linear Algebra" by Bernstein, Gelfand and Gelfand. In particular, I am trying to work through Prop. 3, where we introduce functors
$F: C^b(\Lambda(V)) \rightarrow C^b(S(V^*))$ and
$G: C(S(V^*)) \rightarrow C(\Lambda(V))$.
The goal of the proof is to show these functors define an equivalence of derived categories.
I have two particular questions:
1) In the proof, it is first demonstrated that $F$ and $G$ are adjoint. While I can prove this, I do not understand how it helps the argument; I cannot find a source which connects adjoint functors with equivalences on the derived category level.
2) In both BGG and in Gelfand-Manin "Methods of Homological Algebra", the next step is to show that $F$ and $G$ lift to derived functors, and that they form an equivalence of categories; both sources simply say use the Koszul complex for this step. As for the lifting, I know I need to demonstrate that $F$ and $G$ map acyclic complexes to acyclic complexes, but I don't see how to use the acyclicity of the Koszul resolution here. Moreover, once this is done, I'm stuck again on showing that $F_D$ and $G_D$ actually form an equivalence of categories. How does all of this follow from the properties of the Koszul complex? | 390 | 1,467 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2024-30 | latest | en | 0.9276 |
https://davidmazza.net/canterbury/determining-sufficient-sample-size.php | 1,680,245,903,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949573.84/warc/CC-MAIN-20230331051439-20230331081439-00201.warc.gz | 229,027,762 | 9,535 | # Determining Sufficient Sample Size
(PDF) DETERMINING SUFFICIENCY OF SAMPLE SIZE IN. Understanding Power and Rules of Thumb for Determining Sample Sizes Carmen R. Wilson VanVoorhis and Betsy L. Morgan University of Wisconsin ‐ La Crosse This article addresses the definition of power and its relationship to Type I and Type II errors. We discuss the relationship of sample size and power., Calculate the population size. Your research likely has the goal of finding something out about a population, and in order to determine how many observations you need to make (your sample size), it's necessary to know how many total possible observations are available..
### Why Is Sample Size N>=30 Sufficient? – iSixSigma
Determination of Sufficient Sample Size for Linear. 17/5/2014В В· Sample size calculation is always an essential step during the planning of scientific studies. An insufficient or small sample size may not be able to demonstrate the desired difference, or estimate the frequency of the event of interest with acceptable precision., reduces sample size and power. If you anticipate that you will not be able to collect outcome data on some study participants, increase your initial sample size to ensure that you will have sufficient power to detect the impact of the program at the conclusion of the intervention. rule of thumb #2: if the effect size.
17/5/2014В В· Sample size calculation is always an essential step during the planning of scientific studies. An insufficient or small sample size may not be able to demonstrate the desired difference, or estimate the frequency of the event of interest with acceptable precision. determining sufficient sample size for management survey research activities. The choice of the method is informed b y the fact that we intend to primarily describe the sufficient sample sizes
The following are important considerations for determining an appropriate sample size and understanding its role in the conclusions: Although a sample may be of sufficient size to satisfy statistical requirements, it still may not be sufficient to achieve … 30/6/2018 · I’m hoping someone can clarify this for me. Maybe I’m not understanding something here, but I keep reading that a “large sample size” is one that is greater than or equal to 30. And with a sample size of n>=30, you are able to make inferences about the population from the sample. If this is
determining sufficient sample size for management survey research activities. The choice of the method is informed b y the fact that we intend to primarily describe the sufficient sample sizes 1/6/2012В В· This standards article uses a series of scenarios to assist pediatric researchers in not only determining an adequate trial sample size but also how to proceed when this sample size may be difficult to achieve. Recommendations for practice are summarized in Table 1.
The problem of determining sufficient sample size during recursive estimation of the parameters of single-input single-output dynamic systems is considered in this paper. Mainly, the problem mentioned reduces to that of determining a random moment of ceasing of recursive estimator calculation when the given accuracy of the estimates is achieved. Determining Sample Size. Term 2, 2006 Advanced Methods in Biostatistics, II 2 GOALS • Review of the inputs for determining sample size • Compare sample sizes for Parallel, Crossover and Factorial designs Goal is to: have sufficient power to choose between two simple hypotheses
determining sufficient sample size for management survey research activities. The choice of the method is informed b y the fact that we intend to primarily describe the sufficient sample sizes 17/5/2014В В· Sample size calculation is always an essential step during the planning of scientific studies. An insufficient or small sample size may not be able to demonstrate the desired difference, or estimate the frequency of the event of interest with acceptable precision.
The following are important considerations for determining an appropriate sample size and understanding its role in the conclusions: Although a sample may be of sufficient size to satisfy statistical requirements, it still may not be sufficient to achieve … The sample sizes listed in this table are for zero failures or errors. In looking at the hypothetical example we discussed earlier in the article, an RPN of 320 and a confidence interval of 95% and a reliability of 95%, this translates to a sample size of 59 with zero allowable failures.
17/5/2014В В· Sample size calculation is always an essential step during the planning of scientific studies. An insufficient or small sample size may not be able to demonstrate the desired difference, or estimate the frequency of the event of interest with acceptable precision. 27/11/2015В В· We suggest that the size of a sample with sufficient information power depends on (a) the aim of the study, (b) sample specificity, (c) use of established theory, (d) quality of dialogue, and (e) analysis strategy. We present a model where these elements of information and their relevant dimensions are related to information power.
The following are important considerations for determining an appropriate sample size and understanding its role in the conclusions: Although a sample may be of sufficient size to satisfy statistical requirements, it still may not be sufficient to achieve … In determining sample size it is generally sufficient to act as if the population is infinite and ignore the finite population correction (fpc) factor. The subsequent sections talk about sample sizes for confidence intervals, confidence intervals on sample size and power, and the specification of power. Controlled Vocabulary Terms
Determining Sample Size: How to Ensure You Get the Correct Sample Size. How many responses do you really need for statistically sound results? This simple question is a never-ending quandary for researchers who use statistically based calculations to answer different questions. Calculate the population size. Your research likely has the goal of finding something out about a population, and in order to determine how many observations you need to make (your sample size), it's necessary to know how many total possible observations are available.
18/12/2017 · Determining sample size based on confidence level and margin of error. View more lessons or practice this subject at http://www.khanacademy.org/math/ap-stati... 30/6/2018 · I’m hoping someone can clarify this for me. Maybe I’m not understanding something here, but I keep reading that a “large sample size” is one that is greater than or equal to 30. And with a sample size of n>=30, you are able to make inferences about the population from the sample. If this is
### Determining Sample Size with RAT-STATS Forensus Group
Methods of Determining Sample Sizes 2013 - Wiley Series. Tables for determining the sufficient sample size were given as adapted from Krejcie and Morgan (1970) and Bartlett, et al., (2001). The main objective of this study is to explore the procedures for determining a sufficient sample size for management survey research activities., Tables for determining the sufficient sample size were given as adapted from Krejcie and Morgan (1970) and Bartlett, et al., (2001). The main objective of this study is to explore the procedures for determining a sufficient sample size for management survey research activities..
### DETERMINATION OF SUFFICIENT SAMPLE SIZE FOR LINEAR
Determination of Sufficient Sample Size for Linear. 30/6/2018 · I’m hoping someone can clarify this for me. Maybe I’m not understanding something here, but I keep reading that a “large sample size” is one that is greater than or equal to 30. And with a sample size of n>=30, you are able to make inferences about the population from the sample. If this is The problem of determining sufficient sample size during recursive estimation of the parameters of single-input single-output dynamic systems is considered in this paper. Mainly, the problem mentioned reduces to that of determining a random moment of ceasing of recursive estimator calculation when the given accuracy of the estimates is achieved..
The following are important considerations for determining an appropriate sample size and understanding its role in the conclusions: Although a sample may be of sufficient size to satisfy statistical requirements, it still may not be sufficient to achieve … Therefore we will not be also to use the aforeside successive procedure for the determination of sufficient sample size, but, on the other hand, we may determine the efficiency of RLS by it. Such a problem is solved here by identification of the processes in pipe-lines.
Calculate the population size. Your research likely has the goal of finding something out about a population, and in order to determine how many observations you need to make (your sample size), it's necessary to know how many total possible observations are available. Tables for determining the sufficient sample size were given as adapted from Krejcie and Morgan (1970) and Bartlett, et al., (2001). The main objective of this study is to explore the procedures for determining a sufficient sample size for management survey research activities.
The sample sizes listed in this table are for zero failures or errors. In looking at the hypothetical example we discussed earlier in the article, an RPN of 320 and a confidence interval of 95% and a reliability of 95%, this translates to a sample size of 59 with zero allowable failures. Therefore we will not be also to use the aforeside successive procedure for the determination of sufficient sample size, but, on the other hand, we may determine the efficiency of RLS by it. Such a problem is solved here by identification of the processes in pipe-lines.
Calculation of sample size. The use of statistical formulas for determining the sample size implies, first of all, the choice of a significant benchmark for the measures to be made based on the results provided by the qualitative research to be performed, usually, the researcher has, in this sense, two alternatives: 27/11/2015В В· We suggest that the size of a sample with sufficient information power depends on (a) the aim of the study, (b) sample specificity, (c) use of established theory, (d) quality of dialogue, and (e) analysis strategy. We present a model where these elements of information and their relevant dimensions are related to information power.
Determining Sample Size. Term 2, 2006 Advanced Methods in Biostatistics, II 2 GOALS • Review of the inputs for determining sample size • Compare sample sizes for Parallel, Crossover and Factorial designs Goal is to: have sufficient power to choose between two simple hypotheses The sample sizes listed in this table are for zero failures or errors. In looking at the hypothetical example we discussed earlier in the article, an RPN of 320 and a confidence interval of 95% and a reliability of 95%, this translates to a sample size of 59 with zero allowable failures.
1/6/2012В В· This standards article uses a series of scenarios to assist pediatric researchers in not only determining an adequate trial sample size but also how to proceed when this sample size may be difficult to achieve. Recommendations for practice are summarized in Table 1. Calculate the population size. Your research likely has the goal of finding something out about a population, and in order to determine how many observations you need to make (your sample size), it's necessary to know how many total possible observations are available.
The sample sizes listed in this table are for zero failures or errors. In looking at the hypothetical example we discussed earlier in the article, an RPN of 320 and a confidence interval of 95% and a reliability of 95%, this translates to a sample size of 59 with zero allowable failures. The problem of determining sufficient sample size during recursive estimation of the parameters of single-input single-output dynamic systems is considered in this paper. Mainly, the problem mentioned reduces to that of determining a random moment of ceasing of recursive estimator calculation when the given accuracy of the estimates is achieved.
Determining Sample Size. Term 2, 2006 Advanced Methods in Biostatistics, II 2 GOALS • Review of the inputs for determining sample size • Compare sample sizes for Parallel, Crossover and Factorial designs Goal is to: have sufficient power to choose between two simple hypotheses Determining Sample Size: How to Ensure You Get the Correct Sample Size. How many responses do you really need for statistically sound results? This simple question is a never-ending quandary for researchers who use statistically based calculations to answer different questions.
30/6/2018 · I’m hoping someone can clarify this for me. Maybe I’m not understanding something here, but I keep reading that a “large sample size” is one that is greater than or equal to 30. And with a sample size of n>=30, you are able to make inferences about the population from the sample. If this is Determining Sample Size. Term 2, 2006 Advanced Methods in Biostatistics, II 2 GOALS • Review of the inputs for determining sample size • Compare sample sizes for Parallel, Crossover and Factorial designs Goal is to: have sufficient power to choose between two simple hypotheses
24/7/2019 · Sample Size Calculator Determines the minimum number of subjects for adequate study power ClinCalc.com » Statistics » Sample Size Calculator. of different equations to determine the minimum number of subjects that need to be enrolled in a study in order to have sufficient statistical power to detect a treatment effect. 1. Determining Sample Size. Term 2, 2006 Advanced Methods in Biostatistics, II 2 GOALS • Review of the inputs for determining sample size • Compare sample sizes for Parallel, Crossover and Factorial designs Goal is to: have sufficient power to choose between two simple hypotheses
This workshop outlines how to calculate an appropriate sample size (n) to address the objectives of a research project. Participants will be led through essential steps for the design of a study: specifying the outcome variable, outlining hypothesis tests, estimating the variance or other “nuisance parameters,” determining power to detect 2/9/2012 · Calculation of exact sample size is an important part of research design. It is very important to understand that different study design need different method of sample size calculation and one formula cannot be used in all designs. In this short review we tried to educate researcher regarding
## determining sample power
Why Is Sample Size N>=30 Sufficient? – iSixSigma. determining sufficient sample size for management survey research activities. The choice of the method is informed b y the fact that we intend to primarily describe the sufficient sample sizes, reduces sample size and power. If you anticipate that you will not be able to collect outcome data on some study participants, increase your initial sample size to ensure that you will have sufficient power to detect the impact of the program at the conclusion of the intervention. rule of thumb #2: if the effect size.
### Standard 4 Determining Adequate Sample Sizes American
Determination of Sufficient Sample Size for Linear. Understanding Power and Rules of Thumb for Determining Sample Sizes Carmen R. Wilson VanVoorhis and Betsy L. Morgan University of Wisconsin ‐ La Crosse This article addresses the definition of power and its relationship to Type I and Type II errors. We discuss the relationship of sample size and power., 17/5/2014 · Sample size calculation is always an essential step during the planning of scientific studies. An insufficient or small sample size may not be able to demonstrate the desired difference, or estimate the frequency of the event of interest with acceptable precision..
This can be risky if the sample size is very small because it’s less likely to reflect the whole population; try to get the largest trial study that you can, and/or make a conservative estimate for . Often a small trial study is worth the time and effort. The following are important considerations for determining an appropriate sample size and understanding its role in the conclusions: Although a sample may be of sufficient size to satisfy statistical requirements, it still may not be sufficient to achieve …
This workshop outlines how to calculate an appropriate sample size (n) to address the objectives of a research project. Participants will be led through essential steps for the design of a study: specifying the outcome variable, outlining hypothesis tests, estimating the variance or other “nuisance parameters,” determining power to detect reduces sample size and power. If you anticipate that you will not be able to collect outcome data on some study participants, increase your initial sample size to ensure that you will have sufficient power to detect the impact of the program at the conclusion of the intervention. rule of thumb #2: if the effect size
In determining sample size it is generally sufficient to act as if the population is infinite and ignore the finite population correction (fpc) factor. The subsequent sections talk about sample sizes for confidence intervals, confidence intervals on sample size and power, and the specification of power. Controlled Vocabulary Terms In determining sample size it is generally sufficient to act as if the population is infinite and ignore the finite population correction (fpc) factor. The subsequent sections talk about sample sizes for confidence intervals, confidence intervals on sample size and power, and the specification of power. Controlled Vocabulary Terms
Calculate the population size. Your research likely has the goal of finding something out about a population, and in order to determine how many observations you need to make (your sample size), it's necessary to know how many total possible observations are available. Determining Sample Size. Term 2, 2006 Advanced Methods in Biostatistics, II 2 GOALS • Review of the inputs for determining sample size • Compare sample sizes for Parallel, Crossover and Factorial designs Goal is to: have sufficient power to choose between two simple hypotheses
30/6/2018 · I’m hoping someone can clarify this for me. Maybe I’m not understanding something here, but I keep reading that a “large sample size” is one that is greater than or equal to 30. And with a sample size of n>=30, you are able to make inferences about the population from the sample. If this is reduces sample size and power. If you anticipate that you will not be able to collect outcome data on some study participants, increase your initial sample size to ensure that you will have sufficient power to detect the impact of the program at the conclusion of the intervention. rule of thumb #2: if the effect size
The sample sizes listed in this table are for zero failures or errors. In looking at the hypothetical example we discussed earlier in the article, an RPN of 320 and a confidence interval of 95% and a reliability of 95%, this translates to a sample size of 59 with zero allowable failures. 27/11/2015В В· We suggest that the size of a sample with sufficient information power depends on (a) the aim of the study, (b) sample specificity, (c) use of established theory, (d) quality of dialogue, and (e) analysis strategy. We present a model where these elements of information and their relevant dimensions are related to information power.
18/12/2017В В· Determining sample size based on confidence level and margin of error. View more lessons or practice this subject at http://www.khanacademy.org/math/ap-stati... The problem of determining sufficient sample size during recursive estimation of the parameters of single-input single-output dynamic systems is considered in this paper. Mainly, the problem mentioned reduces to that of determining a random moment of ceasing of recursive estimator calculation when the given accuracy of the estimates is achieved.
30/6/2018 · I’m hoping someone can clarify this for me. Maybe I’m not understanding something here, but I keep reading that a “large sample size” is one that is greater than or equal to 30. And with a sample size of n>=30, you are able to make inferences about the population from the sample. If this is 24/7/2019 · Sample Size Calculator Determines the minimum number of subjects for adequate study power ClinCalc.com » Statistics » Sample Size Calculator. of different equations to determine the minimum number of subjects that need to be enrolled in a study in order to have sufficient statistical power to detect a treatment effect. 1.
27/11/2015В В· We suggest that the size of a sample with sufficient information power depends on (a) the aim of the study, (b) sample specificity, (c) use of established theory, (d) quality of dialogue, and (e) analysis strategy. We present a model where these elements of information and their relevant dimensions are related to information power. 17/5/2014В В· Sample size calculation is always an essential step during the planning of scientific studies. An insufficient or small sample size may not be able to demonstrate the desired difference, or estimate the frequency of the event of interest with acceptable precision.
This can be risky if the sample size is very small because it’s less likely to reflect the whole population; try to get the largest trial study that you can, and/or make a conservative estimate for . Often a small trial study is worth the time and effort. 24/7/2019 · Sample Size Calculator Determines the minimum number of subjects for adequate study power ClinCalc.com » Statistics » Sample Size Calculator. of different equations to determine the minimum number of subjects that need to be enrolled in a study in order to have sufficient statistical power to detect a treatment effect. 1.
The problem of determining sufficient sample size during recursive estimation of the parameters of single-input single-output dynamic systems is considered in this paper. Mainly, the problem mentioned reduces to that of determining a random moment of ceasing of recursive estimator calculation when the given accuracy of the estimates is achieved. The formula for determining sample size to ensure that the test has a specified power is given below: where О± is the selected level of significance and Z 1-О± /2 is the value from the standard normal distribution holding 1- О±/2 below it.
Therefore we will not be also to use the aforeside successive procedure for the determination of sufficient sample size, but, on the other hand, we may determine the efficiency of RLS by it. Such a problem is solved here by identification of the processes in pipe-lines. This workshop outlines how to calculate an appropriate sample size (n) to address the objectives of a research project. Participants will be led through essential steps for the design of a study: specifying the outcome variable, outlining hypothesis tests, estimating the variance or other “nuisance parameters,” determining power to detect
Understanding Power and Rules of Thumb for Determining Sample Sizes Carmen R. Wilson VanVoorhis and Betsy L. Morgan University of Wisconsin ‐ La Crosse This article addresses the definition of power and its relationship to Type I and Type II errors. We discuss the relationship of sample size and power. Tables for determining the sufficient sample size were given as adapted from Krejcie and Morgan (1970) and Bartlett, et al., (2001). The main objective of this study is to explore the procedures for determining a sufficient sample size for management survey research activities.
Therefore we will not be also to use the aforeside successive procedure for the determination of sufficient sample size, but, on the other hand, we may determine the efficiency of RLS by it. Such a problem is solved here by identification of the processes in pipe-lines. Tables for determining the sufficient sample size were given as adapted from Krejcie and Morgan (1970) and Bartlett, et al., (2001). The main objective of this study is to explore the procedures for determining a sufficient sample size for management survey research activities.
determining sufficient sample size for management survey research activities. The choice of the method is informed b y the fact that we intend to primarily describe the sufficient sample sizes Calculate the population size. Your research likely has the goal of finding something out about a population, and in order to determine how many observations you need to make (your sample size), it's necessary to know how many total possible observations are available.
Determining Sample Size: How to Ensure You Get the Correct Sample Size. How many responses do you really need for statistically sound results? This simple question is a never-ending quandary for researchers who use statistically based calculations to answer different questions. 18/12/2017В В· Determining sample size based on confidence level and margin of error. View more lessons or practice this subject at http://www.khanacademy.org/math/ap-stati...
2/9/2012 · Calculation of exact sample size is an important part of research design. It is very important to understand that different study design need different method of sample size calculation and one formula cannot be used in all designs. In this short review we tried to educate researcher regarding The following are important considerations for determining an appropriate sample size and understanding its role in the conclusions: Although a sample may be of sufficient size to satisfy statistical requirements, it still may not be sufficient to achieve …
2/9/2012 · Calculation of exact sample size is an important part of research design. It is very important to understand that different study design need different method of sample size calculation and one formula cannot be used in all designs. In this short review we tried to educate researcher regarding The following are important considerations for determining an appropriate sample size and understanding its role in the conclusions: Although a sample may be of sufficient size to satisfy statistical requirements, it still may not be sufficient to achieve …
Calculation of sample size. The use of statistical formulas for determining the sample size implies, first of all, the choice of a significant benchmark for the measures to be made based on the results provided by the qualitative research to be performed, usually, the researcher has, in this sense, two alternatives: 24/7/2019В В· Sample Size Calculator Determines the minimum number of subjects for adequate study power ClinCalc.com В» Statistics В» Sample Size Calculator. of different equations to determine the minimum number of subjects that need to be enrolled in a study in order to have sufficient statistical power to detect a treatment effect. 1.
reduces sample size and power. If you anticipate that you will not be able to collect outcome data on some study participants, increase your initial sample size to ensure that you will have sufficient power to detect the impact of the program at the conclusion of the intervention. rule of thumb #2: if the effect size determining sufficient sample size for management survey research activities. The choice of the method is informed b y the fact that we intend to primarily describe the sufficient sample sizes
### (PDF) DETERMINING SUFFICIENCY OF SAMPLE SIZE IN
DETERMINING SUFFICIENCY OF SAMPLE SIZE IN MANAGEMENT. 18/12/2017В В· Determining sample size based on confidence level and margin of error. View more lessons or practice this subject at http://www.khanacademy.org/math/ap-stati..., reduces sample size and power. If you anticipate that you will not be able to collect outcome data on some study participants, increase your initial sample size to ensure that you will have sufficient power to detect the impact of the program at the conclusion of the intervention. rule of thumb #2: if the effect size.
determining sample power. determining sufficient sample size for management survey research activities. The choice of the method is informed b y the fact that we intend to primarily describe the sufficient sample sizes, determining sufficient sample size for management survey research activities. The choice of the method is informed b y the fact that we intend to primarily describe the sufficient sample sizes.
### Determining Sample Size with RAT-STATS Forensus Group
Methods of Determining Sample Sizes 2013 - Wiley Series. Calculate the population size. Your research likely has the goal of finding something out about a population, and in order to determine how many observations you need to make (your sample size), it's necessary to know how many total possible observations are available. This workshop outlines how to calculate an appropriate sample size (n) to address the objectives of a research project. Participants will be led through essential steps for the design of a study: specifying the outcome variable, outlining hypothesis tests, estimating the variance or other “nuisance parameters,” determining power to detect.
• Determination of Sufficient Sample Size for Linear
• Determining Sufficient Sample Size CSCAR
• This can be risky if the sample size is very small because it’s less likely to reflect the whole population; try to get the largest trial study that you can, and/or make a conservative estimate for . Often a small trial study is worth the time and effort. The formula for determining sample size to ensure that the test has a specified power is given below: where О± is the selected level of significance and Z 1-О± /2 is the value from the standard normal distribution holding 1- О±/2 below it.
Tables for determining the sufficient sample size were given as adapted from Krejcie and Morgan (1970) and Bartlett, et al., (2001). The main objective of this study is to explore the procedures for determining a sufficient sample size for management survey research activities. 19/8/2017В В· The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In this video I have discussed a very simple way to determine the Sample size with reference.
Determining Sample Size. Term 2, 2006 Advanced Methods in Biostatistics, II 2 GOALS • Review of the inputs for determining sample size • Compare sample sizes for Parallel, Crossover and Factorial designs Goal is to: have sufficient power to choose between two simple hypotheses Understanding Power and Rules of Thumb for Determining Sample Sizes Carmen R. Wilson VanVoorhis and Betsy L. Morgan University of Wisconsin ‐ La Crosse This article addresses the definition of power and its relationship to Type I and Type II errors. We discuss the relationship of sample size and power.
The sample sizes listed in this table are for zero failures or errors. In looking at the hypothetical example we discussed earlier in the article, an RPN of 320 and a confidence interval of 95% and a reliability of 95%, this translates to a sample size of 59 with zero allowable failures. Calculate the population size. Your research likely has the goal of finding something out about a population, and in order to determine how many observations you need to make (your sample size), it's necessary to know how many total possible observations are available.
The problem of determining sufficient sample size during recursive estimation of the parameters of single-input single-output dynamic systems is considered in this paper. Mainly, the problem mentioned reduces to that of determining a random moment of ceasing of recursive estimator calculation when the given accuracy of the estimates is achieved. In determining sample size it is generally sufficient to act as if the population is infinite and ignore the finite population correction (fpc) factor. The subsequent sections talk about sample sizes for confidence intervals, confidence intervals on sample size and power, and the specification of power. Controlled Vocabulary Terms
Determining Sample Size. Term 2, 2006 Advanced Methods in Biostatistics, II 2 GOALS • Review of the inputs for determining sample size • Compare sample sizes for Parallel, Crossover and Factorial designs Goal is to: have sufficient power to choose between two simple hypotheses 19/8/2017 · The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In this video I have discussed a very simple way to determine the Sample size with reference.
1/6/2012В В· This standards article uses a series of scenarios to assist pediatric researchers in not only determining an adequate trial sample size but also how to proceed when this sample size may be difficult to achieve. Recommendations for practice are summarized in Table 1. 18/12/2017В В· Determining sample size based on confidence level and margin of error. View more lessons or practice this subject at http://www.khanacademy.org/math/ap-stati...
Determining Sample Size: How to Ensure You Get the Correct Sample Size. How many responses do you really need for statistically sound results? This simple question is a never-ending quandary for researchers who use statistically based calculations to answer different questions. determining sufficient sample size for management survey research activities. The choice of the method is informed b y the fact that we intend to primarily describe the sufficient sample sizes
2/9/2012В В· Calculation of exact sample size is an important part of research design. It is very important to understand that different study design need different method of sample size calculation and one formula cannot be used in all designs. In this short review we tried to educate researcher regarding In determining sample size it is generally sufficient to act as if the population is infinite and ignore the finite population correction (fpc) factor. The subsequent sections talk about sample sizes for confidence intervals, confidence intervals on sample size and power, and the specification of power. Controlled Vocabulary Terms
This workshop outlines how to calculate an appropriate sample size (n) to address the objectives of a research project. Participants will be led through essential steps for the design of a study: specifying the outcome variable, outlining hypothesis tests, estimating the variance or other “nuisance parameters,” determining power to detect In determining sample size it is generally sufficient to act as if the population is infinite and ignore the finite population correction (fpc) factor. The subsequent sections talk about sample sizes for confidence intervals, confidence intervals on sample size and power, and the specification of power. Controlled Vocabulary Terms
19/8/2017В В· The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In this video I have discussed a very simple way to determine the Sample size with reference. The problem of determining sufficient sample size during recursive estimation of the parameters of single-input single-output dynamic systems is considered in this paper. Mainly, the problem mentioned reduces to that of determining a random moment of ceasing of recursive estimator calculation when the given accuracy of the estimates is achieved.
Understanding Power and Rules of Thumb for Determining Sample Sizes Carmen R. Wilson VanVoorhis and Betsy L. Morgan University of Wisconsin ‐ La Crosse This article addresses the definition of power and its relationship to Type I and Type II errors. We discuss the relationship of sample size and power. The sample sizes listed in this table are for zero failures or errors. In looking at the hypothetical example we discussed earlier in the article, an RPN of 320 and a confidence interval of 95% and a reliability of 95%, this translates to a sample size of 59 with zero allowable failures.
30/6/2018 · I’m hoping someone can clarify this for me. Maybe I’m not understanding something here, but I keep reading that a “large sample size” is one that is greater than or equal to 30. And with a sample size of n>=30, you are able to make inferences about the population from the sample. If this is Calculate the population size. Your research likely has the goal of finding something out about a population, and in order to determine how many observations you need to make (your sample size), it's necessary to know how many total possible observations are available.
27/11/2015В В· We suggest that the size of a sample with sufficient information power depends on (a) the aim of the study, (b) sample specificity, (c) use of established theory, (d) quality of dialogue, and (e) analysis strategy. We present a model where these elements of information and their relevant dimensions are related to information power. Determining Sample Size: How to Ensure You Get the Correct Sample Size. How many responses do you really need for statistically sound results? This simple question is a never-ending quandary for researchers who use statistically based calculations to answer different questions.
Calculation of sample size. The use of statistical formulas for determining the sample size implies, first of all, the choice of a significant benchmark for the measures to be made based on the results provided by the qualitative research to be performed, usually, the researcher has, in this sense, two alternatives: In determining sample size it is generally sufficient to act as if the population is infinite and ignore the finite population correction (fpc) factor. The subsequent sections talk about sample sizes for confidence intervals, confidence intervals on sample size and power, and the specification of power. Controlled Vocabulary Terms
18/12/2017В В· Determining sample size based on confidence level and margin of error. View more lessons or practice this subject at http://www.khanacademy.org/math/ap-stati... 27/11/2015В В· We suggest that the size of a sample with sufficient information power depends on (a) the aim of the study, (b) sample specificity, (c) use of established theory, (d) quality of dialogue, and (e) analysis strategy. We present a model where these elements of information and their relevant dimensions are related to information power.
Therefore we will not be also to use the aforeside successive procedure for the determination of sufficient sample size, but, on the other hand, we may determine the efficiency of RLS by it. Such a problem is solved here by identification of the processes in pipe-lines. 27/11/2015В В· We suggest that the size of a sample with sufficient information power depends on (a) the aim of the study, (b) sample specificity, (c) use of established theory, (d) quality of dialogue, and (e) analysis strategy. We present a model where these elements of information and their relevant dimensions are related to information power.
24/7/2019В В· Sample Size Calculator Determines the minimum number of subjects for adequate study power ClinCalc.com В» Statistics В» Sample Size Calculator. of different equations to determine the minimum number of subjects that need to be enrolled in a study in order to have sufficient statistical power to detect a treatment effect. 1. Calculation of sample size. The use of statistical formulas for determining the sample size implies, first of all, the choice of a significant benchmark for the measures to be made based on the results provided by the qualitative research to be performed, usually, the researcher has, in this sense, two alternatives:
1/6/2012В В· This standards article uses a series of scenarios to assist pediatric researchers in not only determining an adequate trial sample size but also how to proceed when this sample size may be difficult to achieve. Recommendations for practice are summarized in Table 1. 19/8/2017В В· The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In this video I have discussed a very simple way to determine the Sample size with reference.
This can be risky if the sample size is very small because it’s less likely to reflect the whole population; try to get the largest trial study that you can, and/or make a conservative estimate for . Often a small trial study is worth the time and effort. Determining Sample Size. Term 2, 2006 Advanced Methods in Biostatistics, II 2 GOALS • Review of the inputs for determining sample size • Compare sample sizes for Parallel, Crossover and Factorial designs Goal is to: have sufficient power to choose between two simple hypotheses
In determining sample size it is generally sufficient to act as if the population is infinite and ignore the finite population correction (fpc) factor. The subsequent sections talk about sample sizes for confidence intervals, confidence intervals on sample size and power, and the specification of power. Controlled Vocabulary Terms The sample sizes listed in this table are for zero failures or errors. In looking at the hypothetical example we discussed earlier in the article, an RPN of 320 and a confidence interval of 95% and a reliability of 95%, this translates to a sample size of 59 with zero allowable failures. | 8,416 | 41,761 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2023-14 | latest | en | 0.888274 |
https://www.jiskha.com/questions/1749922/determine-whether-each-sequence-is-arithmetic-geometric-or-neither-if-the-sequence-is | 1,597,174,199,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738819.78/warc/CC-MAIN-20200811180239-20200811210239-00448.warc.gz | 713,513,747 | 5,797 | # arithmetic geometric
Determine whether each sequence is arithmetic geometric or neither if the sequence is arithmetic give the common difference if geometric give the common ratio 1. 6,18,54,162, 2. 4,10,16,22 3. 1,1,2,3,5,8 4. 625,125,25,5 5. 5,8,13,21,34
1. 👍 0
2. 👎 0
3. 👁 546
1. 1.
6 , 18 , 54 , 162
Geometric sequence. Common ratio 3
2.
4 , 10 , 16 , 22
Arithmetic sequence. Common difference 6
3.
1 ,1 , 2 , 3 , 5 , 8
Neither, Fibonacci sequence:
1 + 1 = 2 , 1 + 2 = 3 , 2 + 3 = 5 , 3 + 5 = 8
4.
625 , 125 , 25 , 5
Geometric sequence. Common ratio 1 / 5
5.
5 , 8 , 13 , 21 , 34
Neither, Fibonacci sequence:
5 + 8 = 13 , 8 + 13 = 21 , 13 + 21 = 34
1. 👍 0
2. 👎 0
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https://webwork.libretexts.org/webwork2/html2xml?answersSubmitted=0&sourceFilePath=Library/UBC/setOptimization/hockey.pg&problemSeed=1234567&courseID=anonymous&userID=anonymous&course_password=anonymous&showSummary=1&displayMode=MathJax&problemIdentifierPrefix=102&language=en&outputformat=libretexts | 1,627,276,287,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046152000.25/warc/CC-MAIN-20210726031942-20210726061942-00189.warc.gz | 619,806,124 | 3,378 | Consider the demand for tickets to see a specific hockey team play. The price of the ticket can be related to the quantity demanded (q) by the function: $p=199-0.01 q$. When the arena is not close to full capacity the total cost can be expressed by the function: $Cost=79 q + 5,000,000$.
Find marginal revenue (MR) as a function of quantity demanded.
$MR =$
Let $p^*$ and $q^*$ be the price and quantity demanded where profit is maximized.
$p^* =$ $q^* =$
The hockey players union has negotiated a deal requiring the team owner to pay an extra \$1,000,000 a year in salaries to the players. What should the new ticket price ($p_1$) be to ensure that profit is maximized.
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# Electoral or Popular Vote for President? Can Americans do Fractions?
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United States electoral college, votes by state LOC 2008626928
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Bush II and Trump were both elected President by winning the electoral college, while losing the popular vote. Putting aside voter suppression, caging, registration stripping, removing voting booths in Democratic districts, interstate crosscheck, and other tricks Republicans engaged in (See gregpalast.com), does this really represent the will of the people? No, not really. It's a perverse result, but let's not throw out the electoral college baby with the plurality takes-all bathwater, that really needs to go.
I've been told that one reason for the Electoral college is that the first 5 or so elections would have been decided by New York City otherwise. Everyone agrees it's meant to give smaller, rural states more say in our federal system. Full disclosure, I'm from a small state (Vermont), so I like the concept. But as in all other "winner takes all" elections in the US, the outcome is idiotic if the "winner" is allowed to win with a plurality. Let me give you some examples:
Bill Clinton gets 40.13% of the vote, George HW Bush gets 35.87% of the vote, and Ross Perot gets 23.32% of the vote.
Do the math: 35.87 (Bush) + 23.32 (Perot) = 59.19% of the people voted against Clinton and he still wins all 8 electoral votes. That's a landslide against Clinton. How stupid is that? See for yourself: https://en.wikipedia.org/wiki/1992_United_States_presidential_election_in_Colorado
How about 1980 in Massachusetts: Reagan gets 41.90%, Carter gets 41.75%, and Independent John Anderson gets 15.15%.
Do the math: 41.75 (Carter) + 15.15 (Anderson) = 56.9% voted against Reagan and he still wins all 14 electoral votes. Really dumb.
https://en.wikipedia.org/wiki/1980_United_States_presidential_election_in_Massachusetts
How about the pivotal Florida "hanging chad" election in 2000 decided by the Supreme Court stopping the recount:
George W. Bush 48.847%, Al Gore 48.838%, Ralph Nader 1.635%, and other candidates .68%.
Do the math: 48.838 (Gore) + 1.635 (Nader) + .68 (others) = 51.153% voted against Bush and he still wins all 25 electoral votes. Winner takes all is a total farce.
https://en.wikipedia.org/wiki/2000_United_States_presidential_election_in_Florida
The country is not blue and red by state. Every state is a purple mix:
US voter Registration by county:
https://en.wikipedia.org/wiki/Red_states_and_blue_states#/media/File:Gastner_map_purple_byarea_bycounty.png
Nebraska and Maine already allocate some electoral votes by Congressional District. The solution is much simpler. Allocate electoral votes by percentage of the vote received. I know that's proportional representation, and it's something those libtard, communist, pinko, fags in Europe and nearly every other democracy in the world use, but maybe that's not the problem. Maybe Americans just can't do fractions?
Let's go back to Colorado in 1992:
Gary Flomenhoft Social Media Pages:
Gary Flomenhoft is a Vermont decentralist and secessionist who denies the legitimacy of the US government, which consistently commits all four Nuremburg war crimes: crimes against peace (aggressive war), conspiracy to commit crimes against (more...)
The views expressed herein are the sole responsibility of the author and do not necessarily reflect those of this website or its editors.
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View geodesy.py
from math import fmod, modf, sqrt, degrees, radians, sin, cos, atan2 # Mean Earth radius defined by IUGG. (Unit: meters) # ref. https://en.wikipedia.org/wiki/Earth_radius#Mean_radius EARTH_RADIUS = 6371009. def distance((lat1, lng1), (lat2, lng2)): """Get approximate geographical distance between 2 coordinates in meters.
Last active Oct 7, 2015
Python SortedList
SortedList is a list-like class that always keeps items sorted. `heaplist.SortedList` is faster than `bisectlist.SortedList` but with lesser functions.
Here are some test results:
### bisectlist.SortedList
``````Test with 10000 random numbers...
Raw list takes 1.01116704941 seconds
Raw list, sort once takes 0.00338888168335 seconds
``````
Created Apr 10, 2012
Recursively list files
View locate.py
import os, fnmatch def locate(pattern, root=os.curdir): '''Locate all files matching supplied filename pattern in and below supplied root directory.''' for path, dirs, files in os.walk(os.path.abspath(root)): for filename in fnmatch.filter(files, pattern): yield os.path.join(path, filename) if __name__ == '__main__':
Created Feb 15, 2012
Windows Script Decoder 1.8 (Decoding JScript.Encoded)
Created Dec 7, 2011
Multimethods in Python < http://www.artima.com/weblogs/viewpost.jsp?thread=101605 >
View mm.py
registry = {} class MultiMethod(object): def __init__(self, name): self.name = name self.typemap = {} def __call__(self, *args): types = tuple(arg.__class__ for arg in args) # a generator expression! function = self.typemap.get(types) if function is None:
Last active Sep 27, 2015
Fetch top 100 popular photos from Flickr
View fetch-by-tag.py
import re import json import os from urllib.request import urlopen, urlretrieve from glob import glob config = { 'api_key': 'YOUR_API_KEY', 'sort': 'interestingness-desc', 'per_page': 100
Created Sep 8, 2011
Automatic post latest smiley on your timeline (Plurk API 1.0)
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hw5soln - ME 365 Homework Set 5 Out September 22 2011 Due...
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ME 365 Homework Set 5 Out September 22 , 2011 Due September 29, 2011 Problem No. 1 Each member of a class of 50 students is given a piece of the same metal (or what is said to be the same metal) and told to find its density. From the 50 results the mean and the standard deviation are calculated. Given the following tabulation of the observed number of values within each internal, Bin k Values of in bin k Observations O k in bin k 1 Below 12 2 Between and 13 3 Between and 11 4 Above 14 (a) Determine 2 assuming a Gaussian distribution. Solution: Using table A of the appendix to chapter 4: The area under the normal distribution curve for the interval to is 68.27%. From this the probability for each interval can be determined: Bin 1 & Bin 4: P 1 P 4 1 0.6827 2 0.15865 Bin 2 & Bin 3: P 2 P 3 0.6827 2 0.34135 Multiplying each probability by the total number of measurements, 50, the expected number of values in each bin is determined and the following table can be constructed. Bin k Values of in bin Observations O k Expected E k O k E k 2 E k 1 Below 12 7.9325 2.085667 2 Between and 13 17.0675 0.969360 3 Between and 11 17.0675 2.156998 4 Above 14 7.9325 4.640978 2 9.853003 (b) State your reasons for either accepting or rejecting the Gaussian hypothesis.
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{[ snackBarMessage ]} | 474 | 1,660 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.78125 | 4 | CC-MAIN-2018-17 | latest | en | 0.837927 |
https://math.stackexchange.com/questions/4810443/given-u-n-n-a-sequence-of-i-i-d-random-variables-u0-1-find-convergence | 1,708,980,002,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474663.47/warc/CC-MAIN-20240226194006-20240226224006-00056.warc.gz | 393,358,004 | 35,070 | # Given $(U_n)_n$ a sequence of i.i.d random variables $U[0,1]$, find convergence of $1_{(0,1/n)}(U_1)$ and $1_{(0,1/n)}(U_n)$
Given $$(U_n)_n$$ a sequence of i.i.d random variables $$U[0,1]$$. I want to find the convergence in probability and a.s of the sequences $$X_n = 1_{(0,1/n)}(U_1)$$ and $$Y_n = 1_{(0,1/n)}(U_n)$$.
I don't understand why $$X_n$$ and $$Y_n$$ would converge to different values, given that the variables $$U_i$$ are i.i.d. Since $$\lim_{n\to\infty}P(|X_n| > 1/n) = 0$$ my guess is that $$X_n \xrightarrow{P} 0$$ and the same goes for $$Y_n$$.
What can I say about the convergence a.s. though?
• Both converge to $0$ in probability, as you pointed out. $X_n$ converges also to $0$ pointwise a.s. $Y_n$ does too, but along SUBSEQUENCE (that is the best one can say when a sequence converges in probability) Nov 19, 2023 at 22:36
• @Mittens You mean that there is a subsequence $X_{n_k} \xrightarrow{c.s.} 0$ but it is not true that $X_n \xrightarrow{c.s.} 0$? Nov 19, 2023 at 22:44
• No, I am saying that $X_n\xrightarrow{n\rightarrow\infty}0$ a.s, and that there is a subsequence $Y_{n_k}$ such that $Y_{n_k}\xrightarrow{k\rightarrow\infty}0$. Nov 19, 2023 at 22:46
• How can I show that $X_n \xrightarrow 0$ a.s though? Nov 19, 2023 at 22:50
• Because once $U_1(\omega)$ is observed, then for $n> 1/U_1(\omega)$, $X_n(\omega)=0$. Nov 19, 2023 at 22:55
$$P(Y_n>\frac 1 2)=\frac 1 n$$ So Borel Cantelli Lemma (and independence of $$(Y_n)$$ shows that $$Y_n >\frac 1 2$$ infinitely often with probability $$1$$. So $$(Y_n)$$ does not converge to $$0$$ a.s. Since $$Y_n \to 0$$ in probability it cannot converge a.s to anything other than $$0$$.
Of course, $$X_n(\omega) \to 0$$ for every $$\omega$$ so $$X_n \to 0$$ a.s. Ignore points where $$U(\omega)=0$$ or $$1$$ because these events have probability $$0$$.
• Great! Can we use Borel-Cantelli lemma as well to show that $X_n \to X$ a.s? Nov 20, 2023 at 0:33
• Thar hardly requires a proof. If $0<x<1$ then $1_{(0,\frac 1 n)} (x)=0$ for all $n$ sufficiently large, so $1_{(0,\frac 1 n)} (x) \to 0$. @PeterSampodiras Nov 20, 2023 at 4:33 | 786 | 2,114 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 24, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.75 | 4 | CC-MAIN-2024-10 | latest | en | 0.815229 |
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11-05-2015, 07:18 PM #81
derek.john.evans
Human being with feelings
Join Date: Feb 2011
Posts: 217
Quote:
Originally Posted by mrlimbic Yes that's it. It is like ducking but for panning instead of volume (pucking?!!) It seems I could do it as a multichannel effect (like ducking) or via envelope generation and stick the envelope to the pan parameter of another item.
Cool. Yea, I can see a use for that with left/right panned instruments which go mono based on the stereo field of the drum track. I can see a number of ways to implement this, depending on how fancy you want it.
Via the DAW, you would modulate a pan parameter of an effect (eg: volume_pan), and use "audio control signal" which tracks audio coming from channel 4. This channel would be sent over from the drum beat (to channels 3+4) and converted to MS, which means channel 4 would be the drum stereo field.
Via a compressor. A little harder, but, you compress a tracks side (S) in MS mode. The detector input of the compessor again would be the side (S) signal sent from a drum track.
Via code. O, my. A lot of algorithms are running though my head.
Start with a basic pan effect for channels 1+2. Calculate MS for 1+2. Calculate a envelope follower for the side (S) of 3+4. Apply the envelope to the (S) of 1+2. Convert MS back to LR and output to 1+2.
This is a quick implementation. EDIT: Only tested at srate=44100. Im not sure I got the decay calculation correct in relation to srate.
Code:
```desc: Pan Ducker (The Pucker)
slider1:0<-1,1>Pan
slider2:10<0,20>Puck Level
slider3:50<0,100>Puck Decay
@init
sc = 6 / log(2);
@slider
sin = sin(slider1 * \$pi * 0.5);
pan0 = (1 - sin) * 0.5;
pan1 = (sin + 1) * 0.5;
decay = slider3 / srate;
@sample
spl0 *= pan0;
spl1 *= pan1;
in0 = spl0 + spl1;
in1 = spl0 - spl1;
in3 += (sqrt(abs(spl2 - spl3)) - in3) * decay;
in1 *= cos(atan(in3 * slider2));
spl0 = (in0 + in1) * 0.5;
spl1 = (in0 - in1) * 0.5;```
If you pan a guitar to the left (via the effect), and send the drums to channels 3+4, you will hear the guitar pump to the center when the drums hit off center.
Another idea I have is, track the average angles of 2 stereo tracks using atan2(). Again, use a decay or average over time.
This should get you two angles which you want to separate (push apart). Calculate the desired angles. ie: 45 degrees apart and again, apply a decay to soften the shift.
Then you know how much to push the angles apart via cos/sin rotation. Its all 2D maths. I come from a 3D background, so I see LR as being XY, and therefore vector maths apply.
In theory, you could have an effect with 8 stereo inputs, with a stereo field repulsion of each stereo tracks average angle.
Hope that's not too much babble, but, yea, I see some potential ideas here.
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11-06-2015, 03:57 AM #82
mrlimbic
Human being with feelings
Join Date: Nov 2009
Location: UK
Posts: 589
Quote:
Originally Posted by derek.john.evans Cool. Yea, I can see a use for that with left/right panned instruments which go mono based on the stereo field of the drum track. I can see a number of ways to implement this, depending on how fancy you want it. Via the DAW, you would modulate a pan parameter of an effect (eg: volume_pan), and use "audio control signal" which tracks audio coming from channel 4. This channel would be sent over from the drum beat (to channels 3+4) and converted to MS, which means channel 4 would be the drum stereo field. Via a compressor. A little harder, but, you compress a tracks side (S) in MS mode. The detector input of the compessor again would be the side (S) signal sent from a drum track.
Yes in the end I ended up doing pretty the first one. I used M/S encoder and parameter modulation to control pan from only the S channel. It it a little hard to fine tune but seems to work.
To generate a pan envelope might still be a useful thing to do as you can then fine tune more easily if some points are off.
I'm sure I saw someone mention a script that generates a volume envelope from audio levels but can't find it now. You could take the input of that from the M/S encoder to get a stereo width envelope.
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11-06-2015, 09:39 AM #83
mrlimbic
Human being with feelings
Join Date: Nov 2009
Location: UK
Posts: 589
I've just tried out your Pucker code instead of the parameter modulation method I used yesterday but can't seem to get it to work.
It doesn't seem to pan with the sounds am using.
See screenshot. Am trying to pan the mbira to follow the harp wherever it goes.
I render all four channels just to check the send from harp was working and so could view the 'panned' output.
Attached Images
Screen Shot 2015-11-06 at 16.36.18.jpg (50.8 KB, 282 views)
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11-06-2015, 08:02 PM #84
derek.john.evans
Human being with feelings
Join Date: Feb 2011
Posts: 217
Quote:
Originally Posted by mrlimbic I've just tried out your Pucker code instead of the parameter modulation method I used yesterday but can't seem to get it to work. It doesn't seem to pan with the sounds am using. See screenshot. Am trying to pan the mbira to follow the harp wherever it goes. I render all four channels just to check the send from harp was working and so could view the 'panned' output.
I think it might be because you are expecting that code to behave like the modulated pan you have been using. The code currently decreases the side (S) of 1+2 as the side (S) of 3+4 increases.
Therefore, you pan a mono signal to the left or right, and then it will pan to the center as 3+4 becomes more stereo.
The issue is, side (S) doesn't contain LR information. Its the combination of MS which gives you that info.
So, here is where you need to think up some coding ideas.
One idea, is to just implement a modulation style effect. So, have two pans for the effect. ie: A start pan, and a duck pan. And then modulate between the two based on the level of the side of 3+4.
Or, you can forget the side (S) idea, and calculate the running levels of LR for 3+4. Then, apply those levels to 1+2 in reverse. ie: So, as 3+4 moves left, 1+2 moves right.
The complexity of this depends on if you want to handle pre-panned 1+2 signals. ie: Imagine two stereo drum tracks and what the algorithm would be to mix those together in such a way that LR signals are separated as much as possible.
So, many ideas. Sounds like you are getting closer to what you want to code.
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06-03-2016, 06:15 AM #85 SaschArt Human being with feelings Join Date: Aug 2013 Posts: 190 Array for scales: Code: ```slider1:5<0,11,1{Chromatic,Dorian,Harmonic Minor,Locrian,Lydian,Major,Melodic Minor,Mixolydian,Natural Minor,Pentatonic Major,Pentatonic Minor,Phrygian,Whole Tone}>Scale @init arr_scale = 500; //init the array arr_scale[12]="111111111111"; //Chromatic arr_scale[13]="101101010110"; //Dorian arr_scale[14]="101101011001"; //Harmonic Minor arr_scale[15]="110110011010"; //Locrian arr_scale[16]="101010110101"; //Lydian arr_scale[17]="101011010101"; //Major arr_scale[18]="101101010101"; //Melodic Minor arr_scale[19]="101011010110"; //Mixolydian arr_scale[20]="101101011010"; //Natural Minor arr_scale[21]="101010010100"; //Pentatonic Major arr_scale[22]="100101010010"; //Pentatonic Minor arr_scale[23]="110101011010"; //Phrygian arr_scale[24]="101010101010"; //Whole Tone scale=-1; @slider scale != slider1 ? ( scale = slider1; scale_size = 0; i=0; while (i<12) ( strcmp(strcpy_substr(#,arr_scale[scale+12],i,1), "1")==0 ? ( arr_scale[scale_size]=i; scale_size+=1; ); i+=1; ); );``` arr_scale will contain scores from each scale.
06-03-2016, 06:28 AM #86 SaschArt Human being with feelings Join Date: Aug 2013 Posts: 190 Split string in array: Code: ```function splitString(str,sep,arr) local(i,pos) ( i=pos=0; #reg="%S"; #reg+=sep; #reg+="*"; string_pos+=1; len=strlen(str); while (match(#reg,strcpy_from(#,str,pos),string_pos) && i<555) ( arr[i]=string_pos; pos+=strlen(string_pos)+1; i+=1; string_pos+=1; ); pos>0 ? arr[i]=strcpy_from(string_pos,str,pos); ); arr1=0; splitString("C;C#;D;D#;E;F;F#;G;G#;A;A#;B",";",arr1);```
08-22-2016, 12:11 PM #87 teatime Human being with feelings Join Date: Aug 2016 Location: South Africa Posts: 42 Quick Sine This is a dirt-cheap quadratic approximation of a sine: B = 4/\$PI; C = -4/(\$PI*\$PI); function quicksine(x) local(y) ( y = B*x + C*x*abs(x); y = 0.225 * (y * abs(y) - y) + y; y; ); Haven't listened to it, but it does pretty well as an LFO. NB: Only valid between -PI and PI. Discovered here: http://forum.devmaster.net/t/fast-an...ne-cosine/9648 I recommend following the link, there are varying levels of accuracy to be had with this approximation, depending on what you're optimising for.
09-07-2016, 04:55 AM #88 geraintluff Human being with feelings Join Date: Nov 2009 Location: mostly inside my own head Posts: 299 FFT for large sizes I wanted to use (I)FFT to generate samples of size 65536 and above, so I wrote a function to perform larger FFTs. As much work as possible is still done by the built-in functions - this just Cooley-Tukey factorises the large FFT into two smaller ones. It performs the permutations (part of the algorithm), and needs some working memory (for any sensible FFT size, 256 slots is all it needs - see fft_big()'s implementation for details). I've thought about a version that doesn't need this working memory, but it may or may not be slower. Usage: Code: ```fft_big(buffer, 65536, working_mem); buffer[1] = 1; ifft_big(buffer, 65536, working_mem);``` Code: Code: ```// working_space must be 2*sizeB big function fft_ab(block, sizeA, sizeB, working_space) local(N, i, j, twiddle_amount, twiddle_r, twiddle_i, Nbits, shiftleftbits, shiftrightbits, bitmask, index1, source_index, target_index, bitmask, tmp_r, tmp_i) ( N = sizeA*sizeB; i = 0; // Perform the stepwise FFTs while (i < sizeA) ( j = 0; // Copy to working area while (j < sizeB) ( working_space[j*2] = block[(i + j*sizeA)*2]; working_space[j*2 + 1] = block[(i + j*sizeA)*2 + 1]; j += 1; ); fft(working_space, sizeB); fft_permute(working_space, sizeB); // Copy back, with twiddle factors j = 0; while (j < sizeB) ( twiddle_amount = -i*j/N; twiddle_r = cos(twiddle_amount*2*\$pi); twiddle_i = sin(twiddle_amount*2*\$pi); block[(i + j*sizeA)*2] = working_space[j*2]*twiddle_r - working_space[j*2 + 1]*twiddle_i; block[(i + j*sizeA)*2 + 1] = working_space[j*2]*twiddle_i + working_space[j*2 + 1]*twiddle_r; j += 1; ); i += 1; ); // Perform the in-place FFTs j = 0; while (j < sizeB) ( fft(block + j*sizeA*2, sizeA); fft_permute(block + j*sizeA*2, sizeA); j += 1; ); // Permute Nbits = 1; while ((1<>shiftrightbits); target_index > index1; ); target_index == index1 ? ( // This index is the shortest in its permutation group tmp_r = block[target_index*2]; tmp_i = block[target_index*2 + 1]; source_index = ((target_index<>shiftrightbits); while (source_index != index1) ( block[target_index*2] = block[source_index*2]; block[target_index*2 + 1] = block[source_index*2 + 1]; target_index = source_index; source_index = ((target_index<>shiftrightbits); ); block[target_index*2] = tmp_r; block[target_index*2 + 1] = tmp_i; ); index1 += 1; ); ); // working_space needs to be 256 big (128 complex numbers), unless you're doing FFTs of more than 4194304 (2^22) function fft_big(block, N, working_space) local(sizeB) ( N > 32768 ? ( sizeB = 1<<7; (N/sizeB) > 32768 ? sizeB = 1<<11; (N/sizeB) > 32768 ? sizeB = 1<<13; fft_ab(block, N/sizeB, sizeB, working_space); ) : ( fft(block, N); fft_permute(block, N); ); ); // working_space must be 2*sizeB big function ifft_ab(block, sizeA, sizeB, working_space) local(N, i, j, twiddle_amount, twiddle_r, twiddle_i, Nbits, shiftleftbits, shiftrightbits, bitmask, index1, source_index, target_index, bitmask, tmp_r, tmp_i) ( N = sizeA*sizeB; // Permute Nbits = 1; while ((1<>shiftrightbits); target_index > index1; ); target_index == index1 ? ( // This index is the shortest in its permutation group tmp_r = block[target_index*2]; tmp_i = block[target_index*2 + 1]; source_index = ((target_index<>shiftrightbits); while (source_index != index1) ( block[target_index*2] = block[source_index*2]; block[target_index*2 + 1] = block[source_index*2 + 1]; target_index = source_index; source_index = ((target_index<>shiftrightbits); ); block[target_index*2] = tmp_r; block[target_index*2 + 1] = tmp_i; ); index1 += 1; ); // Perform the in-place IFFTs j = 0; while (j < sizeB) ( fft_ipermute(block + j*sizeA*2, sizeA); ifft(block + j*sizeA*2, sizeA); j += 1; ); i = 0; // Perform the stepwise IFFTs while (i < sizeA) ( j = 0; // Copy to working area, with anti-twiddle factors while (j < sizeB) ( twiddle_amount = i*j/N; twiddle_r = cos(twiddle_amount*2*\$pi); twiddle_i = sin(twiddle_amount*2*\$pi); working_space[j*2] = block[(i + j*sizeA)*2]*twiddle_r - block[(i + j*sizeA)*2 + 1]*twiddle_i; working_space[j*2 + 1] = block[(i + j*sizeA)*2]*twiddle_i + block[(i + j*sizeA)*2 + 1]*twiddle_r; j += 1; ); fft_ipermute(working_space, sizeB); ifft(working_space, sizeB); j = 0; while (j < sizeB) ( block[(i + j*sizeA)*2] = working_space[j*2]; block[(i + j*sizeA)*2 + 1] = working_space[j*2 + 1]; j += 1; ); i += 1; ); ); function ifft_big(block, N, working_space) local(sizeB) ( N > 32768 ? ( sizeB = 1<<7; (N/sizeB) > 32768 ? sizeB = 1<<11; (N/sizeB) > 32768 ? sizeB = 1<<13; ifft_ab(block, N/sizeB, sizeB, working_space); ) : ( fft_ipermute(block, N); ifft(block, N); ); );``` The fft_ab() and ifft_ab() functions let you specify the split, but in my speed tests there wasn't much difference (about 3%), and (x, 128) was a good choice. You shouldn't need to use the *_ab() functions, just *_big().
10-15-2016, 07:10 PM #89 chronocepter Human being with feelings Join Date: Apr 2010 Posts: 230 Hey, not sure if in the right place... but.. JS:Osciloscope maximum length is too short. I put some more here: g_maxlen_ms=10000; and it becomes way more useful. I do not know how to adjust the mousewhell it backs to "2" seconds. Just requesting this 10 seconds become a default feature for good. __________________ "Another pointless experiment in synthetic stupidity." - Piz http://soundcloud.com/chronocepter/tracks - for friends
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-- Cockos ---- REAPER 5 ---- Reaper 3 ---- Reaper 2 ---- Reaper 1 Contact Us - Çockos Incorporated - Archive - Top | 4,696 | 16,163 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2019-30 | latest | en | 0.84777 |
http://us.metamath.org/mpegif/2pm13.193VD.html | 1,534,900,472,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221219242.93/warc/CC-MAIN-20180822010128-20180822030128-00205.warc.gz | 416,869,457 | 7,942 | Mathbox for Alan Sare < Previous Next > Nearby theorems Mirrors > Home > MPE Home > Th. List > Mathboxes > 2pm13.193VD Structured version Unicode version
Theorem 2pm13.193VD 29189
Description: Virtual deduction proof of 2pm13.193 28811. The following User's Proof is a Virtual Deduction proof completed automatically by the tools program completeusersproof.cmd, which invokes Mel O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. 2pm13.193 28811 is 2pm13.193VD 29189 without virtual deductions and was automatically derived from 2pm13.193VD 29189. (Contributed by Alan Sare, 8-Feb-2014.) (Proof modification is discouraged.) (New usage is discouraged.)
1:: 2:1: 3:2: 4:1: 5:3,4: 6:5: 7:6: 8:2: 9:7,8: 10:9: 11:10: 12:2,11: 13:12: 14:: 15:14: 16:15: 17:14: 18:16,17: 19:18: 20:15: 21:19: 22:20,21: 23:22: 24:23: 25:15,24: 26:25: qed:13,26:
Assertion
Ref Expression
2pm13.193VD
Proof of Theorem 2pm13.193VD
StepHypRef Expression
1 idn1 28837 . . . . 5
2 simpl 445 . . . . 5
31, 2e1_ 28900 . . . 4
4 simpl 445 . . . . . . . . . . 11
53, 4e1_ 28900 . . . . . . . . . 10
6 simpr 449 . . . . . . . . . . 11
71, 6e1_ 28900 . . . . . . . . . 10
8 pm3.21 437 . . . . . . . . . 10
95, 7, 8e11 28961 . . . . . . . . 9
10 sbequ2 1662 . . . . . . . . . 10
1110imdistanri 674 . . . . . . . . 9
129, 11e1_ 28900 . . . . . . . 8
13 simpl 445 . . . . . . . 8
1412, 13e1_ 28900 . . . . . . 7
15 simpr 449 . . . . . . . 8
163, 15e1_ 28900 . . . . . . 7
17 pm3.2 436 . . . . . . 7
1814, 16, 17e11 28961 . . . . . 6
19 sbequ2 1662 . . . . . . 7
2019imdistanri 674 . . . . . 6
2118, 20e1_ 28900 . . . . 5
22 simpl 445 . . . . 5
2321, 22e1_ 28900 . . . 4
24 pm3.2 436 . . . 4
253, 23, 24e11 28961 . . 3
2625in1 28834 . 2
27 idn1 28837 . . . . 5
28 simpl 445 . . . . 5
2927, 28e1_ 28900 . . . 4
3029, 4e1_ 28900 . . . . . . 7
3129, 15e1_ 28900 . . . . . . . . . 10
32 simpr 449 . . . . . . . . . . 11
3327, 32e1_ 28900 . . . . . . . . . 10
34 pm3.21 437 . . . . . . . . . 10
3531, 33, 34e11 28961 . . . . . . . . 9
36 sbequ1 1947 . . . . . . . . . 10
3736imdistanri 674 . . . . . . . . 9
3835, 37e1_ 28900 . . . . . . . 8
39 simpl 445 . . . . . . . 8
4038, 39e1_ 28900 . . . . . . 7
41 pm3.21 437 . . . . . . 7
4230, 40, 41e11 28961 . . . . . 6
43 sbequ1 1947 . . . . . . 7
4443imdistanri 674 . . . . . 6
4542, 44e1_ 28900 . . . . 5
46 simpl 445 . . . . 5
4745, 46e1_ 28900 . . . 4
48 pm3.2 436 . . . 4
4929, 47, 48e11 28961 . . 3
5049in1 28834 . 2
5126, 50impbii 182 1
Colors of variables: wff set class Syntax hints: wb 178 wa 360 wceq 1654 wsb 1660 This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1556 ax-5 1567 ax-17 1628 ax-9 1669 ax-8 1690 ax-11 1764 This theorem depends on definitions: df-bi 179 df-an 362 df-ex 1552 df-sb 1661 df-vd1 28833
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```pfeformat: true;
(%o1) true
(%i2) m:matrix([1,2,3],[a,4,7],[1,5,7]);
[ 1 2 3 ]
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http://www.solutioninn.com/now-consider-a-modified-version-of-problem-270-where-the | 1,506,397,925,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818694719.89/warc/CC-MAIN-20170926032806-20170926052806-00649.warc.gz | 565,131,507 | 7,579 | # Question: Now consider a modified version of Problem 2 70 where the
Now consider a modified version of Problem 2.70 where the defense is also allowed to roll multiple dice. Each player’s highest roll is compared with the other player’s highest roll, their second highest roll is compared with the other player’s second highest roll, etc. As before, any ties go to the defense.
(a) Suppose both players roll two dice. In this case, there are two armies to be lost since there are two dice comparisons (highest vs. highest and lowest vs. lowest). Find each of the following probabilities:
(i) Offense wins both comparisons (and thus defense loses two armies).
(ii) Offense wins one comparison and defense wins the other (and thus each lose one army).
(iii) Defense wins both comparisons (and thus offense loses two armies).
(b) Repeat all the calculations in part (a) for the scenario where the offense rolls three dice and the defense rolls two dice. As before, there are two comparisons to be made in this scenario (highest vs. highest and second highest vs. second highest).
Sales1
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Dans le document Interpolation schemes in percolation theory (Page 132-146)
Then, the proof follows similar lines of reasoning as the proof of (5.5.1) and (5.5.2) from Lemma 5.5.1 at the end of Section 5.5.1, choosing the prefactor δ appearing in (5.5.40) suitably small (recall that L = L(ε) is fixed) to obtain an analogue of the differential inequality (5.5.14). We omit further details.
5.6 Sharpness for finite-range models
In this section we prove Proposition 5.1.3. Fix L≥0 andδ ∈(0,1), we set
ω={ωh :h∈R}, where ωh :=TδL≥h}, h∈R (5.6.1) (recall Tδ from the paragraph preceding the statement of Proposition 5.1.3). To be specific, we assume thatωis sampled in the following manner. There exists a collection of i.i.d. uniform random variables U = {Ux : x ∈ Zd} independent of the process Z (recall the definition from Section 5.3.1) underP such that, for h∈R,
ωh(x) =
0 if Ux ≤δ/2,
1ϕLx≥h if Ux ∈(δ/2,1−δ/2), 1 if Ux ≥1−δ/2.
(5.6.2) We proceed to verify that ω satisfies the following properties:
(a) Lattice symmetry. For all h ∈ R, the law of ωh is invariant with respect to translations ofZd, reflections with respect to hyperplanes and rotations by π/2.
(b) Positive association. For all h ∈ R, the law of ωh is positively associated, i.e., any pair of increasing events satisfies the FKG-inequality.
(c) Finite-energy. There exists cFE ∈(0,1) such that for any h∈R, P[ωh(x) = 0|ωh(y) for all y6=x]∈(cFE,1−cFE).
(d) Bounded-range i.i.d. encoding. Let{V(x) :x∈Zd}denote a family of i.i.d. ran-dom variables (e.g. uniform in [0,1]). Then, for everyh∈R, there exists a (mea-surable) function g = gh : RZd → {0,1}Zd such that the law of g((V(x))x∈Zd) is the same as that of ωh and, for any x ∈ Zd, gx((vy)y∈Zd) depends only on {vy :y ∈BL(x)}. Thus, in particular,ωh is an L-dependent process.
Property (a) is inherited from corresponding symmetries of the laws of U and ϕL. In view of (5.6.2), (5.3.2) and (5.3.7), ωh is an increasing function of the independent collection (U,Z), and Property (b) follows by the FKG-inequality for independent random variables. Still by (5.6.2), (5.3.2) and (5.3.7), Properties (c) and (d) hold: for the former, takecFE =δ/2; for the latter one can use V(x) to generate the independent random variables Ux and Z`(˜z), for all 0≤`≤L and ˜z ∈ {x, x+12ei,1≤i≤d}. We will use another property of ωh, whose proof is more involved. We therefore state it as a separate lemma.
Lemma 5.6.1. The field ω satisfies the following:
(e) Sprinkling property. For every pair h < h0 ∈ R, there exists ε = ε(h, h0) > 0 such thatωh stochastically dominatesωh0∨ηε, whereηε is a Bernoulli percolation with density ε independent of ωh0. Henceforth we will denote this domination byωh ωh0 ∨ηε.
Proof. We assume by suitably extending the underlying probability space that there existsη={ηε :ε∈(0,1)}withηindependent ofωandηεdistributed as i.i.d. Bernoulli variables with density ε. We will progressively replace the threshold h with h0 in a finite number of steps. To this end we claim that for anyκ >0 there existsε >0 such that for anyh∈[h, h0] andL∈ L, whereLcomprises all the (finitely many) translates of the sub-lattice 10LZd, we have
ωhωh+κ∨ηεL, (5.6.3)
where ηεL(x) = ηε(x) if x ∈ L and ηεL(x) = 0 otherwise. Let us first explain how to derive property (e) from (5.6.3): choosingκ:= h|L|0−h givesωh ωh+κ∨ηεL, for suitable ε = ε(h, h0, L, d) > 0 and any choice L, so that iterating this over the lattices in L gives
ωh ωh+|L|κ∨ _
L∈L
ηLεh0 ∨ηε, as desired.
By approximation, it suffices to verify (5.6.3) for all fields restricted to a finite set Γ ⊂ Zd. Let ωh(S) := {ωh(x) :x ∈ S} for S ⊂Zd and define similarly ηε(S), ηεL(S).
Notice thatωhh+κ ∨ωh and ωh+κ∨ηLε are both increasing functions of (ωh+κ, ωh) and (ωh+κ, ηεL) respectively. Therefore it suffices to show that, conditionally on any realization ofωh+κ, the field ωh(Γ) stochastically dominates ηLε(Λ). To this end we fix an ordering{x1, x2, . . .} of the vertices in Γ such that all the vertices inL∩Γ appear before all the vertices inLc∩Γ. In view of [101, Lemma 1.1], it then suffices to show that for any k ≥1, with Λk ={x1, . . . , xk−1} (Λ0 =∅),
P-a.s., P[ωh(xk) = 1|A, A0]≥ε·1xkL, (5.6.4) where A := {ωh(x) = σ(x), x ∈ Λk}, A0 := {ωh+κ(x) = σ0(x), x ∈ Λ}, for arbitrary σ, σ0 ∈ {0,1}Zd with σ ≥ σ0 (as ωh ≥ ωh+κ). We now show (5.6.4) and assume that xk∈L (the other cases are trivial). To this end let us first define, for any x∈Zd, the pair of events
T(x) :={Ux ∈/ (δ/2,1−δ/2)} and U(x) := \
y∈BL(x)\{x}
T(y). (5.6.5)
Notice that, in view of (5.6.2), T(x) corresponds to the event that the noise at x is triggered. We then write, with U =U(xk),
P[ωh(xk) = 1|A, A0]≥P[ωh(xk) = 1| U, A, A0]·P[U |A, A0]. (5.6.6) We will bound the two probabilities on the right-hand side separately from below. It follows from the definition ofωhin (5.6.2) thatωh+κ(y) =ζ(y) on the eventT(y), where
ζ(y) = 1Uy≥1−δ/2. Consequently, decomposing A0, we obtain, with A01 := {ωh+κ = σ0 on Γ∩BL(xk)c} and A02 :={ζ =σ0 onBL(xk)\ {xk}}, that
p:= P[ωh(xk) = 1| U, A, A0] =P[ωh(xk) = 1| U, A, ωh+κ(xk) =σ0(xk), A01, A02]. However, in view of definition (5.6.2), (5.6.5) and the fact that L is 10L-separated, it follows that both {ωh(xk) = 1, ωh+κ(xk) = σ0(xk)} and {ωh+κ(xk) = σ0(xk)} are where the equality in the second line follows by (5.6.2) and (5.6.5) upon conditioning on ωh(x), x∈ Λk, ωh+κ(y), y∈ (Λ\BL(xk))∪ {xk} and 1ϕL
y≥h+κ, y ∈BL(xk)\ {xk}, and the final lower bound follows by distinguishing whether ρ(y) 6= σ0(y) (in which case the given conditional probability equals 1) or not, and using (5.6.2). Overall, the right-hand side of (5.6.6) is thus bounded from below by ε := ε0(δ/2)|BL|, which implies (5.6.4) and completes the verification of (e).
The rest of this section is devoted to deriving Proposition5.1.3from Properties (a)–
(e). We prove in two parts that ˜h(δ, L) ≥h(δ, L) and h(δ, L) = h∗∗(δ, L) ≥ ˜h(δ, L) which together imply ˜h(δ, L) =h(δ, L) =h∗∗(δ, L), as asserted.
We first argue that ˜h(δ, L) ≥ h(δ, L). As a consequence of Properties (a)–(c) and (e), one can adapt the argument in [75] in the context of Bernoulli percolation
— see also [74, Chap. 7.2] — to deduce that ωh percolates in “slabs”, i.e., for every h < h(δ, L), there exists M ∈Nsuch that
But this implies h≤˜h(δ, L), as desired.
The proof of h(δ, L) =h∗∗(δ, L)≥˜h(δ, L) on the other hand follows directly from the exponential decay of ωh in the subcritical regime. More precisely, we claim that for every h > h(δ, L), there exists c=c(h)>0 such that
P[0←ωh ∂BR]≤exp(−cR), for every R ≥0, (5.6.8) which implies that h(δ, L) =h∗∗(δ, L), cf. (5.1.4) (recall that h∗∗(δ, L) ≥ ˜h(δ, L), as explained below (5.1.12) for δ = 0 and L = ∞). We therefore focus on the proof of (5.6.8). For each h ∈ R, consider the family of processes γε := ωh ∨ηε indexed by ε ∈ [0,1] where ηε is a Bernoulli percolation with density ε independent of ωh. Let εcc(h)∈[0,1] denote the critical parameter of the family of percolation processes {γε : ε ∈ [0,1]} and suppose for a moment that for every 0 ≤ ε < εc(h), there exists c=c(h, ε)>0 such that for everyR ≥1,
θR(ε) :=P[0←→γε ∂BR]≤exp(−cR). (5.6.9) Then (5.6.8) follows immediately by takingε= 0 in caseεc(h)>0 for allh > h(δ, L).
But the latter holds by the following reasoning. From Property (e), we see that whenever h > h(δ, L), choosingh0 = (h(δ, L) +h)/2, one hasωh0 ωh∨ηε0 for some ε0 > 0, whence ε0 ≤ εc(h) as ωh0 is subcritical. The remainder of this subsection is devoted to proving (5.6.9).
For this purpose, we use the strategy developed in the series of papers [58,57, 59]
to prove subcritical sharpness using decision trees. This strategy consists of two main parts. In the first part, one bounds the varianceθR(1−θR) using the OSSS inequality from [125] by a weighted sum of influences where the weights are given by revealment probabilities of a randomized algorithm (see (5.6.14) below). Then in a second part one relates these influence terms to the derivative ofθR(ε) with respect toεto deduce a system of differential inequalities of the following form:
θR0 ≥β R
ΣRθR(1−θR), (5.6.10)
where ΣR :=PR−1
r=0 θr and β =β(ε) : (0,1)→(0,∞) is a continuous function. Using purely analytical arguments – see [58, Lemma 3.1] – one then obtains (5.6.9) forε < εc. In our particular context, we apply the OSSS inequality for product measures (see [58] for a more general version) and for that we use the encoding of ωh in terms of {V(x) :x∈Zd}provided by Property (d). In view of this,1ER with ER={0←→γε ∂BR} can now be written as a function of independent random variables (V(x) :x∈BR+L) and (ηε(x) : x ∈ BR). Using a randomized algorithm very similar to the one used in [59, Section 3.1] (see the discussion after the proof of Lemma 5.6.2 below for a more detailed exposition), we get
X
x∈BR+N
InfV(x)+ X
x∈BR
Infηε(x) ≥cL−(d−1) R
ΣRθR(1−θR), (5.6.11) where InfV(x) := P[1ER(V, ηε) 6= 1ER( ˜V, ηε)] with ˜V being the same as V for every vertex except atxwhere it isresampled independently, and Infηε(x) is defined similarly.
In order to derive (5.6.10) from (5.6.11), we use the following lemma.
Lemma 5.6.2. There exists a continuous function α : (0,1) → (0,∞) such that for all R≥1,
θR0 (ε)≥α(ε) X
x∈BR+L
InfV(x)+ X
x∈BR
Infηε(x)
. (5.6.12)
Proof. Since the derivative is with respect to the parameter of the Bernoulli component of the process, it follows from standard computations that
θ0R=P[ωh(0) = 0] X
x∈BR
P[Pivx].
where Pivx is the same event as in Section 5.5 (see below (5.5.6)) with χt replaced by γε. Now, on the one hand, Infηε(x) ≤ P[Pivx]. On the other hand, since V(x) affects the states of vertices only in BL(x) by Property (d), one immediately gets InfV(x) ≤ P[Piv(BL(x))], where Piv(BL(x)) – called the pivotality of the box BL(x) – is the event that 0 is connected to ∂BR in γε∪BL(x) where as it is not in γε\BL(x).
In fact, due to finite-energy property of ωh, we can write
P[Piv(BL(x))]≤(cFE(1−ε))−c0LdP[Piv(BL(x)), γε(y) = 0 for all y∈BL(x)]. If we start on the event on the right-hand side and then open the vertices insideBL(x) one by one inγε until 0 gets connected to ∂BR, which must happen by the definition of Piv(BL(x)). The last vertex to be opened is pivotal for the resulting configuration.
This implies that
P[Piv(BL(x)), ηε(y) = 0 for all y∈BL(x)]≤ε−c0Ld X
y∈BL(x)
P[Pivy]. Combining all these displays yields (5.6.12).
To conclude, we now give a full derivation of (5.6.11) for sake of completeness. To this end let us define a randomized algorithm T which takes (V(x) : x ∈ BR+L) and (ηε(x) : x∈ BR) as inputs, and determines the event ER by revealing V(x), ηε(x) one by one as follows:
Definition 5.6.3 (Algorithm T). Fix a deterministic ordering of the vertices in BR and choose j ∈ {1, . . . , R} uniformly and independently of (V, ηε). Now set x0 to be the smallest x ∈ ∂Bj in the ordering and reveal ηε(x0) as well as V(y) for all y ∈ BL(x0). Set E0 := {x0} and C0 := {x0} if γε(x0) = 1 and C0 := ∅ otherwise. At each stept ≥1, assume that Et−1 and Ct−1 have been defined. Then,
— If the intersection of BR with the set (∂outCt−1 ∪∂Bj)\Et−1 is non-empty, let x be the smallest vertex in this intersection and set xt := x, Et := Et−1 ∪ {xt}.
Reveal ηε(xt) as well as V(y) for all y ∈ BL(xt) and set Ct := Ct−1 ∪ {xt} if γε(xt) = 1 and Ct :=Ct−1 otherwise.
— If the intersection is empty, halt the algorithm.
In words, the algorithm T explores the clusters in γε of the vertices in ∂Bj. By applying the OSSS inequality [125] to 1ER and the algorithmT, we now get
Var[1ER] =θR(1−θR)≤ X
x∈BR+L
θV(x)(T) InfV(x)+ X
x∈BR
θηε(x)(T) Infηε(x), (5.6.13) where the functionθ·(T), called the revealment of the respective variable, is defined as θV(x)(T) :=π[Treveals the value of V(x)], (5.6.14) and θηε(x)(T) is defined in a similar way. Here π denotes the probability governing the extension of (V, ηε) which accommodates the random choice of layer j, which is independent of (V, ηε).
Let us now bound the revealments for V(x) and ηε(x). Notice that since V(x) affects the state of vertices only in BL(x) by Property (d), V(x) is revealed only if there is an explored vertex y ∈ BL(x)∩ BR. The vertex y, on the other hand, is explored only ify is connected to ∂Bj in γε. We deduce that
θV(x)(T)≤ 1 R
R
X
j=1
P[(BL(x)∩BR)←→γε ∂Bj]≤ 1 R
R
X
j=1
X
y∈BL(x)∩BR
P[y←→γε ∂Bj], where in the last step we used a naive union bound. Forηε(x), it is even simpler:
θηε(x)(T)≤ 1 R
R
X
j=1
P[x←→γε ∂Bj].
Now (5.6.11) follows by plugging the previous two displays into (5.6.13) combined with the translation invariance of γε implied by Property (a) and the triangle inequality.
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Dans le document Interpolation schemes in percolation theory (Page 132-146) | 10,144 | 29,388 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2022-21 | latest | en | 0.822831 |
http://slideplayer.com/slide/2606020/ | 1,527,061,819,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794865456.57/warc/CC-MAIN-20180523063435-20180523083435-00132.warc.gz | 263,812,993 | 25,287 | # Rational Functions and Models
## Presentation on theme: "Rational Functions and Models"— Presentation transcript:
Rational Functions and Models
4.6 Identify a rational function and state its domain Identify asymptotes Interpret asymptotes Graph a rational function by using transformations Graph a rational function by hand Copyright © 2010 Pearson Education, Inc.
Rational Function A function f represented by
where p(x) and q(x) are polynomials and q(x) ≠ 0, is a rational function. Copyright © 2010 Pearson Education, Inc.
Rational Function The domain of a rational function includes all real numbers except the zeros of the denominator q(x). The graph of a rational function is continuous except at x-values where q(x) = 0. Copyright © 2010 Pearson Education, Inc.
Example 1 For each rational function, determine any horizontal or vertical asymptotes. a) b) c) Copyright © 2010 Pearson Education, Inc.
Example 1 Solution a) b) Is a rational function - both numerator and denominator are polynomials; domain is all real numbers; x2 + 1 ≠ 0 Is NOT a rational function Denominator is not a polynomial; domain is {x | x > 0} Copyright © 2010 Pearson Education, Inc.
Example 1 Solution continued c)
Is a rational function - both numerator and denominator are polynomials; domain is {x | x ≠1, x ≠ 2} because (x – 1)(x – 2) = 0 when x = 1 and x = 2. Copyright © 2010 Pearson Education, Inc.
Vertical Asymptotes The line x = k is a vertical asymptote of the graph of f if f(x) g ∞ or f(x) g –∞ as x approaches k from either the left or the right. Copyright © 2010 Pearson Education, Inc.
Horizontal Asymptotes
The line y = b is a horizontal asymptote of the graph of f if f(x) g b as x approaches either ∞ or –∞. Copyright © 2010 Pearson Education, Inc.
Finding Vertical & Horizontal Asymptotes
Let f be a rational function given by written in lowest terms. Vertical Asymptote To find a vertical asymptote, set the denominator, q(x), equal to 0 and solve. If k is a zero of q(x), then x = k is a vertical asymptote. Caution: If k is a zero of both q(x) and p(x), then f(x) is not written in lowest terms, and x – k is a common factor. Copyright © 2010 Pearson Education, Inc.
Finding Vertical & Horizontal Asymptotes
(a) If the degree of the numerator is less than the degree of the denominator, then y = 0 (the x-axis) is a horizontal asymptote. (b) If the degree of the numerator equals the degree of the denominator, then y = a/b is a horizontal asymptote, where a is the leading coefficient of the numerator and b is the leading coefficient of the denominator. Copyright © 2010 Pearson Education, Inc.
Finding Vertical & Horizontal Asymptotes
(c) If the degree of the numerator is greater than the degree of the denominator, then there are no horizontal asymptotes. Copyright © 2010 Pearson Education, Inc.
Example 4 For each rational function, determine any horizontal or vertical asymptotes. Solution g(x) is a translation of f(x) left one unit and down 2 units. The vertical asymptote is x = 1 The horizontal asymptote is y = 2 g(x) = f(x + 1) 2 Copyright © 2010 Pearson Education, Inc.
Example 4 For each rational function, determine any horizontal or vertical asymptotes. a) b) c) Copyright © 2010 Pearson Education, Inc.
Example Solution a) Degree of numerator and denominator are both 1. Since the ratio of the leading coefficients is 6/3, the horizontal asymptote is y = 2. When x = –1, the denominator, 3x + 3, equals 0 and the numerator, 6x – 1 does not equal 0, so the vertical asymptote is x = 1 Copyright © 2010 Pearson Education, Inc.
Example Solution continued a) Here’s a graph of f(x).
Example Solution continued b)
Degree of numerator is one less than the degree of the denominator so the x-axis, or y = 0, is a horizontal asymptote. When x = ±2, the denominator, x2 – 4, equals 0 and the numerator, x + 1 does not equal 0, so the vertical asymptotes are x = 2 and x = 2. Copyright © 2010 Pearson Education, Inc.
Example Solution continued b) Here’s a graph of g(x).
Example Solution c) Degree of numerator is greater than the degree of the denominator so there are no horizontal asymptotes. When x = –1, both the numerator and denominator equal 0 so the expression is not in lowest terms: g(x) = x – 1, x ≠ –1. There are no vertical asymptotes. Copyright © 2010 Pearson Education, Inc.
Example Solution c) Here’s the graph of h(x). A straight line with the
Slant, or Oblique, Asymptotes
A third type of asymptote, which is neither vertical nor horizontal, occurs when the numerator of a rational function has degree one more than the degree of the denominator. Copyright © 2010 Pearson Education, Inc.
Slant, or Oblique, Asymptotes
The line y = x + 1 is a slant asymptote, or oblique asymptote of the graph of f. Copyright © 2010 Pearson Education, Inc.
Graphs and Transformations of Rational Functions
Graphs of rational functions can vary greatly in complexity. We begin by graphing and then use transformations to graph other rational functions. Copyright © 2010 Pearson Education, Inc.
Example 5 Sketch a graph of and identify any asymptotes. Solution
Vertical asymptote: x = 0 Horizontal asymptote: y = 0 Copyright © 2010 Pearson Education, Inc.
Example 6 Use the graph of to sketch a graph of Include all asymptotes
Example 6 Solution g(x) is a translation of f(x) left 2 units and then a reflection across the x-axis. Vertical asymptote: x = –2 Horizontal asymptote: y = 0 g(x) = –f(x + 2) Copyright © 2010 Pearson Education, Inc.
Example 7 Let a) Use a calculator to graph f. Find the domain of f.
b) Identify any vertical or horizontal asymptotes. c) Sketch a graph of f that includes the asymptotes. Copyright © 2010 Pearson Education, Inc.
Example 7 Solution a) Here’s the calculator display using “Dot Mode.” The function is undefined when x2 – 4 = 0, or when x = ±2. The domain of f is D = {x|x ≠ 2, x ≠ –2}. Copyright © 2010 Pearson Education, Inc.
Example 7 Solution b) When x = ±2, the denominator x2 – 4
= 0 (the numerator does not), so the vertical asymptotes are x = ±2. Degree of numerator = degree of denominator, ratio of leading coefficients is 2/1 = 2, so the horizontal asymptote is y = 2. Copyright © 2010 Pearson Education, Inc.
Example 7 Solution c) Here’s another version of the graph.
Graphing Rational Functions by Hand
Let define a rational function in lowest terms. To sketch its graph, follow these steps. STEP 1: Find all vertical asymptotes. STEP 2: Find all horizontal or oblique asymptotes. STEP 3: Find the y-intercept, if possible, by evaluating f(0). Copyright © 2010 Pearson Education, Inc.
Graphing Rational Functions by Hand
STEP 4: Find the x-intercepts, if any, by solving f(x) = 0. (These will be the zeros of the numerator p(x).) STEP 5: Determine whether the graph will intersect its nonvertical asymptote y = b by solving f(x) = b, where b is the y-value of the horizontal asymptote, or by solving f(x) = mx + b, where y = mx + b is the equation of the oblique asymptote. Copyright © 2010 Pearson Education, Inc.
Graphing Rational Functions by Hand
STEP 6: Plot selected points as necessary. Choose an x-value in each interval of the domain determined by the vertical asymptotes and x-intercepts. STEP 7: Complete the sketch. Copyright © 2010 Pearson Education, Inc.
Example 8 Graph Solution STEP 1: Vertical asymptote: x = 3
STEP 2: Horizontal asymptote: y = 2 STEP 3: f(0) = , y-intercept is Copyright © 2010 Pearson Education, Inc.
Example 8 Solution continued STEP 4: Solve f(x) = 0 The x-intercept is
Example 8 Solution continued
STEP 5: Graph does not intersect its horizontal asymptote, since f(x) = 2 has no solution. STEP 6: The points are on the graph. STEP 7: Complete the sketch (next slide) Copyright © 2010 Pearson Education, Inc.
Example 8 Solution continued STEP 7 | 1,997 | 7,795 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.59375 | 5 | CC-MAIN-2018-22 | latest | en | 0.845413 |
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Credits 6.00
Teaching method Contact hours Lecture 24 Tutorial 18 Practical 24 Independent study 0
Course coordinator(s) dr. C Dobre dr. EJ Bakker Lecturer(s) dr. LMW Akkermans dr. EJH Korendijk dr. WT Kruijer G Korontzis dr. ing. M Knotters dr. C Dobre dr. ing. MPH Verouden C Zheng SE Wilson dr DJ Brus dr. SK Schnabel dr. JK Kampen dr. JA Hageman drs. LCP Keizer dr. B Engel prof. dr. FA van Eeuwijk ir. SLGE Burgers dr. ir. E Heuvelink dr. EJ Bakker dr. G Gort DV Bustos Korts V Avagyan S Gugushvile G Bartzis JG Velazco AP Languillaume Examiner(s) dr. EJ Bakker dr. G Gort
English
### Assumed knowledge on:
MAT-15303 Statistics 1 + MAT-15403 Statistics 2 or MAT-14303 Basic Statistics or MAT-15403 Statistics 2.
The student should be familiar with 1) The principles of probability calculus and the subjects: estimation, construction of confidence intervals and hypothesis testing from statistical inference 2) Application of these principles to inference about central values (mean or success probability) for the 1-sample and 2-sample situations, in case of Normal observations and binary (0,1) observations 3) Methods of analysis for simple (one explanatory variable) linear regression.
(To refresh this knowledge, (parts of) chapters 1 to 6 and 11 of the book can be studied.)
### Contents:
Per week we will have 2 lectures of two hours each (for groups up to 120 students) 2 computer practicals of two hours each (for groups of 20 students with 2 teachers / 1 teacher with one student assistant) and one T16 tutorial (of 2 hours) where students will do exercises with pen and paper (max 32 students supervised by 1 teacher and 1 student assistant).
### Learning outcomes:
After successful completion of this course students are expected to (within the limits of the subjects treated) be able to:
- translate a research question into a statistical hypothesis: make a plan (type of design or sampling procedure) for the data collection.
- choose an appropriate model with an understanding of the ingredients of the model in relation to the data;
- analyse the data (with SPSS);
- interpret the results and form conclusions relevant for the actual problem.
### Activities:
- study the book and make exercises;
- computer practicals (compulsory): (learn how to) use SPSS and PQRS, work on case studies.
### Examination:
- written test with open questions and multiple choice questions, which needs to be passed (contribution to final mark: 100%).
- computer practical (attendance compulsory) has to result in a pass.
### Literature:
R. Lyman Ott; Longnecker, M.T. (2010). An Introduction to Statistical Methods and Data Analysis. 6th ed. 1296p.
Lecture notes available in English. (available: WUR-shop).
Programme Phase Specialization Period Compulsory for: BAS Animal Sciences BSc 1AF, 1MO, 2AF, 2MO, 5MO, 6MO BPW Plant Sciences BSc 1AF, 1MO, 2AF, 2MO, 5MO, 6MO BEB Economics and Governance BSc 2MO MAM Aquaculture and Marine Resource Management MSc 2MO, 5MO, 6MO BIN International Development Studies BSc B: Economics of Development 5MO MOA Organic Agriculture MSc C: Double Degree Agroecology 1MO, 2MO, 5MO MOA Organic Agriculture MSc 1AF, 1MO, 5MO, 6MO MAS Animal Sciences MSc 1AF, 1MO, 2MO, 2AF, 5MO, 6MO MFT Food Technology MSc G: Sensory Science 1MO MES Environmental Sciences MSc 2AF, 5MO MPS Plant Sciences MSc D: Plant Breeding and Genetic Resources 1MO, 2MO, 5MO, 6MO MPS Plant Sciences MSc C: Natural Resource Management 1MO, 2MO, 5MO, 6MO MPB Plant Biotechnology MSc 1AF, 1MO, 2AF, 2MO, 5MO, 6MO MNH Nutrition and Health MSc D: Sensory Science 1MO MBF Bioinformatics MSc 1AF, 2AF, 6MO MID International Development Studies MSc B: Economics of Development 1AF MFQ Food Quality Management MSc 1AF, 6MO | 1,036 | 3,745 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2022-27 | latest | en | 0.762469 |
https://gmatclub.com/forum/the-results-of-the-company-s-cost-cutting-measures-are-evident-in-its-227782.html | 1,555,784,931,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578529962.12/warc/CC-MAIN-20190420180854-20190420202854-00274.warc.gz | 425,228,393 | 50,863 | GMAT Question of the Day - Daily to your Mailbox; hard ones only
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# The results of the company’s cost-cutting measures are evident in its
Author Message
Retired Moderator
Joined: 18 Sep 2014
Posts: 1107
Location: India
The results of the company’s cost-cutting measures are evident in its [#permalink]
### Show Tags
24 Oct 2016, 09:28
Source: OG13
The results of the company’s cost-cutting measures are evident in its profits, which increased five percent during the first three months of this year after it fell over the last two years.
A. which increased five percent during the first three months of this year after it fell
B. which had increased five percent during the first three months of this year after it had fallen
C. which have increased five percent during the first three months of this year after falling
D. with a five percent increase during the first three months of this year after falling
E. with a five percent increase during the first three months of this year after having fallen
My problem in this question is I agree that profits vs it filters A and B.
with phrase filters D and E leaving C.
but i could not understand after falling over last two years part. Can someone explain?
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4485
Re: The results of the company’s cost-cutting measures are evident in its [#permalink]
### Show Tags
24 Oct 2016, 14:51
Nevernevergiveup wrote:
The results of the company’s cost-cutting measures are evident in its profits, which increased five percent during the first three months of this year after it fell over the last two years.
A. which increased five percent during the first three months of this year after it fell
B. which had increased five percent during the first three months of this year after it had fallen
C. which have increased five percent during the first three months of this year after falling
D. with a five percent increase during the first three months of this year after falling
E. with a five percent increase during the first three months of this year after having fallen
My problem in this question is I agree that profits vs it filters A and B.
with phrase filters D and E leaving C.
but i could not understand after falling over last two years part. Can someone explain?
Dear Nevernevergiveup,
I'm happy to respond.
First of all, I am going to mention several pieces of etiquette about posting questions.
1) When you post a SC question, always always always underline the relevant portion. I did that for you here.
2) Always cite the source as a specifically as possible. This is from the OG13, SC #90.
3) When you discuss the text in your question, always set off words from the text in quote mark. For clarity, I prefer to use quote marks and a different color.
For #3, here's what I mean. You wrote:
My problem in this question is I agree that profits vs it filters A and B.
with phrase filters D and E leaving C.
but i could not understand after falling over last two years part. Can someone explain?
That is extremely hard to understand because you did not punctuate correctly. Here's how it should look:
My problem in this question is I agree that "profits" vs "it" filters A and B.
"with" phrase filters D and E leaving C.
but i could not understand "after falling over last two years" part. Can someone explain?
You see, it's actually considered rude to ask someone a question but then make mistake that requires the person helping you to expend additional effort. When you are asking for help, it's appropriate to be as respectful and as accommodating as possible.
Finally, I am going to say that your question is a poor question, simply because it is not clear. Any question that says no more than "I don't understand X" is not a thoughtful question. You did tell me what you understood about the rest of the SC question: that's good. What about the phrase "after falling over last two years" do you not understand? What do you think it means? How do you think it ought to be said? Are you asking for the meaning? Are you asking for the grammatical form and why it's right? What exactly is your question?
I will suggest this blog:
Asking excellent question is one of the habits of excellence that will accelerate your GMAT studies.
Does all this make sense?
Mike
_________________
Mike McGarry
Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Retired Moderator
Joined: 18 Sep 2014
Posts: 1107
Location: India
Re: The results of the company’s cost-cutting measures are evident in its [#permalink]
### Show Tags
24 Oct 2016, 22:12
Nevernevergiveup wrote:
The results of the company’s cost-cutting measures are evident in its profits, which increased five percent during the first three months of this year after it fell over the last two years.
A. which increased five percent during the first three months of this year after it fell
B. which had increased five percent during the first three months of this year after it had fallen
C. which have increased five percent during the first three months of this year after falling
D. with a five percent increase during the first three months of this year after falling
E. with a five percent increase during the first three months of this year after having fallen
I agree the profits is the subject which increases/decreases here and is a plural word. Therefore pronoun it cannot refer to to profits as per subject-verb rule. thereby options A and B are incorrect.
with phrase is appropriate here removing options D and E leaving out C as the remaining correct choice.
but in option C, I could not understand how we can define a past event(that too which happened before profits increased in verb+ing form i.e., present continuous tense form)
Is there anything specific regarding time period mentioned as over last two years.
Now did you understand my query? Sorry for troubling you earlier.
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4485
Re: The results of the company’s cost-cutting measures are evident in its [#permalink]
### Show Tags
25 Oct 2016, 10:51
Nevernevergiveup wrote:
Nevernevergiveup wrote:
The results of the company’s cost-cutting measures are evident in its profits, which increased five percent during the first three months of this year after it fell over the last two years.
A. which increased five percent during the first three months of this year after it fell
B. which had increased five percent during the first three months of this year after it had fallen
C. which have increased five percent during the first three months of this year after falling
D. with a five percent increase during the first three months of this year after falling
E. with a five percent increase during the first three months of this year after having fallen
I agree the profits is the subject which increases/decreases here and is a plural word. Therefore pronoun it cannot refer to to profits as per subject-verb rule. thereby options A and B are incorrect.
with phrase is appropriate here removing options D and E leaving out C as the remaining correct choice.
but in option C, I could not understand how we can define a past event(that too which happened before profits increased in verb+ing form i.e., present continuous tense form)
Is there anything specific regarding time period mentioned as over last two years.
Now did you understand my query? Sorry for troubling you earlier.
Dear Nevernevergiveup,
Thank you! Now I understand your question.
This is a subtle point about the present particle, the -ing participle. If there is a main verb and then a phrase with a present participle modifies this main clause, the action in the present participle is understood to occur at the same time as the main verb.
1) Obama serves as US President, enacting policies to benefit citizens.
All in the present.
2) Grant served as US President, enacting policies to benefit citizens.
Grant's service was in the past (1869-1877), and the "enacting" matches this, also in the past.
3) Mike McGarry will serve as US President, enacting policies to benefit citizens.
In this extremely unlikely scenario, my hypothetical service is in the future, and the "enacting" matches this, also in the future.
Thus, the "present participle" is not always present--it is "present" to the time of the main verb, and thus can represent a past or future action.
Now, if we want to indicate that the secondary action took place at a time other than the time of the main verb, we would have to use a perfect participle (e.g. "having enacted") or use a subordinate clause rather than a participle.
Does all this make sense?
Mike
_________________
Mike McGarry
Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Current Student
Joined: 10 Aug 2017
Posts: 25
Location: Austria
GMAT 1: 710 Q49 V40
GPA: 3.54
The results of the company’s cost-cutting measures are evident in its [#permalink]
### Show Tags
16 Aug 2017, 05:13
Dear Mike,
after reading your reply in the thread, I would like to know, whether in the choice C "which have increased five percent during the first three months of this year after had been falling" would be grammatically more correct, as the increase is occurring in a period after the period in which the profits were falling.
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4485
Re: The results of the company’s cost-cutting measures are evident in its [#permalink]
### Show Tags
16 Aug 2017, 15:17
oderebek wrote:
Dear Mike,
after reading your reply in the thread, I would like to know, whether in the choice C "which have increased five percent during the first three months of this year after had been falling" would be grammatically more correct, as the increase is occurring in a period after the period in which the profits were falling.
Dear oderebek,
I'm happy to respond. :-)
My friend, your question indicates some confusions on a few issues. The distinction of tenses, say past vs. present perfect vs. past perfect, is a distinction among full verbs. Full verbs and only full verb have the complete range of tenses.
In order for the "-ing" form of a verb to function as a full verb, it would have to be accompanied by some auxiliary verb
is falling = present progressive
was falling = past progressive
has been falling = present perfect progressive
had been falling = past perfect progressive
Those are all full verbs: any of them could be the main verb of an independent clause.
When "falling" appears by itself, without an auxiliary verb, it is NOT a full verb. It is participle or a gerund. There are present and past participles: present participles are alway active (e.g. buying, selling, hearing, seeing, etc.) and past participles are passive (e.g. bought, sold, heard, seen, etc.) The issue with tenses and participles is subtle, because the "present" participle actually can take on the tense of the main verb.
He entered town, driving well above the speed limit. (The "driving" is a past action.)
He is entering town right now, driving well above the speed limit. (The "driving" is a present action.)
I predict that he will enter town, driving well above the speed limit. (The "driving" is a future action.)
For GMAT purposes, gerunds don't have tense at all.
In this sentence, in the phrase "after falling," the word "after" is a preposition, and the object of a preposition has to be a noun or something acting in a noun-role. The form of a verb that acts in a noun-roll is a gerund, so "falling" here is a gerund, an grammatical form that inherently has no tense at all.
In your question, you asked if we start with a gerund, something that has absolutely no tense, can we add auxiliary verbs to it to give it a tense. With all due respect, my friend, do you see how what you were asking is grounded in multiple misunderstandings? Among other things, you were misunderstanding one part of speech, a gerund, for an entirely different part of speech, a full verb.
Does all this make sense?
Mike :-)
_________________
Mike McGarry
Magoosh Test Prep
Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Re: The results of the company’s cost-cutting measures are evident in its [#permalink] 16 Aug 2017, 15:17
Display posts from previous: Sort by | 2,927 | 12,907 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.421875 | 3 | CC-MAIN-2019-18 | latest | en | 0.967528 |
http://www.cr.ie.u-ryukyu.ac.jp/hg/CbC/CbC_gcc/file/tip/libquadmath/math/atan2q.c | 1,607,207,682,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141750841.83/warc/CC-MAIN-20201205211729-20201206001729-00296.warc.gz | 108,489,882 | 4,210 | ...
author Shinji KONO Mon, 25 May 2020 18:13:55 +0900 1830386684a0
line wrap: on
line source
```
/* e_atan2l.c -- long double version of e_atan2.c.
* Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
*/
/*
* ====================================================
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* atan2q(y,x)
* Method :
* 1. Reduce y to positive by atan2l(y,x)=-atan2l(-y,x).
* 2. Reduce x to positive by (if x and y are unexceptional):
* ARG (x+iy) = arctan(y/x) ... if x > 0,
* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
*
* Special cases:
*
* ATAN2((anything), NaN ) is NaN;
* ATAN2(NAN , (anything) ) is NaN;
* ATAN2(+-0, +(anything but NaN)) is +-0 ;
* ATAN2(+-0, -(anything but NaN)) is +-pi ;
* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
* ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
* ATAN2(+-INF,+INF ) is +-pi/4 ;
* ATAN2(+-INF,-INF ) is +-3pi/4;
* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
static const __float128
tiny = 1.0e-4900Q,
zero = 0.0,
pi_o_4 = 7.85398163397448309615660845819875699e-01Q, /* 3ffe921fb54442d18469898cc51701b8 */
pi_o_2 = 1.57079632679489661923132169163975140e+00Q, /* 3fff921fb54442d18469898cc51701b8 */
pi = 3.14159265358979323846264338327950280e+00Q, /* 4000921fb54442d18469898cc51701b8 */
pi_lo = 8.67181013012378102479704402604335225e-35Q; /* 3f8dcd129024e088a67cc74020bbea64 */
__float128
atan2q(__float128 y, __float128 x)
{
__float128 z;
int64_t k,m,hx,hy,ix,iy;
uint64_t lx,ly;
GET_FLT128_WORDS64(hx,lx,x);
ix = hx&0x7fffffffffffffffLL;
GET_FLT128_WORDS64(hy,ly,y);
iy = hy&0x7fffffffffffffffLL;
if(((ix|((lx|-lx)>>63))>0x7fff000000000000LL)||
((iy|((ly|-ly)>>63))>0x7fff000000000000LL)) /* x or y is NaN */
return x+y;
if(((hx-0x3fff000000000000LL)|lx)==0) return atanq(y); /* x=1.0L */
m = ((hy>>63)&1)|((hx>>62)&2); /* 2*sign(x)+sign(y) */
/* when y = 0 */
if((iy|ly)==0) {
switch(m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
case 2: return pi+tiny;/* atan(+0,-anything) = pi */
case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
/* when x is INF */
if(ix==0x7fff000000000000LL) {
if(iy==0x7fff000000000000LL) {
switch(m) {
case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
case 2: return 3*pi_o_4+tiny;/*atan(+INF,-INF)*/
case 3: return -3*pi_o_4-tiny;/*atan(-INF,-INF)*/
}
} else {
switch(m) {
case 0: return zero ; /* atan(+...,+INF) */
case 1: return -zero ; /* atan(-...,+INF) */
case 2: return pi+tiny ; /* atan(+...,-INF) */
case 3: return -pi-tiny ; /* atan(-...,-INF) */
}
}
}
/* when y is INF */
if(iy==0x7fff000000000000LL) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
/* compute y/x */
k = (iy-ix)>>48;
if(k > 120) z=pi_o_2+0.5Q*pi_lo; /* |y/x| > 2**120 */
else if(hx<0&&k<-120) z=0; /* |y|/x < -2**120 */
else z=atanq(fabsq(y/x)); /* safe to do y/x */
switch (m) {
case 0: return z ; /* atan(+,+) */
case 1: {
uint64_t zh;
GET_FLT128_MSW64(zh,z);
SET_FLT128_MSW64(z,zh ^ 0x8000000000000000ULL);
}
return z ; /* atan(-,+) */
case 2: return pi-(z-pi_lo);/* atan(+,-) */
default: /* case 3 */
return (z-pi_lo)-pi;/* atan(-,-) */
}
}
``` | 1,461 | 3,756 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2020-50 | latest | en | 0.609538 |
https://www.inchcalculator.com/numbers-to-words-converter/ | 1,720,966,561,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514580.77/warc/CC-MAIN-20240714124600-20240714154600-00221.warc.gz | 716,346,532 | 16,819 | # Numbers to Words Converter
Use our numbers to words calculator to convert any number into word form. Enter numbers in decimal format or scientific E notation.
## Number in Word Form:
three hundred and twenty-five
Learn how we calculated this below
## How to Convert a Number to Words
Writing large numbers in word form can initially seem daunting, but with a few guidelines and a systematic approach, it becomes a manageable task. Follow along to see how to write out numbers using words.
To effectively write large numbers in words, it is essential to understand place values. Place values help in breaking down numbers into smaller, manageable parts. The following table shows the place values for numbers up to the trillion:
• Hundreds: (100-999)
• Thousands: (1,000-999,999)
• Millions: (1,000,000-999,999,999)
• Billions: (1,000,000,000-999,999,999,999)
• Trillions: (1,000,000,000,000-999,999,999,999,999)
Each segment of a large number can be broken down into these categories, making it easier to convert into words.
Use the following steps to translate a number into word form:
### Step One: Break Down the Number
Start by dividing the number into smaller groups of three digits, starting from the right. For example, the number 1234567890 can be broken into 1,234,567,890.
Each group (billions, millions, thousands, and ones) will be handled separately.
### Step Two: Write Each Group in Words
Translate each group of three digits into words starting from the right. The first segment on the right is the hundreds value. For instance, the number 890 can be written as eight hundred and ninety.
Continue doing this for each group, moving from right to left and advancing the group as you go.
So, for the second group 567 in the example number above, write it out using thousands instead of hundreds, e.g. five hundred and sixty-seven thousand.
### Step Three: Combine the Groups
Now, combine all the groups, ensuring you maintain their correct place values. Since we worked from right to left, be sure to reverse the resulting number to get the groups in the correct order.
Putting it all together, the number 1,234,567,890 from the example above in words is: one billion, two hundred and thirty-four million, five hundred and sixty-seven thousand, eight hundred and ninety.
• Hyphens: Use hyphens for numbers between twenty-one (21) and ninety-nine (99).
• Consistency: Be consistent with your style. If you start using the word “and,” continue using it in the same way for each group in the entire number.
• Complex Numbers: For very large or complex numbers, consider writing them in a more readable format. For example, 1,000,000,000,000 can be written as “one trillion” instead of “one thousand billion.”
## Names of Large Numbers
Table showing the names in word form for large numbers from one to a googol.
Number Value Number of Zeros Name
1 0 One
10 1 Ten
100 2 Hundred
1000 3 Thousand
106 6 Million
109 9 Billion
1012 12 Trillion
1018 18 Quintillion
1021 21 Sextillion
1024 24 Septillion
1027 27 Octillion
1030 30 Nonillion
1033 33 Decillion
1036 36 Undecillion
1039 39 Duodecillion
1042 42 Tredecillion
1045 45 Quattuordecillion
1048 48 Quindecillion
1051 51 Sexdecillion
1054 54 Septendecillion
1057 57 Octodecillion
1060 60 Novemdecillion
1063 63 Vigintillion
1066 66 Unvigintillion
1069 69 Duovigintillion
1072 72 Trevigintillion
1075 75 Quattuorvigintillion
1078 78 Quinvigintillion
1081 81 Sexvigintillion
1084 84 Septenvigintillion
1087 87 Octovigintillion
1090 90 Novemvigintillion
1093 93 Trigintillion
1096 96 Untrigintillion
1099 99 Duotrigintillion
10100 100 Googol | 948 | 3,619 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.15625 | 4 | CC-MAIN-2024-30 | latest | en | 0.867937 |
http://oeis.org/A125072 | 1,619,119,901,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618039604430.92/warc/CC-MAIN-20210422191215-20210422221215-00432.warc.gz | 73,672,927 | 4,004 | The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A125072 a(n) = number of exponents in the prime-factorization of n which are triangular numbers. 3
0, 1, 1, 0, 1, 2, 1, 1, 0, 2, 1, 1, 1, 2, 2, 0, 1, 1, 1, 1, 2, 2, 1, 2, 0, 2, 1, 1, 1, 3, 1, 0, 2, 2, 2, 0, 1, 2, 2, 2, 1, 3, 1, 1, 1, 2, 1, 1, 0, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 2, 3, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 0, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 1, 0, 1, 3, 1, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,6 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 FORMULA Additive with a(p^e) = A010054(e). - Antti Karttunen, Jul 08 2017 EXAMPLE The prime-factorization of 360 is 2^3 *3^2 *5^1. There are two exponents in this factorization which are triangular numbers, 1 and 3. So a(360) = 2. MATHEMATICA f[n_] := Length @ Select[Last /@ FactorInteger[n], IntegerQ[Sqrt[8# + 1]] &]; Table[f[n], {n, 110}] (* Ray Chandler, Nov 19 2006 *) PROG (PARI) A010054(n) = issquare(8*n + 1); \\ This function from Michael Somos, Apr 27 2000. A125072(n) = vecsum(apply(e -> A010054(e), factorint(n)[, 2])); \\ Antti Karttunen, Jul 08 2017 CROSSREFS Cf. A010054, A125073, A125029, A125070. Sequence in context: A083661 A029369 A255315 * A162642 A139146 A340489 Adjacent sequences: A125069 A125070 A125071 * A125073 A125074 A125075 KEYWORD nonn AUTHOR Leroy Quet, Nov 18 2006 EXTENSIONS Extended by Ray Chandler, Nov 19 2006 STATUS approved
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Last modified April 22 15:23 EDT 2021. Contains 343177 sequences. (Running on oeis4.) | 822 | 1,924 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2021-17 | latest | en | 0.570579 |
https://gpuzzles.com/mind-teasers/guess-the-word/ | 1,508,745,514,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187825812.89/warc/CC-MAIN-20171023073607-20171023093607-00650.warc.gz | 711,433,788 | 10,995 | • Views : 60k+
• Sol Viewed : 20k+
# Mind Teasers : Guess The Word
Difficulty Popularity
The first two letters of an English word refer to a man, the first three refer to a woman, the first four to a great man and the whole word to a great woman.
Guess the word ?
Discussion
Suggestions
• Views : 70k+
• Sol Viewed : 20k+
# Mind Teasers : Maths Logical Brain Teaser
Difficulty Popularity
A man of faith visits the holy land where three temple are erected in a row offering a surreal divinity to the place. Awestruck at the sight of the magnificent temples, he visits the first temple where he finds that the number of flowers in his basket increases to double the number as soon as he sets his foot inside the temple. Astonished by the miracle he is completely happy and seeks it as a blessing of his god. He offers a few flowers to the stone idol of god and moves out.
Then he visits the second temple, where the same miracle happens again. The number of flowers in his basket again double up in number. With a smile on his face, he offers a few of flowers to the stone idol again and walks out after praying.
The moment he enters the third temple, the number of flowers increases to double again. Now he feels entirely blessed. He offers all the flowers at the feet of the stone idol and walks out in a moment of bliss.
When he walks out, he has no remaining flowers with him. He offered equal number of flowers at each of the temple. What is the minimum number of flowers he had before entering the first temple? How many flowers did he offer at each temple?
• Views : 70k+
• Sol Viewed : 20k+
# Mind Teasers : Interesting Bet Puzzle
Difficulty Popularity
In a bowl, there are several chits with distinct numbers on them. You have to choose any two of them at random.
Will you accept the 2 to 1 bet that the numbers will be relatively prime will you accept it?
For instance:
If the numbers you pick are 6 and 13, you lose \$1.
If the numbers you pick are 5 and 25, you win \$2.
• Views : 60k+
• Sol Viewed : 20k+
# Mind Teasers : Guard Door Riddle
Difficulty Popularity
You are in a strange place which is guarded by two guards.One of the guard always say truth while other always lies.You don't know the identity of the two.You can ask only one question to go out from there.
• Views : 60k+
• Sol Viewed : 20k+
# Mind Teasers : Who Am I Hot Cold Riddle
Difficulty Popularity
I am hot but if you remove first two alphabets then I will become really cold. Who am I ?
• Views : 80k+
• Sol Viewed : 20k+
# Mind Teasers : Spatial Trivia Physics Puzzle
Difficulty Popularity
As shown in picture, there are four gears with the following specification
* Gear A has 60 teeth
* Gear B has 40 teeth
* Gear C has 20 teeth
* Gear D has 60 teeth
* Every minute, Gear B makes 15 complete turns.
What is the relative speed of Gear A and Gear B?
• Views : 70k+
• Sol Viewed : 20k+
# Mind Teasers : Classy Age Riddle
Difficulty Popularity
Dean Sam and Castiel are three brothers.
Interestingly their current age is prime.
What's more interesting that difference between their ages is also prime.
How old are they ?
• Views : 80k+
• Sol Viewed : 20k+
# Mind Teasers : New Answer Riddle
Difficulty Popularity
There is a puzzle which can be asked all day with a different correct answer each time. What is the puzzle ?
• Views : 70k+
• Sol Viewed : 20k+
# Mind Teasers : Sherlock Holmes Anne Cipher Puzzle
Difficulty Popularity
Anne was found dead in the central park of London.
There are six suspects "hazard", "Costa", "Pedro", "Willian", "Terry" and "courtois".
Anne has written the murdered name in cipher on the floor as "dqvxf".
Police were unable to solve the mystery so they called Sherlock.
After a minute, Sherlock was able to decipher the cipher and ask the police to capture the murderer.
Who is the murderer?
• Views : 60k+
• Sol Viewed : 20k+
# Mind Teasers : Pattern Age Puzzle
Difficulty Popularity
If neha is 10
Both Sonali and priyanka is 15
Both sadaf and tanu is 10.
how much is prinka by the same system ?
• Views : 60k+
• Sol Viewed : 20k+
# Mind Teasers : Sports Cricket Brain Teaser
Difficulty Popularity
Shihar Dhawan and Virat Kohli were batting on 94.
Seven runs were required to win by the team and only three balls were left.
At the end, both of them secured a century without being out.
How can this be feasible?
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17 October | 1,204 | 4,886 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2017-43 | latest | en | 0.961624 |
https://www.convert-measurement-units.com/convert+kBit+s.php | 1,713,446,027,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817206.54/warc/CC-MAIN-20240418124808-20240418154808-00783.warc.gz | 632,753,856 | 12,646 | Convert kBit/s (Data rate)
## Convert kBit/s
numbers in scientific notation
Direct link to this calculator:
https://www.convert-measurement-units.com/convert+kBit+s.php
# Convert kBit/s:
1. Choose the right category from the selection list, in this case 'Data rate'.
2. Next enter the value you want to convert. The basic operations of arithmetic: addition (+), subtraction (-), multiplication (*, x), division (/, :, ÷), exponent (^), square root (√), brackets and π (pi) are all permitted at this point.
3. From the selection list, choose the unit that corresponds to the value you want to convert, in this case 'kBit/s'.
4. The value will then be converted into all units of measurement the calculator is familiar with.
5. Then, when the result appears, there is still the possibility of rounding it to a specific number of decimal places, whenever it makes sense to do so.
With this calculator, it is possible to enter the value to be converted together with the original measurement unit; for example, '436 kBit/s'. In so doing, either the full name of the unit or its abbreviation can be used. Then, the calculator determines the category of the measurement unit of measure that is to be converted, in this case 'Data rate'. After that, it converts the entered value into all of the appropriate units known to it. In the resulting list, you will be sure also to find the conversion you originally sought. Regardless which of these possibilities one uses, it saves one the cumbersome search for the appropriate listing in long selection lists with myriad categories and countless supported units. All of that is taken over for us by the calculator and it gets the job done in a fraction of a second.
Furthermore, the calculator makes it possible to use mathematical expressions. As a result, not only can numbers be reckoned with one another, such as, for example, '(82 * 66) kBit/s'. But different units of measurement can also be coupled with one another directly in the conversion. That could, for example, look like this: '436 kBit/s + 1308 kBit/s' or '97mm x 74cm x 71dm = ? cm^3'. The units of measure combined in this way naturally have to fit together and make sense in the combination in question.
The mathematical functions sin, cos, tan and sqrt can also be used. Example: sin(π/2), cos(pi/2), tan(90°), sin(90) or sqrt(4).
If a check mark has been placed next to 'Numbers in scientific notation', the answer will appear as an exponential. For example, 7.588 345 609 958 4×1024. For this form of presentation, the number will be segmented into an exponent, here 24, and the actual number, here 7.588 345 609 958 4. For devices on which the possibilities for displaying numbers are limited, such as for example, pocket calculators, one also finds the way of writing numbers as 7.588 345 609 958 4E+24. In particular, this makes very large and very small numbers easier to read. If a check mark has not been placed at this spot, then the result is given in the customary way of writing numbers. For the above example, it would then look like this: 7 588 345 609 958 400 000 000 000. Independent of the presentation of the results, the maximum precision of this calculator is 14 places. That should be precise enough for most applications. | 757 | 3,263 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.390625 | 3 | CC-MAIN-2024-18 | latest | en | 0.859518 |
http://www.perlmonks.org/?node_id=3333;parent=716842 | 1,524,815,607,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125949489.63/warc/CC-MAIN-20180427060505-20180427080505-00506.warc.gz | 482,846,773 | 7,389 | Do you know where your variables are? PerlMonks
### Comment on
Need Help??
Here is your original set
3 2 8 9 -25 5 8 4 4 -3 5 3 -10
First step is adding up consequitive positives and consequitive negatives. The reason for adding up consequitive positives is crystal clear. The only reason, you may pick a negative at any time is it may bring a positive value in future if we keep on going to right. Therefore, to go right and reach a positive value, you must pass through all negatives in the sequence which are in a row. I've made this simplification to see the big picture
Here is the set after this process
22 -25 21 -3 8 -10
At this point, I will start from the end of list, and go to the beginning of list while keeping LOCAL BENEFIT and CURRENT MAX. If the end of list is negative, I will skip it and go left. Otherwise, I will assume it is current maximum that I can reach.
At this point, 8 is assumed to be current maximum, and local benefit is 0.
At the next step, I will update local benefit by adding 8, and -3, and assign it +5. Then my current position will be 21 with this local benefit +5. The current position will take the local benefit if it is positive, or drop it if it is negative or 0. If the current position accepts the local benefit, it will add itself with the local benefit, so 21 + 5 =26 which is now bigger than current maximum, so current maximum will start from the position of 21. If the local benefit is 0 or negative, it will be assigned to 0, and re-calculated from the current position, and its negative value neighbor on its left. If the local benefit is positive, the difference between current position ,and negative neighbor on left will be added up to local benefit. If you follow the procedure above, and reach the last positive on the left, you have done the complete assetment.
Here is the algorithm applied to data set.
22 -25 21 -3 8 -10
-10 droped firstly from the end.
current pos : 8 - current max : 8 - local benefit : 0
STEP 2:
current pos : 21 - current max : 8 - local benefit : 5
21 + 5 = 26 > 8, so update current max
current pos : 21 - current max : 26
STEP 3:
current pos : 22-current max : 26-local benefit : -25+26 =1
22 + 1 = 23 < 26
so current max doesn't change, and local benefit becomes 23 since 0 + 22 + 1 .
Here ( 0 + 22 ) is the value adding up to local benefit. However, since there is no value on left, it becomes 0 instead oa negative neighbor.
The algorithm complexity is linear. The first step is for reduction, and takes linear space and time. However, it is there just reduce the problem size.
The real solution is also linear since you travse from the end of list to the begining while keeping contant extra storage space.
Ok guys, there is the outline of my algorithm
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Notices? | 1,116 | 4,216 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.34375 | 3 | CC-MAIN-2018-17 | latest | en | 0.880539 |
https://www.iovi.com/books/algorithms-manual/leetcode/0172.html | 1,713,360,063,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817153.39/warc/CC-MAIN-20240417110701-20240417140701-00296.warc.gz | 738,289,440 | 13,110 | # 172. Factorial Trailing Zeroes (Easy)
https://leetcode.com/problems/factorial-trailing-zeroes/
Given an integer n, return the number of trailing zeroes in n!.
Example 1:
```Input: 3
Output: 0
Explanation: 3! = 6, no trailing zero.```
Example 2:
```Input: 5
Output: 1
Explanation: 5! = 120, one trailing zero.```
Note: Your solution should be in logarithmic time complexity.
## Solutions
``````class Solution {
// We can imaging that quantity of 2 is always much more than 5. Because every
// even number carries 2 and half of the numbers satisfy this. By contrast, 5 is less than 2.
public int trailingZeroes(int n) {
int ans = 0;
while (n > 0) {
// For the first pass, count how many numbers are multiple of 5
// For the send pass, count how many numbers are multiple of 5 * 5
// Repeat this process until n == 0
ans += n / 5;
n = n / 5;
}
return ans;
}
}
`````` | 258 | 880 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5625 | 4 | CC-MAIN-2024-18 | latest | en | 0.764564 |
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# GMATCLUB VERBAL ATTACK
Author Message
MBA Section Director
Joined: 19 Mar 2012
Posts: 3544
Location: India
GPA: 3.8
WE: Marketing (Energy and Utilities)
Followers: 1512
Kudos [?]: 11836 [14] , given: 1861
### Show Tags
17 Sep 2012, 10:47
14
KUDOS
Expert's post
82
This post was
BOOKMARKED
GMATCLUB VERBAL ATTACK
Hello all
I got my first 760 on MGMAT CAT 2 so I am extremely happy.
With that happiness I have decided to take a break, devoting my time entirely into gmatclub.
So here is what we are going to do
Each week On this forum we will discuss one main topic of Verbal and go over as much we can, covering everything we can share, including resources and questions.
Update:
_________________
If you have any questions
New!
MBA Section Director
Joined: 19 Mar 2012
Posts: 3544
Location: India
GPA: 3.8
WE: Marketing (Energy and Utilities)
Followers: 1512
Kudos [?]: 11836 [8] , given: 1861
WEEK 1: CRITICAL REASONING STRENGTHEN/WEAKEN Questions [#permalink]
### Show Tags
17 Sep 2012, 10:56
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WEEK 1: Strengthen/Weaken/Evaluate the Argument
STRATEGY : Strengthen Question
Which of the following strengthens/ supports/ most justifies/ helps…
Ask to support conclusion/argument in any way- answer can support in a minor or major way!
Stimulus will always be an argument- since you can only strengthen a conclusion, not a fact set. Identify, isolate and assess the premises and conclusion.
Focus on conclusion.
Information in stimulus is suspect. Reasoning errors are present which can be corrected by answer choice.
Strong prephrases possible
Answer choices can bring new information which is not present in stimulus.
While an assumption is necessary to the argument, a strengthen answer might not be essential for the argument to be true.
The correct answer will , at least somewhat, venture outside the scope of the immediate argument (i.e. introduce something new)
How to strengthen?
• Identify the conclusion – your answer choice should help the author and his conclusion
• Personalize the argument- place yourself inside the situation and think how you will react.
• Look for weaknesses in the argument – any gap, hole- that is tailor made to be eliminated as a correct strengthen answer.
• An answer that highlights an assumption of the author will also strengthen the author’s conclusion
• If the argument stimulus talks of a survey, poll- any answer choice which highlights its soundness or establishes its credibility will be correct.
• Correct answer can strengthen just a little or a lot!
• Fixing a weakness of the conclusion
• Validate an assumption made by argument
• Shell Game answers: idea form stimulus altered a little to be wrong
• Out of scope answer: miss the point/conclusion
Whenever a stimulus starts with word ‘Advertisement:’ it will have flawed logic. Be prepared to look out for the gap and address that.
Causality and Strengthen Question
• Eliminate alternate causes
• Show that when the cause occurs, effect occurs
• Show that when the effect is there, cause has occurred
• Show that reverse is not true
• Show that statistical data behind the cause effect conclusion is correct
• Show that when cause doesn’t occur, effect doesn’t occur
In StrnegthenX questions, correct answer choice will mostly have no effect on the argument, or will be out of scope. Be cautious sometimes the answer choice which strengthens the argument is wrongly selected if it strengthens by eliminating an alternate cause which doesn’t occur in stimulus. There is tendency to think that it is out of scope and doesn’t strengthen. E.g. in a question that argues that amphibian population is decreasing because of ozone depletion, an answer choice that their natural habitat is not depleting is not out of scope- but strengthening by eliminating alternate cause of fall in population
BEST APPROACH: SIMPLIFY THE ARGUMENT INTO 1-2 STATEMENTS, and apply choice ONLY to simplified argument. Many choices that seemed relevant otherwise will now not be relevant!
GMATPREP EXAMPLE
Q. Excavation of the ancient city of Kourion on the island of Cyprus revealed a pattern of debris and collapsed buildings typical of towns devestated by earthquakes. Archaeologists have hypothesized that the destruction was due to a major earthquake known to have occured near the island in A.D. 365. Which of the following, if true, most strongly supports the archaeologists' hypothesis?
(A) Bronze ceremonial drinking vessals that are often found in graves dating from years preceding and following A.D. 365 were also found in several graves near Kourion.
(B) No coins minted after A.D. 365 were foundin Kourion, but coins minted before that year were found in abundance
(C) Most modern histories of Cyprus mention that an earthquake occured near the island in A.D. 365.
(D) Several small statues carved in styles current in Cyprus in the century between A.D. 300 and 400 were found in Kourion.
(E) Stone inscriptions in a form of the Greek alphabet that was definitely used in Cyrpus after A.D. 365 were found in Kourion
[Reveal] Spoiler:
Simplified: an earthquake destroyed city. The earthquake happened in year 365. C says that the earthquake happened – that doesn’t strengthen, this is already known to have occurred from the question stem. Reiterate something that is already known – DOES NOT strengthen.
B pinpoints the date at year 365. Correct.
Notes Credit: Vivesomnium, Ron Purewal, Powerscore CR Bible, GMATPrep 2.0
QUESTION SET STRENGTHEN
1. The United States government uses only a household’s cash income before taxes to determine whether that
household falls below the poverty line in a given year; capital gains, non-cash government benefits, and tax credits
are not included. However, yearly cash income is not a fool-proof measure of a given household’s disposable
income. For example, retirees who live off of capital gains from an extensive portfolio could earn hundreds of
thousands of dollars, yet be classified by the government as living in “poverty” because this income is not included
in the calculation. Which of the following, if true, validates the contention that the government’s calculation methods
must be altered in order to provide statistics that measure true poverty?
• For more than 99% of those classified as living in poverty, yearly cash income comprises the vast majority of each
household’s disposable income.
• While the government’s calculation method indicated a 12.5% poverty rate in 2003, the same calculation method
indicated anywhere from a 9% to a 16% poverty rate during the preceding decade.
• Most established research studies conducted by the private sector indicate that the number of people truly living in
poverty in the U.S. is less than that indicated by the government’s calculation method.
• Several prominent economists endorse an alternate calculation method which incorporates all income, not just
cash income, and adjusts for taxes paid and other core expenses.
• The government’s calculation method also erroneously counts those who do not earn income in a given year but
who have substantial assets on which to live during that year.
[Reveal] Spoiler: Question 1 Answer & Explanation
OA: C
The conclusion of the argument is that the government's calculation methods
must be altered in order to provide statistics that measure true poverty. To
support this position, the author first explains how the government’s method
works and then introduces a hypothetical example that would return a "false
positive" - that is, a person who has a large income, yet is classified by the
government as living in poverty. One example, however, is generally not enough
to invalidate an entire method; no method is perfect and there are always a few
results that are not consistent with the overall conclusion. In order to validate, or
strengthen, the conclusion, we need to show that the government’s method is
fundamentally inferior to some alternative that would produce more valid results.
(A) This choice weakens the argument by minimizing the importance of the
author's evidence (the hypothetical retiree with capital gains). According to this
choice, the use of cash income to designate poverty levels is a very sound
method because it provides valid results for more than 99% of those classified as
living in poverty.
(B) This choice shows that the government’s method provided a wide range of
results for the poverty rate over a certain period of time, but it is irrelevant to the
argument at hand. It tells us nothing about whether the method provides relevant
statistics in any given year.
(C) CORRECT. If this statement is true, then the government’s calculation
method seems to overstate the number of people living in poverty, while the
various private sector studies generally agree with each other that the number of
people is lower. Thus, the methods used in the private sector are likely to be
more valid than the government’s method, lending credence to the author's
contention that the government’s method should change.
(D) Although this choice provides an example of people who might agree with the
conclusion (several prominent economists), this choice provides no evidence that
the alternate method they endorse would provide more relevant statistics than
the government’s method.
(E) This choice adds another hypothetical example of how the current method
could include someone in the poverty count who does not actually live in poverty.
It does not, however, address whether there are other calculation methods that
are more accurate than the government’s method.
2. Historically, the drug industry promoted its products to physicians by educating them in their offices or at industry
conferences. In the last 10 years, it has become much more commonplace for drug companies to advertise
prescription drugs directly to consumers, via television advertising and other media. Some public health advocates
have become concerned that patients, encouraged by advertising, may pursue the use of prescription drugs that
may be inappropriate for the individual patient or situation. However, since physicians must prescribe these
medications, there is no reason for such concern. Which of the following pieces of information would be most
• Certain over-the-counter medications are as effective for many common medical conditions as more powerful
nonprescription medications.
• Prescription medication television advertisements directed at the general public only appear on certain programs
and are not seen by many potential consumers.
• Physicians are also subject to prescription drug advertisements that are directed toward consumers.
• Physicians are not susceptible to pressure from patients in determining appropriate courses of treatment, including
drug prescriptions.
• Prescription medicines have been proven to be safe and effective treatments for many patient conditions.
[Reveal] Spoiler: Question 2 Answer & Explanation
The public health advocates are concerned that patients are subjected to
though the drugs may not be clinically appropriate. It is argued that, because
physicians must prescribe the drugs in question, patient pursuit of these
prescription drugs is irrelevant. However, patients who pursue and request
particular prescription drugs may be able to encourage or induce a physician to
prescribe drugs that he or she might not have in the absence of such
encouragement.
(A) The clinical efficacy of certain over-the-counter medications does not address
the public health advocates’ concern regarding patient pursuit of inappropriate
prescription drugs.
(B) The public health advocates’ concern does not rely on every possible
(C) This answer choice states the obvious possibility that physicians may also
irrelevant to the concern expressed by the public health advocates.
advocates’ concern by establishing that physicians are not susceptible to patient
pressure in prescribing inappropriate drugs. As a result, drugs will be prescribed
according to the objective clinical judgment of the prescribing physician,
mitigating the danger of inappropriate use.
(E) That certain prescription medications are safe and effective treatments for
many conditions does not address the concern of inappropriate use expressed
by the public health advocates. Prescription drugs can be safe and effective
when used for certain conditions by various individuals and still be subject to
unhealthy use by other patients.
3. Studies in restaurants show that the tips left by customers who pay their bill tend to be larger when the bill is
presented with the server’s name hand-written on the bill. Psychologists hypothesize that simply seeing a hand-written name makes many consumers feel more of a personal identification with the server, encouraging larger
tips. Which of the following, if true, most strongly supports the psychologists’ interpretation of the studies?
• The effect noted in the studies applies to patrons paying with either credit cards or cash.
• Nametags for servers have not been shown to have any effect on the size of the bill.
• Greeting card companies have found that charities which send holiday cards with handwritten signatures are more
likely to receive donations than those which send cards with printed signatures.
• The studies indicated much larger average tips if the customer ordered alcoholic beverages with his or her meal.
• Many of the restaurants in which the studies were conducted are located in tourist areas, where people are
traveling for leisure activities.
4. Analyst: The pace of technological development brings a constant stream of new devices to the market, and many
of them enjoy commercial success. But announcing new technology too soon after the introduction of a successful
device can backfire. Once consumers hear about the new device, they may stop buying the one currently on sale.
So, if a company wishes to announce the upcoming sale of a new device, it should wait until purchases of the old
device have begun to decline. Which of the following, if true, would best support the analyst’s main assertion?
• New technology often becomes less expensive after an initial surge in sales.
• Media outlets, such as television programs and magazines, often report on the planned introduction of new
devices while the sales of old devices are still strong.
• Many consumers are unable to determine whether new technology is superior to current technology.
• Surveys have shown that some consumers make only one or two technology purchases per year, whereas others
make more frequent purchases.
• Consumers tend to be loyal to technology companies whose products they enjoy using.
5. More and more companies have begun to consume less energy by making themselves more efficient. Over time,
these efforts could place the United States at the forefront of an emerging global market for cleaner technologies.
Such efforts are also essential to tackling the two big energy-related issues of the age: global warming and the
dependence on precarious supplies of oil. The federal government should encourage these efforts by providing the
necessary incentives, whether as loans, direct grants or targeted tax breaks. Which of the following, if true,
provides the most effective support for the argument?
• On the average, Canadian companies are more energy efficient than those in the United States.
• Experts believe that energy efficiency could lower the energy use of the United States to the level of 1995.
• In the past, government incentives have made advances in energy conservation feasible, especially in the auto
industry.
• The dependence on foreign oil is a greater problem in the present than global warming.
• The market for cleaner technologies is currently relatively small because of the infrastructure requirements.
6. State X recently decided to cut state funding for the public library system in County X. To help counteract this cut
in funding, the county library system has increased library late fees from $.10 per day to$.12 per day. Since the
fee increase, library administrators have seen no decline in the number of overdue books. The director of the
county library system concludes that the fee hike has helped to counteract the cut in state funding. Which of the
following statements, if true, most strengthens the director’s claim?
• Since the fee increase, library administrators have noted a significant decrease in the number of books borrowed
each day.
• The library system incurred minor costs to make its visitors aware of the late fee increase.
• Since the fee increase, there has been no significant change in the average number of days that books are
overdue before they are returned.
• The library system in County X tracks its books through a very advanced database system, allowing library
administrators to have access to very accurate statistics on the number of overdue books at any given time.
• Since the reduction in state funding, the library system in County X has eliminated 10% of its staff, creating a 2%
reduction in costs.
7. In the 18th and 19th centuries, it was believed in many coastal American cities that the waterfront was an
undesirable location for residential buildings. As a result, much of the waterfront in these cities was never developed
aesthetically and instead was left to industry and commerce. Today, however, waterfront properties are generally
seen as prestigious, as evidenced by the large sums paid for homes along the beach front. A developer who
wishes to make a large profit would be wise to buy urban waterfront lots and erect residential buildings on them.
Which of the following, if true, most strongly supports the claim made about urban waterfront properties?
• People today have more money, relatively speaking, to spend on real estate than they did in previous centuries.
• Homeowners will be willing to spend large sums on residential properties in traditionally industrial or commercial
districts.
• Many urban waterfront lots are available for purchase.
• Many coastal American cities are encouraging developers to rehabilitate the waterfront through tax incentives.
• Properties in interior residential districts in coastal American cities are significantly more expensive than those
along the waterfront.
8. Charter schools are independent public schools that are given greater autonomy in exchange for increased
accountability. Charter school operators are freed from many of the regulations of the traditional public school
bureaucracy, thereby allowing them to pursue more innovative educational ideas than non-charter public schools
can pursue. At the same time, charter schools are held accountable for achieving specific educational outcomes
and are closed down if those outcomes are not met. Which of the following, if true, best supports the assertion
that students attending charter schools will, on average, perform better on assessments of writing ability than
• Students who attend schools that emphasize order and discipline perform worse on assessments of writing ability
than students who attend schools that do not emphasize order and discipline.
• The majority of students who score in the 99th percentile on assessments of writing ability attend charter schools.
• Public schools that operate outside of the traditional public school bureaucracy spend more time teaching students
writing than do traditional public schools.
• Students who attend schools that are allowed to experiment with their writing curricula perform better on
assessments of writing ability than students who attend schools that have less flexible curricula.
• There are far more students attending non-charter public schools than students attending charter schools.
9. Officials of the Youth Hockey League and parents of players in the league have become concerned with the number
of flagrant fouls occurring during league games. This past season, the number of flagrant fouls was double the
number from the season before. League officials plan to reduce the number of such fouls during the coming
season by implementing mandatory suspensions for players who commit flagrant fouls. Which of the following
statements, if true, provides the best evidence that the officials’ plan will be effective?
• Most serious injuries occurring during league games are a direct result of flagrant fouls.
• League referees have been trained to recognize flagrant fouls and to report incidents involving such fouls.
• Parents of players in the league are in support of mandatory suspensions for flagrant fouls.
• A similar league suspends players for committing flagrant fouls; this league has a relatively low incidence of
flagrant fouls when compared with the Youth Hockey League.
• Most players in the league strive to be selected for the All-Star team, and league rules state that no player with a
record of suspension shall be selected for the All-Star team.
10. Almost every modern kitchen today is equipped with a microwave oven, mainly because microwave ovens offer a
fast and convenient way of cooking and reheating food. Indeed, it has become a standard appliance in most
households. Studies have shown, however, that microwave ovens are not completely safe and their use has
occasionally resulted in serious injury. Because of this, some consumer advocates argue that microwave ovens
should not be so readily accepted as a standard appliance until they can be certified to be completely safe. Which
of the following, if true, would most strengthen the argument of the consumer advocates?
• Microwave ovens have taken much of the joy out of cooking.
• There have been many reported incidences of people who have been scalded by liquids superheated in microwave
ovens.
• Absolute safety is the only criterion by which an appliance should be judged to be acceptable as “standard.”
• There is no such thing as a completely safe appliance.
• Stoves and ovens that use natural gas consume energy much more efficiently than microwave ovens.
OAs in 24 Hours followed by a set of 10 700-800 level WEAKEN questions
Please discuss solutions and other questions in this area.
Lets make this our very own verbal workbook
Cheers.
Next Week's Topic
Inference and Boldface
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### Show Tags
17 Sep 2012, 10:59
1
KUDOS
Expert's post
Source: Online forums
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### Show Tags
17 Sep 2012, 13:30
1
This post was
BOOKMARKED
C D A B E D C B D C
I'm here to discuss. Good bank
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### Show Tags
17 Sep 2012, 13:39
1
KUDOS
Expert's post
You got around 5 wrong
lets see if we have a couple of more answers and then we shall hit the explanations what say?
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### Show Tags
17 Sep 2012, 14:30
Ya
Waiting other responses from members.
In the meantime I would rechek my answers. I'll print it, set a timer and see
They was tough, however
Edit: C D C B C B D C D C
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### Show Tags
17 Sep 2012, 19:19
Check the edited post above
Included a set of strategies.
Feel free to add something if missed
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### Show Tags
18 Sep 2012, 00:23
My answers are listed below. I took 24 min for all of them.
C D C E C C B D E B.
I got 2 of them wrong. One wrong answer is acceptable but other one is not.
Also, we must discuss question 4 because i'm not happy with the explanation floating around for that one.
Cheers!
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### Show Tags
18 Sep 2012, 02:07
souvik101990 wrote:
GMATCLUB VERBAL ATTACK
Hello all
I got my first 760 on MGMAT CAT 2 so I am extremely happy.
With that happiness I have decided to take a break, devoting my time entirely into gmatclub.
Good going dude, What resources did you use to get into 750+ zone. You seem to have indicated Thursdays with Ron and e-GMAT.
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The question is not can you rise up to iconic! The real question is will you ?
MBA Section Director
Joined: 19 Mar 2012
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### Show Tags
18 Sep 2012, 02:10
AbhiJ wrote:
souvik101990 wrote:
GMATCLUB VERBAL ATTACK
Hello all
I got my first 760 on MGMAT CAT 2 so I am extremely happy.
With that happiness I have decided to take a break, devoting my time entirely into gmatclub.
Good going dude, What resources did you use to get into 750+ zone. You seem to have indicated Thursdays with Ron and e-GMAT.
Hey Abhi
E-gmat was great but I kind of found it a but mechanical though
Thursdays with Ron, remains to be the BEST free resource out there.
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### Show Tags
18 Sep 2012, 02:16
2
KUDOS
Expert's post
3
This post was
BOOKMARKED
STRENGTHEN SET OFFICIAL EXPLANATIONS
CDCBCCBDEC
1.
The conclusion of the argument is that the government's calculation methods
must be altered in order to provide statistics that measure true poverty. To
support this position, the author first explains how the government’s method
works and then introduces a hypothetical example that would return a "false
positive" - that is, a person who has a large income, yet is classified by the
government as living in poverty. One example, however, is generally not enough
to invalidate an entire method; no method is perfect and there are always a few
results that are not consistent with the overall conclusion. In order to validate, or
strengthen, the conclusion, we need to show that the government’s method is
fundamentally inferior to some alternative that would produce more valid results.
(A) This choice weakens the argument by minimizing the importance of the
author's evidence (the hypothetical retiree with capital gains). According to this
choice, the use of cash income to designate poverty levels is a very sound
method because it provides valid results for more than 99% of those classified as
living in poverty.
(B) This choice shows that the government’s method provided a wide range of
results for the poverty rate over a certain period of time, but it is irrelevant to the
argument at hand. It tells us nothing about whether the method provides relevant
statistics in any given year.
(C) CORRECT. If this statement is true, then the government’s calculation
method seems to overstate the number of people living in poverty, while the
various private sector studies generally agree with each other that the number of
people is lower. Thus, the methods used in the private sector are likely to be
more valid than the government’s method, lending credence to the author's
contention that the government’s method should change.
(D) Although this choice provides an example of people who might agree with the
conclusion (several prominent economists), this choice provides no evidence that
the alternate method they endorse would provide more relevant statistics than
the government’s method.
(E) This choice adds another hypothetical example of how the current method
could include someone in the poverty count who does not actually live in poverty.
It does not, however, address whether there are other calculation methods that
are more accurate than the government’s method.
2.
The public health advocates are concerned that patients are subjected to
though the drugs may not be clinically appropriate. It is argued that, because
physicians must prescribe the drugs in question, patient pursuit of these
prescription drugs is irrelevant. However, patients who pursue and request
particular prescription drugs may be able to encourage or induce a physician to
prescribe drugs that he or she might not have in the absence of such
encouragement.
(A) The clinical efficacy of certain over-the-counter medications does not address
the public health advocates’ concern regarding patient pursuit of inappropriate
prescription drugs.
(B) The public health advocates’ concern does not rely on every possible
(C) This answer choice states the obvious possibility that physicians may also
irrelevant to the concern expressed by the public health advocates.
advocates’ concern by establishing that physicians are not susceptible to patient
pressure in prescribing inappropriate drugs. As a result, drugs will be prescribed
according to the objective clinical judgment of the prescribing physician,
mitigating the danger of inappropriate use.
(E) That certain prescription medications are safe and effective treatments for
many conditions does not address the concern of inappropriate use expressed
by the public health advocates. Prescription drugs can be safe and effective
when used for certain conditions by various individuals and still be subject to
unhealthy use by other patients.
3.
This argument concerns a potential explanation for larger tips on the part of
restaurant patrons. The explanation provided is that customers are more
generous toward servers that leave their hand-written name on the bill due to a
greater degree of personal identification with the server, which encourages larger
tips. The correct answer will either support the fact that a hand-written name
strengthens personal identification, or that personal identification encourages
larger tips.
(A) The fact that the effect applies equally regardless of the method of payment
is not relevant to the conclusion.
(B) The argument does not address the size of the bill; rather, it addresses the
size of the tip. This choice is irrelevant.
(C) CORRECT. This answer choice provides further evidence that a hand-written name or signature generates a greater form of personalization and
emotional connection among recipients, leading to more donations.
(D) The impact of alcoholic beverages on tipping behavior is irrelevant.
(E) The location of the restaurants and leisure pursuits of the patrons are
irrelevant to the argument.
4.
The conclusion is that a company should wait until purchases of an old device
have begun to decline before announcing a new device. The basis for this claim
is that consumers stop buying the old device. We are asked to strengthen the
argument.
(A) The typical drop in the price of new technology does not influence whether a
company should wait until sales of an old technology begin to decline before
introducing a new one.
(B) CORRECT. This choice states that media outlets such as television and
magazines often report on the planned introduction of new devices while sales of
old devices are still strong. The argument requires that consumers "hear about
the new device"; stories in the media provide a means for consumers to do so.
(C) If many consumers are unable to determine the superiority of new
technology, then they might be less swayed to wait for a new, recently
announced device than otherwise. As a result, this claim may be seen to weaken
the analyst's assertion.
(D) The number of technology purchases per year does not directly relate to this
argument. The argument is about waiting until the consumer demand declines
before announcing a new technology. However frequently consumers typically
purchase technology, some will be ready to buy the old device when news of the
upcoming device gets out -- and according to the argument, this news will cause
some of those consumers to wait.
(E) The passage makes no mention of whether the technologies belong to the
same company or different companies.
5.
The argument claims that federal incentives should be provided to encourage
energy efficiency. The argument also notes that companies are already working
in this direction and that this trend will ease the environmental and energy
pressures that currently trouble the world. Supporting this argument could involve
providing evidence of possible success for these efforts toward their goals.
(A) This choice is an irrelevant comparison. That Canadian companies are more
efficient has no bearing on efforts in the United States or the role of government
incentives.
(B) This choice does not strengthen the claim. Experts' claims are not the same
as reality. Furthermore, the choice does not say whether reducing energy use to
the 1995 level is a significant decrease, nor does it provide any information to
strengthen the link between government incentives and reduced energy use.
(C) CORRECT. This choice provides evidence that government incentives are
effective. Thus, this choice confirms an assumption that the conclusion is
feasible.
(D) This choice is an irrelevant distinction. It does not matter to the argument’s
conclusion if one of these issues is a greater problem than the other in the
present.
(E) The passage asserts that the United States should be at the forefront of an
emerging market for cleaner technologies; i.e., the market will be significant in
the future. The size of the market at present is irrelevant to the argument.
6.
The director concludes that the fee hike has helped to counteract the cut in state
funding. In other words, the director believes that increasing the late fees has led
to increased revenue from late fees. While the size of the fee itself is one
important factor, there are other factors that also have an effect on the amount of
revenue generated from late fees: the number of overdue books and the number
of days that books are overdue before they are returned. It’s very possible that
the fee increase would prompt more borrowers to return their books on time; this
would reduce the number of late fees being paid, reducing revenue from late
fees. Further, it’s possible that the fee increase would prompt more borrowers to
return their already overdue books sooner than they would otherwise. This would
reduce the average amount of each late fee, reducing revenue from late fees.
The argument explicitly states that there has been no decline in the number of
overdue books, but it says nothing about the number of days that books are
overdue before they are returned. A statement that rules out the possibility that
borrowers are returning their already overdue books sooner than they would
have if they were still being charged the original lower overdue fee would
strengthen the director’s claim.
(A) A decrease in the number of borrowed books has no bearing on the revenue
generated from late fees if the number of overdue books remains unchanged.
The question explicitly states that the number of overdue books has not changed.
(B) If anything, this statement weakens the argument. The costs incurred to
implement the new fees would cut into the revenue generated from these new
fees.
(C) CORRECT. This statement rules out the possibility that the library system is
losing revenue as a result of borrowers returning overdue books earlier than they
would otherwise.
(D) The argument has explicitly stated that the number of overdue books has not
changed. This is a stated premise that we must take as factual information,
regardless of the quality of the database being used to track such information.
(E) The elimination of other unrelated costs has no bearing on whether the library
system has successfully increased revenues through late fees.
7.
The conclusion is that a developer who wishes to make a large profit would be
wise to buy urban waterfront lots and erect residential buildings on them. The
basis for that claim is that people pay large sums for beach front homes. We are
(A) This choice states that people have more buying power today than in
previous centuries. This does not strengthen the claim that a developer will make
money on urban waterfront properties.
(B) CORRECT. This choice states that homeowners will be willing to spend large
sums of money on residential properties in traditionally industrial or commercial
districts. Since we know from the argument that urban waterfronts have
traditionally been industrial, this fact strengthens the claim that a developer can
make a profit on urban waterfront properties.
(C) This choice states that many urban waterfront lots are available for purchase.
This does not suggest, however, that a developer will be able to sell them after
he or she builds on them.
(D) This choice states that many coastal cities are giving tax breaks to
developers who rehabilitate the waterfront. But this does not suggest that anyone
(E) This choice states that properties in the interior of cities are more expensive
than those on the waterfront. Although waterfront properties are therefore
cheaper to acquire, this does not necessarily mean that a developer can make a
8.
The question asks for information that will support the conclusion that students
attending charter schools will, on average, perform better on assessments of
writing ability than students attending traditional public schools. The passage
specifies that charter schools differ from non-charter public schools in that
charter schools have more freedom to innovate and that they are held
accountable for meeting specific educational outcomes. One way to support the
conclusion is to demonstrate that one of the two differences cited between
charter and non-charter public schools is somehow tied to higher performance on
writing assessments.
(A) While the passage mentions that charter schools themselves are freed from
many regulations, no information is presented about any difference in emphasis
with respect to order and discipline between charter and non-charter public
schools. As such, it is impossible to tell whether this information would support
the conclusion in the question.
(B) This choice presents information only about those students who score at the
very highest level of the writing assessments. However, this presents no
information about the difference, on average, between all charter school students
and non-charter public school students. It is possible, for example, that while the
students who perform at the highest level on writing assessments are those who
attend charter schools, on average non-charter public school students perform
better.
(C) There is no necessary link between the amount of time spent teaching writing
and student performance on writing assessments. For example, a good teacher
who spends one hour teaching writing may have a more positive impact on
student performance than a poor teacher who spends three hours teaching
writing.
(D) CORRECT. The passage specifies that charter schools have more freedom
to pursue innovative educational ideas than non-charter public schools. It follows
that charter schools are allowed to experiment with their curricula to a greater
degree than non-charter public schools. This choice links this difference to higher
student achievement on assessments of writing ability.
(E) The number of students attending charter vs. non-charter schools has no
bearing on the conclusion. The conclusion focused on student performance on
average, thereby eliminating raw numbers of students as relevant to this
measure.
9.
League officials plan to reduce the number of flagrant fouls by implementing
mandatory suspensions for players who commit such fouls. This plan will work
only if the punishment serves to deter players from committing flagrant fouls.
(A) The cause of injuries has no bearing on whether suspensions will deter
players from committing flagrant fouls.
(B) While the referees’ effectiveness in recognizing and reporting flagrant fouls
will surely aid in the implementation of the new policy, this has no bearing on
whether the policy will deter players from committing flagrant fouls.
(C) The parents’ opinion has no bearing on whether the suspensions will deter
players from committing flagrant fouls.
(D) While we might conclude that the other, similar league has a low incidence of
flagrant fouls because it suspends players who commit such fouls, we have no
evidence to show that the suspensions actually deter players from committing
fouls. It is entirely possible that the other league has a low incidence of flagrant
fouls for other reasons. For example, maybe the players in the other league are
just inherently less aggressive.
(E) CORRECT. If players want to make the All-Star team, and if a record of
suspension precludes these players from being selected for the team, then
players are less likely to commit fouls that will lead to suspensions.
10.
The passage makes the premise that microwave ovens are not completely safe.
This is followed by a conclusion by the consumer advocates that microwave
ovens should not be accepted as standard appliances. Since there is nothing in
the passage that provides an explicit link between the safety of microwave ovens
and their acceptability as standard appliances, the consumer advocates’
conclusion is based on an assumption (i.e., an implied premise) that “an
appliance should be accepted as standard only if it is found to be completely
safe.” The most effective way to strengthen such a conclusion is to show that
such an assumption is indeed true.
(A) The strength of the consumer advocates’ argument hinges upon the link
between the level of safety of microwave ovens and the rationale for their
acceptance in the home. Any lack of joy in microwave cooking is not relevant to
the argument.
(B) Providing a specific example of how a person might be injured, even
seriously, by a microwave oven may provide emotional support for the consumer
advocates’ position, but does little to strengthen the argument logically: the
possibility of injury has already been stipulated as a premise.
(C) CORRECT. This choice best strengthens the argument by making explicit the
assumption upon which the consumer advocates’ argument was based.
(D) If no appliance is completely safe, then the consumer advocates’ argument is
absurb: no appliance is, or ever will be, acceptable as “standard” in a modern
kitchen. This choice weakens the conclusion.
(E) The relative energy efficiency of gas vs. microwave cooking is not relevant to
this argument.
Please feel free to post particular question doubts, and I will be happy to clarify as much as I can.
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### Show Tags
18 Sep 2012, 02:18
Capricorn369 wrote:
My answers are listed below. I took 24 min for all of them.
C D C E C C B D E B.
I got 2 of them wrong. One wrong answer is acceptable but other one is not.
Also, we must discuss question 4 because i'm not happy with the explanation floating around for that one.
Cheers!
Please let me know which OA do you find debatable?
BTW All questions in this set are taken from MGMAT
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18 Sep 2012, 02:41
I got 4 wrong :
The level is 700 800 how did you say ??
My errors on 6 and 7 OK, but 8 and 9 are silly
In general MGMAT is more difficult than the exam ??
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18 Sep 2012, 02:59
First, I only mentioned the level of difficulty, because I anticipated that a lot of people would ask that question. There should be ABSOLUTELY nothing called level of difficulty, and you should not be bothered about it even if there is.
Second, I have taken 3 MGMAT CATs and 3 GMATPreps
I think GMATPrep quant is not harder than that of MGMAT albeit a bit trickier.
But GMATPrep Verbal is definitely a notch on the higher side.
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18 Sep 2012, 11:33
souvik101990 wrote:
Capricorn369 wrote:
My answers are listed below. I took 24 min for all of them.
C D C E C C B D E B.
I got 2 of them wrong. One wrong answer is acceptable but other one is not.
Also, we must discuss question 4 because i'm not happy with the explanation floating around for that one.
Cheers!
Please let me know which OA do you find debatable?
BTW All questions in this set are taken from MGMAT
I would like to discuss question number 4.
I'm not satisfied with the given OA/OE. Can someone illustrate?
Cheers!
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18 Sep 2012, 11:42
Analyst: The pace of technological development brings a constant stream of new devices to the market, and many
of them enjoy commercial success. But announcing new technology too soon after the introduction of a successful
device can backfire. Once consumers hear about the new device, they may stop buying the one currently on sale.
So, if a company wishes to announce the upcoming sale of a new device, it should wait until purchases of the old
device have begun to decline.
Which of the following, if true, would best support the analyst’s main assertion?
• New technology often becomes less expensive after an initial surge in sales. irrilevant
• Media outlets, such as television programs and magazines, often report on the planned introduction of new correct
devices while the sales of old devices are still strong.
• Many consumers are unable to determine whether new technology is superior to current technology. we care about the sales not technology
• Surveys have shown that some consumers make only one or two technology purchases per year, whereas others
make more frequent purchases. irrilevant
• Consumers tend to be loyal to technology companies whose products they enjoy using. loyal is not the point
is not good to announce new devices and at the same time sell the old ones, because the latter fall and all customers go to the new devices BUT is media magazine and so on report that new devices are annonce and at the same time the old devices are still sold.
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18 Sep 2012, 12:12
Capricorn369 wrote:
souvik101990 wrote:
Capricorn369 wrote:
My answers are listed below. I took 24 min for all of them.
C D C E C C B D E B.
I got 2 of them wrong. One wrong answer is acceptable but other one is not.
Also, we must discuss question 4 because i'm not happy with the explanation floating around for that one.
Cheers!
Please let me know which OA do you find debatable?
BTW All questions in this set are taken from MGMAT
I would like to discuss question number 4.
I'm not satisfied with the given OA/OE. Can someone illustrate?
Cheers!
4. Analyst: The pace of technological development brings a constant stream of new devices to the market, and many
of them enjoy commercial success. But announcing new technology too soon after the introduction of a successful
device can backfire. Once consumers hear about the new device, they may stop buying the one currently on sale.
So, if a company wishes to announce the upcoming sale of a new device, it should wait until purchases of the old
device have begun to decline. Which of the following, if true, would best support the analyst’s main assertion?
• New technology often becomes less expensive after an initial surge in sales.
• Media outlets, such as television programs and magazines, often report on the planned introduction of new
devices while the sales of old devices are still strong.
• Many consumers are unable to determine whether new technology is superior to current technology.
• Surveys have shown that some consumers make only one or two technology purchases per year, whereas others
make more frequent purchases.
• Consumers tend to be loyal to technology companies whose products they enjoy using.
Conclusion of this argument
So, if a company wishes to announce the upcoming sale of a new device, it should wait until purchases of the old
device have begun to decline
A. This has almost nothing to do with the argument as this is talking about the sales after the announcement and the release of the new device.
B. This seems to strengthen because if, according to the author, the company does not announce the new device, the media will have nothing to report and sales of the old device will remain strong.
C. As long as their indecisiveness doesn't hamper their buying tendencies, do we need to care?
D.This means almost everything. It means some people may buy the device while some people wont. In any case, we can draw much from this statement.
E. Loyalty can be proved both by purchasing new stuffs from the same company or by not purchasing anything at all(from that or any other company).
Hope this helps
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18 Sep 2012, 12:36
carcass wrote:
Analyst: The pace of technological development brings a constant stream of new devices to the market, and many
of them enjoy commercial success. But announcing new technology too soon after the introduction of a successful
device can backfire. Once consumers hear about the new device, they may stop buying the one currently on sale.
So, if a company wishes to announce the upcoming sale of a new device, it should wait until purchases of the old
device have begun to decline.
Which of the following, if true, would best support the analyst’s main assertion?
• New technology often becomes less expensive after an initial surge in sales. irrilevant
• Media outlets, such as television programs and magazines, often report on the planned introduction of new correct
devices while the sales of old devices are still strong.
• Many consumers are unable to determine whether new technology is superior to current technology. we care about the sales not technology
• Surveys have shown that some consumers make only one or two technology purchases per year, whereas others
make more frequent purchases. irrilevant
• Consumers tend to be loyal to technology companies whose products they enjoy using. loyal is not the point
is not good to announce new devices and at the same time sell the old ones, because the latter fall and all customers go to the new devices BUT is media magazine and so on report that new devices are annonce and at the same time the old devices are still sold.
While announcing new technology -> wait until purchases of the old device have begun to decline -> announce the upcoming sale of a new device.
How the aforesaid sequence is aligned with answer option 2, I don't see any correlation.
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18 Sep 2012, 12:42
Capricorn369 wrote:
carcass wrote:
Analyst: The pace of technological development brings a constant stream of new devices to the market, and many
of them enjoy commercial success. But announcing new technology too soon after the introduction of a successful
device can backfire. Once consumers hear about the new device, they may stop buying the one currently on sale.
So, if a company wishes to announce the upcoming sale of a new device, it should wait until purchases of the old
device have begun to decline.
Which of the following, if true, would best support the analyst’s main assertion?
• New technology often becomes less expensive after an initial surge in sales. irrilevant
• Media outlets, such as television programs and magazines, often report on the planned introduction of new correct
devices while the sales of old devices are still strong.
• Many consumers are unable to determine whether new technology is superior to current technology. we care about the sales not technology
• Surveys have shown that some consumers make only one or two technology purchases per year, whereas others
make more frequent purchases. irrilevant
• Consumers tend to be loyal to technology companies whose products they enjoy using. loyal is not the point
is not good to announce new devices and at the same time sell the old ones, because the latter fall and all customers go to the new devices BUT is media magazine and so on report that new devices are annonce and at the same time the old devices are still sold.
While announcing new technology -> wait until purchases of the old device have begun to decline -> announce the upcoming sale of a new device.
How the aforesaid sequence is aligned with answer option 2, I don't see any correlation.
http://gmatclub.com/forum/gmatclub-verbal-attack-139074.html#p1122812
Note that the media CAN ONLY REPORT if the company itself "plans" it
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18 Sep 2012, 13:54
Capricorn369 wrote:
carcass wrote:
Analyst: The pace of technological development brings a constant stream of new devices to the market, and many
of them enjoy commercial success. But announcing new technology too soon after the introduction of a successful
device can backfire. Once consumers hear about the new device, they may stop buying the one currently on sale.
So, if a company wishes to announce the upcoming sale of a new device, it should wait until purchases of the old
device have begun to decline.
Which of the following, if true, would best support the analyst’s main assertion?
• New technology often becomes less expensive after an initial surge in sales. irrilevant
• Media outlets, such as television programs and magazines, often report on the planned introduction of new correct
devices while the sales of old devices are still strong.
• Many consumers are unable to determine whether new technology is superior to current technology. we care about the sales not technology
• Surveys have shown that some consumers make only one or two technology purchases per year, whereas others
make more frequent purchases. irrilevant
• Consumers tend to be loyal to technology companies whose products they enjoy using. loyal is not the point
is not good to announce new devices and at the same time sell the old ones, because the latter fall and all customers go to the new devices BUT is media magazine and so on report that new devices are annonce and at the same time the old devices are still sold.
While announcing new technology -> wait until purchases of the old device have begun to decline -> announce the upcoming sale of a new device.
How the aforesaid sequence is aligned with answer option 2, I don't see any correlation.
Sorry
If the media announce a new plan this come from the company (apple says: we have the new iPhone) then if this is possible, and is possible to have storg sales of old devices the argument is weaken. The plan is not feasible, B say that is feasible because we have reports about this, due to something that the companies say
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Display posts from previous: Sort by | 12,424 | 57,888 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.1875 | 3 | CC-MAIN-2017-04 | latest | en | 0.86554 |
http://4busydads.com/articles/what-does-ops-stand-for-in-baseball-statistics.html | 1,653,521,695,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662594414.79/warc/CC-MAIN-20220525213545-20220526003545-00226.warc.gz | 492,208 | 29,485 | # What Does Ops Stand For In Baseball Statistics
## What Does OPS Mean in Baseball – What is a Good OPS?
Baseball may just be the perfect sport for math nerds, according to some experts. The OPS package, for example, incorporates formulae from various statistics, which makes it really fascinating to use. However, despite the fact that it appears to be a convoluted method, the outcome is clear: calculating OPS, or on-base plus slugging, may be a rapid way to determine a player’s true contribution to his club. OPS (on-base percentage) is a unique baseball statistic that is explained in detail in this article.
## How is OPS Calculated?
OPS is one of those statistics that must be interpreted in conjunction with other data in order to make sense. To compute On-base plus slugging, we’ll need two statistics: first, the number of times a player has reached base.
• Percentage of time spent on base (OBP). It is a cold, hard statistic that measures how many times a player gets on base by any method in comparison to the total number of at-bats they have had throughout their career. It makes no difference how a player gets on base in the OBP game. Were they tainted with something? Walked? Did they make contact? It everything contributes to their overall batting average (OBP)
• Slugging average (SLG). Unlike other stats, this one is a system that measures the quality of a player’s strikes. The batting average of a baseball player, for example, does not tell you how often they hit the ball
• It just tells you how often they scored a hit. SLG includes the quality of those hits into the calculation by including the amount of bases reached as a component of the equation. An individual player might theoretically have a slugging average of 4.000, which would result in an optimum ratio of home runs to at-bats. That is to say, if a player only has one at-bat and hits a home run, his slugging average will be 4.000 points higher than normal. An SLG of 1.000 indicates that a single was hit in a single at-bat, and so on.
Keep in mind that there are some uncommon instances (such as sacrifice flies) that do not count toward at-bats and, as a result, have no meaningful influence on either of these statistics. The terms OBP and SLG are certainly familiar to you; OBP is a rate measure, and SLG is a rate and quality metric. When you combine the two metrics, on-base plus slugging, you get a more complete picture of a player’s ability to smash the ball hard. What is the formula for calculating it? Simply add the two numbers together.
## What is a Good OPS in Baseball?
For fans of Major League Baseball, it might be difficult to make sense of how OPS works on sometimes. What does it have to say about the look of the plates? What is the overall quality of the ballpark in which they are playing during the season? What is the total number of bases they have amassed? To obtain a real understanding of what a good OPS is, it’s helpful to first establish a standard of comparison. Here are a few of the top OPS in Major League Baseball history:
• With an OPS of 1.1636, Babe Ruth is the all-time leader
• Mike Trout is among the all-time OPS greats who are still active, with a career average of around 1.0000
• Barry Bonds ranks 4th on the list as of 2020, with an OPS of approximately 1.05
• Lou Gehrig ranks third with an OPS of 1.07
• And Ted Williams of the Boston Red Sox is the only other player outside of Babe Ruth who has an OPS of 1.1 or higher over his This is among players who have accumulated at least 3,000 at-bats.
Of course, this only provides us only one end of the range to work with. What about the overall average of the league? A look at the data for Major League Baseball reveals that the league average in on-base plus slugging is often between 0.700 and 0.800.
## What is the Highest OPS in Baseball History?
Already, we’ve shown you the player who has the greatest careerOPS, Babe Ruth of the New York Yankees, in our previous post. His 1.1636 OPS over that many at-bats may never be surpassed, putting him in the running for the title of greatest hitter of all time. However, this is merely one method of looking at the stats. Season-to-season comparisons of metrics such as on-base percentage (OPS) are important because they reveal exactly how spectacularly certain players have reached the pinnacle of their careers.
• Babe Ruth, 1920: 1.3791
• Barry Bonds, 2001: 1.3785
• Babe Ruth, 1921: 1.3586
• Babe Ruth, 1923: 1.3089
• Babe Ruth, 2004: 1.4217
• Babe Ruth, 2002: 1.3807
• Bab
Eventually, Ted Williams enters the picture, having posted the 7th-best offensive season in baseball history. When Rogers Hornsby appears on the list, it is at the thirteenth position that a fourth player is included.
## What about High OPS Seasons in Recent Years?
• Juan Soto of the Washington Nationals had the best OPS in 2020, batting 1.1846 with a 1.1846 on-base percentage. That was good enough for the 25th greatest OPS season in baseball history
• In 2019, Christian Yelich of the Milwaukee Brewers hit 1.1001, which was strong enough for a season in the top 100 of all-time OPS rankings
## Are there Better Stats than OPS?
A hitter’s talent can be evaluated by adding up his or her slugging % or slugging average with his or her on-base percentage, which some may argue is a rudimentary method of doing so. However, it is possible that there is more to it than you realize. After all, on-base percentage (OBP) includes at-bats, walks, sacrifice flies, and the number of times a batter is hit by a pitch. Overall, the OPS statistic takes a variety of factors into consideration, including at-bats and total bases. Hits, walks, HBP, and even sacrifice fly are all accounted for in the overall calculation.
Optimal team performance (OPS) is popular because when calculated for an entire team, it has a strong correlation with how many runs the team has scored. This is why many people consider it to be an effective tool to evaluate a batter’s offensive output on a consistent basis.
The OPS+ statistic, which takes this statistic and “normalizes” it across the league, is also available. A player’s OPS+ takes into account external factors such as the ballpark in which he or she was hitting. It is calculated such that an OPS of 100 represents the league average, which provides people with an immediate understanding of how a player’s offensive productivity compares to the rest of the team. As a result, the statistics of a Cubs player may differ from those of a Dodgers player, who in turn may differ from the statistics of a Cardinals player or a White Sox player.
When a player is free agent, OPS+ is important because he or she may benefit from primarily playing in a smaller ballpark where it is easier to hit home runs, which can increase his or her value.
## Conclusion
The on-base average and slugging percentage, when combined, can provide useful information on a player’s offensive performance in the big leagues. However, like with any other sabermetrics in baseball, it’s not always simple to quantify everything without actually seeing it firsthand in action.
## Similar Posts
In baseball, what exactly is a putout? What is Batter’s Eye? What Does the Abbreviation QAB Mean in Baseball? Baseball GM (General Manager of Baseball) What is the definition of a hold in baseball? Bases are being stolen in baseball. In baseball, what exactly is a quality start? In baseball, there is a magic number. What is the role of a baseball manager? Baseball with a Can of Corn What Is the Meaning of Batting Average? What is a Knuckleball and how does it work? Coach on the Baseball Bench What is a No-Hitter, exactly?
Baseball Doubleheader in the horizon Baseball is a hit-and-run sport.
What is a Spitball Pitch, and how does it work?
## On-base plus slugging – Wikipedia
A player’s on-base plus slugging (OPS) % is derived as the sum of his on-base percentage and slugging percentage, and it is a sabermetric baseball statistic. The ability of a player to get on base as well as hit for power, two crucial offensive qualities, are both illustrated in this illustration. Among Major League Baseball, a batter with an OPS of.800 or greater is considered to be in the highest tier of hitters. Typically, the league leader in OPS will have a score that is close to, and occasionally even above, 1.000.
## Equation
Where OBP represents on-base percentage and SLG represents slugging average, we have the following equation. These averages have been established. – the numerator “H + BB +HBP” essentially means “number of trips to first base at the very least” – the denominator “AB + BB + SF +HBP” basically means “total plate appearances,” but does not include sacrifice bunts. A hitter is not granted a “AB” despite the fact that he steps to the plate (BB or HBP) or puts the ball into play and is ruled out, but the action allows a run to score (as in the SF scenario) even though he has made a trip to the plate.
To compute a batter’s total number of trips to the plate, the four counts (AB + BB + SF + HBP) must be used in conjunction. andwhere:
• H stands for hits
• BB stands for bases on balls
• HBP stands for times hit by pitch
• AB stands for at bats
• SF stands for sacrifice fly
• TB stands for total bases.
OPS may be expressed as follows in a single equation:
## History
The Hidden Game of Baseball, written by John Thorn and Pete Palmer in 1984, was the first book to make on-base plus slugging popular. The New York Times then began publishing the names of the top performers in this statistic in its weekly “By the Numbers” box, a feature that ran for four years and was widely adopted. Peter Gammons, a baseball journalist, popularized and evangelized the statistic, which was then picked up by other writers and announcers. Its popularity grew over time, and by 2004, it was featured on baseball cards produced by Topps Baseball Cards.
Examples include Thorn’sTotal Baseballencyclopedia and theStrat-O-Matic Computer Baseballgame, both of which contained manufacturing information in their early editions.
The availability of its components, OBP and SLG, as well as the fact that team OPS corresponds highly with the number of runs scored, contributed to the rise in popularity of OPS.
## An OPS scale
Bill James, in his essay titled “The 96 Families of Hitters,” classifies hitters into seven separate groups based on their offensive power:
Category Classification OPS range
A Great .9000 and higher
B Very good .8334 to.8999
C Above average .7667 to.8333
D Average .7000 to.7666
E Below average .6334 to.6999
F Poor .5667 to.6333
G Very poor .5666 and lower
This basically converts the ordinal scale into a seven-point ordinal scale for OPS. It is possible to provide a subjective reference for OPS numbers by substituting quality labels for the A–G categories, such as excellent (A), very good (B), good (C), average (D), fair (E), bad (F), and very poor (G).
With at least 3,000 plate appearances through August 5, 2020, the top 10 Major League Baseball players in terms of lifetime OPS were as follows:
1. Babe Ruth has a 1.1636 rating
2. Ted Williams has a 1.1155 rating
3. Lou Gehrig has a 1.0798 rating
4. Barry Bonds has a 1.0512 rating
5. Jimmie Foxx has a 1.0376 rating
6. Hank Greenberg has a 1.0169 rating
7. Rogers Hornsby has a 1.0103 rating
8. Mike Trout has a 1.0009 rating
9. Manny Ramirez has a 0.9823 rating
10. Mark McGwire has a 0.9823
The top four hitters were all left-handed, which was a rarity. Jimmie Foxx has the best career on-base percentage (OPS) of any right-handed batter in baseball history. The following are the best 10 single-season performances in Major League Baseball (all by left-handed hitters):
1. 1.4217 for Barry Bonds in 2004
2. 1.3807 for Barry Bonds in 2002
3. 1.3791 for Babe Ruth in 1920
4. 1.3785 for Barry Bonds in 2001
5. Babe Ruth in 1921
6. Babe Ruth in 1923
7. 1.2875 for Ted Williams in 1941
8. 1.2778 for Barry Bonds in 2003
9. Babe Ruth in 1927
10. Ted Williams in 1957
11. 1.2582 for Babe Ruth in 1927
12. 1.2566 for Ted
During the 1925 season, Rogers Hornsby batted 1.2449, which ranked him 13th on the all-time list of single-season marks for right-handed hitters. For right-handed pitchers since 1935, Mark McGwire’s 1.2224 OPS in 1998 ranks 16th all-time and is the greatest single-season mark for a right-hander.
OPS+, or modified OPS, is a metric that is closely connected to OPS. OPS+ is an adjusted OPS that takes into account the park and league in which the player played, but does not take into account fielding position. The league average is defined as having an OPS+ of 100 points. An OPS+ of 150 or above is exceptional, and a score of 125 or higher is very good, but an OPS+ of 75 or below is mediocre. OPS+ may be calculated using the following equation:where *lgOBP is the league’s park adjusted OBP (excluding pitchers hitting) and *lgSLG is the league’s park adjusted SLG (excluding pitchers hitting).
Due to the additive nature of the two components of OPS+, for example a player with an OBP and SLG that are both 50 percent over average in both categories will have an OPS+ of 200 (twice the league average OPS+), while having an OPS that is only 50 percent above the league average.
As an approximate (but not accurate) estimate, a player with an OPS+ of 150 generates 50 percent more runs in a given series of plate appearances than a player with an OPS+ of 100 throughout the course of a similar set of plate appearances (though see clarification above, under “History”).
Through the completion of the 2019 season, the following players ranked in the top twenty in their respective career OPS+ rankings (minimum 3,000 plate appearances):
1. Babe Ruth has 206 hits
2. Ted Williams has 190
3. Barry Bonds has 182
4. Lou Gehrig has 179
5. Mike Trout has 176
6. Rogers Hornsby has 175
7. Mickey Mantle has 172
8. Dan Brouthers has 170
9. Joe Jackson has 170
10. Ty Cobb has 168
11. Pete Browning has 163
12. Jim Foxx has 163
13. Mark McGwire has 163
14. Dave Orr has 162
15. Stan Musial has 159
16. Hank Greenberg
These are the only players on this list who are exclusively right-handed batters: Browning, Hornsby, Foxx, Trout, McGwire, Allen, Mays, and Thomas are the only players on this list who are exclusively right-handed batters. Mantle is the only player in the group who can transition from one position to another. The following were the best single-season performances:
1. Barry Bonds has 268 hits in 2002
2. Barry Bonds has 263 hits in 2004
3. Barry Bonds has 259 hits in 2001
4. Fred Dunlap has 258 hits in 1884 *
5. Babe Ruth has 256 hits in 1920
6. Babe Ruth has 239 hits in 1921
7. Babe Ruth has 239 hits in 1923
8. Ted Williams has 235 hits in 1941
9. Ted Williams has 233 hits in 1957
10. Ross Barnes has 231 hits in 1876 **
11. Barry Bonds has 231 hits in 2003
* – Fred Dunlap’s remarkable 1884 season took place in the Union Association, which some baseball experts believe is not a legitimate major league in the traditional sense. It is possible that Ross Barnes was helped by a rule that declared a bunt fair if it rolled in fair territory for the first time. When this regulation was lifted, he did not perform nearly as well as he had previously, but injuries may have played a major role in this, since his fielding numbers also fell. If Dunlap’s and Barnes’ seasons were to be removed from the list, two more Ruth seasons (1926 and 1927) would be added to the list.
Barnes, the lone right-handed hitter on the list, would also be eliminated as a result of this.
## Criticism
Despite the fact that it is a straightforward computation, OPS is a contentious statistic. On-base percentage and slugging percentage are both taken into consideration when calculating OPS. On-base %, on the other hand, is a greater predictor of run production. Linear weights are used to construct statistics such as thewOBA, which capitalizes on this distinction. Furthermore, the components of OPS are not always equal (for example, league-average slugging percentages are frequently 75–100 points higher than league-average on-base percentages).
1. For further information, visit the Wayback Machine
2. John Thorn and Pete Palmer, “The Hidden Game of Baseball,” on pages 69-70
3. Alan Schwarz, “The Numbers Game,” on pages 165-233
4. Mr. James and Mr. Bill The 96 Hitter Families have been identified. The Bill James Gold Mine, 2009, p.24
5. “Career LeadersRecords for OPS”.Baseball-Reference.com. RetrievedJuly 26,2019
6. “Single-Season Records for OPS”.Baseball-Reference.com. RetrievedJuly 26,2019
8. “Single- Michael Lewis is a writer who lives in the United Kingdom (203). Moneyball: The Art of Winning an Unfair Game
9. “2019 Major League Baseball Standard Batting”.Baseball-Reference.com
## References
• John Thorn and Pete Palmer are co-authors of this work (1984). Baseball’s “Secret Game” is a little known fact. Schwarz, Alan
• Doubleday & Company, ISBN 0-385-18283-X
• Doubleday & Company, ISBN 0-385-18283-X (2004). The Game of Numbers. Books published by Thomas Dunne Books (ISBN 0-312-32222-4)
## On Base Plus Slugging (OPS) All Time Leaders on Baseball Almanac
When Branch Rickey and Allan Roth invented the on base percentage statistic in the 1950s, they were looking for a way to track the number of times a player reached any base. The sacrifice fly designation was not included in the initial version, but when it was formally adopted in 1984, it was included using the procedure outlined in the preceding section. Later, Slugging Average was established, and the two were merged to form On Base Plus Slugging, which stands for On Base plus Slugging. The player must have played a minimum of 1,000 career games in order to be included on this list of the one-thousand greatest on base plus slugging leaders.
• “Similar to a dog who has never been given table scraps.
• I’m pretty curious.
• I’m hoping to be able to do so this year, and I’m hoping it will be possible.
• I have set a one-year goal for myself.” The Baseball Digest published an article by Todd Helton (May 2004) Babe Ruth owns the record for most wins in the American League, and Manny Ramirez is the only current player who “appears” to be in with a chance.
• Perhaps the 1.000 OPS Club should be established by Baseball Almanac as a new “club” inside the organization.
What do you think of the on-base plus slugging percentage? Like this one, do you find it interesting to argue and debunk complicated statistics like this one? Bring your friends and family to join us onBaseball Fever, where we have a forum dedicated to the discussion of SABRMetric statistics.
## How to Calculate OPS in Baseball
Baseball statistics have long been a significant aspect of the game. When talking about baseball and its many leagues, terms such as batting average, runs batted in, hits, runs, and more have become standard. However, as baseball has progressed throughout the years, the statistics have gotten very intricate. It might be difficult to keep up with the new-age language, which includes statistics such as on-base percentage (OBP), slugging percentage (SLG), and wins above replacement (WAR), among others.
Initially glanced at, it appears to be a difficult figure to compute and comprehend, however it can be simply broken down into a series of steps.
## 1. Understanding and Calculating On Base Percentage
On Base Percentage (also known as On Base Percentage or OBP) is a crucial statistic in baseball and the first important statistic required to comprehend On Base Percentage (also known as OPS). Quite literally, the On Base Percentage tracks how many times an individual player gets on base. In order to compute this, you tally up a player’s hits, walks, and times hit by a pitch, and then divide the total by the number of plate appearances the player has made (at bats plus walks plus hit by pitch plus sacrifice flies).
## 2. Understanding and Calculating Slugging Percentage
The slugging percentage, abbreviated as SLG, is the other important statistic in the calculation of the OPS. Although similar to calculating on-base percentage (OBP), SLG is used to assess the overall quality of hits made by a player rather than amount of base hits made. It does this by giving a numerical value to each base (single = 1, double = 2, etc.) and assessing the type of hit a player receives when he smacks the ball. The formula for calculating SLG is Singles + Doubles x 2 + Triples x 3, + Home Runs x 4 divided by the number of at bats.
## 3. Calculating and Understanding OPS
So, now that we’ve learned how to compute OBP and SLG, it’s important to remember that OPS is basically On Base Percentage plus Slugging, which makes it much simpler to calculate. To compute on-base percentage and slugging % for a player, multiply their on-base percentage by their slugging percentage. For example, a player with an OBP of.280 and an SLG of.500 will have an OPS of.780 if he also has an OBP of.280 and an SLG of.500. This statistic practically reflects the best of both worlds between the two statistics because it evaluates both the amount of time a player spends on base and the quality of their hits.
## What Is OPS in Baseball? Well, It Measures…
There are several approaches of evaluating baseball players, as well as numerous schools of thought on the most effective method of doing so. The earned run average (ERA) of a pitcher is widely considered to be the most reliable conventional statistic for determining his or her performance. Ops, on the other hand, has become a common measure for evaluating hitters in order to quantify their overall effectiveness. As a result, what exactly is OPS in baseball? On-base plus slugging (also known as OPS) is a statistic that attempts to assess a hitter’s overall effectiveness by combining two figures that reflect how well he is at reaching base and hitting for power: on-base percentage and slugging percentage.
We’ll go through everything from what OPS is to why it’s important and how to calculate it in detail. In the meanwhile, let’s get down to business and answer the burning question.
## What Is a Batter’s OPS?
In addition to On-Base, On-Base Plus The slugging percentage of a player is the sum of the player’s on-base percentage and slugging percentage. The on-base percentage (OPS) of a player demonstrates his or her ability to reach base and hit for power. On-base Plus is a slang term for Slugging percentage, often known as On-base percentage (OBP), is a combination of a batter’s On-base percentage (OBP) and Slugging percentage (SP) (SLG). The stat was created to analyze a batter’s ability to reach base and hit for power, which are the two key tasks that are regarded to be the most significant for hitters in baseball at the time of its creation.
You may calculate an OPS by adding these two values together, and voilà, the league OPS for 2019 was.758.
These prices, on the other hand, will alter over time as more and more people join the club.
Because a batter’s OPS tends to hold up better over time than counting figures, it may be used to evaluate batters even when comparing two players who have a significant difference in playing time.
## How Do You Calculate OPS?
As we previously discussed, On-Base Plus is a type of military base. Slugging percentage, often known as on-base percentage and slugging percentage, is the sum of a player’s on-base percentage and slugging percentage. Put another way, you can compute an OPS by simply putting the two numbers together. The on-base percentage (OPS) of a hitter cannot be calculated, however, without these data. Because the complete OPS calculation is lengthy and difficult to compute on its own, it is preferable to calculate OBP and SLG separately and then combine them.
1. In order to do so, sum up all of the hits, walks, and hit by pitches, then divide the total by the number of at-bats plus walks, sacrifice flies, and hit by pitches to get the on-base percentage.
2. As a consequence, the calculation for OBP looks somewhat like this: At bats + walks + hit by pitch / (at bats + walks + hit by pitch + sacrifice flies) = On Base Percentage (OBP).
3. Simply combine the two figures together to obtain the overall probability of success (OPS) for each situation.
4. Using the on-base percentage calculation, the values for hits (30), walks (10), and HBPs (5) total up to 45 when multiplied together.
5. The hitter’s on-base percentage is calculated by dividing 45 by 120, which equals.375.
6. On the batting average side, the total bases from singles (15), doubles (10), triples (15), and home runs (20) add up to a total of a.600 slugging percentage.
For the purposes of illustration, the entire equation is written as follows: With all of that work spread out in front of you, it’s usually better to compute the two figures individually in order to keep everything a bit more organized.
## Why Is OPS a Good Stat?
On-base Plus Slugging is one metric that has remained mostly concealed in plain sight throughout history and has just lately been recognized as being significant. In the world of so-called “advanced” metrics, on-base percentage (OPS) is one of the simplest to compute and utilize. It is comprised of the two values created by the two most significant talents for hitters: reaching base and hitting for power. Because of these two elements, on-field performance (OPS) is a simple metric for fans to locate, compute, and understand.
• OPS, on the other hand, is by no means impenetrable.
• According to theSporting News’ evaluation of on-base percentage (OPS), David Ortiz topped all of Major League Baseball with a 1.021 OPS in 2016, yet in 2000, same score would have matched him for 16th place in the league.
• Because OPS is sensitive to changes in ballpark dimensions and league-wide adjustments, it is not the be-all and end-all metric.
• This statistic is far more sophisticated, since it normalizes a player’s OPS based on league and park considerations, with 100 serving as a reference point for comparison.
## What Is a Good OPS in Baseball?
According to what we discussed previously, OPS standards can shift over time as leagues and ballparks evolve. But there are still broad numbers that are deemed to be excellent or harmful in some way, shape or form. At any point in time in history, an OPS of over.800 has been deemed good, with an OPS of over.900 considered very good, and an OPS of 1.000 or greater considered extraordinary. On the other hand, an OPS of less than 700 is regarded bad, and anything less than 600 is considered extremely poor.
## When Did OPS Become a Stat in Baseball?
On-base Plus is made up of several components. Slugging (both on-base percentage and slugging percentage) has been around for a very long time. Branch Rickey was a pioneer in the development of the on-base percentage statistic in the 1940s and 1950s, and he was credited with inventing the concept. A metric known as “Extra Base Power” was also established by him, and he even reasoned that the two statistics might be combined to determine an individual batter’s total performance. Apparently, Rickey was decades ahead of his time in terms of thinking.
However, it wasn’t until the rise of sabermetrics in the late 1990s and early 2000s that baseball began to take the overall OPS (as well as its components) seriously.
The on-base percentage (OPS) is not regarded an official statistic by Major League Baseball, despite the fact that it is well known and highly accepted today.
After reading this, the next time you see a batter’s OPS, you will have a better understanding of whether you should be optimistic about him or if you should be concerned.
## Highest Career OPS
Babe Ruth, who is in the Hall of Fame, holds the record for the best career On-base Plus Slugging percentage with a 1.164 OPS throughout his 22-year professional baseball career. Seven batters have concluded their careers with an OPS greater than 1.000, with Mike Trout now straddling the line between the two categories.
## Highest Single Season OPS
Barry Bonds owns the single-season record for the greatest On-Base Plus Slugging percentage (1.422) with a mind-boggling 1.422 in 2004. He also established an MLB record with an on-base percentage of.609 and a slugging percentage of.812, both of which were the highest ever recorded.
## What Is Batting Average?
The batting average demonstrates a player’s ability to put the ball in play and advance to the next base. The batting average of a hitter is derived by dividing the total number of hits he has received by the total number of at-bats he has had. It is important in measuring a player’s performance at the bat, but it does not take into consideration walks, sacrifices, and other factors.
### Related Articles
• What is the definition of a Designated Hitter in baseball? What is the definition of MVR in baseball? A Comprehensive Guide to the Rule
• What Is the Meaning of WAR in Baseball? The Complete Guide to Getting Started
• What is the definition of WHIP in baseball
• In baseball, the term “left on base” (LOB) refers to the number of runners who have been left on base.
## What Does Ops Mean In Baseball? Details Explained
The most recent update was made on July 3, 2021 by Percentage that is correct! Ops adds the on-base percentage and slugging percentage together to come out with a value that identifies them as one. The Ops can combine how well a batter can hit for average and power with how well he can hit for a good strikeout rate. It is also employed in the examination of pitchers. When this is done, it is referred as as Ops against. The on-base percentage (sometimes known as the slugging percentage) is a sabermetric statistic in baseball that is used to measure a player’s overall performance.
## Ops Scale
Categories Classifications Ops Range A Great Higher than.9000 B Very good Ranging from.8334 to.8999 C Above average Ranging from.7667 to.8333 D Average Ranging from.7000 to.7666 E Below average Ranging from.6334 to.6999 F Poor .5667 to.6333 G Very poor Lower than.5666
This table separates the Ops categories into seven groups on a seven-point ordinal scale. Quality labels such as excellent(A), very good(B), above average(C), average(D), below average(E), poor(F), extremely poor(G) and poor(H) might be replaced with more descriptive ones (G). All of these categories contribute to the creation of a subjective reference for operational values.
## Ops- Meaning
First and foremost, the abbreviation ‘Ops’ refers to On-Base percentage plus slugging performance. The Ops statistic is derived from the sabermetric movement, which began several decades ago and is still in use today. It is used to capture the value of a batter using a straightforward heuristic.
## Calculations
You must have deduced from the name and meaning of Ops that obtaining the Ops is the result of multiplying two separate values together. Both of these metrics are: Ops= On-base percentage (OBP) + Slugging percentage (SLP). Of course, the two figures that are being put together to form the Ops are generated in the following ways: On-base percentage (OBP) is calculated as follows: (hits + walks + hits-by-pitch) / (at-bats + walks + hits-by-pitch + sacrifice flies) x 100. In this equation, Slugging Percentage(SLP)=/AB.
## History
We’ll start with the history of OBP and then go on to SLP because these two components are what make up the Ops. When Branch Rickey was establishing the Brooklyn Dodgers into a National League juggernaut in the 1940s or 1950s, he established the Organization of Baseball Prospects (OBP). The second factor is referred to as the slugging percentage (SLG). We’ll get back to you on this later. SLG has been in use since the 1800s, according to prominent major league baseball historian John Thorn, who claims that it was first used as an official MLB statistic in 1923 before becoming an official MLB statistic in 1923.
The concept of combining two separate averages in order to obtain a more accurate measure was both reasonable and excessive. As you can see, the calculations used to calculate the Ops are straightforward.
## Why Should I Use Ops Stats?
The on-base percentage plus the slugging percentage is a standard measure that is simple to understand and use. Because it calculates based on the two most crucial jobs of a batter, which are getting on base and having the ability to hit the ball, Ops is considered to be beneficial. While Ops is a fantastic tool, it is lacking in several areas, such as league-wide offense, which changes on a regular basis. As an example, David Ortiz had the greatest Ops of the season last year with 1.021, which was the best in the league.
Another area in which Ops fails is that it does not take into consideration park variables.
It fails to recognize that when a player plays on his home field, he is more likely to perform well and enhance his stats.
## According To Ops Record, Which Pitcher Has The Fastest Throw Of All Time?
Take into consideration the fact that a quick fastball is a lot faster than it used to be. Aroldis Chapman holds the record for throwing the quickest fastball ever recorded in big league baseball history. On September 24, 2010, he set a new world speed record with a throw that reached 105.1 miles per hour. 105.8 miles per hour is the speed at which this pitch was recorded. Chapman’s pitch has grown by about a mile per hour throughout the course of his career. A pitch that was previously recorded at 105MPH may now be observed at 106MPH, according to the data.
## What Is The Downside Of Ops?
The only reason why some individuals believe that the Ops should not be employed is because to mathematical considerations. Despite the fact that we have said several times in this text that Ops is a statistic, we have not highlighted that it is not mathematically sound in any way. We’ve previously indicated that a ballplayer’s on-base percentage and slugging percentage are combined to make his overall offensive performance (Ops). Yes, we both believe that these two numbers are ideal for determining a player’s overall ability to play the game.
## Who Invented The Ops system?
Pete Palmer, please! The guy responsible for developing the Ops system took the time to explain how he came to develop a decent system and why it is still effective after so many years. He shared with us some of the positive steps he had taken, and he also stated that it would take several years to achieve perfection with this technique. The Ops strategy is clearly geared toward evaluating players on the offensive side of the field. All he did was try to make a connection between hitting and the team’s success in 1960.
## What Does The Ops System Require To Be Perfect?
When the Cubs games are shown on the Marquee Sports Network, the beginning line-ups are featured with the statistic ‘Ops’ next to every name, indicating that the player was injured.
For example, the Ops statistic is useful since it informs us far more than most other statistics, like as the batting average number, do. The problem with the Ops data is that they lack context, which is important for fans to understand. More context is required for the Ops statistics to be ideal.
## Conclusion
Basically, we all know what it is: the Ops system is used to track the statistics of baseball players, and we all know how it works. With this approach, a player’s overall performance is expressed as a % of his or her total.
## On-base plus slugging
On-base plus slugging (sometimes known as on-base percentage and slugging percentage) is a baseball statistic that is computed as the sum of a player’s on-base percentage and slugging percentage. This method is excellent for determining a player’s offensive worth since it considers both the ability to get on base and the ability to hit for power, which are two crucial hitting talents, and it is simple to use. In Major League Baseball, a player with an OPS of.900 or more is considered to be in the highest tier of offensive skill.
## Formula
Where OBP represents on-base percentage and SLG represents slugging percentage, we have the following fundamental formula: These percentages are defined as follows and in which locations:
• The letters H, BB, and HBP stand for hits, bases on balls, and times hit by pitch respectively. The letters AB stand for at bats, SF stands for sacrifice fly, and TB stands for total bases.
Because the denominators of OBP and SLG are different, it is feasible to rewrite the calculation for OPS using a common denominator in order to simplify the expression. Mathematics says that this statement is the same as the simple sum of OBP and SLG, which is as follows:
## Interpretation of OPS
It is possible to modify the equation for OPS using a common denominator because OBP and SLG have separate denominators, although this is not recommended. Mathematically speaking, this statement is the same as the simple sum of OBP and SLG:
## History
The Hidden Game of Baseball, written by John Thorn and Pete Palmer in 1984, was the first book to make the concept of on-base plus slugging prominent. The New York Times then began publishing the names of the top performers in this statistic in its weekly “By the Numbers” box, a feature that ran for four years and garnered widespread attention. The statistics were popularized by baseball journalist Peter Gammons, who utilized them and spread the word about them to other writers and announcers.
The Major League Baseballplayers with a lifetime on-base percentage greater than 1.000 are as follows (through 2005, current players are shown in bold):
1. Babe Ruth has a 1.1636 rating
2. Ted Williams has a 1.1155 rating
3. Lou Gehrig has a 1.0798 rating
4. Barry Bonds has a 1.0533 rating
5. Albert Pujols has a 1.0490 rating
6. Todd Helton has a 1.0404 rating
7. Hank Greenberg has a 1.0169 rating
8. Rogers Hornsby has a 1.0103 rating
9. Manny Ramirez has a 1.0076 rating
10. Babe Ruth has a 1.16
Albert Pujols has the best career on-base percentage (OPS) of any right-handed batter in baseball history. The following are the best 10 single-season performances in Major League Baseball (all by left-handed hitters):
1. 1.4217 for Barry Bonds in 2004
2. 1.3807 for Barry Bonds in 2002
3. 1.3791 for Babe Ruth in 1920
4. 1.3785 for Barry Bonds in 2001
5. Babe Ruth in 1921
6. Babe Ruth in 1923
7. 1.2874 for Ted Williams in 1941
8. 1.2778 for Barry Bonds in 2003
9. Babe Ruth in 1927
10. Ted Williams in 1957
11. 1.2582 for Babe Ruth in 1927
12. 1.2566 for Ted
Rogers Hornsby set the record for the greatest single-season batting average for a right-handed batter in 1925 with a 1.2449 mark (13th on the all-time list). Since 1925, Mark McGwire has had the greatest single-season OPS for a right-hander, with a 1.2224 mark in 1998.
OPS+, or Adjusted OPS, is a metric that is closely connected to OPS. OPS+ is an adjusted OPS that takes into account the park and league in which the player played, but does not take into account fielding position.
The league average is defined as having an OPS+ of 100 points. An OPS+ of 150 or greater is considered exceptional, indicating that the player’s overall OPS was 50 percent better than the national average after adjusting for park.
According to lifetime leaders in OPS+ (minimum 3000 plate appearances, current players in bold), the following players were the best through 2005:
1. Babe Ruth has 207 hits
2. Ted Williams has 190
3. Barry Bonds has 184
4. Lou Gehrig has 179
5. Rogers Hornsby has 175
6. Mickey Mantle has 172
7. Dan Brouthers has 170
8. Joe Jackson has 170
9. Ty Cobb has 167
10. And the list goes on.
The following were the best single-season performances:
1. Barry Bonds has 275 hits in 2002
2. Barry Bonds has 262 hits in 2001
3. Barry Bonds has 260 hits in 2004
4. Babe Ruth has 256 hits in 1920
5. Fred Dunlap has 250 hits in 1884
6. Babe Ruth has 239 hits in 1921
7. Babe Ruth has 239 hits in 1923
8. Ted Williams has 235 hits in 1941
9. Ted Williams has 233 hits in 1957
10. Ross Barnes has 231 hits in 1876
11. Barry Bonds has 231 hits in 2003
12. Barry Bonds
• Sabermetrics, on-base percentage, slugging percentage, and other metrics
## Notes
• John Thorn and Pete Palmer are co-authors of this work (1984). Baseball’s “Secret Game” is a little known fact. ISBN 0-385-18283-X
• Alan Schwarz, Doubleday & Company, ISBN 0-385-18283-X (2004). The Game of Numbers. Thomas Dunne Books (ISBN 0-312-32222-4)
• Thomas Dunne Books (ISBN 0-312-32222-4)
## What does OPS stand for?
When it comes to baseball statistics, the ability to get on base and hit for power is referred to as the ability to get on base. Simply combining a player’s OBP and SLG results in the calculation of this statistic. The player’s overall offensive rating (OPR) is represented by the number you get. An OPS of.9000 or greater is excellent, and it is often held by the league’s top scorer. Barry Bonds, with a 1.4217 OPS in 2004, has the greatest single-season OPS mark in baseball history. Babe Ruth holds the record for the best all-time OPS with a 1.1636.
### Example
“The fact that no one on our squad has an OPS of.7000 or above is beyond comprehension to me. Yeah, we’re a bunch of jerks.”
### Related Slang
OBP On-base Percentage avg Batting average ERA Earned run average RBI Runs batted in HR Home run Cycle Single, double, triple, and home run MLB Major League Baseball AB At bat
### Usage
“The fact that no one on our squad has an OPS of.7000 or above baffles me completely. Exactly. We’re terrible.”
#### OPS definition
This article provides an explanation of what the abbreviation “OPS” stands for. The Slangit team has authored and collated the definition, example, and related words given above. If you have any questions, please contact us. We are regularly adding new slang phrases, acronyms, and abbreviations to our database to keep it up to date. Please let us know if you have any suggestions for new terms or updates to current ones.
## What is OPS in Baseball? (Detailed Explanation)
We rely on the generosity of our readers. If you make a purchase after clicking on one of our affiliate links, we may receive a commission. In addition, we get commissions from eligible Amazon sales because we are an Amazon affiliate. More and more new statistical categories have been introduced into Major League Baseball in recent years as a result of an effort to better assess nearly every aspect of baseball, from the velocity of a ball flying off a bat to the speed at which thrown balls spin, and much more.
In baseball, what is the OPS (on-base percentage)?
The overall batting average of a batter is calculated by multiplying his or her ability to reach base successfully by another statistic that represents the strength of the batter’s swing.
OBP and SLG are the acronyms for on-base percentages.
## How Do You Calculate OPS?
The mathematical formula is straightforward: OBP (on-base percentage) plus SLG (slugging average) equals OPS. A player’s at-bat value is calculated using this method, which is simple to understand. What I mean is, on average, how much is produced by each at bat? Over the years, the popularity and impact of the OPS category has expanded very moderately in both popularity and influence. It’s essentially a byproduct of a surge in interest in on-base percentage that began in the 1990s with sabermetrics and the publication of the book “Moneyball,” as well as a broader focus by statisticians on what factors most influence the production of runs.
not just all singles, but doubles, triples, and home runs). For a while, the category was referred to simply as “production,” because the goal is to evaluate a batter’s ability to generate runs.
## An Overview of Baseball’s OPS
Baseball statistics are more popular than statistics for almost every other sport, with the exception of football. Beginning with the introduction of the box score in the late 1880s, newspapers attempted to express all the action of a baseball game in a small printed “box,” with the names of players followed by their exploits in single games. It was a failure, and the box score was scrapped. With the introduction of the new box scores, a limited number of categories were created to track the hitting (and pitching) accomplishments of the players.
The “batting average” of a batter may be calculated by dividing the number of at bats by the number of hits.
However, by the mid-20th century, baseball experts believed they could gain even more insight from the stats.
An summary of the situation:
### On-Base Percentage: How Good Batters are at Avoiding Outs
On-base percentage (OBP) dates back to the 1940s, when Brooklyn Dodgers executive Branch Rickey, with the assistance of statistician Allan Roth, developed the concept over a period of several years. Essentially, it is a fundamental indicator of a batter’s ability to reach at least first base when compared to the total amount of at bats he has accumulated. “Getting on base” refers to reaching first base by any methods possible, including base hits, base on balls, and being hit by a pitch. As an example, if a hitter batted 10 times and reached at least first base on each of those ten occasions, his OBP would be 1.000.
For old-time baseball fans who are particularly familiar with batting average, the on-base percentage statistic should be greater than the batting average category, in general (but typically not by a lot).
Obp became increasingly valuable in the 1990s, as new evidence from what is now known as sabermetrics revealed that getting on base is more significant for scoring runs (and hence winning games) than simply having a high batting average during the season.
### Slugging Percentage: How Many Bases Per Hit
Over the years, one underappreciated baseball statistic has been “total bases,” which refers to how many total bases a batter has gained as a result of his or her hits. A single base hit earns a hitter one base to count, while a home run earns a batter four bases to count in total. The theory is that the more power and, consequently, extra-base hits a batter generates, the more effective he will be in terms of driving in runs to help his team win a game. A batter’s slugging percentage is the number of bases he or she gets on each at bat.
As an example, if a player hits a home run (worth four bases) but does not hit anything else in his first ten at-bats, his SLG is.400.
Slugging percentages can approach 1.000, and league leaders frequently achieve this level of performance. Generally speaking, the line between an ordinary slugger and an excellent slugger is.900.
### OBP vs. SLG in Baseball
Over the years, one underappreciated baseball statistic has been “total bases,” which refers to the total number of bases a batter has gained as a result of his or her hits. From a single base hit (which counts as one base) all the way up to and including a home run (which counts as four bases). The theory is that the more power and, consequently, extra-base hits a batter generates, the more productive he will be in terms of driving in runs to help his team win games in the future. How many bases do you get each at bat?
One B multiplied by two B multiplied by three B multiplied by three B multiplied by three B multiplied by four AB A batter’s SLG is calculated as follows: If he hits a home run (worth four bases) but does not hit anything else in his first ten at-bats, his SLG is 400.
Slugging percentages can be higher than 1.000, and league leaders frequently achieve this level of performance.
## Is OPS a Good Stat? Why, and Why Not?
In baseball, the on-base percentage (OPS) is valued because it indicates whether a batter is hitting with power or not. Having a lot of “pop” in the lineup is preferred by baseball managers because it results in more runs (RBIs) than non-power hitting. Fans also appreciate power, to paraphrase a well-known television commercial. It is possible to calculate how frequently a hitter safely reaches first base as well as how many times his hits result in his gaining further bases using the OPS formula.
• The term for this is slugging, mashing, or driving the ball in baseball jargon.
• Sluggers hit long or extremely hard balls that wreak havoc in the outfield and allow base runners to run amok around the bases in the middle of the game.
• They “create” the runs that are required to win baseball games.
• Sluggers are similar to batters in terms of power.
## What is a Good OPS in Baseball?
Anything in the vicinity of a 1.000 OPS is considered excellent. Anything with a score of more than 1.000 is extraordinary. League leaders frequently have winning percentages in excess of 1.000 at the end of the season. This is true for the current season as well. By the middle of June in 2021, three players had an OPS of or better than 1,000: Vladimir Guerrero Jr.
(tops the list with 1.089), Jesse Winker, and Nick Castellanos. Ronald Acuna Jr. (.989), Kris Bryant (.959), and Shohei Ohtani (.951), all of whom are stars in the Major League Baseball, were among those who came close to the “very good” threshold.
## Can OPS Judge Pitchers, Too?
The answer is yes, but it is employed less frequently than in the case of hitters. It’s referred to as “slugging-percentage against,” and it simply measures how many total bases pitchers allow for each hit. The same is true for “average against,” and so on. Teams are interested in learning which pitchers are most prone to yielding a high number of base hits (avg against), as well as who of those pitchers is allowing the most extra-base hits (SPA). Anything and everything you can think of that may be used to evaluate a baseball player’s performance is being counted and evaluated right now.
## Final Words on Baseball’s OPS Statistical Category
There is no one way to assess how well a hitter contributes to the production of runs that enable the team to win a baseball game. Most of the time, it is necessary to take into account more than one measuring instrument, which is essentially what the OPS is. The on-base percentage (OPS) measures how frequently a hitter gets to second base safely, so avoiding outs, while also displaying how many extra-base hits he slugs out. It assesses a hitter’s ability to get on base as well as hit with power, with the latter implying a higher likelihood of producing more runs.
### Question:Which batter recorded the highest OPS, both for a season, and lifetime?
Answer:Only batters with a minimum of 3,000 at-bats are included for this career record. Babe Ruth is the all-time leader in on-base percentage (OPS), with 1.1636 during his career. Ruth, Barry Bonds, and Ted Williams each had the top 10 OPS figures in a single season, with Bonds’ 1.4217 in 2004 setting the record for the best single-season OPS total ever. Likewise, Bonds has the No. 2 position with a 1.3807 in 2002, while Ruth had the position with a 1.3791 in 1920.
### Q.:Who was the best MLB player for total bases?
A.:Hank Aaron, who has amassed a total of 6,856 total bases over his career. Babe Ruth set the record for most hits in a season with 457 in 1921. To everyone’s surprise, the very next season, Rogers Hornsby broke the National League record for total bases, which remains today, with 450 total bases! Many old-timers believe that total bases is an extremely essential statistic to use in evaluating hitters. (In addition, total bases have a significant role in a batter’s OPS.) Take a look at these more resources: What is the record for the highest-scoring Major League Baseball game in history?
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# Probability
The "at most" and "at least" topic confuses me
Could you briefly describe both and post a small example to help explain each?
Thanks
#### Solution Preview
I just want to use an example to give an expanation.
<br>
<br>Example. If we toss a coin three times, the possible outcomes are {HHH,HHT,HTH,THH,HTT,THT,TTH,TTT}, where H and T represent the outcome of each tossing ...
#### Solution Summary
The solution discusses the "at most" and "at least" topic.
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