url stringlengths 6 1.61k | fetch_time int64 1,368,856,904B 1,726,893,854B | content_mime_type stringclasses 3 values | warc_filename stringlengths 108 138 | warc_record_offset int32 9.6k 1.74B | warc_record_length int32 664 793k | text stringlengths 45 1.04M | token_count int32 22 711k | char_count int32 45 1.04M | metadata stringlengths 439 443 | score float64 2.52 5.09 | int_score int64 3 5 | crawl stringclasses 93 values | snapshot_type stringclasses 2 values | language stringclasses 1 value | language_score float64 0.06 1 |
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https://www.doorsteptutor.com/Exams/NSTSE/Class-8/Questions/Topic-Mathematics-0/Part-127.html | 1,603,981,430,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107904287.88/warc/CC-MAIN-20201029124628-20201029154628-00347.warc.gz | 678,915,728 | 15,850 | # Mathematics [NSTSE (National Science Talent Search Exam- Unified Council) Class 8]: Questions 813 - 814 of 1201
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### Passage
Directions: The following pie-charts show the distribution of herbivores and carnivores in seven different forests A, B, C, D, E, F and G.
Distribution of Herbivores and Carnivores in Seven Different Forests A, B, C, D, E, F and G.
## Question 813 (5 of 5 Based on Passage)
Edit
### Question
MCQ▾
What is the ratio between the animals that are herbivores in forest D and the animals that are carnivores in forest E?
### Choices
Choice (4)Response
a.
b.
c.
d.
## Question 814
Mathematics
Edit
### Question
MCQ▾
The table shows the number of three different brands of watches sold by a certain store. The data are represented by the pie chart type diagram which shows a semicircle divided into six equal sectors. The angle of sector representing the number of Rolex watches sold is:
Brand Number of watches Rolex 35 Omega 60 Citizen 45
### Choices
Choice (4)Response
a.
b.
c.
d. | 324 | 1,328 | {"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-2020-45 | latest | en | 0.80905 |
https://www.mrexcel.com/board/threads/using-sumproduct-with-a-row-of-discontinuous-data-rather-than-a-column.803652/ | 1,725,761,653,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700650958.30/warc/CC-MAIN-20240908020844-20240908050844-00485.warc.gz | 888,819,229 | 19,824 | # Using SUMPRODUCT with a row of discontinuous data rather than a column?
#### thenapolitan
##### Board Regular
Hey All,
I've been reading articles on mrexcel.com for quite some time, but only now am not able to come up with an answer to my question. Not sure if there is a post for this, but curious if someone could help.
Right now I am using =SUMPRODUCT(--(B5:B25>E5:E25)) to return a count when B5:B25>E5:E25. This works great.
I had to convert the columns into rows and the data is set up strangely. I can rearrange the data if necessary, but I need all the data to be in the same row.
So, I tried =SUMPRODUCT(--((J3,L3,N3,P3,R3,T3,V3,X3,Z3,AB3)>(K3,M3,O3,Q3,S3,U3,W3,Y3,AA3,AC3))) - (can you see that the data is discontinuous?) To me, this makes two arrays with 10 items each for comparison, but that is not working.
Any ideas on how to set up something the same as =SUMPRODUCT(--(B5:B25>E5:E25)) but in rows with items that I select manually?
Thanks for any feedback you could give me.
Cheers,
Chris
### Excel Facts
What is =ROMAN(40) in Excel?
The Roman numeral for 40 is XL. Bill "MrExcel" Jelen's 40th book was called MrExcel XL.
Try this:
=SUMPRODUCT(--(J3:AB3*MOD(COLUMN(J3:AB3)-1,2)>K3:AC3*MOD(COLUMN(K3:AC3),2)))
Hello Chris, welcome to MrExcel
If you have a header row with some sort of common text in the columns belonging to the first set, e.g. with "x" in each of these cells:
J2,L2,N2,P2,R2,T2,V2,X2,Z2,AB2
Then this formula will count how many of those cells are > than the cell immediately to the left
=SUMPRODUCT((J3:AB3>K3:AC3)*(J\$2:AB\$2="x"))
Try this:
=SUMPRODUCT(--(J3:AB3*MOD(COLUMN(J3:AB3)-1,2)>K3:AC3*MOD(COLUMN(K3:AC3),2)))
Dude! Awesome! Thanks!
You're most welcome.
Well, now I've come up with my next question - How would I do that same math if each of those cells are 20 different items entered in a userform?
Here are the cells being entered into the table on the button click:
myNewColumn.Range.Cells(1, 10) = tbTeam1_1Man_Game1.Text
myNewColumn.Range.Cells(1, 11) = tbTeam2_1Man_Game1.Text
myNewColumn.Range.Cells(1, 12) = tbTeam1_2Man_Game1.Text
myNewColumn.Range.Cells(1, 13) = tbTeam2_2Man_Game1.Text
myNewColumn.Range.Cells(1, 14) = tbTeam1_3Man_Game1.Text
myNewColumn.Range.Cells(1, 15) = tbTeam2_3Man_Game1.Text
myNewColumn.Range.Cells(1, 16) = tbTeam1_1Man_Game2.Text
myNewColumn.Range.Cells(1, 17) = tbTeam2_3Man_Game2.Text
myNewColumn.Range.Cells(1, 18) = tbTeam1_2Man_Game2.Text
myNewColumn.Range.Cells(1, 19) = tbTeam2_1Man_Game2.Text
myNewColumn.Range.Cells(1, 20) = tbTeam1_3Man_Game2.Text
myNewColumn.Range.Cells(1, 21) = tbTeam2_2Man_Game2.Text
myNewColumn.Range.Cells(1, 22) = tbTeam1_1Man_Game3.Text
myNewColumn.Range.Cells(1, 23) = tbTeam2_2Man_Game3.Text
myNewColumn.Range.Cells(1, 24) = tbTeam1_2Man_Game3.Text
myNewColumn.Range.Cells(1, 25) = tbTeam2_3Man_Game3.Text
myNewColumn.Range.Cells(1, 26) = tbTeam1_3Man_Game3.Text
myNewColumn.Range.Cells(1, 27) = tbTeam2_1Man_Game3.Text
myNewColumn.Range.Cells(1, 28) = tbTeam1_Doubles.Text
myNewColumn.Range.Cells(1, 29) = tbTeam2_Doubles.Text
I guess I would need to add something similar to what you gave me, but with all those variables. Seems like it could be similar logic, but not sure with all those items:
myNewColumn.Range.Cells(1, 30) = SUMPRODUCT(--(J3:AB3*MOD(COLUMN(J3:AB3)-1,2)>K3:AC3*MOD(COLUMN(K3:AC3),2)))
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Go back | 1,409 | 4,416 | {"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-2024-38 | latest | en | 0.887258 |
http://www.online-betting.me.uk/news/goal-scoring-stats-football-betting-strategies.html | 1,495,913,564,000,000,000 | text/html | crawl-data/CC-MAIN-2017-22/segments/1495463609054.55/warc/CC-MAIN-20170527191102-20170527211102-00136.warc.gz | 751,360,525 | 13,683 | Goal scoring stats – football betting strategies
Still scoring goals!
/
Whenever I look at stats I’m drawn towards those denoting GOALS. Don’t know why but I am.
Every match depends on goals for it’s outcome and some sides are more adept at scoring than others. Of such things fortunes are made and lost.
In the PREMIERSHIP season there are 380 matches played. The highest number of different scores amassed in a season has been 32. (2003/04).
For the most part you can say that there will be between 4 and 10 matches where the score will appear only ONCE in a season. Usually where the home side score 6 0r even 7 times.
However, go to the other end of the scale and there are nine scores which are well worth scrutiny.
These scores are, of course, the most likely to occur in your average match.
Checking through the last eight seasons results, these scores have occurred 2,182 times. From a total of 3,040 games.
That’s a percentage figure of 71.77. Current season’s figures are 66.19%. Perhaps we can expect a glut to bring up the average.
The scores in question are set out below. From left to right each seasons total, from 2010/11 backing down to 2003/04.
``` Total.
0 - 0 25 32 42 26 34 32 30 41 262. 20
1 - 0 40 33 42 43 40 54 43 35 330. 24
0 - 1 14 26 30 31 35 28 36 27 227. 15
1 - 1 52 39 34 52 45 32 54 42 350. 35
2 - 0 30 34 34 34 31 40 34 26 263. 19
0 - 2 13 16 16 23 17 23 11 18 137. 15
2 - 1 40 42 36 29 42 30 30 34 283 20
1 - 2 24 19 25 21 20 26 17 28 180. 30
2 - 2 27 21 18 17 15 11 22 19 150. 10
Total 265 262 277 276 279 276 277 270 2182.```
The last column is this season, before matches played 20/03/12.
What do these stats teach us?
Well, for a start, the last two seasons fall a little below expectations. The other six seasons show a remarkable consistency.
The three winning away totals are amongst the lowest four totals.
The three home win scores have the best returns, 876 (40.14%). The three draw scores are next best with 762 (34.92) and the three away winning scores return just 544 successes. Being (24.93%).
How best can these stats be turned to good use? Should you fancy a home win the three scores, 1 – 0, 2 – 0 and 2 – 1 should be employed. At approximate prices of 10.0, 14.5 and 10.0 respectively 100pts would return 368pts. This would give a leeway to further investment should that prove necessary and still achieve an overall profit.
A more cautious approach would be to take the above three hoped for winning scores and combine with the draw scores @ 12.0, 8.0 and 17.0. These scores would return a total of 185.67pts. Again allowing for further investment if thought necessary.
There are many ways to use these stats. Even backing all nine scores in any match you would still make a profit at the average returns.
Another useful choice would be to take the home or away trio and, using other stats add either one or maybe two of the three draw scores. The combinations are many and using experiences derived down the ages a profitable set of choices can be made.
I have checked out four scenarios using the following criteria. Home team favourite at odds against. Using the mythical 100pts again the total return would be 132.50. The second example is the favourite playing away at odds against. Here the return would be 131.74pts. Next is the favourite at home but at odds-on. Return 139.65pts. Finally, the favourite playing away but being offered at odds-on. This one returns 136.90pts.
Good match choices are necessary of course but it shouldn’t be too hard to find at least one close match from the usual league fixture lists. As always when looking at scoring capabilities of any two sides, it is important to refer to historical results between the pair. Herein will be found many good leads to their scoring abilities.
The nine scores above would return profit in seven of ten matches if long term stats are accurate. However the returns would not cover the losses incurred in the other three matches. Although at average returns the total loss would be around 50pts. It should be within the remit of an experienced forecaster to overcome this loss figure and turn a nice profit on a regular basis.
Especially at this time of the season when concentrating on the teams whose season is virtually over. Those with nothing to play for other than a reasonable position in the table. These sides tend to freewheel, especially when playing a similarly placed team.
As usual these stats should give a good basis for those who like to build their own strategies. Any strategy that is used should be “paper-trialled” over a reasonable period of time and different staking methods applied to each of them. A backers strength is usually based on the amount of study put into the selection method. The more midnight oil being burned the likelier an increase in profits.
Incidentally, matches between ” nothing to play for sides” tend to end with low “card points”. When league points aren’t so essential these sides don’t seem to give the referee too many chances to waive his cards.
Bet sensibly and only with money you can afford to lose. | 1,397 | 5,297 | {"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-2017-22 | latest | en | 0.714577 |
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# GMAT-Prep CR2
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21 Dec 2008, 10:24
The mayor proposes to kill tiger sharks which attacks tourists. If tiger sharks are killed, then the small sharks which tiger sharks feed on, will increase in population. Since those small sharks feed on fish, it will impact the commerially important fisheries. So only (D) provides the best reasoning. (E) states the not all(which means atleast some) of the tourists either swim or surf. So mayor's proposal would still be valuable to protect those tourists.
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21 Dec 2008, 11:24
In the exam I could have almost skipped the correct answer.
Mayor's proposal is to kill tiger sharks within one mile of the shore and this action will boost economy. On the contrary, if tiger sharks get killed, small sharks will thrive and continue to gobble fishes, affecting economy. Hence, D is correct.
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22 Dec 2008, 10:23
scthakur wrote:
In the exam I could have almost skipped the correct answer.
Mayor's proposal is to kill tiger sharks within one mile of the shore and this action will boost economy. On the contrary, if tiger sharks get killed, small sharks will thrive and continue to gobble fishes, affecting economy. Hence, D is correct.
Ohh!!! missed it completely.
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Re: GMAT-Prep CR2 [#permalink] 22 Dec 2008, 10:23
Display posts from previous: Sort by | 725 | 2,597 | {"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} | 3.890625 | 4 | CC-MAIN-2017-43 | longest | en | 0.887426 |
http://freehitcountercode.com/what-is-next-number/ | 1,695,326,048,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506029.42/warc/CC-MAIN-20230921174008-20230921204008-00127.warc.gz | 23,174,466 | 18,189 | # What Is Next Number
What Is Next Number: Unveiling the Mystery of Number Sequences
Numbers have always fascinated humanity, serving as a universal language that transcends borders and cultures. From the ancient Egyptians who used numbers to measure land boundaries to the modern-day mathematicians solving complex equations, numbers have played a vital role in our lives. One intriguing aspect of numbers is their ability to form sequences, leading us to the concept of “What Is Next Number.” This article will explore the enigmatic world of number sequences, unraveling their patterns, and providing a glimpse into the future.
Understanding Number Sequences
Number sequences are arrangements of numbers that follow a specific pattern or rule. These sequences can be finite or infinite, and their patterns can be found in various mathematical concepts and real-life phenomena. The beauty lies in their predictability, as once you recognize the pattern, you can determine the next number in the sequence. However, some sequences can be complex, requiring a deeper understanding of mathematical principles.
Types of Number Sequences
The world of number sequences is vast and diverse, encompassing various types. Let’s delve into some of the most common types:
1. Arithmetic Sequences: In an arithmetic sequence, each number (except the first one) is obtained by adding a constant difference to the previous number. For example, the sequence 3, 7, 11, 15, 19… follows the pattern of adding 4 to each previous number.
2. Geometric Sequences: Geometric sequences, on the other hand, involve multiplying a constant ratio to obtain the next number. For instance, the sequence 2, 6, 18, 54, 162… follows the pattern of multiplying each previous number by 3.
3. Fibonacci Sequence: The Fibonacci sequence is a famous sequence where each number is the sum of the two preceding ones – 0, 1, 1, 2, 3, 5, 8, 13, 21… It is intriguing to observe the spirals formed by Fibonacci numbers in nature, such as the arrangement of leaves on a stem or the seeds in a sunflower.
4. Prime Numbers: Prime numbers are a sequence of numbers that can only be divided by 1 and themselves without leaving any remainder. The sequence starts with 2, 3, 5, 7, 11, 13, 17, 19… and continues infinitely. Prime numbers have captivated mathematicians for centuries due to their unique properties.
Q1: How can I identify the pattern in a number sequence?
A: To identify the pattern in a number sequence, carefully observe the differences or ratios between consecutive numbers. Look for a constant difference or ratio that applies to all the numbers in the sequence. It may require trial and error or knowledge of different sequence types.
Q2: Can number sequences be random?
A: While some sequences may appear random, most follow a specific pattern or rule. However, the complexity of the pattern may make it difficult to identify, leading to the misconception of randomness.
Q3: Why are number sequences important?
A: Number sequences have practical applications in various fields, including mathematics, computer science, statistics, and finance. They also enhance critical thinking and logical reasoning skills by challenging individuals to identify patterns.
Q4: Are there any unsolved number sequences?
A: Yes, there are several unsolved number sequences that continue to baffle mathematicians. One famous example is the Collatz conjecture, which states that for any positive integer, repeatedly applying specific operations will eventually lead to the sequence 4, 2, 1, 4, 2, 1… | 749 | 3,561 | {"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} | 4.5625 | 5 | CC-MAIN-2023-40 | latest | en | 0.914802 |
https://community.betterlesson.com/community/lesson/6626/telling-time-30-minute-intervals?from=consumer_breadcrumb_dropdown | 1,642,470,948,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320300658.84/warc/CC-MAIN-20220118002226-20220118032226-00354.warc.gz | 250,977,834 | 10,708 | # Lesson: Telling Time: 30 minute intervals
Tara Smith E.l. Haynes Pcs Washington, DC
2843 Views
3 Favorites
### Lesson Objective
Objective: SWBAT tell time to the half hour and be introduced to telling time on a digital clock
### Lesson Plan
Materials Needed: analog clocks (can be made from paper plate or card stock), digital clock (alarm clock), pencil, index cards, and Do Now worksheet.
Vocabulary: digital clock, minutes, one-half, half-past, hour, o'clock, minute hand, and hour hand.
-----
Do Now (5-7 min): Students begin the lesson by reviewing how to tell time to the hour with a worksheet.
Opening (3-5 min): Teacher begins by discussing the differences between digital and a clock with hands. Then discusses the differences between the hour and minute hand. A chart can be made to hang in the classroom.
Teacher then moves to show 3 o'clock on a demonstration clock and asks the class, "What time does this clock show right now?" The teacher then moves the minute hand halfway around the clock to the 6 while the students count by 5s. Once the teacher reaches the 6, then teacher should ask the following questions of the class:
How many minutes have passed?
Where does the minute hand point?
Where does the hour hand point?
What time is it?
Finally, the teacher should state the objective at the end of the opening. For example, "Great job everyone, Today we are going to master telling tiem to the half-hour, or half-past, and spend a short time looking at the similarities between digital and analog clocks. Let's get started!
Direct Instruction (7-10 min): The teacher writes three-thirty, 3:30, and half-past 3 on the board. While continuing to move the minute hand around to the 12 the students count by fives. The teacher explains that these each communicate the same time.
The teacher then presents both an analog and digital clock to the class, each displaying 4:30. Calling on three students the teacher asks for three different ways to say the time. To check for engagement, the teacher can quickly poll the class for which clock they find easier to tell time on. Once results are in, the teacher points out that 4:30 on the digital clock is just as easy as 1:30 on the analog clock, pointing out that "just remember the 6 = 30 minutes!" The students are then asked to practice counting by 5s starting at the 1.
Guided Practice (10 min):
The teacher then shows the class 5:00, and asks a student to tell the time. She then moves the minute hand to 5:30 and asks the following questions of the class:
How much time has passed?
What time is it now?
The teacher then repeats this process 2-5 more times depending on how well the class understands the concept. The students then break into math partners to try the activity on their own.
Independent Practice (10 min):
Students break into groups of 2. Each group has a demonstration analog clock and a ten index cards with times written on them (5:00, 7:00, 3:00, etc). One student displays a time on the index card to the student holding the demonstration clock. The student should move the minute and hour hand to display the time. Then the student should move the minute hand to make the time move to half-past. The student holding the demonstration clock should then ask the other student the following questions: How much time has passed? What time is it? Each student should complete 5 index cards and then switch the demonstration clock to the other student. The teacher should circulate the room to assisting students.
Closing (3-5 min):
Teacher calls then attention of the class back to him/her and gives the students 2 minutes to clean up their workspace. They quickly review the three ways to communication times to the half-hour both orally and on the demonstration clocks. Finally, the students complete the 5 question quiz.
### Lesson Resources
Clock Face for Demonstration Clocks Activity 954 Arrows for Demonstration Clock Activity 754 Do Now_differentiated Starter / Do Now 600 Do Now_time to hour Starter / Do Now 569 | 894 | 4,035 | {"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} | 3.75 | 4 | CC-MAIN-2022-05 | latest | en | 0.926902 |
https://fresherbell.com/quizdiscuss/quantitative-aptitude/if-rs-782-be-divided-into-three-parts-proportional | 1,686,344,141,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224656833.99/warc/CC-MAIN-20230609201549-20230609231549-00671.warc.gz | 315,400,925 | 9,418 | Quiz Discussion
If Rs. 782 be divided into three parts, proportional to 1/2 : 2/3 : 3/4, then the first part is:
Course Name: Quantitative Aptitude
• 1]
Rs. 182
• 2]
Rs. 190
• 3]
Rs. 196
• 4]
Rs. 204
Solution
No Solution Present Yet
Top 5 Similar Quiz - Based On AI&ML
Quiz Recommendation System API Link - https://fresherbell-quiz-api.herokuapp.com/fresherbell_quiz_api
# Quiz
1
Discuss
A policeman starts to chase a thief. When the thief goes 10 steps the policeman moves 8 steps and 5 steps of the policeman are equal to 7 steps of the thief. The ratio of the speed of the policeman and the thief is = ?
• 1]
25 : 28
• 2]
25 : 26
• 3]
28 : 25
• 4]
56 : 25
Solution
2
Discuss
Two numbers are in the ratio 3 : 5 If 9 is subtracted from each the new numbers are in the ratio 12 : 23 The smaller number is
• 1]
28
• 2]
33
• 3]
49
• 4]
55
Solution
3
Discuss
The ratio of the ages of a, b, c, d is 8:10:7:9 respectively. The oldest person is 9 years older than the youngest person. Find the age of a?
• 1]
22
• 2]
23
• 3]
24
• 4]
25
Solution
4
Discuss
What number has a 5:1 ratio to the number 10?
• 1]
42
• 2]
50
• 3]
55
• 4]
62
Solution
5
Discuss
A, B and C enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4. After 2 months, A withdraws half of his capital and after 10 months, a profit of Rs. 378 is divided among them. What is B's share ?
• 1]
160
• 2]
180
• 3]
172
• 4]
144
Solution
6
Discuss
The fourth proportional to 5, 8, 15 is:
• 1]
18
• 2]
24
• 3]
19
• 4]
20
Solution
7
Discuss
The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?
• 1]
3 : 3 : 10
• 2]
10 : 11 : 20
• 3]
23 : 33 : 60
• 4]
Cannot be determined
Solution
8
Discuss
If a: b = 7: 5, b: c = 9: 11, find a: b: c?
• 1]
63: 14: 55
• 2]
63: 45: 55
• 3]
14: 14: 15
• 4]
7: 14: 15
Solution
9
Discuss
If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
• 1]
2 : 5
• 2]
3 : 7
• 3]
5 : 3
• 4]
7 : 3
Solution
10
Discuss
Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:
• 1]
27
• 2]
33
• 3]
49
• 4]
55
# Quiz | 869 | 2,374 | {"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} | 3.640625 | 4 | CC-MAIN-2023-23 | longest | en | 0.81675 |
http://www.ck12.org/analysis/Finding-Zeros-of-Polynomials/?by=community | 1,490,866,236,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218193288.61/warc/CC-MAIN-20170322212953-00546-ip-10-233-31-227.ec2.internal.warc.gz | 463,520,404 | 15,385 | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# Finding Zeros of Polynomials
## If a given value is a root, the function equals zero when x is the value
Levels are CK-12's student achievement levels.
Basic Students matched to this level have a partial mastery of prerequisite knowledge and skills fundamental for proficient work.
At Grade (Proficient) Students matched to this level have demonstrated competency over challenging subject matter, including subject matter knowledge, application of such knowledge to real-world situations, and analytical skills appropriate to subject matter.
Advanced Students matched to this level are ready for material that requires superior performance and mastery.
## Finding Rational and Real Zeros
This lesson shows you how to find all the rational and real-number solutions of a polynomial.
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This indicates how strong in your memory this concept is
0
## Finding Rational and Real Zeros
by EPISD Algebra 2 Team //at grade
This lesson shows you how to find all the rational and real-number solutions of a polynomial.
MEMORY METER
This indicates how strong in your memory this concept is
0
## Factoring and Solving Polynomial Functions
by Millard Public School Omaha, NE (www.mpsomaha.org) //at grade
This lesson shows you how to find all the rational and real-number solutions of a polynomial.
MEMORY METER
This indicates how strong in your memory this concept is
0
## Finding Rational and Real Zeros
This lesson shows you how to find all the rational and real-number solutions of a polynomial.
MEMORY METER
This indicates how strong in your memory this concept is
0 | 370 | 1,712 | {"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} | 3.15625 | 3 | CC-MAIN-2017-13 | latest | en | 0.862406 |
http://mammarosa.eu/bmw-750il-wiring-diagram-diagram | 1,606,180,580,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141169606.2/warc/CC-MAIN-20201124000351-20201124030351-00527.warc.gz | 69,751,417 | 13,460 | # Bmw 750il Wiring Diagram
• Wiring Diagram
• Date : November 24, 2020
## Bmw 750il Wiring Diagram
750il
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Bmw 750il Wiring DiagramWhich Statement Describes the Shaded Area from the Venn Diagram? ? What does the following information to tell you about the shape of a Venn diagram? Well, you know that it is a place which includes a pair of intersecting circles and if there aren't any other circles which areabutting or touching each other in some manner. You can also know that if two circles intersect in this form then they will have two things. The next statement describes the measurements of the Venn diagram. If two circles are set up to coincide with each other in size and a third circle is placed in the middle then the dimension which the fourth circle will probably occupy is unknown. We can say that the purpose that makes up the middle circle is the largest measurement of the Venn diagram. A definition is necessary to discuss this since you could be asking yourself how to look at the middle circle. When this is viewed from anorientation angle then it would look as a square. We could also say that the quantity inside the square is bounded by the horizon and the upper and underside of the Venn diagram. The lines that we draw the Venn diagram are parallel to the lines which connect the points in the corners of this square. The first feature of a Venn diagram is the fact that it can have any number of circles. This is a characteristic that some people do not like about this diagram. They do not enjoy the fact that it can seem with many different dimensions. It is more pleasing to them to think of a specific Venn diagram with just one dimension. The second and third most interesting characteristics of this diagram would be that each circle is located in the corner of the square. This means that the middle of this square is a circle and can be located in the corner. There are no empty points. Therefore, this attribute is particularly exciting as it allows us to produce any form that we need. Now, let us look at the next feature, which is the drawing paper. You have created a good rectangle and you are able to manipulate it with your fingers to create shapes. Do this for some time until you see a pattern appearing. Now draw a place that touches two of the corners of the newspaper. You may now have one circle and two triangles. You may use your fingers to locate the third circle and create the form that you see. The circles are in the corners and are the triangle, but the outside edges are clearly summarized. Ultimately, we can talk about the center line. The center line is joined to every one of the other lines . Due to this, the lines out of the middle line are visually distinct from the lines inside the center line. | 713 | 3,124 | {"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} | 3.28125 | 3 | CC-MAIN-2020-50 | latest | en | 0.942174 |
https://pendulumedu.com/qotd/angle-bisector-of-a-triangle-28-february-2022 | 1,701,330,923,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100172.28/warc/CC-MAIN-20231130062948-20231130092948-00478.warc.gz | 524,355,881 | 53,971 | Question of The Day28-02-2022
In a △ABC, the bisector of ∠B and ∠C meets at I, If ∠A = 120° what is the measure of ∠BIC?
Correct Answer : a ) 150°
Explanation :
According to the question
The bisector of ∠B and ∠C meets at I
∠A = 120°
We know that
If the bisector of ∠B and ∠C of △ ABC meet at I, then ‘I’ will be the incenter of △ ABC
We know that
⇒∠I = 90° + ∠$$A \over 2$$
Substituting the values
⇒ ∠I=90+$$120 \over 2$$
⇒∠I = 150°
Hence, (a) is the correct answer.
0 | 190 | 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": 0, "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} | 4.21875 | 4 | CC-MAIN-2023-50 | latest | en | 0.872099 |
http://nrich.maths.org/public/leg.php?code=31&cl=1&cldcmpid=182 | 1,501,246,840,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500550967030.98/warc/CC-MAIN-20170728123647-20170728143647-00619.warc.gz | 234,346,758 | 10,174 | # Search by Topic
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https://oneconvert.com/unit-converters/length-converter/feet-to-cm | 1,713,548,448,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817442.65/warc/CC-MAIN-20240419172411-20240419202411-00641.warc.gz | 399,821,945 | 31,136 | # Convert foot to centimeter
## What is a Foot?
A foot is a unit of size widely utilized in different methods of dimension. It is predominantly employed in the imperial strategy, which remains prevalent in certain nations, like the USA and the UK. In this system, a foot corresponds to 12 inches or one-third of a lawn.
The notion of the ft as a unit of measurement dates back to ancient times. It has been employed by diverse civilizations throughout history, with differing lengths contingent upon the region. However, the standardized foot is generally acknowledged today as the international foot. It is precisely defined as 0.3048 meters.
Ft has a connection to feet through the historical origin of the term; there is a theory that in ancient times was roughly equal to the weight of one foot.
The foot is frequently employed for measuring height, length, or distance. It is generally utilized in day-to-day life to approximate the height of objects, gauge room dimensions, or ascertain someone's height.
Although numerous nations have embraced the metric technique, the foot still finds usage in certain regions due to historical and cultural factors. It is noteworthy that the metric system is generally favored in scientific and technical fields owing to its simplicity and consistency.
## What is a centimeter?
A centimeter, a metric unit of measurement, represents a fraction of a meter, precisely one-hundredth. The metric structure originated in France during the late 18th century as a response to the need for a standardized and universally accepted size system.
It aimed to alleviate the confusion from using multiple measure systems, facilitating international trade and communication. The metric was meticulously designed, with units interconnected through powers of ten derived from base units.
The centimeter finds extensive application in everyday life, determining clothing sizes and estimating individuals' height. Moreover, it is paramount in scientific analysis, projection, and diverse enterprises that depend on accurate sizes. The metric structure, including the cm, has garnered widespread global adoption, promoting consistency and fostering seamless multinational collaboration.
To conclude, the cm is a fundamental metric unit for measuring length. Its integration into the MS has significantly enhanced measurement precision and streamlined global communication.
## How to Convert foot to cm
The next options can be operated to restore feet to cm:
Formula method:
• There are 0.032808399 feet in one cm.
• Split the feet by 0.032808399 to reach the equal in centimeters.
Decimal point method:
• Diverge the digit of feet by 0.032808399 to transform it into cm.
• Split the cm by 30.48 to reach the equivalent in ft.
Modification Table:
• Create a simple conversion table with the ft importance in one column and their corresponding cm values in the other.
These methods allow you to convert feet to centimeters manually and without relying on an online service.
To convert foot to centimeter , the formula is used,
$C=F*30.48$
where the ft to cm value is substituted to get the answer from Length Converter.
1 ft
=
30.48 cm
1 cm
=
0.0328 ft
Example: convert 15 ft to cm:
15 ft
=
15
x
30.48 cm
=
457.2 cm
## foot to centimeter Conversion Table
Approximately 0.032 feet are equal to one centimeter. This means that a centimeter is about 0.032 times longer than a foot. For example, if 1 cm is measured, it corresponds to about 0.0329 feet. If you measure 150 feet in cm, A conversion factor of 0.032 feet to centimeters establishes the ratio between feet to cm.
foot (ft) centimeter (cm)
0.01 ft 0.3048 cm
0.1 ft 3.048 cm
1 ft 30.48 cm
2 ft 60.96 cm
3 ft 91.44 cm
5 ft 152.4 cm
10 ft 304.8 cm
20 ft 609.6 cm
50 ft 1524 cm
100 ft 3048 cm
1000 ft 30480 cm
### Popular Unit Conversions Length
The most used and popular units of length conversions are presented for quick and free access. | 871 | 3,941 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "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-2024-18 | latest | en | 0.952681 |
http://www.telegraph.co.uk/culture/books/3669867/Mnemony-clever-ways-to-remember-stuff.html | 1,519,213,157,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891813608.70/warc/CC-MAIN-20180221103712-20180221123712-00669.warc.gz | 540,769,306 | 25,243 | Telegraph.co.uk
Wednesday 14 February 2018
# Mnemony clever ways to remember stuff
This year, the runaway favourite for the bestsellers list is I Before E (Except After C) by Judy Parkinson. It is the perfect stocking filler for every parent who has ever worried about what their child is not being taught at school, introducing the concept of mnemonics - simple memory aides that, once learnt, fix the information in the brain. In fact, parents may also want to jog their own memories, too
### SPELLING IT OUT
Is it Affect or Effect?
The RAVEN mnemonic is useful here. Remember: Affect, Verb; Effect, Noun. For example, the woman was affected by the effect of the film.
Desert (as in Sahara) or Dessert (as in crème brûlée)?
The sweet one has two SugarS.
Stationery or Stationary?
Think of the initial 'e' in 'envelope' for stationery', or keep in mind: PEns are items of stationEry. CArs when parked are stationAry.
### THINK OF A NUMBER
The Metric System
To remember the order of kilometre (1,000 metres), hectometre (100 metres), decametre (10 metres), metre, decimetre (1/10 of a metre), centimetre (1/100 of a metre) and millimetre (1/1000 of a metre), say to yourself: King Henry Died Mightily Drinking Chocolate Milk, or Kippers Hardly Dare Move During Cold Months.
The Value of Pi
The Greek letter is a mathematical constant and begins 3.141, although it has an infinite number of decimal places. The traditional way to remind yourself of this is a mnenomic where the number of letters in each word corresponds to a digit. So Pi to six decimal places is: How I wish I could calculate Pi = 3.141592.
### GEOGRAPHICALLY SPEAKING
Learning Directions
The four main compass directions are North, South, East and West. In clockwise order that could be Never Eat Shredded Wheat, or Never Eat Slimy Worms.
The Seven Continents of the World
To remember Europe, Asia, Africa, Australia, Antarctica, North America, South America many swear by the phrase Eat An Apple As A Nice Snack.
The Great Lakes of North America
The five Great Lakes from west to east are Superior, Michigan, Huron, Erie and Ontario. As SMHEO is less than memorable, these short pithy sentences are far more effective: Sally Made Henry Eat Onions, or Sergeant Major Hates Eating Oranges. From east to west, try: Old Elephants Have Much Skin.
### ANIMAL MAGIC
Camels: One Lump or Two?
How do you remember which camel has one hump, and which has two? A Bactrian camel's back is shaped like the letter B - it has two humps. A dromedary's back is shaped like the letter D - so it only has one hump.
Elephants Never Forget
What's the difference between an Indian elephant and an African elephant? It's all in the ears, as the rhyme proves: India's big, and its elephant there features?/ But Africa's bigger with much bigger creatures.
Insect Stings
What home remedies are there if you are stung by a bee or a wasp? Use Ammonia for a Bee sting?/ And Vinegar for a Wasp sting?/ B follows A and W follows V.
### THE WORLD OF SCIENCE
The Common Magnetic Materials
The four commonest magnetic elements are Nickel, Iron, Copper and Steel, which can be remembered by the pithy saying: Nick Irons Creased Shirts.
The Parts of an Atom
PEN is one of the simplest acronyms ever: Proton, Electron, Neutron.
The Order of the Planets
Since August 2006, when Pluto was downgraded, the planets in our solar system are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune - or My Very Educated Mother Just Sent Us Nuts.
Temperatures in Celsius
Here's a simple rhyme to help you decide whether to take an overcoat: "30°C is hot/20°C is nice/10°C is cold/0°C is ice".
### HISTORICAL THOUGHTS
The Greek Philosophers
The names of the three most important Greek philosophers, in order of their dates of birth and influence are: Socrates (469-399 BC), Plato (c.429-c.347 BC), Aristotle (384-322 BC). Imagine them meditating in a health SPA. Or think of the phrase: Smart People of Athens.
British Royal Dynasties
From William the Conqueror to the current Queen there have been eight major royal houses: Norman, Plantagenet, Lancaster, York, Tudor, Stuart, Hanover, Windsor. Or No Point Letting Your Trousers Slip Half Way
The Great Fire of London, 1666
To remember the year, think of the three sixes in 1666 resembling smoking chimneys on the skyline of London.
Nelson's Injuries
In 1794, at the Siege of Cavi, he lost the sight in his right eye. Three years later, at Santa Cruz, his right arm had to be amputated. So think EAR: Eye, Arm - Right.
### RELIGIOUS MATTERS
The Ten Commandments
To remember the list of rules given in the Old Testament, try: One idle damn Sunday, Dad killed cheating thief and lied to cover it. That is: one God; no idols; don't swear; keep the Sabbath; honour your father (and mother); don't kill; don't commit adultery; don't steal; don't bear false witness; don't covet.
The Seven Deadly Sins
To remember Anger, Pride, Covetousness, Lust, Sloth, Envy, Greed, what about All Private Colleges Leave Serious Educational Gaps?
### FINALLY…
Few people need tips on drinking alcohol, but some drinkers swear by the advice offered in this rhyme: Beer on whisky? Very risky! Whisky on beer, never fear… Or this warning quote says it succinctly and honestly: Never mix grape with the grain.
• 'I Before E (Except After C): Old-School Ways to Remember Stuff' by Judy Parkinson (Michael O'Mara) is available for £9.99 + 99p. To order, please call Telegraph Books on 0870 428 4112 or visit books.telegraph.co.uk.
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More from the web | 1,441 | 5,770 | {"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-2018-09 | latest | en | 0.906249 |
https://www.geeksforgeeks.org/check-if-a-tree-can-be-split-into-k-equal-connected-components/?ref=rp | 1,590,797,914,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347406785.66/warc/CC-MAIN-20200529214634-20200530004634-00061.warc.gz | 730,543,755 | 30,081 | # Check if a Tree can be split into K equal connected components
Given Adjacency List representation of a tree and an integer K., the task is to find whether the given tree can be split into K equal Connected Components or not.
Note: Two connected components are said to be equal if they contain equal number of nodes.
Examples:
Input: N = 15, K = 5
Beow is the given tree with Number nodes = 15
Output: YES
Explanation:
Below is the 5 number of Connected Components can be made:
## Recommended: Please try your approach on {IDE} first, before moving on to the solution.
Approach:
The idea is to use Depth First Search(DFS) traversal on the given tree of N nodes to find whether the given tree can be split into K equal Connected Components or not. Following are the steps:
1. Start DFS Traversal with the root of the tree.
2. For every vertex not visited during DFS traversal, recursively call DFS for that vertex keeping the count of nodes traverse during every DFS recursive call.
3. If the count of nodes is equals to (N/K) then we got our one of the set of Connected Components.
4. If the total number of the set of Connected Components of (N/K) nodes is equal to K. Then the given graph can be split into K equals Connected Components.
Below is the implementation of the above approach:
## C++
`// C++ program to detect whether ` `// the given Tree can be split ` `// into K equals components ` `#include ` `using` `namespace` `std; ` ` ` `// For checking if the graph ` `// can be split into K equal ` `// Connected Components ` `int` `flag = 0; ` ` ` `// DFS Traversal ` `int` `DFS(vector<``int``> adj[], ``int` `k, ` ` ``int` `i, ``int` `x) ` `{ ` ` ` ` ``// Intialise ans to 1 ` ` ``int` `ans = 1; ` ` ` ` ``// Traverse the adjacency ` ` ``// for vertex i ` ` ``for` `(``auto``& it : adj[i]) { ` ` ``if` `(it != k) { ` ` ``ans += DFS(adj, i, it, x); ` ` ``} ` ` ``} ` ` ` ` ``// If number of nodes is ` ` ``// greater than x, then ` ` ``// the tree cannot be split ` ` ``if` `(ans > x) { ` ` ``flag = 1; ` ` ``return` `0; ` ` ``} ` ` ` ` ``// Check for requirement ` ` ``// of nodes ` ` ``else` `if` `(ans == x) { ` ` ``ans = 0; ` ` ``} ` ` ``return` `ans; ` `} ` ` ` `// A utility function to add ` `// an edge in an undirected ` `// Tree ` `void` `addEdge(vector<``int``> adj[], ` ` ``int` `u, ``int` `v) ` `{ ` ` ``adj[u].push_back(v); ` ` ``adj[v].push_back(u); ` `} ` ` ` `// Driver's Code ` `int` `main() ` `{ ` ` ``int` `N = 15, K = 5; ` ` ` ` ``// Adjacency List ` ` ``vector<``int``> adj[N + 1]; ` ` ` ` ``// Adding edges to List ` ` ``addEdge(adj, 1, 2); ` ` ``addEdge(adj, 2, 3); ` ` ``addEdge(adj, 2, 4); ` ` ``addEdge(adj, 4, 5); ` ` ``addEdge(adj, 5, 6); ` ` ``addEdge(adj, 5, 7); ` ` ``addEdge(adj, 4, 8); ` ` ``addEdge(adj, 4, 9); ` ` ``addEdge(adj, 8, 11); ` ` ``addEdge(adj, 10, 11); ` ` ``addEdge(adj, 11, 14); ` ` ``addEdge(adj, 9, 12); ` ` ``addEdge(adj, 12, 15); ` ` ``addEdge(adj, 12, 13); ` ` ` ` ``// Check if tree can be split ` ` ``// into K Connected Components ` ` ``// of equal number of nodes ` ` ``if` `(N % K == 0) { ` ` ``// DFS call to Check ` ` ``// if tree can be split ` ` ``DFS(adj, -1, 1, N / K); ` ` ``} ` ` ` ` ``// If flag is 0, then the ` ` ``// given can be split to ` ` ``// Connected Components ` ` ``cout << (flag ? ``"NO"` `: ``"YES"``); ` ` ` ` ``return` `0; ` `} `
## Java
`// Java program to detect whether ` `// the given Tree can be split ` `// into K equals components ` `import` `java.util.*; ` ` ` `class` `GFG ` `{ ` ` ` `// For checking if the graph ` `// can be split into K equal ` `// Connected Components ` `static` `int` `flag = ``0``; ` ` ` `// DFS Traversal ` `static` `int` `DFS(Vector adj[], ``int` `k, ` ` ``int` `i, ``int` `x) ` `{ ` ` ` ` ``// Intialise ans to 1 ` ` ``int` `ans = ``1``; ` ` ` ` ``// Traverse the adjacency ` ` ``// for vertex i ` ` ``for` `(``int` `it : adj[i]) { ` ` ``if` `(it != k) { ` ` ``ans += DFS(adj, i, it, x); ` ` ``} ` ` ``} ` ` ` ` ``// If number of nodes is ` ` ``// greater than x, then ` ` ``// the tree cannot be split ` ` ``if` `(ans > x) { ` ` ``flag = ``1``; ` ` ``return` `0``; ` ` ``} ` ` ` ` ``// Check for requirement ` ` ``// of nodes ` ` ``else` `if` `(ans == x) { ` ` ``ans = ``0``; ` ` ``} ` ` ``return` `ans; ` `} ` ` ` `// A utility function to add ` `// an edge in an undirected ` `// Tree ` `static` `void` `addEdge(Vector adj[], ` ` ``int` `u, ``int` `v) ` `{ ` ` ``adj[u].add(v); ` ` ``adj[v].add(u); ` `} ` ` ` `// Driver's Code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ``int` `N = ``15``, K = ``5``; ` ` ` ` ``// Adjacency List ` ` ``Vector []adj = ``new` `Vector[N + ``1``]; ` ` ``for``(``int` `i= ``0``; i < N + ``1``; i++) ` ` ``adj[i] = ``new` `Vector(); ` ` ` ` ``// Adding edges to List ` ` ``addEdge(adj, ``1``, ``2``); ` ` ``addEdge(adj, ``2``, ``3``); ` ` ``addEdge(adj, ``2``, ``4``); ` ` ``addEdge(adj, ``4``, ``5``); ` ` ``addEdge(adj, ``5``, ``6``); ` ` ``addEdge(adj, ``5``, ``7``); ` ` ``addEdge(adj, ``4``, ``8``); ` ` ``addEdge(adj, ``4``, ``9``); ` ` ``addEdge(adj, ``8``, ``11``); ` ` ``addEdge(adj, ``10``, ``11``); ` ` ``addEdge(adj, ``11``, ``14``); ` ` ``addEdge(adj, ``9``, ``12``); ` ` ``addEdge(adj, ``12``, ``15``); ` ` ``addEdge(adj, ``12``, ``13``); ` ` ` ` ``// Check if tree can be split ` ` ``// into K Connected Components ` ` ``// of equal number of nodes ` ` ``if` `(N % K == ``0``) { ` ` ``// DFS call to Check ` ` ``// if tree can be split ` ` ``DFS(adj, -``1``, ``1``, N / K); ` ` ``} ` ` ` ` ``// If flag is 0, then the ` ` ``// given can be split to ` ` ``// Connected Components ` ` ``System.out.print(flag==``1` `? ``"NO"` `: ``"YES"``); ` `} ` `} ` ` ` `// This code is contributed by Rajput-Ji `
## C#
`// C# program to detect whether ` `// the given Tree can be split ` `// into K equals components ` `using` `System; ` `using` `System.Collections.Generic; ` ` ` `class` `GFG ` `{ ` ` ` `// For checking if the graph ` `// can be split into K equal ` `// Connected Components ` `static` `int` `flag = 0; ` ` ` `// DFS Traversal ` `static` `int` `DFS(List<``int``> []adj, ``int` `k, ` ` ``int` `i, ``int` `x) ` `{ ` ` ` ` ``// Intialise ans to 1 ` ` ``int` `ans = 1; ` ` ` ` ``// Traverse the adjacency ` ` ``// for vertex i ` ` ``foreach` `(``int` `it ``in` `adj[i]) { ` ` ``if` `(it != k) { ` ` ``ans += DFS(adj, i, it, x); ` ` ``} ` ` ``} ` ` ` ` ``// If number of nodes is ` ` ``// greater than x, then ` ` ``// the tree cannot be split ` ` ``if` `(ans > x) { ` ` ``flag = 1; ` ` ``return` `0; ` ` ``} ` ` ` ` ``// Check for requirement ` ` ``// of nodes ` ` ``else` `if` `(ans == x) { ` ` ``ans = 0; ` ` ``} ` ` ``return` `ans; ` `} ` ` ` `// A utility function to add ` `// an edge in an undirected ` `// Tree ` `static` `void` `addEdge(List<``int``> []adj, ` ` ``int` `u, ``int` `v) ` `{ ` ` ``adj[u].Add(v); ` ` ``adj[v].Add(u); ` `} ` ` ` `// Driver's Code ` `public` `static` `void` `Main(String[] args) ` `{ ` ` ``int` `N = 15, K = 5; ` ` ` ` ``// Adjacency List ` ` ``List<``int``> []adj = ``new` `List<``int``>[N + 1]; ` ` ``for``(``int` `i= 0; i < N + 1; i++) ` ` ``adj[i] = ``new` `List<``int``>(); ` ` ` ` ``// Adding edges to List ` ` ``addEdge(adj, 1, 2); ` ` ``addEdge(adj, 2, 3); ` ` ``addEdge(adj, 2, 4); ` ` ``addEdge(adj, 4, 5); ` ` ``addEdge(adj, 5, 6); ` ` ``addEdge(adj, 5, 7); ` ` ``addEdge(adj, 4, 8); ` ` ``addEdge(adj, 4, 9); ` ` ``addEdge(adj, 8, 11); ` ` ``addEdge(adj, 10, 11); ` ` ``addEdge(adj, 11, 14); ` ` ``addEdge(adj, 9, 12); ` ` ``addEdge(adj, 12, 15); ` ` ``addEdge(adj, 12, 13); ` ` ` ` ``// Check if tree can be split ` ` ``// into K Connected Components ` ` ``// of equal number of nodes ` ` ``if` `(N % K == 0) { ` ` ``// DFS call to Check ` ` ``// if tree can be split ` ` ``DFS(adj, -1, 1, N / K); ` ` ``} ` ` ` ` ``// If flag is 0, then the ` ` ``// given can be split to ` ` ``// Connected Components ` ` ``Console.Write(flag==1 ? ``"NO"` `: ``"YES"``); ` `} ` `} ` ` ` `// This code contributed by Rajput-Ji `
Output:
```YES
```
Time Complexity: O(V + E), where V is the number of vertices and E is the number of edges
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# 11ProbHw1 - IEOR 3658 Probability Prof Mariana...
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IEOR 3658 Assignment #1 Probability September 13, 2011 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #1 – due September 21st, 2011 1. Consider two subsets A,B Ω and suppose x 1 ,x 2 A , x 2 B , but x 1 / B . For each of the following statements, determine whether it is true, possibly true (not enough information is available to decide), or false: (a) A B (b) B A (c) A = B (d) A 6 = B (e) ∅ ⊂ A (f) A = Ω (g) B B 2. Draw Venn diagrams and find a simple expression for the following events: (a) ( E F ) ( E F c ) (b) ( E F ) ( E c F ) ( E F c ) (c) ( E F ) ( F G ) 3. Let E , F and G be three events. Find expressions for the following events: (a) only F occurs (b) both E and F but not G occur (c) at least one event occurs (d) none occurs (e) at most two occur 4. Let A,B,C be three subsets of Ω about which it is known that A = B C and also A = B C . For each of the following, state whether it is true, possibly true, or false:
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# Sue: Commercial flights currently contribute more carbon dio
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Status: PLAY HARD OR GO HOME
Joined: 25 Feb 2014
Posts: 179
Location: India
Concentration: General Management, Finance
Schools: Mannheim
GMAT 1: 560 Q46 V22
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Sue: Commercial flights currently contribute more carbon dio [#permalink]
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05 Jul 2014, 00:10
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Sue: Commercial flights currently contribute more carbon dioxide to the atmosphere in one year than does the whole of Africa. If we want to reduce global warming we need to restrict the number of flights we take.
Dave: Did you know that by taking one inter-continental flight you cause more pollution than you would in twelve months of car travel?
Dave’s response to Sue’s comment serves to
A. reinforce Sue’s contention that flights are a major contributor to increased carbon dioxide levels
B. add more weight to her contention that we should reduce the number of flights we take
C. mitigate the force of her argument by suggesting that there is an alternative approach
D. suggest an alternative that will reduce the effect of pollution
E. question whether she really understands the severity of global warming
all the best peeps..hope u all get it right
[Reveal] Spoiler: OA
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Re: Sue: Commercial flights currently contribute more carbon dio [#permalink]
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07 Jul 2014, 02:35
Quote:
Sue: Commercial flights currently contribute more carbon dioxide to the atmosphere in one year than does the whole of Africa. If we want to reduce global warming we need to restrict the number of flights we take.
Dave: Did you know that by taking one inter-continental flight you cause more pollution than you would in twelve months of car travel?
Dave’s response to Sue’s comment serves to
A. reinforce Sue’s contention that flights are a major contributor to increased carbon dioxide levels
B. add more weight to her contention that we should reduce the number of flights we take
Dave is only elaborating Sue's argument by giving a fact. He nowhere comments about reducing the number of flights one takes.
@vards : Could you please post the OE..need to know why is the option A incorrect.
Thank you.
Manager
Status: PLAY HARD OR GO HOME
Joined: 25 Feb 2014
Posts: 179
Location: India
Concentration: General Management, Finance
Schools: Mannheim
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GPA: 3.1
Re: Sue: Commercial flights currently contribute more carbon dio [#permalink]
### Show Tags
07 Jul 2014, 03:30
2
KUDOS
Shalabh09 wrote:
Quote:
Sue: Commercial flights currently contribute more carbon dioxide to the atmosphere in one year than does the whole of Africa. If we want to reduce global warming we need to restrict the number of flights we take.
Dave: Did you know that by taking one inter-continental flight you cause more pollution than you would in twelve months of car travel?
Dave’s response to Sue’s comment serves to
A. reinforce Sue’s contention that flights are a major contributor to increased carbon dioxide levels
B. add more weight to her contention that we should reduce the number of flights we take
Dave is only elaborating Sue's argument by giving a fact. He nowhere comments about reducing the number of flights one takes.
@vards : Could you please post the OE..need to know why is the option A incorrect.
Thank you.
Hello friend..!
here u go..hope it helps u clear ua doubts..
OE
Since Dave’s comments don’t challenge what Sue says, we can eliminate answers E and C (mitigate = lessen). His comments reinforce what she says and so A sounds tempting but is wrong since Dave talks about pollution in general and doesn’t mention carbon dioxide. Of the remaining choices, B is best since Dave does give information that suggests, like Sue, that we should take fewer flights. (D is incorrect mainly because Dave is not talking about the ‘effect’ of pollution. Note how careful you have to be that all the words in an answer are exactly right.
Please consider kudos if it helped u
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Re: Sue: Commercial flights currently contribute more carbon dio [#permalink]
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21 Dec 2015, 23:30
Hello from the GMAT Club VerbalBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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Re: Sue: Commercial flights currently contribute more carbon dio [#permalink] 21 Dec 2015, 23:30
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## Introduction
Pythagorean Theorem is a fundamental concept in geometry that helps us understand the relationship between the sides of a right triangle. It is named after the ancient Greek mathematician Pythagoras, who discovered this relationship. To reinforce and practice this theorem, teachers often provide students with worksheets that contain various problems related to the Pythagorean Theorem. In this article, we will explore the benefits of using Pythagorean Theorem worksheets in PDF format, and provide you with some samples and frequently asked questions.
## The Benefits of Pythagorean Theorem Worksheets PDF
1. Accessibility: Worksheets in PDF format are easily accessible and can be downloaded and printed from any device. Students can work on them at their own convenience, whether it’s in the classroom or at home.
2. Convenience: PDF worksheets can be easily shared with students via email or online platforms. Teachers can also upload them to a learning management system for students to access.
3. Variety: Pythagorean Theorem worksheets PDF come in a wide range of difficulty levels and formats. This allows teachers to cater to the different needs and abilities of their students.
4. Practice: Worksheets provide ample opportunities for students to practice applying the Pythagorean Theorem to solve problems. By regularly practicing with these worksheets, students can reinforce their understanding of the concept and improve their problem-solving skills.
## Sample Pythagorean Theorem Worksheets PDF
Here are five sample Pythagorean Theorem worksheets in PDF format:
1. Worksheet 1: Introduction to Pythagorean Theorem
This worksheet introduces students to the Pythagorean Theorem and provides them with basic problems to solve. It includes a variety of right triangles with known side lengths.
2. Worksheet 2: Applications of Pythagorean Theorem
This worksheet focuses on real-world applications of the Pythagorean Theorem. It includes problems related to finding the distance between two points on a coordinate plane, determining the height of a building, and more.
3. Worksheet 3: Pythagorean Triples
This worksheet explores the concept of Pythagorean Triples, which are sets of three positive integers that satisfy the Pythagorean Theorem. Students are required to identify and generate Pythagorean Triples.
4. Worksheet 4: Word Problems
This worksheet presents word problems that require students to apply the Pythagorean Theorem to solve. It includes problems related to finding the length of a ladder leaning against a wall, determining the distance between two ships, and more.
5. Worksheet 5: Challenging Problems
This worksheet contains challenging problems that require students to think critically and apply the Pythagorean Theorem in unique ways. It includes problems related to irregular shapes, finding missing side lengths, and more.
1. What is the Pythagorean Theorem?
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
2. How do Pythagorean Theorem worksheets help students?
Pythagorean Theorem worksheets provide students with practice problems that help them reinforce their understanding of the concept and improve their problem-solving skills. They also help students apply the theorem to real-world scenarios.
3. Are Pythagorean Theorem worksheets suitable for all grade levels?
Yes, Pythagorean Theorem worksheets can be adapted to different grade levels by adjusting the difficulty of the problems. Teachers can provide simpler problems for younger students and more complex problems for older students.
4. Can I create my own Pythagorean Theorem worksheets?
Yes, you can create your own Pythagorean Theorem worksheets using various online worksheet generators or by designing them manually. However, using pre-made worksheets in PDF format saves time and ensures a consistent quality.
5. Can Pythagorean Theorem be applied only to right triangles?
Yes, the Pythagorean Theorem is specifically applicable to right triangles, where one angle measures 90 degrees. It does not apply to other types of triangles.
## Tags
1. Pythagorean Theorem
2. Worksheets
3. PDF
4. Geometry
5. Right Triangle
6. Math Practice
7. Problem Solving
8. Education
9. Learning Tools
10. Teaching Resources | 888 | 4,472 | {"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} | 3.640625 | 4 | CC-MAIN-2024-22 | latest | en | 0.919977 |
https://schoollearningcommons.info/question/90-of-40-30-of-then-the-the-value-of-is-24829127-19/ | 1,652,973,079,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662529538.2/warc/CC-MAIN-20220519141152-20220519171152-00253.warc.gz | 566,472,788 | 14,185 | ## √90% of 40 = 30% of x, then the the value of x is??
Question
√90% of 40 = 30%
of x, then the the value of x is??
in progress 0
8 months 2021-09-23T10:20:02+00:00 1 Answer 0 views 0 | 80 | 188 | {"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} | 3.296875 | 3 | CC-MAIN-2022-21 | latest | en | 0.731016 |
https://maeckes.nl/Term%20GB.html | 1,716,906,227,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059139.85/warc/CC-MAIN-20240528123152-20240528153152-00329.warc.gz | 307,682,606 | 2,205 | < 1 2 >
### Term
A term is a basic algebraic expression that consists only of multiplications and divisions with numbers and letters.
##### Explanation
The numbers are called the coefficients. Both the figures and each letter can be raised to a power. In an algebraic expression with various terms these are separated by plus signs and minus signs.
##### Example 1
In a polynomial
the successive terms are added together.
##### Example 2
The binomium can be written as
where all terms have combinations.
##### Example 3
A square with three terms must be calculated term-by-term from left to right
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc | 171 | 667 | {"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-2024-22 | latest | en | 0.89905 |
https://mathoverflow.net/questions/266565/variation-of-the-green-function-with-respect-to-the-metric | 1,563,761,910,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195527458.86/warc/CC-MAIN-20190722010436-20190722032436-00328.warc.gz | 478,206,088 | 31,162 | Variation of the Green function with respect to the metric
Consider a (closed) Riemann surface and let $G(x,y)$ be the Green function of the Laplace-Beltrami operator. We can informally identify $G$ with the two-point correlation function for the Gaussian random field:
$$G(x,y)=\left<\phi(x)\phi(y)\right>=\frac{1}{Z} \int \mathcal{D}\phi\;\phi(x)\phi(y) \exp\left(-\frac{1}{2}\int \left| \nabla\phi(z)\right|^2 dV_g(z)\right).$$ This is easy to vary with respect to the metric $g_{\mu\nu}$:
$$\delta G(x,y)=-\frac{1}{2}\int dV_g(z)\;\delta g^{ij}(z)\left<\phi(x)\phi(y) \nabla_i\phi(z)\nabla_j\phi(z)\right>_c,$$ where $\left<\right>_c$ is the connected correlation function (the disconnected diagram $x\leftrightarrow y,z\leftrightarrow z$ is cancelled by the variation of the partition function). We can use Wick's theorem to compute this, getting
$$\boxed{\frac{\delta G(x,y)}{\delta g^{ij}(z)}=-\nabla_{[i} G(x,z)\nabla_{j]} G(z,y)}$$
(derivatives w.r.t. $z$). This formula looks wickedly similar to the Hadamard variation formula for the variation of the boundary of the domain in flat space. Yet I haven't been able to find any mentions of this in the mathematical literature.
Furthermore, if we define the regularized Green's function (a.k.a. the Robin function) by $$G^R(x)=\lim_{y\to x} \left(G(x,y)-\frac{1}{2\pi}\ln d(x,y)\right),$$ where $d(x,y)$ is the local geodesic distance, then I'm conjecturing the following variational formula: $$\frac{\delta G^R(x)}{\delta g^{ij}(z)}=-\nabla_{i} G(x,z)\nabla_{j} G(x,z)-\frac{1}{4\pi}\nabla_i \nabla_j G(x,z).$$ The second term is motivated by the well-known formula for conformal variations (where it is $\frac{1}{4\pi}\delta_x(z)$) and seems to be necessary to cancel the second order pole in this variation. Edit: this guess turned out to be wrong, see my answer below.
$$\frac{\delta G(x,y)}{\delta g^{\mu\nu}(z)}=(-\nabla_{[\mu}G(z,x)\nabla_{\nu]}G(z,y)+\frac{1}{2}g_{\mu\nu}(z)\nabla_\rho G(z,x)\nabla^\rho G(z,y))+\frac{1}{2V}(G(x,z)+G(z,y))g_{\mu\nu}(z).$$
The traceless part in the brackets represents the quasiconformal variation (which in complex conformal coordinates reduces to just $8\partial_z G(z,x)\partial_z G(z,y)$, as found in the literature). The last "trace" term is the conformal variation, which is not probed by the path integral because it only shows up at finite volume.
I believe this formula to be correct based on the independence of conformal and quasiconformal variations. The resulting tensor is also divergence-free away from $x$ and $y$, as required by general covariance. The more difficult part is proving the following conjecture for the Robin function:
$$\frac{\delta G^{R}\left(x\right)}{\delta g^{\mu\nu}\left(z\right)}=-\nabla_{\mu}G\left(z,x\right)\nabla_{\nu}G^R\left(z\right)+\frac{1}{2}g_{\mu\nu}(z)\nabla_\rho G(z,x)\nabla^\rho G^R(z)+\frac{1}{V}G\left(z,x\right)g_{\mu\nu}\left(z\right)-\frac{1}{4\pi}\nabla_{\mu}\nabla_{\nu}G\left(z_{i},z\right)-\frac{\delta(x,z)}{4\pi}g_{\mu\nu}(z)+\frac{1}{8\pi V}g_{\mu\nu}(z)+\frac{1}{2V}f_{\mu\nu},$$ where $f_{\mu\nu}$ is an unknown symmetric traceless tensor defined by $$\nabla^\mu f_{\mu\nu}=\nabla_\nu G^R,$$ as required by the divergence-free condition on the metric variation of $G^R$. This result is based on the exact formula $$G^R(z)=\frac{1}{4\pi}\int G\left(x,y\right)R\left(y\right)\mathrm{d}V(y)+\frac{1}{V}\zeta^{R}\left(1\right)-c,$$ where $\zeta^{R}(s)=\zeta(s)-\frac{V}{4\pi}\frac{1}{s-1}$ and $\zeta$ is the spectral zeta function of the positive Laplace-Beltrami operator, $c=\frac{1}{2\pi}\left(\gamma-\ln2\right)$ (reference below).
Steiner, Jean, A geometrical mass and its extremal properties for metrics on $S^2$, Duke Math. J. 129, No. 1, 63-86 (2005). ZBL1144.53055. | 1,283 | 3,745 | {"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} | 3.09375 | 3 | CC-MAIN-2019-30 | latest | en | 0.770743 |
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# Lesson Plan 1 _ Coon, C. M.
- Fall 2012
Lesson Plan
Title: Algebraic System of Equations Grade Level: Ninth Grade Time Frame: 45 50 minutes Connection to Standards: NYS Common Core Standards for Mathematics Reasoning with Equations & Inequalities Solve systems of equations: 7. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = 3x and the circle x2 + y2 = 3. Rationale/Purpose: Students should have knowledge of how to solve functions of equations. Students should also know how to the find slope and the y-intercepts. Both of these concepts will help with furthering knowledge in solving systems of equations. For this lesson students will learn how to graph their equations and be able to find the point of intersection graphically and then by solving them algebraically. Students will also be able to state whether the functions are parallel or not by solving them graphically first and then algebraically. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I. Objectives The students will be engaged with the lesson given they are writing down notes and asking questions when they are uncertain about the topic. The students will get 85% - 100% of the Bell Work correct. The students will participate during the lesson by answering questions given by the teacher, whether that is giving thumbs up for understanding, asking what the definitions mean or how to use a certain equation. 85% - 100% of the students will understand the material when given the question. A-REI
## Lesson Plan 1 _ Coon, C. M. - Fall 2012
The students will work on their class work when given time to work on it during class. They will ask questions if they do not understand the material. The class work will be collected at the end of the period and 85% - 100% of the questions will be correct because of time during the class to ask question. Students will use a straight edge when graphing their 4 to 5 equations, with at least 4 of the 5 correct. 85% - 100% of the students will come in with their homework completed.
II.
Required Materials During the class I will need one of the three, a chalkboard, a white board or a smartboard, and I will need worksheets, graph paper, and straight edges.
III.
Bell Ringer: Evaluate the following set of equations and state their slope and y-intercept. 1. 2. 3. B. Step by Step 1. Introduction Go over bell ringer Ask if there are any similarities the students see in the slopes and y-intercepts 2. Body Have students graph Bell Ringer problems Find any intersections between equations as a class on the board Give a worksheet and have students try problems on their own or with a small group
## Lesson Plan 1 _ Coon, C. M. - Fall 2012
Go over algebraic way to find intersections as a class Try examples on the board together Try examples from given class work sheet Ask students if they noticed any similarities between slopes
3. Closure Go over what we did during class Ask questions about the two ways to find intersection and how to tell if the lines are parallel or intersecting. IV. Differentiation A. Advanced If there is a student that is picking up on the material quickly when graphing the equations, I will have the student try to think of a faster way to find the intersections or how to tell if a line will be parallel. If the student excels with finding a faster way to find intersection I will give the student three or four equations to try to find intersections within one problem. I can also have the student tell me how by just looking at the equation if they will know if the equations are parallel or intersecting. V. Homework, if Applicable or Follow-up
Give the students a homework sheet that has similar problems that we did in class. As they go through the homework ask the students to keep in mind any similarities that they may notice about the equations when working on the questions. VI. Assessment/Evaluation A. Assessment of Student(s) Collect the class work to check for understanding and participation See if the students were engaged or not, by if they were participating asking questions, paying attentions or asking each other for help during class work time
## Lesson Plan 1 _ Coon, C. M. - Fall 2012
B. Self-Assessment (Teacher) Make notes to how successful or unsuccessful the lesson was for student comprehension. Make note of anything that needs to be changed for next time o Easier/ harder questions o More examples/ less examples o To give homework or not depending on understanding
Adapted by Snowden, P. L. (2012) from: Carmichael, S. B. (Project Coordinator). (2012). Common core curriculum maps: English language arts, grades 9-12. San Francisco. Jossey-Bass. | 1,051 | 4,808 | {"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} | 3.828125 | 4 | CC-MAIN-2019-39 | latest | en | 0.926015 |
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×
# See solution: 18 Write a polar equation of a conic with the focus at the origin and the
ISBN: 9781305270336 484
## Solution for problem 8 Chapter 10.6
Single Variable Calculus: Early Transcendentals | 8th Edition
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Problem 8
18 Write a polar equation of a conic with the focus at the origin and the given data
Step-by-Step Solution:
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Tuesday, April 5, 2016 Chapter 12 Leadership and Follower-ship 80%-85% are followers 15%-20% are leaders - Leadership - process of guiding and directing the behavior of people in the work environment • formal leadership - officially sanctioned leadership based on the authority of a formal position • informal leadership - unofficial leadership accorded to a person by other members of the organization - Management and Leadership • management - planning and budgeting - organizing and staffing - controlling and problem solving • leadership - setting a direction for the organization - aligning people with that direction - motivating people - Early Trait Theo
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##### ISBN: 9781305270336
Since the solution to 8 from 10.6 chapter was answered, more than 227 students have viewed the full step-by-step answer. Single Variable Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781305270336. The answer to “18 Write a polar equation of a conic with the focus at the origin and the given data” is broken down into a number of easy to follow steps, and 18 words. This textbook survival guide was created for the textbook: Single Variable Calculus: Early Transcendentals, edition: 8. This full solution covers the following key subjects: . This expansive textbook survival guide covers 95 chapters, and 5427 solutions. The full step-by-step solution to problem: 8 from chapter: 10.6 was answered by , our top Calculus solution expert on 03/19/18, 03:29PM.
#### Related chapters
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https://www.exploredatabase.com/2022/02/machine-learning-mcq-hierarchical-agglomerative-clustering-single-and-complete-linkage.html | 1,670,538,802,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711368.1/warc/CC-MAIN-20221208215156-20221209005156-00026.warc.gz | 826,655,051 | 22,557 | Please visit, subscribe and share 10 Minutes Lectures in Computer Science
# Multiple choices questions in Machine learning. Interview questions on machine learning, quiz questions for data scientist answers explained, machine learning exam questions, question bank in machine learning, Hierarchical agglomerative clustering, How to calculate the pairwise distance using single linkage? Complete linkage agglomerative clustering
## Machine Learning MCQ - Hierarchical agglomerative clustering - single linkage and complete linkage
1. After three iterations of Hierarchical Agglomerative Clustering using Euclidean distance between points, we get the 3 clusters: C1 = {2, 4}, C2 = {7, 8} and C3 = {12, 14}. What is the distance between clusters C1 and C2 using Single Linkage and Complete Linkage?
a) 2, 2
b) 3, 4
c) 3, 6
d) 5, 6
************************ | 200 | 860 | {"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-2022-49 | latest | en | 0.770296 |
https://m.ebrary.net/35908/engineering/conservation_laws_with_particle_interaction_collisions | 1,596,940,856,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738380.22/warc/CC-MAIN-20200809013812-20200809043812-00418.warc.gz | 403,509,212 | 4,544 | Home Engineering Computational Transport Phenomena of Fluid-Particle Systems
# Conservation Laws with No Particle Interaction and Collisions
By substituting for p mass, momentum, and energy, the corresponding conservation laws are easily obtained from Maxwell’s equation (2.30). For a case with no particle interaction/collisional contribution,
## Conservation of Mass
Let p = m, since nm = esps = p
## Conservation of Momentum
Let p = mc
Since Pk = p(CC) and (C) = 0
## Conservation of Solid-Phase Fluctuating Energy
Let p = 1 mc2
Note: qk = |p C2Cfc = 2nm(C2C) and since в = C2)
It is easy to derive the conservation equation for the fluctuating energy from Eq. (2.38) as
where Pk = p(CC).
Similarly, we can obtain the equations for the stress tensor (CC). This equation is similar to the Reynolds stress equations in single-phase turbulent flow. However, in the Reynolds stress equation, the average is over a time interval. Here, the averaging is over the velocity space. These averages are not equal as experimentally shown by Tartan and Gidaspow (2004). If we include rotation (Goldshtein and Shapiro 1995) in addition to the translation presented here, we can obtain a balance for the rotational temperature, as in single-phase fluids (Condiff et al. 1965).
Related topics | 309 | 1,294 | {"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-2020-34 | latest | en | 0.885136 |
http://math.stackexchange.com/questions/205486/in-how-many-ways-can-we-colour-n-baskets-with-r-colours?answertab=oldest | 1,462,127,026,000,000,000 | text/html | crawl-data/CC-MAIN-2016-18/segments/1461860116878.73/warc/CC-MAIN-20160428161516-00081-ip-10-239-7-51.ec2.internal.warc.gz | 184,823,013 | 18,333 | In how many ways can we colour $n$ baskets with $r$ colours?
In how many ways can we colour $n$ baskets using up to $r$ colours such that no two consecutive baskets have the same colour and the first and the last baskets also have different colours?
For example, if we take $N=5$ and $r = 4$, and represent the colours by $R,B,Y$ and $G$, then $\langle R,Y,B,G,Y\rangle$ is a valid arrangement whereas $\langle R,R,B,G,Y \rangle$ and $\langle G,B,R,Y,G\rangle$ aren't.
It's is not difficult to solve this one by brute force; however, I would like to see a combinatorial approach. Any thoughts?
-
can someone give a brute force approach?? – user43585 Oct 4 '12 at 10:38
Let $a_n$ be the number of arrangements in which the first and last basket have different colours, and $b_n$ the number of arrangements in which they have the same colour, where in either case adjacent baskets can't have the same colour. Then by adding an admissible basket at the end of such an arrangement we obtain the recurrence
\begin{align} a_{n+1}&=(r-2)a_n+(r-1)b_n\;,\\ b_{n+1}&=a_n\;, \end{align}
and substituting the second equation into the first yields
$$a_{n+1}=(r-2)a_n+(r-1)a_{n-1}\;.$$
The characteristic equation is
$$\lambda^2-(r-2)\lambda-(r-1)=0\;,$$
with solutions $\lambda=-1$ and $\lambda=r-1$. Thus we have
$$a_n=c_1(-1)^n+c_2(r-1)^n\;,$$
and the initial conditions $a_1=0$ and $a_2=r(r-1)$ yield
$$-c_1+c_2(r-1)=0\;,\\ c_1+c_2(r-1)^2=r(r-1)$$
with solution $c_1=r-1$, $c_2=1$. The desired number of arrangements is therefore
$$a_n=(-1)^n(r-1)+(r-1)^n\;.$$
To get the number of arrangements that use all $r$ colours, you can use inclusion/exclusion:
$$\sum_{k=0}^r(-1)^{r-k}\binom rk\left((-1)^n(k-1)+(k-1)^n\right)\;,$$
and the sum over the first term vanishes, leaving
$$\sum_{k=0}^r(-1)^{r-k}\binom rk(k-1)^n\;.$$
-
Why? To get the number of arrangements that use all r colours, you can use inclusion/exclusion: $$\sum_{k=0}^r(-1)^{r-k}\binom rk\left((-1)^n(k-1)+(k-1)^n\right)\;,$$ I don't understand. – Schwarz Nov 7 '12 at 13:09
@Schwarz: Do you understand inclusion/exclusion in general? – joriki Nov 7 '12 at 22:15
I don't understand inclusion/exclusion in general – Schwarz Nov 8 '12 at 2:29
@Schwarz: It would have been more efficient to say that in the first place instead of letting me guess what it is about that statement that you don't understand. This isn't the right place to explain inclusion/exclusion to you; I'd suggest that you read the Wikipedia article, and if you still have a question afterwards, you can ask it on this site as a separate question. – joriki Nov 8 '12 at 5:59
This is now the subject of a separate question. – joriki Nov 8 '12 at 12:35 | 860 | 2,692 | {"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": 1, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2016-18 | latest | en | 0.823113 |
https://gitter.im/FreeCodeCamp/Help/archives/2018/07/23 | 1,561,398,181,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627999620.99/warc/CC-MAIN-20190624171058-20190624193058-00312.warc.gz | 445,958,297 | 34,295 | 23rd
Jul 2018
Karma Drukpa
@coderkarma
Jul 23 2018 00:08
@thekholm80
question
Karma Drukpa
@coderkarma
Jul 23 2018 00:14
NeverMind i got it.
Karma Drukpa
@coderkarma
Jul 23 2018 00:56
``````function average(...nums) {
let sum = 0;
for (const num of nums){
sum += num;
}
return sum/nums.length;
}
console.log(average(2, 6));
console.log(average(2, 3, 3, 5, 7, 10));
console.log(average(7, 1432, 12, 13, 100));
console.log(average());``````
@thekholm80 wondering do you have another way of finding this.
Kyle Holm
@thekholm80
Jul 23 2018 00:57
another way of finding what?
Karma Drukpa
@coderkarma
Jul 23 2018 00:57
also my last test is not passing
avg
Kyle Holm
@thekholm80
Jul 23 2018 00:58
i find averages by adding everything up and dividing by the number of items
Karma Drukpa
@coderkarma
Jul 23 2018 00:58
finding average of unlimited amount of numbers
Kyle Holm
@thekholm80
Jul 23 2018 00:59
what does `console.log(average());` return?
Karma Drukpa
@coderkarma
Jul 23 2018 00:59
nan
not a number
Kyle Holm
@thekholm80
Jul 23 2018 00:59
what should it return?
Karma Drukpa
@coderkarma
Jul 23 2018 00:59
0
Kyle Holm
@thekholm80
Jul 23 2018 00:59
so do that then
if there are numbers passed as parameters, return the average. otherwise, return 0
Karma Drukpa
@coderkarma
Jul 23 2018 01:00
oh i see, i could just add 0 while returning
``````function average(...nums) {
let sum = 0;
for (const num of nums){
sum += num;
}
return sum/nums.length || 0;
}
console.log(average(2, 6));
console.log(average(2, 3, 3, 5, 7, 10));
console.log(average(7, 1432, 12, 13, 100));
console.log(average()); //0``````
I Could use || operator there?
Kyle Holm
@thekholm80
Jul 23 2018 01:01
did you try it?
Karma Drukpa
@coderkarma
Jul 23 2018 01:01
trying..
it worked .
Kyle Holm
@thekholm80
Jul 23 2018 01:02
good job
Karma Drukpa
@coderkarma
Jul 23 2018 01:02
but is that good way of doing it?
Kyle Holm
@thekholm80
Jul 23 2018 01:03
sure
Karma Drukpa
@coderkarma
Jul 23 2018 01:04
ok. thanks
yesterday question, i had to consult with my friend
to get it done. how did you do it ?
closures question?
Kyle Holm
@thekholm80
Jul 23 2018 01:07
``````def running_average():
history = []
def get_average(num):
nonlocal history
history.append(num)
return round(sum(history) / len(history), 2)
return get_average``````
Karma Drukpa
@coderkarma
Jul 23 2018 01:12
is that in python ? does append works like push?
wow that is different
Kyle Holm
@thekholm80
Jul 23 2018 01:12
oh duh
``````function runningAverage() {
let history = [];
return num => {
history.push(num);
return Math.round((history.reduce((a, b) => a + b) / history.length) * 100) / 100;
}
}``````
sorry
Karma Drukpa
@coderkarma
Jul 23 2018 01:15
nice
Anand Potukuchi
@anandpotukchi
Jul 23 2018 04:25
when you wke up in the morning to see 250 unread messages -_-
Karma Drukpa
@coderkarma
Jul 23 2018 04:25
lol
Anand Potukuchi
@anandpotukchi
Jul 23 2018 04:40
howndo I optimize codepen to show fcc test suites
Note: Did'nt bother reading anything - just clicked on the fcc pen
suvi
@sumaya99
Jul 23 2018 04:52
`````` <div class="visitorsdiv">
<div> <label for="visitor">Visitors</label>
<input type="number" id="visitor" name="visitors" value="2"></div>
<div> <label for="check-in">Check-in</label>
<input type="date" id="check-in" name="Check-in" placeholder=""></div>
<div>
<label for="check-out">check-out</label>
<input type="date" id="check-out" name="Check-out" placeholder=""></div>
<input class="continue" type="button" value="Continue">``````
</div>
how can i create an input type date that in the placeholder it should be show day/month/year
but i doesn't work i try all the way
the placeholder turned like that
Rahul
Jul 23 2018 05:28
@sumaya99 You can start with a simple (and working) solution like date-util for polymer that allows you to use a tag like this one:
<date-util format="dd/MM/yyyy"></date-util>
or
<input type="date" data-date="" data-date-format="DD MMMM YYYY">
Anand Potukuchi
@anandpotukchi
Jul 23 2018 06:19
shoudl the survey form be just a design or should it be functional?
coz i guess the one in the example is
Anand Potukuchi
@anandpotukchi
Jul 23 2018 06:57
nobody online?
Claudio Restifo
@Marmiz
Jul 23 2018 07:13
As long as it suffice the user stories you'll be good to go @anandpotukchi
@diomed
Jul 23 2018 07:19
where is 90es.css
Prakash Kumar
@ThePrakashKumar
Jul 23 2018 08:14
What is the problem?
@ezioda004
Jul 23 2018 08:31
@ThePrakashKumar Typo in `arr[i].lenght`
1LifeLess
@1LifeLess
Jul 23 2018 13:40
Please tell me i didn't go nuts, on FreeCodeCamp => splice is working like slice
``````let test= [0,1,2,3,4,5,6].splice(0,2);
console.log(test);``````
can someone go to his account and test it?
@ezioda004
Jul 23 2018 13:49
@1LifeLess `.splice()` also mutates the array and returns the removed chunk.
1LifeLess
@1LifeLess
Jul 23 2018 13:50
@ezioda004 ..hu...so if i want to return the mutated array and not the removed chunk?
@ezioda004
Jul 23 2018 13:51
@1LifeLess
``````const arr = [1, 2, 3];
arr.splice(0, 1);
console.log(arr); //[2, 3]``````
1LifeLess
@1LifeLess
Jul 23 2018 13:52
@ezioda004 huuu.. i see, thank you! :-)
Marc
@MWBauer
Jul 23 2018 14:27
Hey folks. I was wanting to get your opinion on something. I'm making an app that requires a database of recipes. Do you think it better to let the user input the recipe or hardcode it into the app?
@diomed
Jul 23 2018 14:52
@MWBauer porque no los dos?
@ezioda004
Jul 23 2018 14:52
Thats a good taco recipe.
@diomed
Jul 23 2018 14:53
ice cream as well
Marc
@MWBauer
Jul 23 2018 14:55
@diomed no porque
also, no hablo
Kyle Holm
@thekholm80
Jul 23 2018 15:04
yo soy un hombre con mucho queso
@ezioda004
Jul 23 2018 15:17
You need soy sauce?
Kyle Holm
@thekholm80
Jul 23 2018 15:17
Spur
Jul 23 2018 15:17
May i join ? :)
@ezioda004
Jul 23 2018 15:19
Yes, we're about to apply soy sauce to Kyles head on his demand.
Kyle Holm
@thekholm80
Jul 23 2018 15:20
do i get a vote on this plan?
@ezioda004
Jul 23 2018 15:21
Too late hombre.
Karma Drukpa
@coderkarma
Jul 23 2018 15:21
hhahahahha
nalinpuri
@nalinpuri
Jul 23 2018 16:36
hello pls tell me what i am doing wrong in https://codepen.io/nalinpuri/pen/qKeKGL
I want to put the survey at the topbelow the white background at center.
how can i do that
survey text
gishy1
@gishy1
Jul 23 2018 16:38
hello world !!
i need help spacing my nav elements
i tried botttom-border in css and it failed
Ene Catalin
@EneCatalin
Jul 23 2018 16:45
maybe this ?
gishy1
@gishy1
Jul 23 2018 16:47
oh because i summoned the flex god i must continue along that line ?
got you
but is should be able to access the nav elements,no?
Ene Catalin
@EneCatalin
Jul 23 2018 16:49
I suck at css and remmebered flex-boxes
figured they have some auto-sizing
gishy1
@gishy1
Jul 23 2018 16:53
hmm is that why i cant seem to get my boxes to size properly
Yago Estévez
@yagoestevez
Jul 23 2018 16:59
@gishy1 looks like your using flexbox properties in a non-flex element
Also, there are typos
space-between no inbetween
Yago Estévez
@yagoestevez
Jul 23 2018 17:24
Anyone know what this "like" thing is about? https://giant-chronometer.glitch.me/
I wanted to figure it out myself, but Google Finance seems to be down and I the example project above doesn't work...
Kyle Holm
@thekholm80
Jul 23 2018 17:37
@yagoestevez kind of weird, but it looks like the site is tracking user's 'likes' on each stock, recording it and then if you search for 2 stocks it will show how one's 'likes' compares to the other
kind of like some financial popularity contest
@diomed
Jul 23 2018 17:40
@yagoestevez are u on glitch
like registered and all
Alexander R Bott
@Abott1222
Jul 23 2018 17:47
Kyle Holm
@thekholm80
Jul 23 2018 17:47
@Abott1222 oh geez
i don't know how i feel about that
Alexander R Bott
@Abott1222
Jul 23 2018 17:58
@thekholm80 ?
they picked an easy target to emulate, windows lol
Kyle Holm
@thekholm80
Jul 23 2018 17:58
they say they 100% wrote it from scratch - my concern would be security
Alexander R Bott
@Abott1222
Jul 23 2018 17:58
they arent trying to copy linux
Kyle Holm
@thekholm80
Jul 23 2018 17:58
windows isn't best known for being secure, and they have billions invested
Alexander R Bott
@Abott1222
Jul 23 2018 17:58
cant be much worse than windows
^
yup lol
its an interesting project though
Kyle Holm
@thekholm80
Jul 23 2018 17:59
linux is super secure, but they have a massive community of developers
and i'm all about a gaming platform that doesn't require windows. if someone builds that, I'm all for it
Alexander R Bott
@Abott1222
Jul 23 2018 17:59
ya I would wait until they react v1 though hahaha
anyway back to work. just thought you would find that interesting
Kyle Holm
@thekholm80
Jul 23 2018 18:00
it's a good find, thanks
@diomed
Jul 23 2018 18:14
:hearts: favorite & forget
Ene Catalin
@EneCatalin
Jul 23 2018 18:19
at some point opening the saved pages becomes a scary task
Alexander R Bott
@Abott1222
Jul 23 2018 18:35
2 many media queries
Kyle Holm
@thekholm80
Jul 23 2018 18:57
@diomed x
@diomed
Jul 23 2018 18:58
ah yes, my old wallpaper
how nice to see it again
Kyle Holm
@thekholm80
Jul 23 2018 18:59
i'm sad that i'll never be that cool
idris
@idris12
Jul 23 2018 18:59
hello
Laura Veee
@Cyclokitty
Jul 23 2018 19:00
That is a glorious wallpaper
idris
@idris12
Jul 23 2018 19:02
how do i make the lower one on the same line with the first
the lower line is a ul but i used float
@diomed
Jul 23 2018 19:03
by showing code coz we aint screenshot readers
Kyle Holm
@thekholm80
Jul 23 2018 19:04
i used paint
@diomed
Jul 23 2018 19:04
haha.good1
fixed it
@thekholm80 u misunderstood him, he wanted those lower ones above, not above one lowered. lol
so. borked it
Kyle Holm
@thekholm80
Jul 23 2018 19:05
turn it upside down?
@idris12 joking aside, it's hard to suggest anything when we don't know anything about your code
idris
@idris12
Jul 23 2018 19:07
here is the css
@diomed
Jul 23 2018 19:08
thanks for all the screenshots. lol
@idris12 ever heard of codepen.io or https://jsfiddle.net
idris
@idris12
Jul 23 2018 19:09
Kyle Holm
@thekholm80
Jul 23 2018 19:14
how's this?
idris
@idris12
Jul 23 2018 19:20
its very good but the "us" on contact goes underneath
i want all of them to be on one line
Kyle Holm
@thekholm80
Jul 23 2018 19:21
oh i was aiming more at a 'proof of concept' not perfection
you may have to adjust to make it perfect
idris
@idris12
Jul 23 2018 19:22
ok thank you also that justify content is a new one for me
i havent seen that before
Kyle Holm
@thekholm80
Jul 23 2018 19:23
you could put your margins back and use `justify-content: space-between;` instead
@diomed
Jul 23 2018 19:26
watch us rock your world with our web design capabilities
O_o
that may be an overstatement for now
idris
@idris12
Jul 23 2018 19:29
@thekholm80 still no luck
i tried adjusting the margin to move it to the left maybe it will readjust
but its stuck there
@diomed haha
Yago Estévez
@yagoestevez
Jul 23 2018 19:32
@thekholm80 sorry, I was away. So likes are about that... Aright then. Thanks!
@diomed I'm registered on glitch, yes.
@diomed
Jul 23 2018 19:34
@yagoestevez are u mby on support forums
Yago Estévez
@yagoestevez
Jul 23 2018 19:35
Nope
spaniarddev
About that... How can I change my name there? :D
@diomed
Jul 23 2018 19:38
u should ask that on support forums :smiling_imp:
@diomed
Jul 23 2018 19:49
### screech screech
Yago Estévez
@yagoestevez
Jul 23 2018 19:50
hah
Definitely
@diomed
Jul 23 2018 19:51
@yagoestevez if u register, could u ask smth for me?
Kyle Holm
@thekholm80
Jul 23 2018 19:52
\$10 says it's "why did you ban diomed?"
Vaibhav Singh
@vaibhavsingh97
Jul 23 2018 19:52
Hi developers! Help me understand better what difficulty do you face working on side projects, how do you manage your tasks and build a team? What tools and platforms do you use?
bit.ly/2LIGzIN
Yago Estévez
@yagoestevez
Jul 23 2018 19:54
lol
@diomed
Jul 23 2018 19:54
@vaibhavsingh97 I use tools and platforms
Kyle Holm
@thekholm80
Jul 23 2018 19:55
that's an ugly bird
@diomed
Jul 23 2018 19:56
such a bully
Fay Vor
@phavor
Jul 23 2018 20:21
How can I change the color scheme of the ubuntu's default terminal to a color scheme I downloaded from github?
Kyle Holm
@thekholm80
Jul 23 2018 20:22
did the github repo have any instructions?
Fay Vor
@phavor
Jul 23 2018 20:23
Yea, I should go to `preference -> color ->` and then click on `load preset`
but the problem is that, when I click on the color tab there is no `load preset` or anything like that, when I try to change the color, the best I see there is `custom`. There is no way to open the file-system and load any file
Kyle Holm
@thekholm80
Jul 23 2018 20:26
can you share the link to the repo?
Fay Vor
@phavor
Jul 23 2018 20:26
@thekholm80 am trying to configure the new `zsh` and `oh-my-zsh` which I installed earlier today
Kyle Holm
@thekholm80
Jul 23 2018 20:28
did you do this part?
Drop the cobalt2.zsh-theme file in to the ~/.oh-my-zsh/themes/ directory.
Open up your ZSH preferences at ~/.zshrc and change the theme variable to ZSH_THEME=cobalt2.
Fay Vor
@phavor
Jul 23 2018 20:29
yes I did
Kyle Holm
@thekholm80
Jul 23 2018 20:29
and it saved correctly?
Fay Vor
@phavor
Jul 23 2018 20:30
yes I used nano. so I did the normal `ctrl x` `y` and `enter` to save the modification
Kyle Holm
@thekholm80
Jul 23 2018 20:30
i :heart: nano
Fay Vor
@phavor
Jul 23 2018 20:30
lol same here. I can't seem to get a hold on it's pal vim
Kyle Holm
@thekholm80
Jul 23 2018 20:31
i've never even bothered to try
editing config files with nano is too easy
Fay Vor
@phavor
Jul 23 2018 20:31
:laughing:
Kyle Holm
@thekholm80
Jul 23 2018 20:31
i'm not sure what this iTerm2 is
In iTerm2 access the Preferences pane on the Profiles tab.
Fay Vor
@phavor
Jul 23 2018 20:32
It's a terminal app for MacOx users
Kyle Holm
@thekholm80
Jul 23 2018 20:32
that explains why i don't know what it is lol
Fay Vor
@phavor
Jul 23 2018 20:32
zsh is supposed to be the remedy for other linux distros
Kyle Holm
@thekholm80
Jul 23 2018 20:34
i'm looking through zsh's docs to see if they have linux help
Fay Vor
@phavor
Jul 23 2018 20:34
aiit
Kyle Holm
@thekholm80
Jul 23 2018 20:36
cobalt2.itermcolors is for anyone who uses iTerm2 and wants the colours.
Fay Vor
@phavor
Jul 23 2018 20:36
That means, linux users can't use it?
Kyle Holm
@thekholm80
Jul 23 2018 20:37
maybe?
Fay Vor
@phavor
Jul 23 2018 20:39
it :broken_heart: my heart
Kyle Holm
@thekholm80
Jul 23 2018 20:41
sorry. it may be possible to get it working - but i can't spend the rest of the day trying to figure it out
Fay Vor
@phavor
Jul 23 2018 20:45
I'd keep looking around
1LifeLess
@1LifeLess
Jul 23 2018 21:24
damn it didn't let me to add description, well it's React, in JS the way to get date is "new Date()" but in React it throw an error, why?
The solution is to NOT use the "new" keyword, can someone please explain why?
alpox
@alpox
Jul 23 2018 21:27
@1LifeLess `Date()` returns a string with the current time. `new Date()` returns a new date object
1LifeLess
@1LifeLess
Jul 23 2018 21:28
@alpox hmm..i see now...many thanks!
PeterWebDev
@PeterWebDev
Jul 23 2018 23:33
quick review on portfolio please looking to refine it | 5,445 | 15,137 | {"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} | 2.875 | 3 | CC-MAIN-2019-26 | latest | en | 0.748255 |
https://community.powerbi.com/t5/Desktop/Measure-Calculate-until-last-week/m-p/2214400 | 1,643,438,364,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320300573.3/warc/CC-MAIN-20220129062503-20220129092503-00701.warc.gz | 227,282,688 | 95,679 | cancel
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Frequent Visitor
## Measure Calculate until last week
I'm trying to get a measure right.
Certain grades are given and I want to see how they progress every week. For that I try to write a measure that has the average of the grade number and filters until the last week.
Unfortunately I cannot get a dynamic week date where the measure has the current week minus 1 (so that it shows the average until last week). Hope someone can help out.
test =
calculate(AVERAGE(table[number]),WEEKNUM('Calendar'[Date])-1)
1 ACCEPTED SOLUTION
Solution Sage
Hi @MdB ,
First, create a weeknumber column in your calendar table:
WeekNumber = WEEKNUM('Calendar'[Date],2)
Then create a measure like this:
test =
var Maxdate = WEEKNUM(TODAY(),2)-1
return
CALCULATE(AVERAGE('Table'[Number]),'Calendar'[WeekNumber]<=Maxdate)
If I answered your question, please mark it as a solution to help other members find it more quickly.
Solution Sage
Hi @MdB ,
First, create a weeknumber column in your calendar table:
WeekNumber = WEEKNUM('Calendar'[Date],2)
Then create a measure like this:
test =
var Maxdate = WEEKNUM(TODAY(),2)-1
return
CALCULATE(AVERAGE('Table'[Number]),'Calendar'[WeekNumber]<=Maxdate)
If I answered your question, please mark it as a solution to help other members find it more quickly. | 334 | 1,334 | {"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-2022-05 | latest | en | 0.88659 |
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https://geoplatt.com/algebra-online-course-algebra-operation/ | 1,601,511,861,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600402130531.89/warc/CC-MAIN-20200930235415-20201001025415-00066.warc.gz | 364,554,724 | 12,255 | # Algebra Online Course: Algebra Operation
Integers Worksheet Algebra Answer Key : step by step to Start from zero to hero & 18 Reason Why You Really to Practice Much more!
The most importand Thing Concerning algebra and Math is you really need to practise so as to understand the Theories.
There are a great deal of algebra books, tutorials, interactive courses, online tutors and classes which can help you a lot, however minus some homework and training you’re sure to neglect.
You cannot remember the 1000s of algebra theories and equations without any truly understand what each equation really means. What is the reason behind every algebra concept.
An integral element is to just take modest actions. For example learn one algebra equation, then practise it for two or three days, then move ahead into the next.
Move on only if you truly feel comfortable in everything you’ve heard. Every single time you move on into this following algebra concept boost the difficulty of the equations or even the exercises you’re trying to address.
Practice this procedure and so on you’ll observe your brain will have the ability to absorb math and algebra quicker and easier. You will begin to enjoy it.
The following thing is that algebra takes you to apply certain rules. You’ll come across these elementary rules in a lot of equations and algebra concepts. The more you practise the basic algebra rules the better you will become at learning more and different difficult algebra concepts.
Lots of folks learning algebra miss out to the basic rules. In the end they screw up everything. Keep in mind, rules are all everywhere. Our society is based on rules. Same goes for algebra. Treat algebra rules like a game and you will like it.
You might wind up wondering. . Why can I find math and algebra? That is a good question. You have to ask your self this question prior to going on. Algebra will allow you to solve problems, make conclusions, apply strategies and a lot more. If you’d like your skills to worth gold then you have to know math and especially algebra. If you’d like your mental powers to attain top level then you’ve got to learn algebra.
If you want math then you definitely know this to be able to go to advanced mathematics you need to know the fundamentals of algebra. Algebra is anywhere in your daily life.
This really is an excellent advantage when trying to learn algebra. Why? As it is possible to get the a real problem and turn it into an algebra equation or concept.
Consistently ask your self. . why? Here is just a simplified example. You walk on the street and you see a girl carrying a birdcage. Inside the bird cage you will find 4 little critters. Unexpectedly the cage’s door opens and among these birds leaks. You can turn this occurrence into a easy algebra equation:
#### 3 – 1 = two
See the reason? Given that’s the very first step! Then it’s going to soon be easy to show live complicated situations in to algebra concepts. Your mind will soon become knowledgeable about the idea. And so on you will be able to show your entire life to algebra!
## Algebra for Beginners: Tips To Become an Algebra Star
Many folks are kind of poor in the area of algebra mathematics. A whole lot of them read books, attend lessons and find out more about the web to obtain information, interactive lessons and web sites which might help them improve their algebra skills.
Interactive learning (e.g. on the web classes ) is a lot more fun and entertaining than reading algebra books. However, can interactive instruction independently help you become an algebra celebrity?
In order to understand math you have to understand the algebra concepts. Learn the fundamentals of algebra effectively, proceed on to harder issues, learn them. Then move forward to even more complex problems. Therefore on.
In the event that you do these steps again and again, your brain will start to adjust and you will enjoy it. In reality, in the event you successfully learn a few algebra concept then you will wish to own more.
Practise is really importand at algebra. You can not expect to learn everything from online classes or turorials. You want to go through the concepts and the principles of algebra again and again as a way to learn them.
An effective technique is to simply take your algebra books and write all the equations and concepts inside a sheet of paper. Keep each concept on a different sheet. Read notes and write down your opinion for every single or algebra concept. Keep this notebook in your pocket and keep filling it using notes. You may not like it in the beginning, but the longer you practise and use this personal algebra notebook the better for you.
You shouldn’t be hasty. Don’t rush. Curl up. Learning Algebra requires time. Take a seat, attempt to work out the concepts. You are one of many. We’ve been around. Welldone! You’ve already created your Algebra Notebook. In case you didn’t recognize this can be really importand.
Here are some more hints:
– you will find thousands of Algebra books on the market that break up algebra to its easiest components. Maybe not many books are good but a few are very unique.
(Tip: Visit college bookstores. They definitely have algebra texts or books that you could borrow or take away). Don’t stick to one book or lesson. Many books explain some algebra theories much better than others. Select a variety of novels or internet courses.
You can find a live coach. Eveeybody needs a tutor from time to time! It’s going to be much easier to study from someone who’s already knowledgeable about the notions of algebra. Some schools provide zero price coaches to help you during the basics of algebra. Just be certain that you receive a one.
Join a site and proceed through some online classes. You may cherish it! There are online communities where folks discuss their algebra issues and help each other. There are plenty of websites that provide free online math courses. Combine them. Have some fun.
Even if you’re a member of the many popular interactive algebra communities you still must research and synthesize a lot. You may combine studying and practising with interactive courses that will be fun. Interactive courses.
r labs, Algebra Tutorials and Books are great but what’s really importand and effectual is to do some assignments.
Remember that the trick is practise. It’s all about understanding the rationale for the concepts and also the steps. By time you will realize that it is a lot easier to adhere to the task. I would like one of the best of luck and hope you’ll become the next algebra star.
## Learn Integers Worksheets [ Adding Integers Different Signs Worksheet ]
If you’ve spent time in Canada in January, you’ve probably experienced a negative integer firsthand. Banks like you to keep negative balances in your accounts, therefore they could charge you loads of interest. Deep sea sailors spend all kinds of period in negative integer land. There are a number of reasons why a comprehension of integers is helpful even if you’re not likely to pursue a bookkeeping or heavy sea diving livelihood.
One tremendously essential reason is that you’ll find lots of senior high school math topics that will rely upon a strong knowledge of integers as well as the rules associated with them.
We’ve included a few hundred integers tips with this particular page to help encourage your students in their pursuit of comprehension. You may also want to receive some of those giant integer number lines to create if you are a teacheror print off a few of our integer number lines. You may even project them on your own whiteboard or make an overhead transparency.
For homeschoolers or those with just one or a few students, the newspaper versions should do. The other thing which we recommend are all integer chips a.k.a. two-color counters. Read about them below.
### Coordinate grid paper
Number lines:
Integer number lines may be used for various mathematics activities including operations with integers, counting, comparing, ordering, etc..
## Assessing & Ordering Integers Worksheets
For students who are just starting with integers, it’s extremely helpful when they may use an integer online to compare integers and to observe how the placement of integers works. They should quickly understand that negative numbers are counter-intuitive since they are probably quite utilised to larger absolute values significance larger numbers.
The opposite is the case, obviously, with negative numbers. Students need to be able to recognize easily that an optimistic number is obviously greater than a negative number and also that between two negative integers, usually the one with the lower absolute value is in fact the increased number. Have students practice with these integers worksheets and follow up with the close proximity comparing integers worksheets.
## Comparing pairs of integers in close proximity
By closing proximity, we mean that the integers being contrasted differ very modest in value. Depending on the scope, we have enabled various differences between the two integers being compared. From the first set at which the range is -9 to 9, the gap between the two numbers is necessarily 1.
With the biggest range, a difference as high as 5 is allowed. These tips can help students further enhance their ability to visualize and conceptualize the notion of negative numbers and also will act as a base for all the additional worksheets with these pages.
Have you heard about two-color counters and also just how they can make your life easier while helping students know integers better? Sure, you could simply teach them exactly the the ++, +-+, also — rules, but chances are they would have no color in their own lives.
Two-color counters are usually plastic chips that typically come with yellowish on one side and red on the opposite hand. They do come in other colors, so you’ll have to employ your own colors in our description.
Adding with two-color counters is truly quite straightforward. You mimic the first number with a pile of chips reversed into the appropriate side and also you model the next number having a pile of chips reversed into the right side, then you mash them completely, simply take out the zeros (if any) and sew! You have your own answer. As there are a few confused faces in the audience, let’s clarify a little further.
As soon as we state, the correct sidewe suggest usage red for negative numbers and yellowish for favorable numbers. You would model -5 together with five red 7 and chips with seven yellow chips. Mashing them together ought to be right forward. As you’re adding, you put the 2 sets of chips together, being careful not to flip some of them at the process, obviously. Taking out the zeros means removing as many pairs of yellow and reddish chips as you can. You try this because -1 and 1 if added together equals zero (this will be identified as the zero principle).
If you eliminate the zeros, you don’t change the solution whatsoever. The benefit of removing the zeros, nevertheless, is the fact that you end up with only one color and as a consequence, the reply to the integer question.
Reference
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Please teach me by explaining to me what this question is asking me to do!
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https://kurz-grossbottwar.de/which/31231952f75fd3fc13d | 1,660,856,685,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882573399.40/warc/CC-MAIN-20220818185216-20220818215216-00380.warc.gz | 318,496,640 | 12,340 | Compound Interest Formula. AS/NZS 1170.2 Wind Load Calculation Example; ASCE 7-10 Wind Load Calculation Example; EN 1991-1-4 Wind Load Calculation Example; NBCC 2015 Snow Load Calculation Example; ASCE 7-16 Wind Load Calculation Example for L-shaped Building; IS 875-3 Wind Load Calculation Example; Wind and Snow Loads for Ground Solar Panels ASCE 7-16 You may also find the following Engineering calculators useful. Torque: M = F*D 2 / 2; Moment of inertia of strip: I x = B*t 3 / 12; Length of strip: L = *n*(D 1 + D 2) / 2; Angle of twist: = [1.25*M*L / (E*I)]*(180 / ); Bending stress: = [2M*(t / 2)] / I x By analyzing the forces and motion of the soil microbody according to the steady-state. Online calculator and formulas for calculating a helix curve Online calculator. If we try 15 steps, we will have 27 cm treads and 20 cm risers. A spiral bevel gear set requires matching of hands; left-hand and right-hand as a pair. This graph is interactive. Tangent Offset. A spiral is a curve in the plane or in the space, which runs around a centre in a special way.
Spiral Curves. The length of the helix spiral is the hypotenuse of a triangle whose other sides are the circumference of the round part and the lead distance formed by the width of the spiral. A round duct with a cross sectional area of 0.6m2 has a perimeter of 2.75m. P denotes Pitch.
1.17 (1/26/98) Changed formula constants to use 1976 US/ICAO Standard Atmosphere instead of 1962 US Standard. calculation of geometrical features of a spiral bevel gear pair is developed according to ISO 23509:2006 standard. R - Radius of Simple Curve. Spiral Curve | Surveying and Transportation Engineering Formula: i = L / ( 6RL s) Where, i - Tangent deflection angle to any point on the curve. You can make a spiral by two motions of a Stair Layout Formula. The Golden Ratio (also known as golden mean, golden section (Latin: sectio aurea), extreme and mean ratio, medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut, and golden number) is the formula that rules arts.. To determine the length of helix/spiral bar, the following formula is used :-. In mathematics, the Fibonacci numbers, commonly denoted F n , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones.The sequence commonly starts from 0 and 1, although some authors omit the initial terms and start the sequence from 1 and 1 or from 1 and 2. To calculate the length d = Winding depth in inches. The rise in prices of goods and services is referred to as inflation. N = Number of turns. (Note: All input Metric units are converted to English units for Numbers; Blog; Shop; Calculator Compount Interest. So, Total Length of the spiral bar is. That way, the equation for a golden spiral with an initial radius of one will be: The growth factor b is defined as b = (ln ) / right, where right is a right angle. The length of a spiral can be calculated as. Next, an ana-logue face-hobbed bevel gearset is derived that in a third step is converted to a non-generated (Formate) version. On-chip spiral inductors with variable line width layouts are known for their high quality factor (Q-factor). Transition Spirals. You may also find the following Engineering calculators useful. A Golden Spiral created from a Golden Rectangle expands in dimension by the Golden Ratio with every quarter, or 90 degree, turn of the spiral. l = Spiral arc from the TS to any point on the spiral (l = Ls at the SC). The Fibonacci Sequence can be written as a "Rule" (see Sequences and Series). Art Lesson 4 Back to the Art Lessons List What is the Golden Ratio. Try for free the constructor/estimator Spiral Staircase (Rotating / Round / Screw) on stairs-calculator.com. Formulas: r = a * n = / 360 r 1 = a * 360 = r / n l = a / 2 * [ * 1 + + ln( + 1 + ) ] p = l() + r for n1 p = l() - l(-360) + r 1 for n>1 d = a * + a * (-180) for >180 = ( + 2) / [ a * ( + 1) 3/2] Simple Curve Formulas. Delta(s) = 0.005 * D * Ls = 0.005 * 2.0000 * 200.00 = 2.0000(ddd) ~ 2-00-00(dms) u = Chord * Sin(Delta(s) * 2 / 3) / n = H/P = Overall Height of the column/pitch = 10/2 = 5. Straight conductor. The Length of a Helix calculator computes the linear length of a spiral of helix if it was pulled straight. In this video you will learn How to find length of Spiral Bar.
Calculation of the project begins with what will be the length of the circle, which according to the rules of geometry is calculated by the formula L = 2R. Calculate Spiral Reinforcement Ratio For a Short Spiral Column With Small Eccentricity: Calculation: Designer/Checker: Input: Metric Units. The Fibonacci numbers may be defined by the recurrence relation Note: This calculation is designed for spiral springs with fixed ends of the spring. Interest Calculator. In addition to a good aesthetic, the ramp is an architectural element that must be able to overcome a certain gap, in a functional and safe way. Function and Types. A logarithmic spiral with 3 turnings and k = 0,19. decimal places. Inside Plumb = tread points vertically (plumb). While a circular curve has a radius that is constant, a spiral curve has a radius that varies Below is a Computations. = AS/NZS 1170.2 Wind Load Calculation Example; ASCE 7-10 Wind Load Calculation Example; EN 1991-1-4 Wind Load Calculation Example; NBCC 2015 Snow Load Calculation Example; ASCE 7-16 Wind Load Calculation Example for L-shaped Building; IS 875-3 Wind Load Calculation Example; Wind and Snow Loads for Ground Solar Panels ASCE 7-16
This of course leads to exponential growth, generally asociated with some kind of spiral structure.
Spiral Curves. The Formula for the Circumference of a Spiral. Elevation Point Of Vertical Curve On Road Calculator. the Calculator will be available after changes in the relevant parameters. Here, n = number of turns of the helical stirrup ( no. To use this online calculator for Flat Spiral Spring Controlling Torque, enter Young's Modulus (E), Width of Spring (b), Thickness Of Spring (t) & Length of spring (L) and hit the calculate button. BLM Irregular Boundary Adjustment. Simple Interest ; Compound Interest ; Trignometric Calculators. L = Length of In this paper, a simplified method for the calculation of a mutual inductance of the planar spiral coil, motivated from the Archimedean spiral, is presented. Notice the recursive formula: An =2An . Round duct and rectangular duct comparison. Pitch (in perpendicular distance) = 3. =nC2 + P2. Calculate the spiral delta and tangent distance to the Spiral Point of Intersection (SPI). Zero Spiral Type Bevel Gears: In zero type of bevel gears, there is no offset teeth design and spiral geometry in teeth. This graph is equilibrium conditions of moment of momentum, Makes A Spiral. The Archimedean spiral is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular These formulas enable an initial theoretical calculation of the spring. Corrected equation for dst12 in intersection section. Spiral Calculations.
(Should have been the distance formula in the first section!) July 24, 2014 at 2:57 pm. Based on an analysis of ohmic and eddy-current losses, we first derive an analytical formula for the metal resistance calculation of a spiral inductor. 9.1 Spring design. to such objects. Inductance. This spiral is found in nature! If one chooses for () a bounded function the spiral is bounded, too. Trigonometric Formulas; Curves. For example 5 and 8 make 13, 8 and 13 make 21, and so on. Here are the simple handbook formulas for the calculation of inductances, which Coil32 does not use, but which can be useful for electronics hobbyists and students. The development of a helix is a straight line. Geometry; Geometry 1D; A helix or helical lines play a role in the representation of spiral stairs, threads and twist drills, for example. Here is how the Flat Spiral Spring Controlling Torque calculation can be explained with given input values -> 2.083E+10 = (10000000000*2*(5^3))/(12*10). Simple Curve Formulas. t = b + = 6 + 5 = 11 mm. Get professional drawings, number of materials, adaptive 3D. A design system is selected now my flow rate is .6 ms , 2 fps 1/5 their flow rate so I would expect a wheel size of around 50cm ( 2.8m / 5 ) with 20 coils to reach my 10m head ( apparently each coil is double the head ? The fundamental equation is as follows: Steel pipe single meter weight calculation (kg / m): W = (outer diameter wall thickness) * wall thickness * 0.02466 = 2408 * 12 * 0.02466 = 712.57 kg / m. The unit for the calculated theoretical weight of steel is kilo grams (kg). Here, n denotes number of turns.
When we make squares with those widths, we get a nice spiral: Do you see how the squares fit neatly together? Planar spiral spring is important for the dimensional miniaturisation of motor-based elastic actuators. 0.58) = 23.8 m. Next, lets determine a pitch of the spiral, while setting the sheet thickness as =5 mm. Curve Layout. Create Coordinates. Spiral staircases save valuable square meters because they occupy a much smaller area than a conventional staircase. Example 1. Select On the basis of Neumanns formula [8] and the equation of the Archimedean spiral [1,13], accurate expressions of mutual inductance of Archimedean spiral coils applicable to arbitrary pitches are derived in this paper, and the corresponding numerical calculation methods are Feedback. But most generally used bevel gear spirals 35 degrees. INSTRUCTIONS: Choose units and enter the following: (H) Height of helix(P) Pitch: distance between turns(D) Diameter of helixLength of Helix (L): The calculator returns the length of the helix in meters. Spiral Curve Calculation - Free download as PDF File (.pdf), Text File (.txt) or read online for free. The Volume of core in Short Axially Loaded Columns with Helical Ties formula is defined as the volume of the core of the given column is calculated using Volume of core = (pi /4)*((Diameter of core)^(2))* Pitch of spiral reinforcement.To calculate Volume of core in Short Axially Loaded Columns with Helical Ties, you need Diameter of core (D c) & Pitch of spiral reinforcement (p). Tip: Detailed information on the calculation of spiral springs can be found in the theoretical section of help. All dimensions are entered in inches and all outputs will be in inches. (by Doug Haluza) 1.16 Direction of Spiral - required Clockwise going up Counter-Clockwise going up. The ramp calculation is one of the most important steps to determine the success of its functionality, a fact that usually causes concerns among several professionals.. Degree of Pitch (calculated): Arc Length (calculated): Notes: * Albina must have Plan View Radius, Overall Height of Bent Section Arc in Plan/Overal Run, Direction of Spiral to produce a spiral. At the beginning of this chapter the development of a face-milled, conjugate spiral bevel gearset is conducted. In this video you will learn How to find length of Spiral Bar. How do you calculate the pitch of a spiral spring? Also, the minimum number of teeth is generally 12. Therefore, the Section IV. Made unit conversions more accurate. Number of spirals = length / spacing of spiral+ 1 = 10000 / 200 + 1 = 50 + 1 = 51 nos. Putting all the value in given A: Total accrued amount i.e.
model. L = length of spiral (m, ft ) n = number of rings. Real And Reactive Power Calculator. C = 2 * Pi * R = Pi * D. This is the well-known formula for the circumfence of a circle, and it can partially be used to figure out the circumference of a spiral! Use this calculator to find the inductance of a multi-layer coil. Parallel conductors ( current in opposite directions) Radius Through Three Points. Formula. The logarithmic spiral is a spiral whose polar equation is given by r=ae^(btheta), (1) where r is the distance from the origin, theta is the angle from the x-axis, and a and b are arbitrary We take this nice of Stair Layout Formula graphic could possibly be the most trending topic gone we allocation it in google plus or facebook. Spiral Curve Offsets. The way of design procedure used in this book allows to define dimensions of a spring with a certain degree of looseness. Parallel conductors ( current in one direction) rw. Real And Reactive Power Calculator. Table 2 The calculations for spiral bevel gears in the Gleason system. The function () of a spiral is usually strictly monotonic, continuous and unbounded.For the standard spirals is either a power function or an exponential function. L - Length of spiral from tangent to any point. Electric Potential Play with it. Spiral: In the plane Click Total Length = No Of Spiral x Radius Of The Pile = 51 x 1.5m = 76.5 meters Solution of a Simple Curve. We have noticed an unusual activity from your IP 207.46.13.50 and blocked access to this website.. C denotes circumference of spiral. I want to make Screw of following. In step four Spiral Curve Layout. Electric Potential Energy Calculator. Ls =Total length of spiral curve from TS to SC (typically the superelevation runoff length, see Section 2A-2 and Section 2A-3). Furthermore, the value of C is calculated by the subsequent formula: C = D = Simple Interest ; Compound Interest ; Trignometric Calculators. Derivation of the exact formula. What is the Inflation Formula? how to calculate the flat form of a flight of screw conveyor. The function () of a spiral is usually strictly monotonic, continuous and unbounded.For the standard spirals is either a power function or an exponential function. Transition Curve Deflection Angle Necessary for Passenger Safety.
of the pitch in total pile length ). However, when the stiffness calculation of the spring arm is based on simple beam bending theory, the results possess substantial errors compared with the stiffness obtained from finite-element analysis (FEA). I find it difficult to apply the formula: 0,1,1, 2, 3, 5, 8. Trip Fuel Consumption Calculator. Formula created by French architect Franois Blondel (1618-1686) verifying coherence between the step height and the going. Spiral reinforcement is used in circular column, pier or pile.
Dparameter. Lathe Operation Cutting Time Calculator. Spiral angles are generally between 20-45 degrees.
. For instance, leaves on the stem of a flower or a branch of a tree often grow in a helical pattern, spiraling aroung the branch as new leaves form further out. D = spiral outside diameter (m, ft ) d = spiral inside diameter or opening (m, ft ) Solution of a Simple Curve. The pressure angle of general spiral bevel gears is 20 degrees. Approach: We can easily find the recursive nature in the above problem. Belt Load. Use this online calculator to know how to use spiral curve to gradually change the curvature and super elevation of road and this is also known as transition curve. L s - Length of spiral. Please enter angles in degrees, here you can convert angle units. Different spirals follow. Spiral Curve Layout. Trigonometric Formulas; Curves. viv rosser says. Outside Stringer = tread points winding up and around OUTSIDE of stairs from top of first rise to upper floor. Section IV. If were working with degrees, This opens in a new window. Abstract. BASIC FORMULAS. A suitable bounded function is the arctan function: . The ideal value is 630mm (24.8"). Therefore, there are five numbers of turns in that spiral bar or column. The person can reach n th stair from either (n-1) th stair or from (n-2) th stair. Refer to the bottom of the page for explanation of input variables and other notes. Here is the TRIR formula: Number of recordable incidents x 200,000 / total number of hours worked in your business over one year. The figure of 200,000 is used as this represents the number of hours 100 full-time employees would log during 50 40-hour weeks during a Here are a number of highest rated Stair Layout Formula pictures upon internet. Choose the number of decimal places, then click Calculate. Single layer Planar spiral coil inductor calculator : The first approximation is based on a modification of an expression developed by Wheeler; the second is derived from electromagnetic principles by approximating the sides of the spirals as current-sheets; and the third is a monomial expression derived from fitting to a large database of inductors (and the exact inductance values). Comparison of Arc and Chord Definitions. please you explain and send calculation. To calculate the exact length of the spiral, we write the equation of the curve in polar coordinates: Here is the distance between the axis as a function of the angle . is average velocity x average velocity / 64.4 = 2.55 foot head. Most of them are produced by formulas. r = Coil radius in inches. x6 for max efficenty size = 9.3 foot dia wheel or 2.8m. Reply. The numerical example used the correct formula. If one chooses for () a bounded function lSpiral length. A spiral curve can be used to provide a gradual transition between tangent sections and circular curves. The Minimum length of a spiral formula is defined as a three-dimensional curve that turns around an axis at a constant or continuously varying distance while moving parallel to the axis is calculated using The calculation formula of the spiral: $$p=[ \frac {l^2}{n^2} - ^2d^2]$$ $$l=n[p^2+(d)^2]$$ In the formula: n - the number of spirals. The fundamental equation is as follows: Steel pipe single meter weight calculation (kg / m): W = (outer diameter wall thickness) * wall thickness * 0.02466 = 2408 * 12 * 0.02466 = 712.57 kg / m. The unit for the calculated theoretical weight of steel is kilo grams (kg). It deems that the errors arise from the spiral length term in the calculation formula. Direction of Spiral - required Clockwise going up Counter-Clockwise going up. 51 nos of the spiral are completed for spiral bar in this length of given column or pile. All equations in Table 2 are also applicable to Gleason bevel gears with any shaft angle. A rectangular duct with an equal cross sectional area has a perimeter of 3.87m. See: Nature, The Golden Ratio, and Fibonacci. Fermats Spiral; API. One of the measures of inflation is the Consumer Price Index Consumer Price Index The Consumer Price Index (CPI) is a measure of the average price of a basket of regularly used consumer commodities compared to a base year. Using the useful line, you will see that the calculated length is 4.18 meters where people will step on. The cutting length of the spiral stirrup is given by the formula. How to calculate cutting length of spiral stirrups and spiral stirrup are used in piles and round column and number of turns and circumference. Fermat's Spiral - The details. Interest Calculator. Method 1: The first method uses the technique of recursion to solve this problem. Hence, for each stair n, we try to find out the number of ways to reach n-1 th stair and n-2 th stair and add them to give the answer for the n NUMBER OF SPIRAL.
Vertical Curves. Because of the: relatively complex i formulas' Scribd is the world's largest social reading and publishing site. We identified it from well-behaved source. The rectangular duct therefore requires more metal for its construction, this adds more weight and costs to the design. At one time when the load is known per square foot: P= G 1 x C (in feet)x W (in feet) At one time when load is known by pounds per hour: P=G 2 / (S x 60) x C (in feet) Annual Nominal interest Rate in percent: r: Rate of interest per year r = R / 100: t: Time period involved in years(i.e. 1. The vertical distance between two step Degree of Pitch (calculated): Arc Length (calculated): Notes: * Albina must have Plan View Radius, Overall Height of When the spiral angle bm = Please confirm that you are not a robot calculation results. L = Inductance in microhenrys (H) Coil dimensions for calculating inductance. Its submitted by paperwork in the best field. Curve Layout. L = 3.14 n (D + d) / 2 (1) where. How is that done? Inside Level = tread points around INSIDE LEVEL, On the Sponsored. C = circumference of the l = Coil length in inches. In this paper, we present an analytical approach to facilitate the design of such inductors. tion of the flow in the gear theoretical developments with definitions of formula symbols. . What is the formula to calculate the length of a spiral? Multi-Layer Coil Inductance Calculator. Note: This calculator is also suitable for flat spiral (pancake, spiderweb, etc.) Trip Fuel Consumption Calculator. Ppitch. The Rule. Spiral reinforcement is used in circular column, pier or pile. BLM Grant Boundary Adjustment. Transition Spirals. However, the final spring design and its functionality must always be tested and confirmed using Spiral Calculations.
I want formula and calculaion of screw flight cutting drawing. | 4,900 | 20,871 | {"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": 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-2022-33 | latest | en | 0.834894 |
https://www.learner.org/series/learning-math-geometry/what-is-geometry/part-c-folding-paper-40-minutes/ | 1,685,899,169,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224650201.19/warc/CC-MAIN-20230604161111-20230604191111-00053.warc.gz | 923,096,572 | 25,408 | # What Is Geometry? Part C: Folding Paper (40 minutes)
## Session 1, Part C
### In This Part:
• Constructions
• Constructing Triangles
• Concurrencies in Triangles
• More Constructions
Geometers distinguish between a drawing and a construction. Drawings are intended to aid memory, thinking, or communication, and they needn’t be much more than rough sketches to serve this purpose quite well. The essential element of a construction is that it is a kind of guaranteed recipe. It shows how a figure can be accurately drawn with a specified set of tools. A construction is a method, while a picture merely illustrates the method.
The most common tools for constructions in geometry are a straightedge (a ruler without any markings on it) and a compass (used for drawing circles). In the problems below, your tools will be a straightedge and patty paper. You can fold the patty paper to create creases. Since you can see through the paper, you can use the folds to create geometric objects. Though your “straightedge” might actually be a ruler, don’t measure! Use it only to draw straight segments. See Note 4 below.
Throughout this part of the session, use just a pen or pencil, your straightedge, and patty paper to complete the constructions described in the problems. Here is a sample construction with patty paper to get you started:
To construct the midpoint of a line segment, start by drawing a line segment on the patty paper.
Next, fold the paper so that the endpoints of the line segment overlap. This creates a crease in the paper.
The intersection of the crease and the original line segment is the midpoint of the line segment.
### Constructions
To construct a perpendicular line, consider that a straight line is a 180° angle. Can you cut that angle in half (since perpendicular lines form right angles, or 90° angles)? To construct a parallel line, you may need to construct another line before the parallel to help you.
### Problem C1
Draw a line segment. Then construct a line that is
1. perpendicular to it
2. parallel to it
3. the perpendicular bisector of the segment (A perpendicular bisector is perpendicular to the segment and bisects it; that is, it goes through the midpoint of the segment, creating two equal segments.)
### Problem C2
Draw an angle on your paper. Construct its bisector. (An angle bisector is a ray that cuts the angle exactly in half, making two equal angles.)
### Problem C3
Illustrate each of these definitions with a sketch using four different triangles. Try to draw four triangles that are different in significant ways — different side lengths, angles, and types of triangles. The first one in definition (a) is done as an example.
1. A triangle has three altitudes, one from each vertex. (An altitude of a triangle is a line segment connecting a vertex to the line containing the opposite side and perpendicular to that side.)
2. A triangle has three medians. (A median is a segment connecting any vertex to the midpoint of the opposite side.)
3. A triangle has three midlines. (A midline connects two consecutive midpoints.)
When you construct medians, you need to do two things: First find the midpoint; then fold or draw a segment connecting that point to the opposite vertex. Except in the case of special triangles (such as an equilateral triangle, and one median in an isosceles triangle), you can’t construct a median with just one fold. When you construct altitudes, you need to construct a perpendicular to a segment, but not necessarily at the midpoint of that segment. And remember that the altitude may fall outside the triangle, so you might want to draw or fold an extension of the sides of the triangle to help you.
### Problem C4
Draw five triangles, each on its own piece of patty paper. Use one triangle for each construction below.
1. Carefully construct the three altitudes of the first triangle.
2. Carefully construct the three medians of the second triangle.
3. Carefully construct the three midlines of the third triangle.
4. Carefully construct the three perpendicular bisectors of the fourth triangle.
5. Carefully construct the three angle bisectors of the fifth triangle.
### VIDEO SEGMENT
In this video segment, participants construct the altitudes, medians, and midlines of their triangles. Compare your solutions to Problem C4 with those in this video segment.
What are the similarities and differences in your results? What conjectures can you make about the constructions you’ve just completed?
You can find this segment on the session video approximately 15 minutes and 40 seconds after the Annenberg Media logo.
Problems C3 and C4 and the Video Segment problems taken from Connected Geometry, developed by Educational Development Center, Inc. p. 32. © 2000 Glencoe/McGraw-Hill. Used with permission. www.glencoe.com/sec/math
### Concurrencies in Triangles
When three or more lines meet at a single point, they are said to be concurrent. The following surprising facts are true for every triangle:
• The medians are concurrent; they meet at a point called the centroid of the triangle. (This point is the center of mass for the triangle. If you cut a triangle out of a piece of paper and put your pencil point at the centroid, you would be able to balance the triangle there.)
• The perpendicular bisectors are concurrent; they meet at the circumcenter of the triangle. (This point is the same distance from each of the three vertices of the triangles.)
• The angle bisectors are concurrent; they meet at the incenter of the triangle. (This point is the same distance from each of the three sides of the triangles.)
• The altitudes are concurrent; they meet at the orthocenter of the triangle.
Triangles are the only figures where these concurrencies always hold. (They may hold for special polygons, but not for just any polygon of more than three sides.) We’ll revisit these points in a later session and look at some explanations for why some of these lines are concurrent. You’ll explore the derivation of such terms as incenter and circumcenter later in Session 5 of this course.
### Problem C5
For each construction in parts a-d, start with a freshly drawn segment on a clean piece of patty paper. Then construct the following shapes:
1. an isosceles triangle with your segment as one of the two equal sides
2. an isosceles triangle whose base is your segment
3. a square based on your segment
4. an equilateral triangle based on your segment
### More Constructions
Think about how you might construct the exact side lengths needed for these squares. For example, the first square will need a side length exactly one half the original. The third square is very difficult!
### Problem C6
1. Construct a square with exactly one-fourth the area of your original square. How do you know that the new square has one-fourth the area of the original square?
2. Construct a square with exactly one half the area of your original square. How do you know that the new square has one half the area of the original square?
3. Construct a square with exactly three-fourths the area of your original square.
### Problem C7
Recall that the centroid is the center of mass of a geometric figure. How could you construct the centroid of a square?
### Problem C8
When you noticed concurrencies in the folds, were you sure that the segments were concurrent? What would convince you that, for example, the medians of every triangle really are concurrent?
### Notes
Note 4
If you are working in a group, you may choose to do all of the construction problems as a group activity. Watch for someone with appropriate solutions (for example, folding the two endpoints to each other, rather than measuring). Ask that person to share the solution and explain why it will always work on any segment. That’s the goal for these problems: to come up with general methods that will always work and that don’t rely on measurement. At the end, leave at least 10 minutes to share methods, even if not everyone is done. Then make a list of conjectures that come from that problem.
### Problem C1
Start by drawing a line segment. Then do the following:
a. Fold the paper so that one of the endpoints of the line segment lies somewhere on the line segment. The crease created defines a line perpendicular to the original line segment.
b. Use the process above to construct a perpendicular line. Then use the same process to construct a line perpendicular to the new line, making sure that this second perpendicular is a different line from the original. Since this third line and the original are each perpendicular to the second line, they are parallel.
c. Fold the paper so that the endpoints of the line segment overlap. Draw a line segment along the crease, intersecting the original line segment. This new line segment is perpendicular to the original one and bisects it, because we used the same process that we used to construct the midpoint in the sample construction.
### Problem C2
Draw an angle on a piece of paper. Next, fold the paper so that the two sides of the angle overlap. The crease created defines a bisector of the angle.
### Problem C3
For parts (a)-(c), draw several triangles, at least one of which has an obtuse angle (to see that the definitions make sense in general). Then draw in the altitudes. Repeat with medians. Repeat with midlines.
a. altitudes:
b. medians:
c. midlines:
### Problem C4
Draw five triangles on separate pieces of patty paper, and then do the following:
a. Pick a side. Fold the paper so that the crease is perpendicular to the side [see Problem C1(a)] and so that it goes through the vertex opposite the side. You may have to extend the line segments of your triangle if the triangle has an angle larger than 90°. (See illustration for an example of what this looks like.) Connect the side with the vertex along the crease. The line segment drawn is the altitude corresponding to the side chosen. Now repeat with the other two sides.
b. Pick a side. Fold the paper so that the endpoints of the chosen side overlap. The midpoint of the side is the point where the side intersects the crease. Using a straightedge, connect the midpoint of the side with the vertex opposite it. Repeat with the other two sides.
c. Pick a side. Find the midpoint of the side by following the construction of question (b). Repeat this construction with the other two sides. Using a straightedge, connect the consecutive midpoints.
d. Pick a side. Construct a perpendicular bisector of the chosen side using the construction from Problem C1(c). Repeat with the other two sides.
e. Pick an angle. Fold the paper so that the two sides of this angle overlap. The crease defines a ray that bisects the chosen angle. Repeat with the other two angles.
### Problem C5
Draw a line segment, and then do the following:
a. Make a crease that goes through one of the endpoints of the original line segment. The crease will extend to the edges of the paper.
Fold the paper along the crease and mark where the second endpoint of the line segment overlaps with the folded piece.
Then unfold the paper and connect the marked point with the point where the original line segment and the crease intersect.
Next, connect the two “free” ends of the two line segments with a straight line. The result is an isosceles triangle, where the original line segment is one of its two equal sides.
b. Construct a perpendicular bisector of the line segment. Choose any point on the perpendicular bisector and connect it with the endpoints of the original line segment. The resulting triangle is isosceles and has the original line segment as its base.
c. Extend the line segment to form a line, being sure to mark the original endpoints of the line segment. Use this line to construct a perpendicular line through the endpoints of the original line segment [see Problem C1(a)].
You should now have two parallel lines, each perpendicular to the original line segment at the endpoints.
Then fold the paper so that the original line segment overlaps the first perpendicular line you drew.
Mark the point on the perpendicular line where the second endpoint falls on this line. (This defines one of the equal, perpendicular sides.)
Perform the same process on the second perpendicular line to define the third side of the square.
Finally, use the straightedge to connect the two points you marked on the perpendicular lines to define the fourth side of the square.
d. Construct the perpendicular bisector of the segment.
Pick one of the two endpoints of the original line segment. Fold the paper along a line that contains the endpoint such that the other endpoint falls on the perpendicular bisector.
Flip your patty paper, and then mark that spot on the bisector.
Connect the marked spot with the two endpoints of the original line segment.
### Problem C6
a. Fold the paper in half to make a rectangle. Fold it in half again by bisecting the longer sides of the rectangle. The resulting square has one-fourth the area of the original one. There are exactly four squares that fit exactly on top of each other, so they must have the same area. Since together they completely make up the original square, each must be one-fourth of the original square.
b. Find the midpoints of all four sides. Connect the consecutive midpoints. The resulting square has one-half the area of the original square. To see this, connect the diagonals of the new square. You will see four triangles inside the square and four triangles outside, all of which have the same area. Half the area of the original square is inside the new square.
c. In order to obtain a square with exactly three-fourths the area of the original square (sides = 1) we need to calculate the sides of the new square:
a • a = 3/4
a2 = 3/4
a = √3/2
So we are looking to construct a square whose sides are equal to √3/2.
Start with a piece of patty paper. Think of the bottom edge as the base of an equilateral triangle.
Fold the vertical midline. The third vertex of the equilateral triangle will be on this midline.
Bring the lower right vertex up to the midline, so that the entire length of the bottom edge is copied from the lower left vertex to the midline.
The distance from the bottom of the midline to this mark is √3/2. It is the height of an equilateral triangle with the side length equal to 1. This can also be easily calculated using the Pythagorean theorem for the right triangle with the sides 1 and 1/2.
Next, fold down from this mark. This is the height of the square.
Fold down the corner so that you can fold the right side in the same amount as the top.
Fold over the right side. This square has area 3/4 of the original square.
### Problem C7
One way to do this is to use a straightedge to draw the two diagonals of the square. The centroid is the point of their intersection. Another is to draw the perpendicular bisectors of two consecutive sides of the square [the same construction as Problem C6(a)]. The intersection of these bisectors is the same centroid.
### Problem C8
Noticing what appear as concurrencies in the folds may lead one to conjecture that concurrencies occur in general. Keep in mind any one construction that suggests this is a special case. Therefore, in order to convince ourselves that they do occur in general, we need to construct a formal proof. | 3,309 | 15,393 | {"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} | 4.75 | 5 | CC-MAIN-2023-23 | longest | en | 0.888902 |
https://statproofbook.github.io/P/blrkc-prior | 1,716,534,647,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058684.66/warc/CC-MAIN-20240524060414-20240524090414-00223.warc.gz | 475,328,452 | 4,564 | Index: The Book of Statistical ProofsStatistical Models ▷ Univariate normal data ▷ Bayesian linear regression with known covariance ▷ Conjugate prior distribution
Theorem: Let
$\label{eq:GLM} y = X \beta + \varepsilon, \; \varepsilon \sim \mathcal{N}(0, \Sigma)$
be a linear regression model with measured $n \times 1$ data vector $y$, known $n \times p$ design matrix $X$ and known $n \times n$ covariance matrix $\Sigma$ as well as unknown $p \times 1$ regression coefficients $\beta$.
Then, the conjugate prior for this model is a multivariate normal distribution
$\label{eq:GLM-N-prior} p(\beta) = \mathcal{N}(\beta; \mu_0, \Sigma_0) \; .$
Proof: By definition, a conjugate prior is a prior distribution that, when combined with the likelihood function, leads to a posterior distribution that belongs to the same family of probability distributions. This is fulfilled when the prior density and the likelihood function are proportional to the model parameters in the same way, i.e. the model parameters appear in the same functional form in both.
Equation \eqref{eq:GLM} implies the following likelihood function:
$\label{eq:GLM-LF} p(y|\beta) = \mathcal{N}(y; X \beta, \Sigma) = \sqrt{\frac{1}{(2 \pi)^n |\Sigma|}} \, \exp\left[ -\frac{1}{2} (y-X\beta)^\mathrm{T} \Sigma^{-1} (y-X\beta) \right] \; .$
Expanding the product in the exponent, we have:
$\label{eq:GLM-LF-s1} p(y|\beta) = \sqrt{\frac{1}{(2 \pi)^n |\Sigma|}} \cdot \exp\left[ -\frac{1}{2} \left( y^\mathrm{T} \Sigma^{-1} y - y^\mathrm{T} \Sigma^{-1} X \beta - \beta^\mathrm{T} X^\mathrm{T} \Sigma^{-1} y + \beta^\mathrm{T} X^\mathrm{T} \Sigma^{-1} X \beta \right) \right] \; .$
Completing the square over $\beta$, one obtains
$\label{eq:GLM-LF-s2} p(y|\beta) = \sqrt{\frac{1}{(2 \pi)^n |\Sigma|}} \cdot \exp\left[ -\frac{1}{2} \left( (\beta - \tilde{X}y)^\mathrm{T} X^\mathrm{T} \Sigma^{-1} X (\beta - \tilde{X}y) - y^\mathrm{T} Q y + y^\mathrm{T} \Sigma^{-1} y \right) \right]$
where $\tilde{X} = \left( X^\mathrm{T} \Sigma^{-1} X \right)^{-1} X^\mathrm{T} \Sigma^{-1}$ and $Q = \tilde{X}^\mathrm{T} \left( X^\mathrm{T} \Sigma^{-1} X \right) \tilde{X}$.
Separating constant and variable terms, we get:
$\label{eq:GLM-LF-s3} p(y|\beta) = \sqrt{\frac{1}{(2 \pi)^n |\Sigma|}} \cdot \exp\left[ -\frac{1}{2} \left( y^\mathrm{T} Q y + y^\mathrm{T} \Sigma^{-1} y \right) \right] \cdot \exp\left[ -\frac{1}{2} (\beta - \tilde{X}y)^\mathrm{T} X^\mathrm{T} \Sigma^{-1} X (\beta - \tilde{X}y) \right] \; .$
In other words, the likelihood function is proportional to an exponential of a squared form of $\beta$:
$\label{eq:GLM-LF-s4} p(y|\beta) \propto \exp\left[ -\frac{1}{2} (\beta - \tilde{X}y)^\mathrm{T} X^\mathrm{T} \Sigma^{-1} X (\beta - \tilde{X}y) \right] \; .$
The same is true for a multivariate normal distribution over $\beta$
$\label{eq:GLM-N-prior-s1} p(\beta) = \mathcal{N}(\beta; \mu_0, \Sigma_0)$ $\label{eq:GLM-N-prior-s2} p(\beta) = \sqrt{\frac{1}{(2 \pi)^p |\Sigma_0|}} \cdot \exp\left[ -\frac{1}{2} (\beta-\mu_0)^\mathrm{T} \Sigma_0^{-1} (\beta-\mu_0) \right]$
exhibits the same proportionality
$\label{eq:GLM-N-prior-s3} p(\beta) \propto \exp\left[ -\frac{1}{2} (\beta-\mu_0)^\mathrm{T} \Sigma_0^{-1} (\beta-\mu_0) \right]$
and is therefore conjugate relative to the likelihood.
Sources:
Metadata: ID: P432 | shortcut: blrkc-prior | author: JoramSoch | date: 2024-01-19, 08:42. | 1,214 | 3,379 | {"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": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.765625 | 4 | CC-MAIN-2024-22 | latest | en | 0.535445 |
https://worldbuilding.stackexchange.com/questions/32973/temperature-on-a-14-days-day-planet | 1,718,203,148,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861173.16/warc/CC-MAIN-20240612140424-20240612170424-00230.warc.gz | 573,945,925 | 41,486 | # Temperature on a 14-days day planet
In this question I asked about temperatures on a planet where a day last 30 days. The data are the same:
• stellar flux of 1.118
• albedo between Earth's and Mars's
• atmospheric composition of 18% oxygen, 13% argon and 69% nitrogen
• sea-land pressure of 0.87 atmospheres
• land covered by water is 13%
• axial tilt and the eccentricity are neglible
If it's useful, this is the map:
How would maximum and minimum temperatures change (between night and day and across latitude) if a day last only 14/15 days? How would this affect the weather?
• How long does a year on the planet last? Jan 22, 2016 at 11:06
• if there is no tilt it does not matter (to the weather) Jan 22, 2016 at 12:15
• So a fortnight is one night Jan 26, 2016 at 21:27
• If "fortnight" means 7 days, yes. Jan 27, 2016 at 13:42
The average equilibrium temperature can be obtained from the Stefan-Boltzmann law, for your data 293.5 K (20 C). Compensating for the Earth-like atmosphere, (+15 K for Earth, closer to +12.5 K for this planet), we have an average temperature of approximately 306 K (33 C). Quite hot, as expected from a higher solar flux, and smaller albedo.
Another useful average we can get from this law is the equatorial average, 311 K without the atmosphere, ~323 K compensated.
Equations for temperature estimations without an atmosphere:
Effective influx: $$= solar flux * (1-albedo)$$
Global average $$= \left(\frac{I_e}{4\sigma}\right)^{\frac{1}{4}}$$
Equatorial average $$= \left(\frac{I_e}{\pi \sigma}\right)^{\frac{1}{4}}$$
Stationary sun-in-zenith average $$= \left(\frac{I_e}{\sigma}\right)^{\frac{1}{4}}$$
Where $$\sigma$$ is the Stefan-Boltzmann constant ($$σ = 5.67×10^{-8} W m^{-2} K^{-4}$$), and $$I_e$$ is the effective influx.
For a rapidly rotating planet, use the equatorial average for the equator temperature, for a very slowly rotating planet, use the sun-in-zenith equation for the peak temperature. For a case in between those extremes, use something in-between those equations.
Your planet seems to be divided into two regions, a lowland and a highland. We find the highest temperature variations on the equator part of the highland, where a necessary low cloud cover gives huge, desert-like variations, reaching almost 90 C shortly after noon (actually 130 degrees C if we calculate the black-body equilibrium, but we must compensate for atmospheric convection), and less than 0 C degrees (perhaps as low as -15 C) shortly before dawn.
In the lowland, the atmosphere, combined with clouds formed by the lakes ,gives more inertia to the system, thereby limiting the variations. (0 - 50 degrees C).
• Can you explain where the +90 and -15 came from? I understand how you got the average from the linked law but not where you got the range. Jan 26, 2016 at 9:20
• That is an estimate obtained from the temperature equilibrium for a stationary surface (for the day) and the temperature drop from 14 days of radiation at night. Jan 26, 2016 at 9:23
• This is a good answer but if there was a bit more detail on how you reached those numbers it would be a great one. For example if it allowed someone coming to the question who had a longer or shorter day than this would they be able to use the information here to produce their own numbers? Jan 26, 2016 at 9:35
• @TimB I added some of the equations, and how to approximate the peak equatorial temperature. Better now? I am new here. Jan 26, 2016 at 9:48
• Yes, this looks great, most likely this answer will get the bounty :). I'll leave it open for a bit longer though as bounty=more views=more upvotes. Was there any particular method used to compensate for the effects of atmosphere? Jan 26, 2016 at 10:16
You're looking at much the same answer as for your previous question.
A lot of the stability in temperature on Earth is caused by the specific heat capacity of water. It warms up more slowly and cools more slowly than the land. Your planet has relatively very little water, which will cause greater temperature variation to start with. On top of that you've got these long days allowing it to heat up and cool down that much more.
During the day it's going to be hell outside, at night hell will freeze over.
The Earth maintains nearly-constant average temperature due to its oceans. Not only do the oceans act like a huge heat-sink, storing and releasing energy as needed, they also move energy from the warm equator to the colder poles. Without oceans, the temperature will only be limited by the heat absorbed by the ground - so not a lot. The atmospheric density is slightly lower than Earth's as well, which means even less temperature regulation.
With only 15% of your world being ocean, my guess is that the global climate of the world would somewhat resemble the climate of Mars, though with slightly higher average temperature. Mars' average maximum and minimum temperatures are -7 to -82 C (19 to -116 F) in the winter, and 4 to -73 C (39 to -99 F) in the summer. However, the long days and nights will grow that gap severely.
I don't have any hard numbers, just guesswork, but my guess is that the cold temperatures will reach past -150 C (-238 F), and the hot temperatures will be at or above the boiling point of water. Human life would struggle to survive in domes; outside of a habitat, no human could survive except at dawn and twilight, near the water.
The daily temperature differences in high and dry places like Colorado's San Luis Valley can swing quite a bit in just 24 hour one summer in the town of Alamosa this happened
August 24, 2002: Record high of 85°, record low of 33° (52° range)
August 25, 2002: Record high of 87°, record low of 30° (57°)
August 26, 2002: Record high of 88°, record low of 31° (57°)
[stats from weather underground]
Back of the envelope gives me the range of boiling point of water to dry ice as possible highs and lows. There also would be a crazy wind blowing from the cold side to the hot as convection currents would be far stronger than earth's. This would damp down the temperature range by a bit by trading it for freezing super hurricanes. | 1,526 | 6,133 | {"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": 7, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2024-26 | latest | en | 0.838628 |
http://www.jiskha.com/display.cgi?id=1224638964 | 1,498,523,821,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320873.54/warc/CC-MAIN-20170626235612-20170627015612-00407.warc.gz | 573,476,518 | 3,800 | # Math
posted by .
How do I write a word problem that matches this expression:10-(2x4)?
• Math -
Ben had \$10.00 to spend. He bought two cups of hot chocolate at the local coffee shop. Each cup of hot chocolate cost \$4.00. How much money did he have left?
• Math -
\$2 | 74 | 275 | {"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-2017-26 | latest | en | 0.952272 |
https://www.noodle.com/learn/details/54387/learn-geometry-how-to-find-the-area-of-a-rectangle | 1,524,645,793,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125947759.42/warc/CC-MAIN-20180425080837-20180425100837-00026.warc.gz | 831,419,146 | 12,353 | ## At A Glance
### Learn Geometry - How to Find the Area of a Rectangle
Bestselling Learn Guitar on Android! http://bit.ly/LearnGuitarAndroid In this video, Mahalo math expert Julie Clark shows you how to find the area of a rectangle. Area of a Rectangle Formula --------------------------------------------------------------------- The first step in finding the area of a rectangle is using the formula A=b x h, where A is the area, b is the base and h is the height.For example, in the figure illustrated below, the rectangle has a base of four and a height of seven. When you plug those numbers into the formula, you find that the area equals four times seven, which equals 28. Read more by visiting our page at: http://www.mahalo.com/learn-geometry-how-to-find-the-area-of-a-rectangle/
Length: 01:15
## Contact
Questions about Learn Geometry - How to Find the Area of a Rectangle
Want more info about Learn Geometry - How to Find the Area of a Rectangle? Get free advice from education experts and Noodle community members. | 225 | 1,032 | {"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-2018-17 | latest | en | 0.817114 |
http://www.solutioninn.com/suppose-that-s-50-k-45- | 1,498,245,295,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320130.7/warc/CC-MAIN-20170623184505-20170623204505-00182.warc.gz | 664,921,160 | 7,230 | # Question: Suppose that S 50 K 45
Suppose that S = \$50, K = \$45, σ = 0.30, r = 0.08, and t = 1. The stock will pay a \$4 dividend in exactly 3 months. Compute the price of European and American call options using a four-step binomial tree.
View Solution:
Sales0
Views85 | 85 | 275 | {"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-2017-26 | longest | en | 0.892876 |
https://forum.arduino.cc/t/current-transformer/644084 | 1,660,210,493,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571246.56/warc/CC-MAIN-20220811073058-20220811103058-00327.warc.gz | 252,617,098 | 7,635 | # Current Transformer
Hello all,
I’m working on a project to measure ac current of an electric motor. I’m using a 2000:1 current transformer (no resistor). I’m using a voltage divider using 2 - 10k resistor and a 345ohm burden resistor. I’m basing everything off from this web site: How to use Non-invasive AC Current Sensors with Arduino – Scidle
I need to measure a max of 20amp. before i hooked the circuit up to the Arduino Nano, i ran the line wire through the coil and powered on the device (1500 watt heater for testing only). using my clamp on meter, it read 12amp on high. i sized the burden resistor until i was getting about 2vac on the coil. I assumed this would be a good stop to start.
My issue is understanding some of the sample code, that is also on that page and i’m hoping someone could help me out.
It is this part of the code and information i don’t fully understand (maybe other parts too).
``````// total = sqrt(SumSqVClamp/numReadings);
// total= (total*(float)2/3); // Rburden=3300 ohms, LBS= 0,004882 V (5/1024)
// // Transformer of 2000 laps (SCT-013-000).
// // 5*220*2000/(3300*1024)= 2/3 (aprox
``````
I’m assume that represents 5v, 220 is the VAC (my case will be 120), 2000 are the number of turns in the CT, 3300 is the burden resistor (345 for mine), 1024 is the sample per volt. when i calculate it all out i come up with 3.39, in my code to make the output from the Nano match my clamp on meter i use 0.028. this was sampling at 3 different currents, 5a, 8a, 12a . i believe this is calculating “I=V/R” but i can’t get my head around it to understand why there is a difference.
For what i need i could just move forward, but i would like to know what I’m missing in understand what is going on.
here is my code:
`````` // Testing using a NANOv3
// Current Transformer 2000:1 - ZDCT004GL
const unsigned int numReadings = 200; //samples to calculate Vrms.
int readingsVClamp[numReadings]; // samples of the CT-In
int readingsGND[numReadings]; // samples of the virtual
float SumSqGND = 0;
float SumSqVClamp = 0;
float VacAmps = 0;
int PinVClamp = A3; // CT In
int PinVirtGND = A4; // Virtual Ground
void setup() {
Serial.begin(9600);
// initialize all the readings to 0:
}
}
void loop() {
// Calculate Current / Amps
// Current Transformer - 2000:1
unsigned int i=0;
SumSqGND = 0;
SumSqVClamp = 0;
VacAmps = 0;
for (unsigned int i=0; i<numReadings; i++)
{
delay(1); //
}
//Calculate Vrms
for (unsigned int i=0; i<numReadings; i++)
{
SumSqVClamp = SumSqVClamp + sq((float)readingsVClamp[i]);
}
// total = sqrt(SumSqVClamp/numReadings);
// total= (total*(float)2/3); // Rburden=3300 ohms, LBS= 0,004882 V (5/1024)
// // Transformer of 2000 laps (SCT-013-000).
// // 5*220*2000/(3300*1024)= 2/3 (aprox)
// 5*120*2000/(345*1024)= 3.3967
// 120000/353280
VacAmps= (VacAmps*(float).028);
Serial.print("Apps: ");
Serial.println(VacAmps);
delay(1000);
}
``````
You might find this page more helpful: Learn | OpenEnergyMonitor
My approach for calibrating the system would be to measure the rms voltage across the burden resistor, for several known currents (as you seem to be doing) and fit a line to that using a least squares program.
There are several websites that will perform that fit for you, then you have a simple equation that gives the current as a result of the rms voltage across the burden resistor.
Burden resistors need to be sized as per the CT spec and not just to give the voltage you want .
If this is a simple CT , then the output is an AC signal which can’t be directly read by the Arduino .
Note also you can loop your primary wire multiple times through the CT to increase the output ( e.g if your load is 5A , if you loop the wire three times through the CT it will read 15A.) This can make better use of the range of the CT.
You can buy AC current transducers that have a DC output and are therefore easier to use
sapman:
Hello all,
I'm working on a project to measure ac current of an electric motor.
What kind of motor?
@MarkT - It's a 1hp / single phase (110vac/60hz) It runs a vacuum pump. part of monitoring the current (and temp) is to warm the pump up before applying the load so it does not overload the circuit. most of the time it is 0c out side when it is running. it also run for days at a time.
@jremington and @hammy -
I did track down my issue down to how the website was do the calculation (or how i was understanding it). I did find a couple burden resistor calculators and some datasheets for current transformers with the formulas to use. it did verify that the resistor size i chose was correct for the Arduino and the max current i will be measuring.
After getting my head around this, it all came down to the following to figure it out:
// Es = Ip * (Rb/Tr) - Calculate burden resistor
// Rb = Tr(Es/Ip) - Es - Max voltage to Arduino (4.5v), Ip - Max Current to be read - Load
// Es = ADCrms * (5/1023) - ADC 10 bits (0-1023)
// Is = (Es/Rb) : Is - Current of secondary, Es - Voltage of secondary, Rb - Burden Resistor
// Ip = (Is*Tr) : Ip - Current of primary, Tr - Current transformer ratio
as i was typing this i went back and looked at his formula and he was multiplying the primary voltage back in, and was actually calculating power/watts and not current. I should have caught that.
thanks --- dane ---
Based on your application and I assume an industrial application I would consider using an AC Current Transducer and forget just using a straight current transformer. I have monitored motor current for assorted pumps running single and poly phase at voltages from 120 to 4160 and if you want to keep this simple I would spend the \$100 USD and get a transducer along these lines.
https://www.crmagnetics.com/ac-current-transducers/average-rms/single-element/cr4410
They are 24 VDC powered and you can get 0 to 20 AAC outputs 0 to 5 VDC. I have seen off the boat versions for under \$50 USD and the link is merely an example but a Google of AC Current Transducers will bring up a dozen hits or more to similar. I have used the CR Magnetics stuff in some harsh environments and some were running 20 years plus when I retired. Your call but for a commercial application you may want to consider something like this.
Ron | 1,728 | 6,373 | {"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-2022-33 | latest | en | 0.843936 |
http://gpl4you.com/discussion.php?q=mcq&company=Capgemini&type=Mathematical%20Skills | 1,556,179,854,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578711882.85/warc/CC-MAIN-20190425074144-20190425100144-00494.warc.gz | 75,673,842 | 17,292 | Company
• The diameter of the driving wheel of a bus in 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 66 kmph?
last reply by Anil • 2 years ago • asked by Kirti reddy
• Suresh borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of 11 years is Rs.8160, how much money did he borrow?
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• There are 10 cig packs each containing an unknown no of cigs( each = Pack has between 50 and 100). One pack has all bad cigs . Each good cig = ( if u can agree that any cig is good) weighs 1gm. Each bad cig weighs = 1.1 gm or .99 gm but all bad cigs weigh same. Using a spring chemical = Balance ( which gives u the exact weight) .find out which pack is bad ,Using the balance only once.
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last reply by Rahul Mittal • 7 years ago • asked by Nandani | 391 | 1,300 | {"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-2019-18 | latest | en | 0.94521 |
http://athensmutualaid.net/angles-of-elevation-and-depression-answer-key-your-ultimate-guide-to-trigonometry/ | 1,721,516,271,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517541.97/warc/CC-MAIN-20240720205244-20240720235244-00428.warc.gz | 2,201,366 | 39,513 | # Cool Angles Of Elevation And Depression Answer Key: Your Ultimate Guide To Trigonometry References
Cool Angles Of Elevation And Depression Answer Key: Your Ultimate Guide To Trigonometry References. The angle of depression is the angle. Some of the worksheets displayed are infinite geometry, angle of elevation depression trig work.
A man is 1.8 m tall. Web trigonometry can be used to solve problems that use an angle of elevation or depression. We have a new and.
### His Angle Of Elevation To.
The angle of depression is the angle. Web angles of elevation and depression worksheet. Web trigonometry can be used to solve problems that use an angle of elevation or depression.
### The Term Angle Of Depression Represents The Angle From The Horizontal.
Web how to solve problems involving angles of elevation or depression Web find distance using right triangles and angles of elevation or depression click create assignment to assign this modality to your lms. He stands 50 m away from the base of a building.
### The Angle Of Elevation Is The Angle Between The Horizontal Line Of Sight And The Line Of Sight Up To An Object.
Use this worksheet to improve your ability to. Lesson 4 of this trigonometry series centres on angles of elevation and depression. Web another example of angles of elevation comes in the form of airplanes.
### Web Means Α = Β.
So, in most problems its doesn’t matter how you draw your diagram because the angle of elevation is equal to angle of depression. The angle which the line of sight makes with the horizontal line passing through the observer’s eye when the object is above the observer is called the angle of elevation. Marshallers, people who signal and direct planes as they are on the landing strip, would.
### He Stands 50 M Away From The Base Of A Building.
For example, if you are standing on the ground looking up at the top of a mountain, you could measure the angle of elevation. An architect wants to calculate the height of a building. Web the figure below shows each of these kinds of angles. | 420 | 2,055 | {"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-2024-30 | latest | en | 0.852061 |
https://au.mathworks.com/matlabcentral/cody/problems/2015-length-of-the-hypotenuse/solutions/2027987 | 1,606,503,092,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141193856.40/warc/CC-MAIN-20201127161801-20201127191801-00305.warc.gz | 199,453,368 | 16,924 | Cody
# Problem 2015. Length of the hypotenuse
Solution 2027987
Submitted on 19 Nov 2019 by Bora Canbula
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
a = 1; b = 2; c_correct = sqrt(5); tolerance = 1e-12 ; assert(abs(hypotenuse(a,b)-c_correct)<tolerance);
2 Pass
a = 3; b = 4; c_correct = 5; tolerance = 1e-12 ; assert(abs(hypotenuse(a,b)-c_correct)<tolerance);
3 Pass
a = 5; b = 12; c_correct = 13; tolerance = 1e-12 ; assert(abs(hypotenuse(a,b)-c_correct)<tolerance);
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Start Hunting! | 228 | 727 | {"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-2020-50 | latest | en | 0.70075 |
https://medium.com/@taposhdr/forecasting-methods-part-i-9440e27466ab | 1,521,779,399,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257648177.88/warc/CC-MAIN-20180323024544-20180323044544-00744.warc.gz | 659,647,374 | 29,893 | # Forecasting Methods : Part I
Recently, I was asked to teach a class on forecasting using Python. I thought my notes would be a good source of information for every one interested in this area and I might learn from my reader’s feedback as well. In this part 1 of the article we will talk about basic forecasting methods — Naive, Average, Moving Average and Weighted Average. In the next parts we will discuss measures of scoring, exponential smoothing techniques, Holt, Holt winters, ARIMA, ARMA and deep learning methods using LSTM.
Incidentally Kaggle also released a competition on forecasting which plans to forecast for 145K time series. However, this article is based on M-competitions data-set. Kaggle’s competition is very similar to M3 competitions held in the past led by forecasting researcher Spyros Makridakis. The goal of the M3 competition was to be able to forecast across multiple (3003) time series. The results and learnings from the M3 competition are summarized in the paper.
In this article set I will review forecasting methods using python. The goal is to develop an intuitive understanding of forecasting for beginners. Finally, I felt there are not many mature libaries for forecasting in python, although statsmod provides ARIMA and ARMA at the time of this writing. Facebook’s prophet also seems to be at an early stage.
We will cover the following forecasting methods as shown below -
### Installing libraries
We will use the following libraries. Majority of these could be installed from pip3.
### Pre-processing Data
For this article, I have downloaded data from M3 competition website. Then we massage the data to get to one series and play with it.
We see for the series N 1 there are a total of 1–47 observations. Out of which many might be empty values, represented in python as NaN. We then melt the data to get to our 1st series N 1. We see the series N 1 is an annual series and has a start date of 1975.
In the code shown below, we get a list of variables that we need to melt(pandas melt function), then we create a date series using pandas date_range function and finally create a time-series Series object series1 with index as the year. We print the series.
Next we split the date into 1/3rds, for training and testing.
Lets plot the test and the training data-sets using matplot lib.
### Forecasting Methods
Now that we have the data in the right form, we begin with our journey of forecasting with humble beginnings of Naive Method.
### Method 1 :Naive Method
This is the most primitive forecasting method. The premise of the naive method is that the expected point is equal to the last observed point:
Naive methods although look so simple (“naive”) are useful to create a baseline and also to compute some metrics such as MdRAE. We will cover metrics in detail in the next section of this series.
Lets see how it looks, when we plot the Naive method along side our data and predict for few (7) years ahead.
### Method 2 (a): Average Forecasting Single Next Period
A little more sophisticated method to forecasting beyond “naive” is average method. Here we believe that a good forecast will be an average of all data points.
### Method 2 (b): Average Forecasting Multiple Periods
Average method applied to the multiple periods, would give a flat line. The idea is to develop a visual representation as we move in our journey of learning forecasting.
### Method 3: Moving Average Forecasting
The idea of using last k periods as a good window to predict the next period is moving average. There are two main types of moving average forecasts: Centered Moving Average and Trailing Moving Average.
#### Centered Moving Average (CMA)
The value at time (t) is calculated as the average of raw observations at, before, and after time (t).
For example, a center moving average with a window of 3 would be calculated as:
centered_mv_avg(t) = mean(observed(t-1), observed(t), observed(t+1))
This method requires knowledge of future values, and as such is used on time series analysis to better understand the dataset.
A center moving average can be used as a general method to remove trend and seasonal components from a time series, a method that we often cannot use when forecasting.
#### Trailing Moving Average (TMA)
The value at time (t) is calculated as the average of the raw observations at and before the time (t).
For example, a trailing moving average with a window of 3 would be calculated as:
traling_mv_average(t) = mean(observed(t-2), observed(t-1), observed(t))
Trailing moving average only uses historical observations and is used on time series forecasting. We will use this for our discussion ahead.
### Method 4 : Weighted Moving Average
The next improvement beyond the moving average, is weighted moving average. Here we assign weights to the last k-periods. The most important thing here to remember is that sum of all weights should be equal to 1.
If you are still with me, then we have looked at the very basic methods of forecasting. I had to create a custom library for this, since none of the major libraries in python had these basic time series methods available. I will make this available through pip soon.
References
Thank you for reading this. Here are the list of references that will be very helpful.
One clap, two clap, three clap, forty?
By clapping more or less, you can signal to us which stories really stand out. | 1,178 | 5,433 | {"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} | 2.953125 | 3 | CC-MAIN-2018-13 | latest | en | 0.955478 |
https://www.teacherspayteachers.com/Product/7th-Grade-Math-7SPA1-FREE-Worksheet-on-Presidential-Polling-Plus-Bacon-2846403 | 1,621,012,511,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243991428.43/warc/CC-MAIN-20210514152803-20210514182803-00076.warc.gz | 1,055,103,010 | 29,448 | DID YOU KNOW:
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# 7th Grade Math: 7.SP.A.1 FREE Worksheet on Presidential Polling Plus Bacon!
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### Description
This 10 question worksheet aligns with Common Core standard 7.SP.A.1. In this worksheet students will determine is samples describe in the problems are representative of the population studied and describe why or why not. Eight of the ten questions are about presidential polling while there is a short break where Chet polls his fellow Glasshouse residents about breakfast. Can be used as an in class assignment, a homework assignment, or individual questions can be used to facilitate class discussion. It doesn't even have to be used in a math class as this topic is relevant to other classes as well! Plus it is free. 4 page PDF.
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### Standards
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Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. | 393 | 1,855 | {"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-2021-21 | latest | en | 0.907995 |
https://projecteuclid.org/journals/annals-of-mathematical-statistics/volume-35/issue-1/Linear-Forms-in-the-Order-Statistics-from-an-Exponential-Distribution/10.1214/aoms/1177703749.full | 1,701,611,044,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100508.23/warc/CC-MAIN-20231203125921-20231203155921-00591.warc.gz | 542,368,749 | 27,255 | March, 1964 Linear Forms in the Order Statistics from an Exponential Distribution
Elliot A. Tanis
Ann. Math. Statist. 35(1): 270-276 (March, 1964). DOI: 10.1214/aoms/1177703749
## Abstract
In testing hypotheses about an exponential distribution with probability density function $p(x; \theta, A) = (1/\theta)e^{-(x - A)/\theta},\quad \text{ for } x \geqq A,\\= 0,\quad \text{ for } x < A,$ where $\theta > 0$, the following questions arise: (1) Are certain linear forms in the order statistics of a random sample of size $n$ from this distribution distributed as chi-square random variables? (2) Are certain linear forms in the order statistics stochastically independent? The first two theorems in Section 2 answer these questions. As a consequence of these two theorems, several results follow which are similar to those pertaining to quadratic forms in normally distributed variables. The characterization theorem in Section 3 was suggested by a result for normally distributed variables. Lukacs [4] proved that if a random sample is taken from a continuous type distribution with finite variance, then the independence of the sample mean and the sample variance characterizes the normal distribution. That is, the independence of the estimates of the two parameters of the normal distribution characterizes that distribution. Now if $X_1 < X_2 < \cdots < X_n$ are the order statistics of a random sample from the exponential distribution $p(x; \theta, A)$, then $X_1$ and $(1/n) \sum^n_{i = 1} (X_i - X_1)$ are estimates of the parameters $A$ and $\theta$, respectively. In Section 3, we prove that the independence of these two statistics characterizes this exponential distribution.
## Citation
Elliot A. Tanis. "Linear Forms in the Order Statistics from an Exponential Distribution." Ann. Math. Statist. 35 (1) 270 - 276, March, 1964. https://doi.org/10.1214/aoms/1177703749
## Information
Published: March, 1964
First available in Project Euclid: 27 April 2007
zbMATH: 0132.39504
MathSciNet: MR158481
Digital Object Identifier: 10.1214/aoms/1177703749 | 531 | 2,066 | {"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-2023-50 | latest | en | 0.826904 |
http://pi.math.cornell.edu/~projcalc/triangle.html | 1,529,583,376,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267864148.93/warc/CC-MAIN-20180621114153-20180621134153-00198.warc.gz | 252,576,158 | 1,411 | Series, Integrals, and Hidden Patterns
(1)The figure below indicates a pattern for the creation of infinitely many boxes inside a triangle in the plane. Suppose the base of the triangle is of length two.
(a) What is the area of the largest box?
(b) What is the total area of the two next largest boxes?
(c) What is the total area of four next largest boxes?
(d) If you drew in more boxes, how many would there be at the next stage? What would their total area be?
(e) What is the total area of the largest box plus the two next largest boxes? What is the total area of the 1+2+4=7 largest boxes together? If we added together the areas of all of the infinitely many boxes insides the triangle, what would the area be, assuming it makes sense to add up infinitely many areas? Should this answer match the total area of the triangle? Does it?
(2)(a) You probably computed the total area of the triangle in part (1) by using geometry. Compute the area now with an integral, by choosing a suitable f(x) and finding the area under (a portion of) its graph.
(b) We know that this integral, like all definite integrals, is in fact the limit of Riemann sums. Can you interpret the pattern of boxes inside the triangle in terms of Riemann sums?
©Copyleft 1996 by Harel Barzilai. "Share and Enjoy." Inspired by Calculus: An Active Approach with Projects p. 125. | 322 | 1,360 | {"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} | 3.296875 | 3 | CC-MAIN-2018-26 | latest | en | 0.931595 |
https://brainmass.com/statistics/dispersion-and-spread-of-data/several-mixed-problems-189524 | 1,601,524,764,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600402130615.94/warc/CC-MAIN-20201001030529-20201001060529-00263.warc.gz | 253,772,812 | 13,816 | Explore BrainMass
# Several mixed problems
This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!
(See attachment for details)
11 A baseball player scored a total of 27 runs in the first 20 games of the season. If he continues at the same pace, how many runs should he score in the 80-game season?
Show Work Below
12 Estimate the result in the following division problem. (Remember to round divisors to the nearest ten and dividends to the nearest hundred.)
612 divided by 32
Show Work Below
13 1,232 is what percent of 220?
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14 Dave invested \$8,500 in a time deposit. What interest will he earn for 2 years if the interest rate is 4.75% compounded annually (at the end of each year)?
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15 Choose the correct greatest common factor of 84, 105 and 147
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16 A saleswoman is working on a 3% commission basis. If she wants to make \$3,000 in one month, how much must she sell?
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17 Find the missing length of the right triangle
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18 The sales tax rate in a state is 8%. If you pay a tax of \$2.50 on an item that you purchase, what is its selling price?
Show Work Below
19 Find the angles of a, b, and c
Show Work Below
a:
b:
c:
20 Find the missing angle:
Show Work Below
21 Find the first and third quartiles, Q1 and Q3, of the following set of numbers.
13, 5, 12, 16, 7, 14, 7, 3, 10, 7
Show Work Below
22 Find the mean, mode and median of the following numbers:
13, 5, 12, 16, 7, 14, 7, 3, 10, 7
Show Work Below
Mean:
Mode:
Median:
Worth 3 points
23 The table below gives the mean temperature (in degrees Fahrenheit) for the month of June over a 6-year period in Town B.
Year 1 2 3 4 5 6 7 8 9 10
Temp. 69° 68.5° 70° 72° 71° 71.5° 70.8° 69.7° 67.7° 68.1°
Make a bar graph using the above data.
Show Work Below
24 Determine the maximum and minimum values of the following set of numbers.
-12, 19, 12, 10, -24, 1, -1
Show Work Below
25 Perform the indicated operations
Show Work Below
26 Label the following equation as "true" or "false. Must prove your answer to get full credit.
|4| + |-4| = |4 + -4|
Show Work Below
27 Find the reciprocal of
Show Work Below
28 Show the prime factorization of the number 117.
Show Work Below
29
Find the area.
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30 Write 58% as a fraction or a mixed number.
Show Work Below
31 The electricity costs of a business increased from \$20,000 one year to \$22,000 the next.
To the nearest whole percent, what was the rate of increase?
Show Work Below
32 Find the area of the figure.
Show Work Below
33 Rewrite the statement, using percent notation.
13 out of 25 college students work at part-time jobs.
Show Work Below
Show Work Below
35 Evaluate the following:
-62 - (-3)3
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36 The length of a box is yd, its height is yd and its width is yd. What is its volume in cubic yards?
Show Work Below
37 Which two triangles are similar?
Show Work Below
38 Subtract
Show Work Below
Show Work Below
40 Which of the numbers 32, 23, 54, and 37 are prime?
Show Work Below
41 What fractional part of an hour is 18 minutes? Simplify your result.
Show Work Below
42 Divide Write the result in simplest form.
Show Work Below
43 Write the following as a common fraction or mixed number.
5.679
Show Work Below
44 For the decimal 8.62354:
What is the place value of 5?
Show Work Below
45 The following pie chart shows the budget for a local company. The total budget is \$899,300. Find the amount budgeted in the category of taxes.
Show Work Below | 982 | 3,596 | {"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-2020-40 | latest | en | 0.922345 |
https://www.crazy-numbers.com/en/15462 | 1,716,232,716,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058293.53/warc/CC-MAIN-20240520173148-20240520203148-00591.warc.gz | 631,761,796 | 3,481 | Warning: Undefined array key "numbers__url_substractions" in /home/clients/df8caba959271e8e753c9e287ae1296d/websites/crazy-numbers.com/includes/fcts.php on line 156
Number 15462: mathematical and symbolic properties | Crazy Numbers
# Everything about number 15462
Discover a lot of information on the number 15462: properties, mathematical operations, how to write it, symbolism, numerology, representations and many other interesting things!
## Mathematical properties of 15462
Questions and answers
Is 15462 a prime number? No
Is 15462 a perfect number? No
Number of divisors 12
List of dividers
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1, 2, 3, 6, 9, 18, 859, 1718, 2577, 5154, 7731, 15462
Sum of divisors 33540
Prime factorization 2 x 32 x 859
Prime factors
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2, 3, 859
## How to write / spell 15462 in letters?
In letters, the number 15462 is written as: Fifteen thousand four hundred and sixty-two. And in other languages? how does it spell?
15462 in other languages
Write 15462 in english Fifteen thousand four hundred and sixty-two
Write 15462 in french Quinze mille quatre cent soixante-deux
Write 15462 in spanish Quince mil cuatrocientos sesenta y dos
Write 15462 in portuguese Quinze mil quatrocentos sessenta e dois
## Decomposition of the number 15462
The number 15462 is composed of:
1 iteration of the number 1 : The number 1 (one) represents the uniqueness, the unique, a starting point, a beginning.... Find out more about the number 1
1 iteration of the number 5 : The number 5 (five) is the symbol of freedom. It represents change, evolution, mobility.... Find out more about the number 5
1 iteration of the number 4 : The number 4 (four) is the symbol of the square. It represents structuring, organization, work and construction.... Find out more about the number 4
1 iteration of the number 6 : The number 6 (six) is the symbol of harmony. It represents balance, understanding, happiness.... Find out more about the number 6
1 iteration of the number 2 : The number 2 (two) represents double, association, cooperation, union, complementarity. It is the symbol of duality.... Find out more about the number 2
## Mathematical representations and links
Other ways to write 15462
In letter Fifteen thousand four hundred and sixty-two
In roman numeral
In binary 11110001100110
In octal 36146
In hexadecimal 3c66
In US dollars
Fatal error: Uncaught Error: Call to undefined function money_format() in /home/clients/df8caba959271e8e753c9e287ae1296d/websites/crazy-numbers.com/templates/sample-number.tpl:180 Stack trace: #0 /home/clients/df8caba959271e8e753c9e287ae1296d/websites/crazy-numbers.com/index.php(8): include() #1 {main} thrown in /home/clients/df8caba959271e8e753c9e287ae1296d/websites/crazy-numbers.com/templates/sample-number.tpl on line 180 | 849 | 3,028 | {"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-2024-22 | latest | en | 0.717458 |
https://codescracker.com/js/js-Math-round.htm | 1,680,280,525,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949644.27/warc/CC-MAIN-20230331144941-20230331174941-00005.warc.gz | 210,259,761 | 5,904 | # JavaScript Math.round() | Round a number to its nearest integer
The JavaScript Math.round() method is used when we need to round a specified number to its nearest integer value. For example:
HTML with JavaScript Code
```<!DOCTYPE html>
<html>
<body>
<p id="xyz"></p>
<script>
let num = 10.51;
document.getElementById("xyz").innerHTML = Math.round(num);
</script>
</body>
</html>```
Output
Please note: While rounding a number using the Math.round() method:
• 10.49 will round to 10
• 10.50 will round to 11
## JavaScript Math.round() Syntax
The syntax of Math.round() method in JavaScript is:
`Math.round(x)`
The parameter x is required, refers to a number.
The Math.round(x) method returns a number indicates to the rounded value of x.
## JavaScript Math.round() Example
HTML with JavaScript Code
```<!DOCTYPE html>
<html>
<body>
<p>Math.round(-5.1) = <span id="span1"></span></p>
<p>Math.round(-5.49) = <span id="span2"></span></p>
<p>Math.round(-5.50) = <span id="span3"></span></p>
<p>Math.round(-5.51) = <span id="span4"></span></p>
<p>Math.round(0) = <span id="span5"></span></p>
<p>Math.round(5.1) = <span id="span6"></span></p>
<p>Math.round(5.49) = <span id="span7"></span></p>
<p>Math.round(5.50) = <span id="span8"></span></p>
<p>Math.round(5.51) = <span id="span9"></span></p>
<script>
document.getElementById("span1").innerHTML = Math.round(-5.1);
document.getElementById("span2").innerHTML = Math.round(-5.49);
document.getElementById("span3").innerHTML = Math.round(-5.50);
document.getElementById("span4").innerHTML = Math.round(-5.51);
document.getElementById("span5").innerHTML = Math.round(0);
document.getElementById("span6").innerHTML = Math.round(5.1);
document.getElementById("span7").innerHTML = Math.round(5.49);
document.getElementById("span8").innerHTML = Math.round(5.50);
document.getElementById("span9").innerHTML = Math.round(5.51);
</script>
</body>
</html>```
Output
Math.round(-5.1) =
Math.round(-5.49) =
Math.round(-5.50) =
Math.round(-5.51) =
Math.round(0) =
Math.round(5.1) =
Math.round(5.49) =
Math.round(5.50) =
Math.round(5.51) =
### Other methods to do similar job
Here are the list of methods that are used to either round a number in other way, or to do similar type of job.
• Math.ceil() - round a number up to its nearest largest integer.
• Math.floor() - round a number up to its nearest smallest integer.
• toFixed() - round a number to particular number of decimals.
• toPrecision() - format a number to specific length.
• Math.trunc() - find the integer part of a number.
JavaScript Online Test
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# What is “Casting Out Nines”? Part 3
Learn the magic behind this amazing mathematical tool.
By
Jason Marshall, PhD
Episode #84
In the past few articles, we’ve learned all about an amazing technique called “casting out nines” that you can use to check whether or not you’ve made errors in your arithmetic. So far we’ve learned what check digits are, how they’re used with casting out nines to check addition problems, and how casting out nines can be used to check subtraction, multiplication, and division problems, too.
But up until now we’ve sidestepped the question of why this seemingly magical trick works—it’s got to be something complicated, right? Well, as you’ll see today, casting out nines is indeed a great magic trick. But, like all magic tricks, it isn’t actually magic. In this case, it’s some fantastic math. And, just like all good magic tricks, once the trick is revealed, the idea behind casting out nines is simple enough that everybody can understand and appreciate it—which is exactly what we’re going to do today.
## Why Does Casting Out Nines Work?
Without a doubt, the most important thing to know about casting out nines is how to use it. So if any of the things I mentioned earlier—stuff like check digits and using casting out nines to check addition, subtraction, multiplication, and division—are unfamiliar to you, I encourage you to go back and take a look at the two earlier articles in this series.
Once you know how to use casting out nines, it’s hard not to be left a little dumbfounded by the fact that it works. It’s weird, right? We just add up all the digits in numbers and compare them and somehow that tells us if the answer can be correct…kind of crazy! Which inevitably leads us wonder: Why does casting out nines work?
## Sum of Remainders = Remainder of Sum
To find out, let’s start by thinking about adding two numbers: 10+11. For reasons that will become clear in a minute, let’s now divide both of these numbers by some number—let’s say 9—and find the two remainders. Well, 10÷9 is equal to 1 with a remainder of 1 and 11÷9 is equal to 1 with a remainder of 2. If we add up those two remainders—does anything seem familiar yet?—we get 1+2=3. Okay, now let’s take a look at what we know to be the answer to 10+11…namely 21. If we divide 21 by 9 like we did to the numbers before, we get 21÷9 is equal to 2 remainder 3 (since 2 x 9 is equal to 18…which is 3 less than 21). Interestingly, you’ll notice that the remainder here, 3, is the same as the sum of the remainders from before. Again, does anything seem familiar about this?
So what have we found? Well, we’ve discovered that the sum of a group of remainders must equal the remainder of the sum (this is really just the distributive property that we’ve talked about before in action). We’ve seen that this is true when we use 9 as the number we divide by, but it doesn’t actually matter what number we divide by to find our remainders. For example, let’s take the same problem from before—10+11=21—but this time let’s divide by 8. So 10÷8 is equal to 1 remainder 2, 11÷8 is equal to 1 remainder 3, and 21÷8 is equal to 2 remainder 5. Which means that the sum of the remainders of the numbers we’re adding—that is 2+3=5—is equal the remainder of the sum!
## Web Bonus Tip: Is This Always True?
If you’re curious and decide to see if this also works when dividing by 7, you’ll find that 10÷7 is equal to 1 remainder 3, 11÷7 is equal to 1 remainder 4, and 21÷7 is equal to 3 remainder 0. So, in this case, the sum of the remainders—3+4=7—is not equal to the remainder of the sum. What happened?! Well, actually, nothing happened and everything still works out just fine…once you know that 7 is the same as 0 when you’re dividing by 7, 8 is the same as 0 when you’re dividing by 8, 9 is the same as 0 when you’re dividing by 9, and so on. The reason is that we aren’t actually doing normal remainder division here, we’re actually doing modular arithmetic and, as you’ll see if you look back at the earlier articles on modular arithmetic, that’s how things work. But for our purposes of understanding how casting out nines works, thinking about things in the simpler terms of normal remainder division works just fine—so we’ll stick to that.
## About the Author
Jason Marshall, PhD
Jason Marshall is the author of The Math Dude's Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way. | 1,132 | 4,611 | {"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-2021-49 | latest | en | 0.914799 |
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# C3 differentiation question help watch
1. Hi can someone help me?
Find the turning points on the curve with equation y=(x^2)(x+1)^8
Determine the nature of each turning points and sketch the curve.
This is what I have done so far
What if the second derivative is still 0? In the answer at the back of the book, it is said this is a minimum? Why??
Thanks a lot!
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2. (Original post by pepperzealot)
Hi can someone help me?
Find the turning points on the curve with equation y=(x^2)(x+1)^8
Determine the nature of each turning points and sketch the curve.
This is what I have done so far
What if the second derivative is still 0? In the answer at the back of the book, it is said this is a minimum? Why??
Thanks a lot!
Posted from TSR Mobile
For which value of x does it say its a minimum. It only has one minimum and maximum, they occur at x=0 and x=-0.2 respectively.
3. (Original post by Phichi)
For which value of x does it say its a minimum. It only has one minimum and maximum, they occur at x=0 and x=-0.2 respectively.
. But in the answer there are two minimums and one maximum.... x=-1 is also at a minimum…I
can not understand how can we know this is a minimum？ If I substitute x=-1in to the second derivative，I will get 0.
4. (Original post by pepperzealot)
. But in the answer there are two minimums and one maximum.... x=-1 is also at a minimum…I
can not understand how can we know this is a minimum？ If I substitute x=-1in to the second derivative，I will get 0.
Paper and MS links?
5. (Original post by pepperzealot)
. But in the answer there are two minimums and one maximum.... x=-1 is also at a minimum…I
can not understand how can we know this is a minimum？ If I substitute x=-1in to the second derivative，I will get 0.
Have you tried sketching the curve by plugging in some sample values of x and seeing what happens?
It should be obvious that this function is >=0 for all values of x, so the 2 values of x where it is actually 0 (x = 0 and x = -1) must be minima. For x > 0 or x < -1 the function just gets bigger and bigger in a positive sense so the curve just increases to infinity.
The only tricky point is what happens between -1 and 0 - the function is positive in this region, so to get from 0 back down to 0 again there must be (at least) one point in between where the curve turns down again and this will be a maximum.
6. (Original post by davros)
Have you tried sketching the curve by plugging in some sample values of x and seeing what happens?
It should be obvious that this function is >=0 for all values of x, so the 2 values of x where it is actually 0 (x = 0 and x = -1) must be minima. For x > 0 or x < -1 the function just gets bigger and bigger in a positive sense so the curve just increases to infinity.
The only tricky point is what happens between -1 and 0 - the function is positive in this region, so to get from 0 back down to 0 again there must be (at least) one point in between where the curve turns down again and this will be a maximum.
Thanks a lot
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Card Game Cheater
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 3619 Accepted Submission(s): 1904
Problem Description
Adam and Eve play a card game using a regular deck of 52 cards. The rules are simple. The players sit on opposite sides of a table, facing each other. Each player gets k cards from the deck and, after looking at them, places the cards face down in a row on the table. Adam’s cards are numbered from 1 to k from his left, and Eve’s cards are numbered 1 to k from her right (so Eve’s i:th card is opposite Adam’s i:th card). The cards are turned face up, and points are awarded as follows (for each i ∈ {1, . . . , k}):
If Adam’s i:th card beats Eve’s i:th card, then Adam gets one point.
If Eve’s i:th card beats Adam’s i:th card, then Eve gets one point.
A card with higher value always beats a card with a lower value: a three beats a two, a four beats a three and a two, etc. An ace beats every card except (possibly) another ace.
If the two i:th cards have the same value, then the suit determines who wins: hearts beats all other suits, spades beats all suits except hearts, diamond beats only clubs, and clubs does not beat any suit.
For example, the ten of spades beats the ten of diamonds but not the Jack of clubs.
This ought to be a game of chance, but lately Eve is winning most of the time, and the reason is that she has started to use marked cards. In other words, she knows which cards Adam has on the table before he turns them face up. Using this information she orders her own cards so that she gets as many points as possible.
Your task is to, given Adam’s and Eve’s cards, determine how many points Eve will get if she plays optimally.
Input
There will be several test cases. The first line of input will contain a single positive integer N giving the number of test cases. After that line follow the test cases.
Each test case starts with a line with a single positive integer k <= 26 which is the number of cards each player gets. The next line describes the k cards Adam has placed on the table, left to right. The next line describes the k cards Eve has (but she has not yet placed them on the table). A card is described by two characters, the first one being its value (2, 3, 4, 5, 6, 7, 8 ,9, T, J, Q, K, or A), and the second one being its suit (C, D, S, or H). Cards are separated by white spaces. So if Adam’s cards are the ten of clubs, the two of hearts, and the Jack of diamonds, that could be described by the line
TC 2H JD
Output
For each test case output a single line with the number of points Eve gets if she picks the optimal way to arrange her cards on the table.
Sample Input
3
1
JD
JH
2
5D TC
4C 5H
3
2H 3H 4H
2D 3D 4D
Sample Output
1
1
2
Source
Statistic | Submit | Discuss | Note
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2 Name: Angles in Triangles Find the measure of the unknown angle in each of the triangles. 1. If m 1 = 40 and m 2 = 80, what is m 3? 2. If m 1 = 50 and m 2 = 75, what is m 3? 3. If m 1 = 50 and m 2 = 80, what is m 3? 4. If the complement of 1 is 80 and m 2 = 80, what is m 3? 5. If the supplement of 2 is 110 and the complement of 3 is 60, what is m 1? 6. If the supplement of 1 is 80 and m 2 = 70, what is m 3? 7. If the supplement of 1 = 40 and m 2 = 30, what is m 3? 8. If the complement of 1 = 60 and m 2 = 80, what is m 3? 9. If m 1 = 80 and the complement of m 2 = 70, what is m 3? 10. If the supplement of 2 is 70 and m 3 = 30, what is m 1?
3 Answer Key 1. [180 - ( ) = 60 ] 2. [180 - ( ) = 55 ] 3. [180 - ( ) = 50 ] 4. [m 1 = = 10 ; m 3 = ( ) = 90 ] 5. [m 2 = = 70 ; m 3 = = 30 ; m 1 = ( ) = 80 ] 6. [m 1 = = 100 ; m 3 = ( ) = 10 ] 7. [m 1 = = 140 ; m 3 = ( ) = 10 ] 8. [m 1 = = 30 ; m 3 = ( ) = 70 ] 9. [m 2 = = 20 ; m 3 = ( ) = 80 ] 10. [m 2 = = 110 ; m 1 = ( ) = 40 ] studyisland.com edmentum.com West 83rd Street Suite 300, 8200 Tower Bloomington, MN EDMENTUM, INC.
4 Name: Exponents, Squares & Cubes Write an equivalent expression for each of these expressions. 1. 2x + 4y + 7x 2-6y 2. 2x 2 (4x 2 + 2x) 3. x(x ) x 2 4. y 2 (x 2 + 1) 5. x 2 (x 2 + 1) Find the square root of each of the following , Find the cube root of each of the following , ,000,000
5 Answer Key 1. 7x 2 + 2x - 2y 2. 8x 4 + 4x 3 3. x x 2 y x 4 + x studyisland.com edmentum.com West 83rd Street Suite 300, 8200 Tower Bloomington, MN EDMENTUM, INC.
6 Name: Spelling Circle the letter of the correct answer. 1. Which of the following words is spelled correctly? A. Golden B. Damppen C. Followwer D. Paintte 2. Which of the following words is spelled correctly? A. Comfortable B. Succesful C. Believeable D. Saden 3. Which of the following words is spelled correctly? A. Shortten B. Beleiveed C. Shopper D. Invadder 4. Which of the following words is spelled correctly? A. Woodden B. Likeable C. Ruler D. Looseen 5. Which of the following words is spelled correctly? A. Faten B. Golfer C. Believeable D. Succesful 6. Which of the following words is spelled correctly? A. Collapseible B. Trapper C. Rober D. Whiteen 7. Which of the following words is spelled correctly? A. Carfull B. Peacful C. Reversible D. Pleasureable 8. Which of the following words is spelled correctly? A. Beautiful B. Guilless C. Exciteable D. Clearley 9. Which of the following words is spelled correctly? A. Agreable B. Allowwance C. Assistent D. Carelessness 10. Which of the following words is spelled correctly? A. Sunny B. Guned C. Stoping D. Steped
7 Answer Key 1. A 2. A 3. C 4. C 5. B 6. B 7. C 8. A 9. D 10. A studyisland.com edmentum.com West 83rd Street Suite 300, 8200 Tower Bloomington, MN EDMENTUM, INC.
8 Name: Multiple-Meaning Words Read the sentence. Pick the choice that uses the bold word in the same way as the original sentence. Circle the letter of the best answer. 1. Lack of money drove Sally to sell her house. A. The blizzard drove Debbie to decide to stay home from work. B. Dad drove us to the mall, but Mom said she would take us home. C. The family drove three hours to see the ocean. D. My older sister drove me to the movies. 2. Matt stroked his dog s back to calm him down. A. The stroke left her paralyzed on the right side of her body. B. The man had a stroke and was not able to walk. C. The girl stroked her doll s hair. D. A stroke affects a person s brain functions. 3. Frank gave his wife roses for their anniversary. A. We watched as the balloons rose to the ceiling. B. Janet planted a rose garden. C. The sun rose slowly in the sky. D. The airplane rose off into the distance. 4. He tried with his might to lift the heavy desk, but it wouldn t budge. A. It took all her might to pry open the stuck window. B. An accident might happen if you re not paying attention to what you re doing. C. According to the weatherman, it might rain tomorrow. D. My mom said that she might take us to the movies this weekend. 5. The duck stuck his bill in the water. A. Our phone bill was due on the last day of the month. B. The eagle had a fish in its bill. C. Grandpa paid the bill at the restaurant. D. We were given a bill for our hotel room during our vacation.
9 6. The rain pounded on the ground. A. The baker pounded the dough for the bread. B. We need a pound of turkey to make the sandwiches. C. Kathy bought a pound of chocolate. D. I sent her a pound of fudge for her birthday. 7. We picked strawberries at the strawberry patch. A. The patch covered his knee. B. Grandma sewed a patch on my backpack. C. The farmer tended his pumpkin patch. D. We taped a patch over the hole in the cushion. 8. I placed the envelope in the mail slot. A. The employer was able to fill the slot in the accounting department. B. Who in the department is qualified to fill the administrative slot? C. Put the quarter in the slot of the vending machine. D. There is an open slot on the baseball team for next year. 9. The maid had to strip the beds when the guests left the room. A. I need to cut a strip of paper for my project. B. My mom told me to strip the wrapping off of the package. C. I needed only one strip of beef to give to the puppy. D. There is only a small strip of grass left in the yard. 10. Old cars were started by a crank in the front of the vehicle. A. When Jill turned the crank, the jack jumped out of the box. B. Mr. Wilson is a crank who likes to yell at his kids in the yard. C. My brother is a real crank when he doesn t get enough sleep. D. I can be the biggest crank when I am hungry. studyisland.com edmentum.com West 83rd Street Suite 300, 8200 Tower Bloomington, MN EDMENTUM, INC.
10 Answer Key 1. A 2. C 3. B 4. A 5. B 6. A 7. C 8. C 9. B 10. A studyisland.com edmentum.com West 83rd Street Suite 300, 8200 Tower Bloomington, MN EDMENTUM, INC.
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### ME3-11 Measuring Perimeter
ME3-11 Measuring Perimeter Goals: Students will estimate and measure perimeters using non-standard units. Prior Knowledge Required: What measurement means Practice and comfort with other forms of linear | 8,412 | 32,614 | {"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-2018-43 | latest | en | 0.828958 |
http://mathhelpforum.com/math-topics/47030-physics-help-print.html | 1,529,530,091,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267863886.72/warc/CC-MAIN-20180620202232-20180620222232-00532.warc.gz | 210,579,512 | 3,082 | Physics help
• Aug 28th 2008, 03:31 PM
Rainy2Day
Physics help
Hello there,
I dont even know where to start with this problem (Headbang) so I hope someone here can spare some time and help me (Happy)
1) Using your calculator verify that sin 0 divided by Cos 0 is equal to tan 0 for angle 0. Try 30 degrees and prove that this result is true in general by using the definitions for sin - and cos 0 and tan 0.
• Aug 28th 2008, 04:00 PM
skeeter
you can do the calculator verification, right?
definitions ...
$\displaystyle \cos{\theta} = \frac{x}{r}$
$\displaystyle \sin{\theta} = \frac{y}{r}$
$\displaystyle \tan{\theta} = \frac{y}{x}$
now, use the above definitions to show that
$\displaystyle \tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}$
• Aug 28th 2008, 04:19 PM
Rainy2Day
Umm how do you exactly do a calculator verification? (Worried)
• Aug 28th 2008, 04:31 PM
skeeter
what kind of calculator do you have?
• Aug 28th 2008, 04:44 PM
Rainy2Day
I got a ti-84 Plus not really sure how to use it though (Doh)
• Aug 28th 2008, 05:07 PM
skeeter
1. press the [MODE] button, move the dark blinking cursor on top of the word degree and press [ENTER].
2. go back to the home screen by pressing [2nd] [MODE].
3. enter the expression sin(0)/cos(0) then [ENTER] ... the calculator will return the value 0.
4. enter tan(0) and [ENTER] ... the calculator will return the same value 0.
5. Do the same operations with other angles ... 30 degrees, 52 degrees, whatever ... you'll see that the sin/cos calculation yield the same value as the tangent calculation. As such, you've verified that sin(x)/cos(x) = tan(x) with the calculator.
• Aug 28th 2008, 05:15 PM
Rainy2Day
Thank you for your help (Rofl)
It is much appreciated (Smirk) | 535 | 1,732 | {"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} | 3.578125 | 4 | CC-MAIN-2018-26 | latest | en | 0.825836 |
https://www.studiesabroad.com/destinations/europe/greece/athens/arts-business-liberal-arts--sciences--honors-courses/ianf3123/Financial-Mathematics-492045 | 1,695,549,074,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506632.31/warc/CC-MAIN-20230924091344-20230924121344-00813.warc.gz | 1,085,998,793 | 20,868 | # Financial Mathematics
The American College of Greece
## Course Description
• ### Course Name
Financial Mathematics
• ### Host University
The American College of Greece
• ### Location
Athens, Greece
• ### Area of Study
Finance, Mathematics
• ### Language Level
Taught In English
• ### Course Level Recommendations
Lower
ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.
### Hours & Credits
• US Credits
3
• Recommended U.S. Semester Credits
3
• Recommended U.S. Quarter Units
4
• ### Overview
DESCRIPTION:
Fundamental concepts of financial mathematics and their application in investment project appraisal, credit transactions and pricing of financial products.
RATIONALE:
To provide students with a solid understanding in compound interest theory, the time value of money and of their application to the analysis of financial transactions, important for advance courses in corporate finance and investment analysis, fixed income and derivatives.
LEARNING OUTCOMES:
As a result of taking this course, students should be able to:
1. Demonstrate understanding of the time value of money and compound interest theory and their application to financial products’ pricing.
2. Apply discounting techniques for investment appraisals and explain their differences.
3. Explain the main factors influencing the term structure of interest rates and calculate spot and forward rates and contracts.
METHOD OF TEACHING AND LEARNING:
In congruence with the teaching and learning strategy of the college, the following tools are used:
− Class lectures, interactive learning (class discussions, group work) and practical problems solved in class.
− Exercises are assigned as homework, the solutions of which are reviewed in class.
− Office hours: students are encouraged to make full use of the office hours of their instructor, where they can ask questions, see their exam paper, and/or go over lecture material.
− Use of blackboard.
− IT sessions in labs, during which the student practices in recoding transactions using special accounting software (Peachtree Complete Accounting).
− A tutoring service provided by the College is also available to students who choose to get additional help.
This site uses cookies to store information on your computer. Some are essential to make our site work; others help us improve the user experience. By using the site, you consent to the placement of these cookies. | 493 | 2,608 | {"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-2023-40 | latest | en | 0.909072 |
https://networkpages.nl/reading-mathematics-in-braille/ | 1,709,065,163,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474686.54/warc/CC-MAIN-20240227184934-20240227214934-00289.warc.gz | 410,211,626 | 23,611 | Bezoek de website voor leraren en scholieren →
Have you ever wondered how people with a severe visual impairment practice and understand mathematics?
In most cases when people practice mathematics they rely heavily on visual information, write down formulas and work out examples, or draw diagrams and graphs. People with a severe visual impairment, who read in braille (from here on braille readers), have to rely on other skills and use other methods to practice and understand mathematics.
In November 2021 Annemiek van Leendert defended her doctoral thesis and received the degree of doctor. The title of her thesis is Improving Reading and Comprehending Mathematical Expressions in Braille.
Her promoters and co-promoters were Prof. Dr. P. H. M. Drijvers and Dr. L. M. Doorman (Freudenthal Institute, Utrecht University) and Prof. Dr. J. van der Steen and Dr. ir. J. J. M. Pel (Erasmus Medical Center, Department of Neuroscience).
Annemiek has been (for more than thirty years) working for Royal Visio, an organization that provides care and education for people with visual impairment. Annemiek received a grant from the Dutch Research Council (NWO) to carry out her doctoral research.
In her research, Annemiek investigated how braille readers can become more proficient in reading and understanding mathematical expressions. She approached this issue from various perspectives.
First, Annemiek did research on how braille readers read and understand mathematical expressions in braille, as well as how to improve their tactile reading strategies. In addition, she looked at the professional development of mathematics teachers teaching braille readers. She developed a course for mathematics teachers where both tactile and auditory perception played an important role.
Finally, Annemiek investigated which mathematical braille notations are used in other countries (three non-European and thirteen European countries), and how specific features of these notations can help braille readers with reading and understanding mathematics.
### Mathematics in Braille
Braille is a system of raised dots that allows people to read with their fingertips. A braille cell consists of six (⠿) or eight dots (⣿). We, therefore, speak of 6-dot or 8-dot braille. A dot can either be felt or not. The braille characters differ from each other in the location of the raised dots. In 6-dot and 8-dot braille it is therefore possible to create a maximum of $2^6 = 64$ and $2^8 = 256$ braille characters.
Braille readers read by moving their fingertips over the braille characters. Words, mathematical expressions, and equations are displayed in braille characters. When reading, the fingertips move from left to right over the braille characters, and each character must be read separately. This is called tactile reading. We can distinguish two braille reading techniques: the conjoint and the disjoint braille reading technique.
In conjoint reading, the index fingers move one or two braille cells from each other. In disjoint reading, the two index fingers explore different parts of the line. Disjoint reading offers more flexibility to braille readers because this technique allows them to combine and compare braille characters that are relatively far apart. This can be useful when reading mathematical expressions and the braille reader, for example, wants to know where the closing parenthesis is or what kind of expression it is.
The letters of the alphabet are depicted in the same way in 6-dot and in 8-dot braille. The letters a, b, and c, for example, are represented as ⠁(a),⠀⠃(b), and ⠉ (c). In 6-dot braille, a number sign (⠼ ) is often used to represent numbers. The numbers 1, 2, and 3 are then displayed as ⠼⠁(1), ⠼⠃(2), and ⠼⠉(3). This is not necessary for 8-dot braille because more combinations are possible. For example, the number 3 can be displayed as ⠩⠀ or as ⢉.
Words and mathematical expressions are displayed in braille characters. Due to the dimensions of the braille cells (⠿ or ⣿) only a limited number of combinations of raised dots is possible. In addition, all braille cells are in a straight line. It's not possible to place a braille character slightly higher or lower (as for example in $2^x$). Braille is, therefore, a linear notation.
In mathematics, complex symbols are often used, such as $\sqrt{}$ for a square root or $\infty$ for infinity. In braille, such symbols must be displayed in dots. That is difficult because the number of dots in a braille cell is limited.
#### Touching mathematics
In 6- dot Dutch mathematical braille notation, mathematical expressions resemble TeX code. An expression is written in linear tex form and then converted to braille. See the table below for some examples.
Note: # stands for number sign (⠼).
We notice right away that there is an essential difference between the mathematical notation in print and in braille. Print readers can use the shape and positions of the symbols to understand the meaning of the expression faster and better. In a fraction, for example, the numerator and denominator are placed one above the other and separated by a line. This is not possible in braille, because braille is a linear output modality, and all braille cells are the same size.
Braille readers must read each braille character individually and one after the other in order to build an overview of the mathematical expression. This demands a lot from the working memory of the braille reader. An additional complication is that the braille characters are quite difficult to distinguish from each other. A reader with typical vision, on the other hand, can make use of the specific shape of symbols and the layout of the expression.
All over the world, different mathematical braille notations are used. In some notations, getting an overview of an expression is facilitated by announcing the structure of an expression or a part of an expression, for example, that it concerns a fraction. Then an expression of the form 'bf x^#2/sqrt(#2) ef' is used, where bf stands for beginning and ef for end of a fraction. Such kind of structure-markers are not used in the Dutch mathematical braille notation.
Annemiek has been looking for other ways to help braille readers build an overview of mathematical expressions. Her research focused on tactile reading strategies that help braille readers to better understand and use the mathematical structure of expressions and equations.
### Making Mathematics Accessible
#### Relieve working memory
As an example, take equation (3) in Table 1. If the braille reader wants to form a picture of the equation, he/she will first read each braille character separately. The braille reader starts at the leftmost braille character and thus moves to the right over the braille characters. Only after reading the first open parenthesis after the '=' sign, the braille reader knows that it is about an equation. The question is whether the braille reader knows, after reading the whole equation, that it concerns an equation of two like fractions. This is what a reader with typical vision sees at a glance, and what helps to find the solution.
Therefore, Annemiek developed an intervention that teaches braille readers to use tactile reading strategies with a focus on the mathematical structure of expressions and equations. Annemiek's intervention is based on a number of assumptions about how braille readers can read and understand mathematical expressions and equations. In Annemiek's research the following didactic concept is central:
Didactic concept
1. The first step to understanding the structure of an expression or an equation is to decode, as accurately as possible, each element of the expression or equation.
2. The second step is to look for relationships between different parts of the expression, or equation.
3. Finally, the exact calculation of the expression or the solution to the equation follows.
This is elaborated in the intervention in the following way:
Intervention
1. For the first step, a conjoint reading style is the most suitable because this reading style is best suited for exact reading. During this exercise, the braille readers are also expected to try and build a global view of the expression or the equation.
2. For the second step, a disjoint reading style seems most appropriate, because it allows the braille reader to physically link and compare different parts of the expression or equation.
3. For the last step, that was performing the exact calculation or finding the solution, different reading styles can be used depending on the type of expression or equation, and on the experience and knowledge of the braille reader.
Figure 1 shows the finger movements (black and gray lines) while reading the expression '24 + 15 ='. In Figure 1(a), the whole process is displayed. Here you can see that the braille reader first reads the entire expression with his left and right index fingers. Then the sum is calculated by first adding the tens and then add the units together (20 + 10 = 30 and 4 + 5 = 9). The disjoint reading style (see Figure 1(c)) supports this process. In the end, both fingers are used to scan the whole expression again.
Figure 1: Schematic representation of the finger movements when reading the expression '24 + 15 =' in braille. The movements of the left and right index finger are shown in light and dark grey, respectively. (a) shows the whole reading process. (b), (c) and (d) represent the successive stages of this process.
### In five steps
The intervention consists of five individual lessons of 45 minutes. Lisan Boonstra contributed to the development and implementation of this intervention. In the first lesson the focus was mainly on decoding the braille characters and on the structure of mathematical expressions. The braille readers learned how to explore the mathematical structure by touch. Think, for example, holding the opening or closing parenthesis.
In the second and third lesson, the braille readers learned to use finger movements that support understanding mathematical expressions and equations. An important strategy, for example, is to read the left and right side of an equation 'simultaneously' with disjoint reading. This makes it possible to compare the expressions to the left and right of the '=' sign. In the last two lessons the students practiced with more challenging expressions and equations to master the aforementioned techniques.
### Didactical responsibility
Annemiek opens her thesis with a quote from Ignacio Estrada: “If a child can't learn the way we teach, maybe we should teach the way they learn.” This dissertation mainly focuses on braille readers aged 12 and 18 years. In the Netherlands, about 50% of these students — that's about forty students — go to regular schools. The mathematical books are converted into braille and the accompanying drawings are transformed into tactile drawings.
Annemiek's research shows that it is important that we as a society, commit ourselves to inclusive education. That's education where knowledge is accessible to all students. The fact that someone has a visual impairment does not mean that he/she has no aptitude for mathematics. From Annemiek’s research, it also turns out that it is very challenging to teach mathematics to braille readers. Mathematics teachers should therefore have plenty of opportunities to delve into this matter. They should be given the opportunity to develop the didactic skills needed to teach braille readers. And of course, new and better tools also help improve mathematical education for braille readers.
### The more personal aspect
Two questions for Annemiek: Annemiek, what do you think when you look back at the past four years?
“I start my dissertation with the aforementioned quote from Ignacio Estrada. That's the essence of what, in my opinion, education is about. During my research, I often realized how complicated it is to teach mathematics to braille readers. There is still much work to be done in that regard. Braille readers shouldn’t be performing poorly in mathematics because we don’t know (yet) how to teach them properly.”
What are your plans for the future?
“I want to continue to support braille readers (and their teachers) in mathematics. I also hope that I can continue to do research. I already have specific plans for a research project on mathematical equations and (tactile and audible) graphs. How can we help braille readers process mathematical equations? Furthermore, I want to commit myself more to mathematics education in developing countries. This concerns mathematics education for all students.”
#### Summary
In her PhD research, Annemiek investigated how braille readers can become more proficient in reading and understanding mathematical expressions. She investigated how braille readers read and understand mathematical expressions in braille, as well as how they can improve their tactile reading strategies. To achieve this goal, Annemiek developed an intervention that teaches braille readers to use tactile reading strategies with attention to the mathematical structure of expressions and equations. She also developed a course for mathematics teachers of braille readers.
"I am very grateful I was given the opportunity to do this research. The steps leading up to it were exciting and challenging. All in all it was a fantastic experience!"
We wish Annemiek all the best with her fantastic commitment to a more inclusive education!
The featured image is by Hans Braxmeier from Pixabay.
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On Friday 24th of September Professor Ton Koonen received a royal distinction “Ridder in the Orde van de Nederlandse Leeuw” during the symposium “Optical Networks – communication fabric of our society”, preceding his valedictory lecture “Light work(s)”. | 3,131 | 15,193 | {"found_math": true, "script_math_tex": 7, "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": 7, "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-2024-10 | latest | en | 0.925514 |
http://mathhelpforum.com/calculus/146964-roots-function.html | 1,527,157,776,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794866201.72/warc/CC-MAIN-20180524092814-20180524112814-00044.warc.gz | 192,148,539 | 8,998 | ## Roots of a function
Hi.
How many roots (zeros) are there to the function:
f(x)=a*cos(x+x1)+b*cos(2*x+x2) (a,b,x1,x2=const)
in the interval [-pi,pi) ?
I'm pretty sure there are either 2 or 4 roots, but I don't have any proof. | 79 | 228 | {"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-2018-22 | latest | en | 0.858471 |
https://www.wesellsonoma.com/2019/10/26/promissory-note-interest-calculator/ | 1,680,256,951,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949598.87/warc/CC-MAIN-20230331082653-20230331112653-00293.warc.gz | 1,182,374,310 | 8,954 | Balloon Mortgage
# Promissory Note Interest Calculator
Balloon Payment Excel This is called a "balloon payment" because it is typically a much larger payment than the earlier, periodic payments. discover a More Collaborative Amortization Tool with Smartsheet Smartsheet is a cloud-based work management platform in a familiar spreadsheet layout.
This borrowing cost is called interest. The extra amount of money you have to pay back in addition to the original amount borrowed. calculating the amount of interest on a note follows a simple.
Whenever a person writes a promissory note that includes interest, it is as if he documents and has witnesses. it is permitted if the borrower added a stipulation that whenever he desired, he could.
Understand the difference between APR and interest rate and how they may affect. is not based on APR, it's based on the interest rate on your promissory note.
Calculate Interest From: The date that interest will start being charged. Generally this is the date that the loan funds are received. If you have an existing loan that you are putting onto the Zimple system, this would be the date interest was paid through (i.e. the end of the prior month)..
Notes Payable Formula 46 l Meaning: how confident the market is in the business. The larger the figure, the more that shareholders are prepared to pay for a share in that company compared with the firm’s historic
A promissory note, or "promise to pay", is a note that details money borrowed from a lender and the repayment structure.The document holds the borrower accountable for paying back the money (plus interest, if any). There are 2 types of promissory notes, secured and unsecured. It’s the old magic of compound interest at work.
About Dates, First Period Interest & Year-End Totals. Important Note About Dates: This calculator supports variable length first periods. That is, the calculator calculates the exact amount of interest due even when the initial period is shorter or longer than the other scheduled periods.
Compound interest, also known as compounded interest, is interest that's calculated both on the initial principal of a deposit or loan, and on all.
refinance balloon mortgage Bankrate Calculator Loan Monthly Payment contract perma-fix environmental services, INC. PESI Files An 8-K Entry into a Material Definitive Agreement – The Loan provides for monthly payments of accrued interest only during the first. the Lender agreed under the terms of the Loan and a Subordination Agreement with our credit facility lender, to.This Mortgage APR Calculator takes all of that into account to determine what your APR will be on a home loan. It will also calculate what your monthly payments will be, as well as showing your interest costs and payments over the entire length of the loan. | 564 | 2,811 | {"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-2023-14 | latest | en | 0.952121 |
http://www.jiskha.com/members/profile/posts.cgi?name=connie&page=6 | 1,369,509,725,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368706121989/warc/CC-MAIN-20130516120841-00061-ip-10-60-113-184.ec2.internal.warc.gz | 535,931,728 | 3,528 | Saturday
May 25, 2013
# Posts by connie
Total # Posts: 200
algerbra 1
The decimal notation for the fraction -9/16 is Round to the nearest hundreth Solve 5x+8x=78 The solution is x= Simplify the answer. Type an integer of decimal. Solve using the addition principle 9.5=p-9.2 The soluation is p=
Algerbra 1
Multiply (-23)(-10)
Algerbra 1
3. In your industrial oven, you bake two baking sheets with 12 scones each, two baking sheets with 20 cookies each, and one baking sheet with 2 scones and 10 cookies. a. Write an expression that illustrates the total cost of all baked goods in the scenario above using the vari...
algerbra 1
5. When managing a business, it is important to take inventory of where your money is spent. You have a monthly budget of \$5,000. Refer to the table below and answer the questions that follow. Round your answers to the nearest tenth of a percent. Category Cost Percentage Labor...
algerbra 1
4. Your profit P is determined by subtracting the cost C, the amount of money it costs to operate a business, from the revenue R, the amount of money you earn from selling your product. Profit can be represented algebraically by the equations: Profit = Revenue - Cost OR P = R ...
algerbra1
2. You are trying to decide how to most efficiently use your oven. You do not want the oven running at a high temperature when you are not baking, but you also do not want to waste a lot of time waiting for the oven to reach the desired baking temperature. The instruction man...
Algerbra1
1.You have recently found a location for your bakery and have begun implementing the first phases of your business plan. Your budget consists of an \$80,000 loan from your family and a \$38,250 small business loan. These loans must be repaid in full within 10 years. a.What inte...
calculus
Steve, The problem has a 39 in front of the "e".
calculus
The full quesiton is "The population of a certain species of fish introduced into a lake is described by the logistic equation G(t) = (12,000) / 1+39e^(-1.2t) where G(t) is the population after t years. Find the point at which the growth rate of this population begins to ...
calculus
What is the derivative of (12,000) / 1+39e^(-1.2t)
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http://acm.timus.ru/problem.aspx?space=5&num=4 | 1,534,630,573,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221213794.40/warc/CC-MAIN-20180818213032-20180818233032-00335.warc.gz | 8,911,424 | 3,635 | ENG RUS Timus Online Judge
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## D. Buttons
Time limit: 2.0 second
Memory limit: 64 MB
### Background
As you surely already know, Yekaterinburg has gotten its right to hold The Summer Olympic Games of the 2032. It is planned that it will be allowed to Russia as a country-organizer to emend a program of the games a bit. So, in order to improve the command result it has been decided to replace the competition in gymnastics by the competition in the new game "Buttons".
The rules of the game are very simple. There’s a small heap of K buttons before two players. The players in turns take buttons from the heap, moreover, at a time one can take a number of buttons from 1 up to L. The one who takes the last button is the winner.
The rules of the Olympic Games will be a bit harder then usual. The one, who is to make a first step according to a lot, has an opportunity to fix a number K with the following restriction to it: 3 ≤ K ≤ 108 (that is the exact number of buttons that has been prepared for the Olympic tournament). The player who is to make the second step fixes a number L that satisfies the following conditions 2 ≤ L < K.
### Problem
A very crucial task is given to your team: you are to write a program that should help the second player to make his choice. In other words, given a number K your program is to find a number L that guaranties a victory to the second player with a proper game of both sides.
So, for instance, there are only three buttons in the heap, the choice L = 2 provides for the victory of the second player. Really, if the first player takes only one button at his turn, the second one wins, taking the two last buttons. On the contrary, if the first one takes two buttons, the second one wins, taking the last button.
### Input
The standard input consists of one line, which contains an only integer number K — a number of buttons in the heap, that has fixed the first player at his turn.
### Output
To the standard output you are to write the only number L — the maximal number of buttons that can be taken at a time which provides for the victory of the second player. If there are several those numbers L, you should write the least. If there are no such numbers, you are to write 0 to the standard output.
### Sample
inputoutput
```3
```
```2
```
Problem Author: Leonid Volkov
Problem Source: Ural State University Internal Contest October'2000 Junior Session
To submit the solution for this problem go to the Problem set: 1023. Buttons | 627 | 2,701 | {"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} | 2.6875 | 3 | CC-MAIN-2018-34 | longest | en | 0.946168 |
https://brainly.com/question/1764 | 1,485,103,609,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560281450.93/warc/CC-MAIN-20170116095121-00534-ip-10-171-10-70.ec2.internal.warc.gz | 785,811,848 | 9,021 | 2014-01-12T22:51:27-05:00
### This Is a Certified Answer
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
5+a over 5 = 17 , 5 +a over 5 times 5 = 17 times 5 , 5+a = 85, 5+a-5=85-5, a= 80
2014-01-13T00:03:33-05:00
### This Is a Certified Answer
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
( 5 + a )/5 = 17 / * 5
5 + a = 85
a = 85 - 5
a = 80 | 234 | 803 | {"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-2017-04 | latest | en | 0.925343 |
https://wecivilengineers.blog/how-to-calculate-number-of-bricks-per-square-meter-m2/ | 1,566,683,411,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027321786.95/warc/CC-MAIN-20190824214845-20190825000845-00449.warc.gz | 704,305,602 | 44,772 | # How to calculate number of Bricks per Square meter (m2)
Quantity of bricks depends upon:
1.Size of Bricks
2.Thickness of wall
•Full or 1 brick thick wall
•Half brick thick wall (Partition wall)
3.Thickness of mortar
#### CASE 1:
Assumptions:-
Size of brick→ 19x9x9 cm (0.19×0.09×0.09 m)
Thickness of mortar = 10 mm
Thickness of wall = Full or 1 brick thick wall
No. of bricks = Volume of brickwork/ volume of 1 brick with mortar
Volume of 1 Brick with mortar = 0.20×0.10×0.10=0.002 m^3
Volume of brickwork = Thickness of wall x Area of brickwork
Volume of brickwork = 0.19mx1m^2 = 0.19 m^3
∴ No. of bricks = 0.19/(0.002) = 95No’s (without wastage)
Consider the wastage percentage as 10 %
Then,
No. of bricks with wastage = 95 + 9.5 =104.5 No’s
If, THICKNESS OF WALL = Half brick thick wall (Partition wall)
Then,
No. of bricks without wastage = 47.5 No’s
No. of bricks with wastage = 52.25 No’s
#### CASE 2:
Size →23x11x7 cm (0.230×0.110×0.070 m)
Thickness of mortar = 10mm (0.01m)
Thickness of wall = full or 1 brick wall
No. of bricks = Volume of brickwork/ volume of 1 brick with mortar.
Volume of 1 Brick with mortar = 0.240×0.120×0.080= 0.002304 m^3.
Volume of brickwork = 1 m^2 x 0.230 m =0.230 m^3
∴ No. of bricks in 1sq.m = 0.230/0.002304 = 99.826 ≊100 No’s (without wastage)
Consider the wastage percentage as 10 %
Then,
No. of bricks with wastage = 99.826+9.982=109.808 ≊110 No’s
If, THICKNESS OF WALL = Half brick wall
Then,
No. of bricks without wastage = 49.913 (50 No’s) (without wastage)
No. of bricks with wastage = 54.904 (55 No’s)(with wastage )
Watch the video given in the link below, for better understanding and detailed explanation
How to calculate number of bricks per Square meter (m2)
Subscribe & Watch Technical video’s related to civil engineering on our YouTube channel We Civil Engineers | 602 | 1,856 | {"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} | 4.5625 | 5 | CC-MAIN-2019-35 | latest | en | 0.849246 |
http://forums.macrumors.com/threads/anyone-ever-take-discrete-mathematics.956031/ | 1,469,858,813,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257832939.78/warc/CC-MAIN-20160723071032-00218-ip-10-185-27-174.ec2.internal.warc.gz | 86,989,139 | 45,590 | # Anyone ever take Discrete Mathematics?
Discussion in 'Mac Programming' started by chrono1081, Jun 29, 2010.
1. ### chrono1081 Expand Collapse macrumors 604
Joined:
Jan 26, 2008
Location:
Isla Nublar
#1
Hi guys.
I have a Discrete Mathematics class coming up and I googled to see what type of math it is and the definitions are all over the place. In fact, most places end up saying things like "No one really knows the precise definition of discrete mathematics blah blah".
So I was wondering if anyone who has taken it for computer science could shed any light on the subject?
The reason I ask is I'm trying to gauge the difficulty of the class since I am an online student who works 84 hours a week (12 hours a day, 7 days a week, as a contractor in a hostile country). If it seems it may be something really difficult to me I would reschedule it until I am back home for good.
I know there is not much of a definite answer to this question but if anyone has taken this class for computer science what kind of things did you learn? We also have to write programs to solve the problems we are learning and from reading excerpts from various books it looks like the class is somewhat closely related to artificial intelligence.
Any help would be greatly appreciated
2. ### mfram Expand Collapse macrumors 6502a
Joined:
Jan 23, 2010
Location:
San Diego, CA USA
#2
Discrete Math covers a lot of stuff. Some of it includes proofs, mathematical induction, set theory, permutations, abstract algebra, generator polynomials, ring theory, Galois Fields... eventually leading to the mathematics associated with Error Correcting codes. Fun stuff. You won't get all of that in one course.
3. ### lee1210 Expand Collapse macrumors 68040
Joined:
Jan 10, 2005
Location:
Dallas, TX
#3
I'm guessing anyone here with a CS degree had to take some sort of discrete math. My course covered a lot of proofs, set theory, graph theory, some recursion, and complexity analysis (O-notation). This was the first course in which the traveling salesman problem was introduced.
In retrospect it was a good course, and all of the information was critical. At the time I hated it, and it was punishingly difficult. We were allowed to do the homework in groups, and 6-8 of us would get together for 4-6 hours a week, also working on things independently, and we'd still have problems finishing. Also, the professor spoke in monotone, and turned off all the lights and closed the blinds to present overhead slides. It was a real battle to stay awake.
It sounds like you have enough on your plate right now. This doesn't sound like the right time to tackle this course, or any course. Good on you if you want to try, but I would really hold off until you can commit more time and energy.
-Lee
4. ### TuffLuffJimmy Expand Collapse macrumors G3
Joined:
Apr 6, 2007
Location:
Portland, OR
#4
Took it. Hardest class ever (so far ). STUDY HARD. I would not recommend taking the class online. It's definitely one class where you want to be at every lecture and have a very available teacher so you can ask a boat load of questions.
just finished my freshman year, btw.
5. ### chrono1081 Expand Collapse thread starter macrumors 604
Joined:
Jan 26, 2008
Location:
Isla Nublar
#5
Thank you guys for all of the info
Well, I called the school to swap out the class with another one but unfortunately I have to take that one in order to move on to the last 300 level course I have and to my 400 level courses, which are all I have left. I can't drop it either since that will put me below full time status and then I'll have to pay more \$\$\$.
Whats worse, is my other class that I have this semester is an "Intro" to 3D modeling and sound which has the students making a short 3D animated film from scratch (meaning I make the models, textures, animation, etc as well as the soundtrack, voiceovers, and sound effects !). Some "intro" huh? Lol. (I'm sooooo glad I started teaching myself Maya a year ago ).
So I am stuck with both classes since they are essentially gateway classes to get to the rest of the courses.
Oh well wish me luck! I'm pretty sure I will need it
(I also started reading my Discrete Mathematics book, it looks quite challenging. I'm going to have to brush up on some data structures I rarely use as well as recursion since that is yet another thing I've only used a handful of times).
6. ### oldMac Expand Collapse macrumors 6502a
Joined:
Oct 25, 2001
#6
Best math class I ever took
I'll chime in to let you know it was one of the easier math classes I took and one of the most interesting. Possibly I found it easier because it was interesting and I had a very good professor. I found my calc series to be much harder and less practical for computer science application.
7. ### mdatwood Expand Collapse macrumors 6502a
Joined:
Mar 14, 2010
Location:
Denver, CO
#7
This. My CS degree required 2 semesters of discrete math. I found them fun, interesting and not all that hard. For me they were much better than calculus.
Discrete math is really a combination of so many other topics that it's hard to sum up in a single post. If you want to know more you should start here.
8. ### lee1210 Expand Collapse macrumors 68040
Joined:
Jan 10, 2005
Location:
Dallas, TX
#8
to oldMac and mdatwood:
Either your way smarter, or your brains work way differently than mine. I guess the professor may have had a lot to do with it, too, but my discrete math class kicked our (myself and my classmates) asses.
There was, basically, a prerequisite ladder, and each step along the way had one course that had about a 20-33% fail rate. You got to repeat one class once, and after that you were out of the program. The discrete math class was one of these. I don't know if this was by design, or the "weeding out" was just a natural effect of a rigorous program, but I was very happy to squeak by some of those classes.
-Lee
9. ### chrono1081 Expand Collapse thread starter macrumors 604
Joined:
Jan 26, 2008
Location:
Isla Nublar
#9
Thats how the school I have now does things, they have plenty of weeding out classes.
I'm actually on my third college. South Hills Business School -> Penn State University -> and now DeVry and DeVry seems to have the nastiest hardest classes out of the three (their physics class is ridiculously tough, the hardest I've ever had). I'm half afraid to see what this class will entail.
I've heard a huge mix of opinions on Discrete Mathematics, some people I know said it was the hardest thing they ever took, others said it was fairly easy.
Looking at the syllabus we go through the entire 700 page book in 8 weeks and have a ton of programming assignments so it looks like it may be a bit of a challenge lol.
Luckily those assignments are console only not MFC so I can write them on my mac
10. ### NT1440 Expand Collapse macrumors G3
Joined:
May 18, 2008
Location:
Hartford, CT
#10
Took it and failed it the first time around. I'm retaking it this fall so I can move on with my CS program.
All I can say is even if it seems easy at first (really was) STUDY YOUR ASS OFF as it will get pretty hard.
Also, I ****ing hate proofs (the reason I failed, which still hasn't been explained to me how it relates to CS more than the fun stuff like logic gates). Can anyone tell me why proofs would become the main focus of a CS type class?
11. ### mdatwood Expand Collapse macrumors 6502a
Joined:
Mar 14, 2010
Location:
Denver, CO
#11
I don't think I'm smarter than anyone. I did have a great teacher (the same one for both classes) and I really like discrete math so I naturally studied more. I didn't do nearly as well in my calculus classes, although I wish I could take them again today because my overall interest in math has gone way up since I graduated years ago.
And you're right, my program had 2 fail out courses - discrete math and the 1st programming class. I managed A's in both because I was interested in the classes I went to a liberal arts school and I remember my grades would come out and they would be A's in my major (CS) and C's in everything else. I even managed to fail Spanish a couple of times
Look at proofs as a thinking exercise. Instead of trying to memorize proofs make sure to understand them. Proofs are useful because they teach you to think logically (deduction, counter example, etc...) and systematically (don't miss steps that mess up your logic). Thinking in this manner is critical when finding hard to track down bugs among other things.
You want really hard? I had this one teacher that expected us to learn additional material while taking the test. I likened it to being taught to multiply and then from there understanding it well enough to learn to do division on the test. Only class I've ever taken that gave me nightmares
12. ### chrono1081 Expand Collapse thread starter macrumors 604
Joined:
Jan 26, 2008
Location:
Isla Nublar
#12
I've managed to pass all of the weeding out classes so far with A's. We had "Intro to computer hardware" which was more like system architecture and dealt with logic gates, memory management and plenty of x86 assembler. That was the first "programming" class I had at DeVry. We had to write data compression and do some low level graphics work. I was so glad I already was well versed in C and C++ because x86 assembler was a whole other animal. I know I was one of only a handful that passed.
Then their awful (as in hard, not awful content wise) physics class. I couldn't believe how insanely difficult it was. I got A's in physics at Penn State and thought I was good at physics. I got an A in DeVry's physics class too but omg seriously the material was so freaking difficult and I had to work hard for it. Of course, being online they engineer everything so that its not googlable and will tease by saying everything is "open books, open notes, open internet". If you don't know the material, you will not pass. I already know two people who failed out of the school cause they thought they didn't need to study and could google the answers. Being a year ahead of them I tried to warn them but to no avail. There are always those who take the lazy way out.
Anyway, I've been reading this Discrete Mathematics book for the past few hours and I have to say it is quite interesting and I can see where it would be quite applicable. (I'm also going to do all of the programming exercises to try and get a head start ) Classes start in 5 days XD
13. ### mdatwood Expand Collapse macrumors 6502a
Joined:
Mar 14, 2010
Location:
Denver, CO
#13
Well good luck and keep up the good attitude!
I love school. I finished my MsCS 2 years ago and am starting to miss taking classes again. I especially enjoyed my Ms because the teachers are less like teachers and more like peers and the classes are more focused. I have thought about a PhD, but there isn't a school nearby that offers anything CS related and I would have to quit my job and go back to ramen noodles. Another thing is that I'm very much a generalist and that doesn't usually fit with a PhD where the goal is often to become an expert in one thing.
If you have anymore school questions be sure to ask. My day job doesn't challenge me in nearly the same ways.
14. ### chrono1081 Expand Collapse thread starter macrumors 604
Joined:
Jan 26, 2008
Location:
Isla Nublar
#14
I would LOVE to go for a Masters. In fact, I plan on it. I've been eying all kinds of places to get a masters (especially DigiPen since I've always wanted to go there and I plan on living in Redmond).
Whats funny is back in high school, I HATED school and didn't even want to go to college. I thought I was bad at math and all the things I failed in high school (physics too).
Then one day it clicked, I wasn't bad at these things, I just had bad teachers. (Really I did, I'd never get my questions answered in math class :/ and this was before I had internet access). I then realized anyone can learn anything, its all how you are exposed to it. If one persons style of teaching doesn't make things click, go online or to a bookstore and find another style.
I then started college (one of my three) and started getting all A's in all of my classes including classes I thought in high school was hard (math, physics). I realized that while school can be important, self study is more important and its the way to get the most out of school. I think thats why I took a shine to online school as much as I did because it let me self study all of the time and I really feel like I am getting my moneys worth out of my education for the first time in my life. (I'll admit though, I was REALLY skeptical at first!).
Sure, there are still lectures and professor interactions, (and all of the online professors at my school are regular professors at various brick and mortar campuses), but a lot of the work is left for the student to research and figure out and I like that. IMO you learn more that way having to solve problems by yourself and being resourceful rather then being spoon fed.
Anyway enough of my tangent. I want a masters....(but first I have to get my bachelors...which will be next summer! )
15. ### pilotError Expand Collapse macrumors 68020
Joined:
Apr 12, 2006
Location:
Long Island
#15
Unless your going to be in education, I wouldn't bother. It has done absolutely nothing for my career.
Looking back, I would have gone for an MBA in finance or international business. They are much more useful degrees down the road. You most likely won't program forever, the MBA degree will take you much farther in preparing you for a CIO or CTO job. I have a buddy who became a COO at a major bank, due mainly to his MBA.
The reality is, an MSCS degree won't teach you all that much more than you will learn in the real world. If you want, you could probably go for an MBA and take 1 or 2 CS classes as an elective.
16. ### nofunsir Expand Collapse macrumors member
Joined:
Dec 30, 2009
Location:
Reno
#16
What IS Discrete Math
Discrete math puts into definable terms all those quirky math ideas you've known your whole life, yet never had a name or defined process for.
For example, proving things. (not necessarily like proofs in geometry/algebra)
If X implies Y, and Y implies Z then you must conclude that X implies Z. Also, notZ implies notX. (there are also symbols you'll learn... and it gets significantly more complicated, but you get the idea.)
Or, "how many ways are there to arrange 6 people from a group of 10 (6 female and 4 male) into 6 chairs, if a male must be at one end of the line of chairs."
Or, "how many numbers between 1 and 1,000,000 are divisible by 11?"
Or things like, "counting to infinity", aka proof by induction: proving a proposition is true because A) you can prove step 1 and B) you can also prove that "if the proposition is true for step n, it is also true for step n+1" --> therefore the initial proposition is proven
Believe it or not, there are actually formulas for these things.
My advice: (I got an A, and not just an A- )
Read the chapter summaries before class. (to familiarize yourself with the confusing terms)
Do a good job on whatever project the teacher gives. (since the tests can be intimidating)
Take your time on tests, this is one of those subjects where the teacher can ask really SUCKY trick questions.
When you're stuck, google the HW questions with quotes around it. Most books ask the exact same questions.
Keep the book.
17. ### saltyzoo Expand Collapse macrumors 65816
Joined:
Oct 4, 2007
#17
For the average person with the proper aptitude and talent for programming, discrete math will be one of the most fun and easiest classes you will take to get your degree.
18. ### mdatwood Expand Collapse macrumors 6502a
Joined:
Mar 14, 2010
Location:
Denver, CO
#18
Everyones mileage is different, but I look at MBAs as a dime a dozen nowadays. Also, unless you get your MBA from one of the big name schools I can't imagine it's going to be the key to landing a job as a COO at a major bank. The big wigs that I know personally at companies have a variety of degrees from business to music to philosophy to nothing at all. Proven ability is more important that anything else out there.
With that said, as a technologist I would never ignore understanding business (software is mostly written to solve business problems). If I was going to go the business route with school I would pick something like finance over a general MBA. There is a school in Chicago that offers a program in financial engineering where you study what a lot of the quant guys do, but I'm getting a little off topic now
In general though, very rarely does getting any degree, except maybe your undergrad, automatically mean a job or more money. Additionally, the longer ago the degree was completed the less it matters. What my MsCS has done for me is that I met a lot of people some of who I am now working with on various projects that may turn into a much better job than I have now. Many of the big tech companies we talk about daily started with a few techies in grad school throwing together an idea.
In short, do what you like, do it well, be passionate about it and things will work out.
19. ### chrono1081 Expand Collapse thread starter macrumors 604
Joined:
Jan 26, 2008
Location:
Isla Nublar
#19
@pilotError - I think education may be something I would enjoy down the road. I think it would be fun to be a computer science teacher at a high school or something. I have friends who are teachers and they all had bachelors degrees but had to go get masters to keep their jobs. I guess its a new requirement in my state.
@nofunsir and saltyzoo - I've noticed the sucky trick questions in the book already I've had to write programs to solve some of them (which is good since its the type of thing I've never written programs for before).
The "how to solve the magicians card trick mathematically" questions are stickers for me because I keep screwing up the rules lol but thats my own careless mistakes. I do think that I will enjoy this class though and I can see it being very applicable, more so then most other math I've taken to computer science.
@mdatwood - I know what you mean about degrees not making more money. I make roughly triple of what my degree holding friends do and I have no degree, but I have PLENTY of experience, they do not.
Unfortunately my experience is in the IT field with regards to hardware such as servers, networking, etc. I have no professional programming experience, only hobbyist, which is what scares me. Whats worse is I know the school I go to now people poke fun at (DeVry), why I don't know because out of the three colleges I went to (Penn State included) DeVry is the only one where I feel like I am getting my moneys worth. Maybe its because they accept pretty much everyone lol. I just don't want an employer to see my resume and assume I am worthless because of the school I picked : / I worked my @\$\$ off to get the grades I have.
To combat the potentially real scenario that I am judged based on my school, I've been working on a portfolio (Hopefully they will judge me by my portfolio). I've taught myself Maya, Logic (still a bit new to this one), Photoshop, Corel Painter, C++, C, Objective-C, Unity3D, ZBrush, and am very proficient in all of them (except for Logic, still learning the ins and outs of that one). I have several completed game projects under my belt where I created everything from scratch. I'm currently revisiting those projects, optimizing my code that I wrote awhile back and redoing the artwork and music.
If you haven't guessed by now I'm trying to a job in the games industry I'll know by next summer if I am successful or not since that is when I graduate XD
This is a HUGE gamble for me since I'm leaving my current job to pursue my dream of being a game programmer. I'll make sure that I make it work.
I'm hoping for a programming job but I'll take anything I can get to get my foot in the door
20. ### mdatwood Expand Collapse macrumors 6502a
Joined:
Mar 14, 2010
Location:
Denver, CO
#20
Chrono,
I'm definitely not saying degrees are useless, especially an undergrad degree since many companies require some sort in order to get through the screening process. Also, getting a CS degree helps the self taught person learn the things they didn't even know they didn't know.
My comment was mainly on advanced degrees. At that point you have to just want the degree for personal satisfaction and growth because they rarely turn into automatic money or jobs.
With the portfolio you have I think you are already way ahead of the curve. The problem you're going to run into is that everyone wants to be a game programmer so companies can pick and chose and they can pay like crap. Not much fun. It sounds like you're very skilled, so if that doesn't work out you can head back corporate programming and make the easy money then do iPhone games on the side. Speaking of, is that something you have already thought about? Doing your own thing making iPhone games has a lot more potential reward than working for a game company.
BTW, I've interviewed tons of people and the large majority have been horrible. I can only wish that someone came in with a portfolio and your attitude
21. ### chrono1081 Expand Collapse thread starter macrumors 604
Joined:
Jan 26, 2008
Location:
Isla Nublar
#21
I didn't think you meant that at all. Sorry I just reread my post and realized it sounded snotty Lol. That wasn't my intent
I agree about the CS degree, sometimes I wish I went that route instead because even though I do a lot of research, there are things that I don't know that I don't know. iTunes U helps a lot in this regard because I always will load up CS lectures and watch them. I feel like my bases are pretty well covered and that I have a good general knowledge of different main areas of computer science but there is always still so much to learn.
As for the corporate programming thing, I have thought about that a lot too. I'd love to work for a game studio just to see what its like in the real world, but unfortunately most places do pay crap and its tough to get in.
Working in a corporate environment and making games on the side is actually pretty appealing to me since (I know this will sound selfish but...) I like to have every aspect of my game under my control and I like to create it all by myself. I know it doesn't work that way in the real world but thats why I like hobbyist game development because hobbyist development usually works that way. I also do like the casual game market more then mainstream because you can pretty much create whatever you want, not just what sells well.
So much to think about and only a year left to do it!
22. Sep 4, 2011
Last edited: Sep 4, 2011
### KikoDoran Expand Collapse macrumors newbie
Joined:
Sep 4, 2011
#22
This may help
In Discrete Math you will find yourself doing a lot of truth tables. Download this widget:
and here are some instructions the developer has to help you input stuff:
http://logik.phl.univie.ac.at/~chris/Logikwidget/index-en.html
Saved me a lot of time when trying to find whether things are logically equivalent, tautologies, or contradictions, etc...
Hope it helps. I took some Doctorate classes when I was stationed in Iraq 5 years ago and I know at times it really kicked my butt with all the reading. Hang in there and don't be overwhelmed by Discrete Math. It isn't that hard if you relax and study hard. It is very helpful in programming logic in general...
Kiko Doran
23. ### mmendoza27 Expand Collapse macrumors 6502
Joined:
Oct 18, 2007
#23
This is a really interesting thread. I was actually just looking ahead at my future classes and I have to take Discrete Mathematics, Mathematical Foundations and Analysis of Algorithms for my BS. These fall under math theory and I can also take electives which could vary across other math subjects such as linear algebra. I'm thinking about picking up a Data Structures book for Java and reading it to prepare myself for these classes coming up. Definitely enjoyed the thread and enjoy seeing other people as enthusiastic as myself about programming.
24. Sep 7, 2011
Last edited: Sep 7, 2011
### mydogisbox Expand Collapse macrumors member
Joined:
Jan 16, 2011
#24
I would actually put it the other way around: Why would you have CS classes where proofs are not the main focus? To understand why you have to look at what Computer Science is. Not to be too pedantic, but Computer Science is science. From the wikipedia entry on science:
Science (from Latin: scientia meaning "knowledge") is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.
So basically, Computer science is the systematic study of computers and computability. The fact that most people get CS degrees in order to get programming (read engineering) positions is, I think, primarily a reflection of two things.
First, computer science as a discipline is not particularly practical. Other fields (such as math or hard sciences) tend to be funded by industry in ways that computer science, for various reasons, isn't. As a result, computer science depends on programmers to boost their # of degrees awarded (although this is changing with the creation of software engineering degrees at some schools).
Second, the study of computers/computability requires proficiency in programming and, conversely, being well versed in what is computable is a valuable trait in a software developer.
So, you ask why Computer Science courses focus on proofs, and, in response, I ask why any CS course would not focus on proofs.
25. ### Sander Expand Collapse macrumors 6502
Joined:
Apr 24, 2008
#25
If I were to get your resume on my desk and would read this thread I was googling around a bit as a preparation for your interview, I'd know what direction I was going to steer the interview.
You seem like a very talented and hard-working all-rounder. You like to take control and responsibility, and finish stuff. That's good, especially since here in The Netherlands, it's not unusual to be offered an unlimited contract from the get-go (i.e., not a temporary or "trial" contract). That means I have to be careful not to hire "one trick ponies", unless we'd be in dire need of a certain specialty. So, that part is covered.
However, we also try to weed out the "prima donnas". I'd make sure I'd present you with some situational questions about having to delegate work to others, and how you'd deal with that. Someone who knows everything better than anyone else is nice and all, but we do have more work than you can handle by yourself. How well do you play with others? Can you let things go? Scoring an A- on the final project because you did your part with an A result and left the other half to a less talented guy who got a B is still better than scoring a C on the total because you finished your 150% of the work with an A but the final 50% never got done at all...
Just some food for thought. | 6,283 | 27,112 | {"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-2016-30 | longest | en | 0.954581 |
https://statmodeling.stat.columbia.edu/2006/03/17/posterior-distributions-vs-bootstrap-distributions/ | 1,601,248,228,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600401582033.88/warc/CC-MAIN-20200927215009-20200928005009-00247.warc.gz | 614,056,139 | 8,797 | ## Posterior distributions vs bootstrap distributions
A Bayesian posterior distribution of a parameter demonstrates the uncertainty that arises from being a priori uncertain about the parameter values. But in a classical setting, we can obtain a similar distribution of parameter estimates through the uncertainty in the choice of the sample. In particular, using methods such as bootstrap, cross-validation and data splitting, we can perform the simulation. It is then interesting to compare the Bayesian posteriors with these. Finally, we can also compare the classical asymptotic distributions of parameters (or functionals of these parameters) with all of these.
Let us assume the following contingency table from 1991 GSS:
Belief in Afterlife Gender Yes No/Undecided Females 435 147 Males 375 134
We can summarize the dependence between gender and belief with an odds ratio. In this case, the odds ratio is simply θ= (435*134)/(147*375)=1.057 – very close to independence. It is usually preferable to work with the natural logarithm of the odds ratio, as its “distribution” is less skewed. Let us now examine the different distributions of log odds ratio (logOR) for this case, using bootstrap, cross-validation, Bayesian statistics and asymptotics.
Asymptotics
The large-sample approximating normal distribution has the mean of log θ, and a particular standard deviation, but the expression is nasty to typeset in HTML.
Bayesian
We have to assume a model. We will simply model the data as arising from a multinomial, using the usual symmetric Dirichlet prior with α=1. The odds ratio is then computed using the probabilities in the posterior, not using the counts.
Bootstrap
logOR is computed as above from the sample but from bootstrap resamples (samples of equal size from the original sample but with replacement).
K-fold Cross-Validation
The data is divided into K groups of approx. equal size, and K “versions” of the logOR are computed by omitting one of the groups and then estimating from the sample.
9:1 Data Splitting
logOR is computed from a random selections (without replacement) of 90% of the data.
Results
10000 samples of logOR were drawn using the above methodologies. We can see that bootstrap, Bayes, asymptotics and 2-fold cross-validation yield very similar distributions of logOR. On the other hand, k-fold cross-validation results in distinctly different distributions. Leave-one-out is not even shown.
Conclusion
Different assumptions lead to different conclusions. And the choice of splitting/cross-validation/bootstrap/asymptotics is the same kind of a prior assumption as is the Bayesian prior. Which assumption is correct? ;) Which assumption is easier to explain? What do assumptions mean?
While 1091 cases are quite a few, if the above experiment was repeated with a much smaller number of cases, the Bayesian approach would start making more sense than others. But when the number of cases is large, there is no major difference. | 611 | 2,986 | {"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} | 3.03125 | 3 | CC-MAIN-2020-40 | latest | en | 0.887575 |
http://nafeducation.org/lib/deleted_neighborhood.htm | 1,547,860,258,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583660877.4/warc/CC-MAIN-20190118233719-20190119015719-00132.warc.gz | 160,288,566 | 2,394 | deleted neighborhood
Deleted Neighborhood
The proper name for a set such as {x: 0 < |xa| < δ}. Deleted neighborhoods are encountered in the study of limits. It is the set of all numbers less than δ units away from a, omitting the number a itself.
Using interval notation the set {x: 0 < |xa| < δ} would be (a – δ, a) ∪ (a, a + δ). In general, a deleted neighborhood of a is any set (c, a) ∪ (a, d) where c < a < d.
For example, one deleted neighborhood of 2 is the set {x: 0 < |x – 2| < 0.1}, which is the same as (1.9, 2) ∪ (2, 2.1). | 177 | 538 | {"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-2019-04 | latest | en | 0.972033 |
http://erikoest.dk/quanti.htm | 1,579,285,394,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250590107.3/warc/CC-MAIN-20200117180950-20200117204950-00186.warc.gz | 59,006,523 | 5,903 | Erik Østergaard - Bit(s) and Byte(s) Quantifiers / Bit(s) og byte(s) angivelser
## Quantifiers - Jargon
In techspeak and jargon, the standard metric prefixes used in the SI (Système International) conventions for scientific measurement have dual uses. With units of time or things that come in powers of 10, such as money, they retain their usual meanings of multiplication by powers of 1000 = 10^3. But when used with bytes or other things that naturally come in powers of 2, they usually denote multiplication by powers of 1024 = 2^(10).
Here are the SI magnifying prefixes, along with the corresponding binary interpretations in common use:
``` prefix decimal binary
kilo- 1000^1 1024^1 = 2^10 = 1,024
mega- 1000^2 1024^2 = 2^20 = 1,048,576
giga- 1000^3 1024^3 = 2^30 = 1,073,741,824
tera- 1000^4 1024^4 = 2^40 = 1,099,511,627,776
peta- 1000^5 1024^5 = 2^50 = 1,125,899,906,842,624
exa- 1000^6 1024^6 = 2^60 = 1,152,921,504,606,846,976
zetta- 1000^7 1024^7 = 2^70 = 1,180,591,620,717,411,303,424
yotta- 1000^8 1024^8 = 2^80 = 1,208,925,819,614,629,174,706,176
```
Here are the SI fractional prefixes:
``` prefix decimal jargon usage
milli- 1000^-1 (seldom used in jargon)
micro- 1000^-2 small or human-scale
nano- 1000^-3 even smaller
pico- 1000^-4 even smaller yet
femto- 1000^-5 (not used in jargon---yet)
atto- 1000^-6 (not used in jargon---yet)
zepto- 1000^-7 (not used in jargon---yet)
yocto- 1000^-8 (not used in jargon---yet)
```
The prefixes zetta-, yotta-, zepto-, and yocto- have been included in these tables purely for completeness and giggle value; they were adopted in 1990 by the '19th Conference Generale des Poids et Mesures'. The binary peta- and exa- loadings, though well established, are not in jargon use either --- yet. The prefix milli-, denoting multiplication by 1000^(-1), has always been rare in jargon (there is, however, a standard joke about the 'millihelen' --- notionally, the amount of beauty required to launch one ship). 'Femto' and 'atto' (which, interestingly, derive not from Greek but from Danish) have not yet acquired jargon loadings, though it is easy to predict what those will be once computing technology enters the required realms of magnitude.
There are, of course, some standard unit prefixes for powers of 10. In the following table, the 'prefix' column is the international standard suffix for the appropriate power of ten; the 'binary' column lists jargon abbreviations and words for the corresponding power of
1. The B-suffixed forms are commonly used for byte quantities; the words 'meg' and 'gig' are nouns that may (but do not always) pluralize with 's'.
``` prefix decimal binary pronunciation
kilo- k K, KB, /kay/
mega- M M, MB, meg /meg/
giga- G G, GB, gig /gig/,/jig/
```
Confusingly, hackers often use K or M as though they were suffix or numeric multipliers rather than a prefix; thus "2K dollars", "2M of disk space". This is also true (though less commonly) of G.
Note that the formal SI metric prefix for 1000 is 'k'; some use this strictly, reserving 'K' for multiplication by 1024 (KB is thus 'kilobytes').
K, M, and G used alone refer to quantities of bytes; thus, 64G is 64 gigabytes and 'a K' is a kilobyte (compare mainstream use of 'a G' as short for 'a grand', that is, \$1000). Whether one pronounces 'gig' with hard or soft 'g' depends on what one thinks the proper pronunciation of 'giga-' is.
Confusing 1000 and 1024 (or other powers of 2 and 10 close in magnitude) --- for example, describing a memory in units of 500K or 524K instead of 512K --- is a sure sign of the marketroid. One example of this: it is common to refer to the capacity of 3.5" (microfloppies) as '1.44 MB'. In fact, this is a completely bogus number. The correct size is 1440 KB, that is, 1440 * 1024 = 1474560 bytes. So the 'mega' in '1.44 MB' is compounded of two 'kilos', one of which is 1024 and the other of which is 1000. The correct number of megabytes would of course be 1440 / 1024 = 1.40625. Alas, this fine point is probably lost on the world forever.
##### My Sources / Mine kilder
Sources: Various books, the Internet, and various encyclopedias.
Kilder: Forskellige bøger, internettet og forskellige leksikoner.
### Computer Data Representation and Number Systems / Computer data repræsentation og talsystemer
©1997 - 1999 Erik Østergaard, Copenhagen, Denmark. | 1,382 | 4,494 | {"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} | 2.90625 | 3 | CC-MAIN-2020-05 | latest | en | 0.806098 |
https://www.meritnation.com/ask-answer/expert-answers/class-7-math/gr7-sb1/page:2 | 1,623,660,610,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487611641.26/warc/CC-MAIN-20210614074543-20210614104543-00122.warc.gz | 802,072,673 | 10,655 | Subject: Maths, asked 2 days, 2 hours ago
Subject: Maths, asked 2 days, 3 hours ago
Subject: Maths, asked 2 days, 17 hours ago
## At the end of the winter season, a shopkeeper earns a profit of Rs 100 by selling a shirt but incurred a loss of Rs 50 on selling a woollen jacket. At the end of sale on one day, he incurred a loss of Rs 200 while he sold 10 jackets. How many shirts did he sell on that day?
Subject: Maths, asked 2 days, 23 hours ago
Subject: Maths, asked 2 days, 23 hours ago
Subject: Maths, asked 2 days, 23 hours ago
Subject: Maths, asked 2 days, 23 hours ago
Subject: Maths, asked 3 days, 5 hours ago
Subject: Maths, asked 3 days, 14 hours ago
## If x=6+(8×¼)-(6÷⅔) then the value of x will be?
Subject: Maths, asked 3 days, 7 hours ago
Subject: Maths, asked 3 days, 23 hours ago
Subject: Maths, asked 3 days, 23 hours ago
Subject: Maths, asked 3 days, 23 hours ago | 277 | 897 | {"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} | 3.078125 | 3 | CC-MAIN-2021-25 | latest | en | 0.960514 |
http://xahlee.info/SpecialPlaneCurves_dir/Intro_dir/aboutThisProject.html | 1,725,801,258,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651002.87/warc/CC-MAIN-20240908115103-20240908145103-00373.warc.gz | 55,081,818 | 2,834 | # Introduction
This personal project started when I was learning calculus in 1993. I found a book Curves and their Properties by Robert C Yates at school library. The book tells various interesting properties that relates different curves. For example, if you roll a parabola along a line, the trace of its focus is a catenary, a shape assumed by a hanging chain. If the parabola rolls on a congruent parabola, the trace of its vertex is a cissoid, a curve used by the Greeks to double the cube.
I wrote some graphical programs in Mathematica to see these properties, partly as a programming exercise. These programs matured into several Mathematica Packages over the years. In summer 1995 I worked as a intern at Wolfram Research Inc., the company that makes Mathematica. There I studied and wrote more Mathematica programs on plane curves as a project.
The goal of the project is to produce materials that demonstrate interesting properties of plane curves visually. Many concepts or properties of plane curves such as cusp, tangent, evolute, involute, envelope, are more readily explained by a illustration or animation. The mathematics in these pages are beginning college level. Overall, this project is designed to educate and entertain.
At Wolfram Research, I got acquainted with the World Wide Web. It seems to be the perfect medium for making my notes public. I started to convert my notes to html in February 1996.
Note that the historical notes about these curves are gathered from second-hand resources. (That is, books and articles written by math historians.)
As of 2004-12, this site contains 80 animations, 110 Geometer's Sketchpad files, 450 illustrations, 90 Mathematica notebooks, and 90 HTML files. I hope you enjoy them.
## Acknowledgement
This project is based on materials from several books (See: bibliography). In the beginning, the main reference and motivation was: Curves and Their Properties by Robert C Yates, 1952.
During my intern at Wolfram, many people have helped me in Mathematica programing. Especially Matthew Cook, Michael Trott, and Robby Villegas. Thanks to Terry Rob who gave me many good advice at a early stage of the project.
There are few companies I like to thank. Wolfram Research, Inc., for letting me work on this project during my intern in 1995. Also thanks to the following companies who donated their software.
• Key Curriculum Press. Geometer's Sketchpad is dynamic geometry software particularly good at doing synthetic Euclidean geometry.
• Cabri Geometry. Cabri Geometry II is a dynamic geometry software particularly good at doing synthetic Euclidean geometry and Projective geometry.
• Pedagoguery Software. GrafEq is a curve plotter specializing in implicitly defined curves.
• http://www.nucalc.com. NuCalc plots both curve and surfaces with dynamic animation capabilities. | 597 | 2,846 | {"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-2024-38 | latest | en | 0.955327 |
http://magoosh.com/gre/2012/is-the-revised-gre-adaptive/ | 1,477,690,465,000,000,000 | text/html | crawl-data/CC-MAIN-2016-44/segments/1476988725475.41/warc/CC-MAIN-20161020183845-00009-ip-10-171-6-4.ec2.internal.warc.gz | 158,524,044 | 35,641 | offers hundreds of practice questions and video explanations. Go there now.
This is a great question, whether you’ve taken the old GRE or are just embarking on your GRE journey.
The short answer is that the new GRE is still adaptive, but in a very different way.
The Adaptive Nature of the Revised GRE
On the old GRE, the test adapted within each section. The computer would assume that every test taker was equal and would start with a mid-range question. If the test taker answered a few questions correctly, the test would become progressively difficult. And if the test taker answered the questions incorrectly, the test would become easier.
The old GRE algorithm is slightly more nuanced than this, but really the details, at this point, are moot. We only care about the revised GRE.
The Revised GRE adapts between sections
A salient difference between the old and revised GRE is that the revised GRE has two sections for math and two sections verbal. The old GRE had one section for each.
That the revised GRE has two sections for each subject is significant – this allowed ETS to make the test make the test adapt between sections.
There is no adaptation within section
The section adaptation is the only adaptation that happens on the new GRE. What this means is that the questions do not change depending on whether you answer them correctly. You can think of it this way – each section is static. Your performance on the first section will determine whether you get an easy section or a difficult section. The easy section is static and the difficult section is static. Again, this means the questions in the section do not change. You could miss the first ten and question 11 will still be question 11. You could work backwards from the last question, nailing all of them, and question 11 is still question 11.
The level of difficulty of questions is random
Even though a section is static it doesn’t mean that, theoretically, it couldn’t become progressively harder. After all, this is what the old old GRE, meaning the paper-based 1990 GRE was like. However, there is no order of difficulty on the Revised GRE. The first question can be the hardest and the last question the easiest. Most likely, the first and last question will be medium ones.
Each question is weighted the same
Do not spend 5 minutes trying to answer the question in which four circles are wedged inside some octagon (actually, that would make an interesting question – but another time!). Each question is weighed the same. So the question that gives you the radius of a circle and asks for the area, which should take no more than 15 seconds, is worth the same as the one about the monstrous polygon.
Can you let up at the end?
Again, each question is weighted the same – and the computer hasn’t “figured you out” the way it supposedly did with the old GRE. Your score on the new GRE is based on how many questions you miss. The point here is that you do not reach a certain level in which the computer “thinks” you are doing very well (à la the old GRE). So do not slack off at the end, thinking you answered most questions correctly and now you’re set.
The only reason I even mention this – as it is counterintuitive – is because many are still operating under the conception of the old GRE, in which you could, at least somewhat, slack off at the end without hurting your score too much.
Takeaways
• The Revised GRE does not adapt within a section, only between sections
• Each question is weighted the same
• Difficult questions and easy questions are randomly mixed throughout the section
if you want to know more about the test check out the Ultimate GRE Guide!
By the way, students who use Magoosh GRE improve their scores by an average of 8 points on the new scale (150 points on the old scale.) Click here to learn more.
67 Responses to Is the Revised GRE Adaptive?
1. Kingsley September 18, 2016 at 8:59 am #
I understand that the gre is adaptive , but my question is , does the scores are affected with the difficulty level? Like with easy level 10 equals 8 and in difficult level 10 equals 12 ????? Help
• Magoosh Test Prep Expert September 21, 2016 at 6:51 am #
Hi Kingsley,
Let’s dive right in. Within each section, all questions contribute equally to your raw score, which is the number of questions you answered correctly. Your raw score is then converted to a scaled score through equating. Here’s what ETS has to say about “equating”:
“The equating process accounts for minor variations in difficulty among the different test editions as well as the differences in difficulty introduced by the section-level adaptation. Thus a given scaled score for a particular measure reflects the same level of performance regardless of which second section was selected and when the test was taken.”
The score is not based on a % correct, but rather on the raw score and then that scaling process mentioned above. Many students assume the raw to equated score conversion will simply mean mapping the raw score onto this new scale, but the process is not so transparent. Imagine a student got got a total of 30 correct, which is a raw score of 30/40. This does not mean that the scaled score should be 160, however. I have seem as much as +/-5 point difference between the approximation (adding raw score to the 130-170 scale) and the actual equated scale. This is because of the relative difficulty of the questions you got and how they scale according to average difficulty.
If we use the rule of thumb above, 65% accuracy across 40 verbal questions (there is no estimate for just half of the verbal questions you would face) would be 26/40 as a raw score, so we could probably reasonably expect the true score to be between 154 and 159 depending on the difficulty of the questions missed and answered correctly. This estimate is true for quant and verbal performance. This means that exactly 30 right could but probably will not result in a 150. I hope this helps illustrate! 🙂
2. Cartoondiablo August 15, 2016 at 2:45 pm #
Do you know what the cut-off for getting the more difficult second section is?
• Magoosh Test Prep Expert August 16, 2016 at 4:00 am #
Hello! Unfortunately, we don’t have specifics to this degree because ETS’ scoring and underlying statistics are secret. The best you can find online is anecdotal evidence from individual students.
3. Bhumik August 14, 2016 at 5:23 am #
i used a kaplan sofware for practice and in quantitive section my 27 ans are right but score shows 151 =21 mark hows this possible and what the trick behind it let me know pls the day after tommorow i appear for Gre revised test pls .
• Magoosh Test Prep Expert August 14, 2016 at 12:57 pm #
Hi Bhumik,
While I can’t comment on the accuracy of the Kaplan tests, getting 27 answers right doesn’t guarantee a score of 157. Remember, the scale from 130-170 has 41 possible scores, first of all. Second, the scaling that happens during equating means that the difficulty level of the questions you answered correctly will play into the score you ultimately get. I typically see a difference of +/- 5 points from the estimate of [questions answered right] + 130.
I hope this helps a little, and good luck on your test! 🙂
4. Akhil June 28, 2016 at 7:23 am #
1. If we perform extremely well on the very first quant section, does that have any impact on the next verbal section?
2. If we perform very poor on the very first verbal section, will the next verbal section be easier than the previous one?
• Magoosh Test Prep Expert June 29, 2016 at 7:14 am #
Hi Akhil 🙂
Good questions! Firstly, your performance on the first quant section does not impact the next verbal section. Your performance on the first quant section only affects the subsequent quant section, while your performance on the verbal section only impacts the subsequent verbal section. Also, if you do not perform very well on the first verbal section, yes, the other verbal section will most likely have a higher percentage of easier questions.
It’s also important to keep in mind that you’ll have an experimental section on the exam, which is not graded. It may be verbal or math and will probably be at the same difficulty level as the hard second section. The experimental section may appear at the beginning, in the middle, or at the end of your exam.
Hope this clears up your doubts 🙂
5. Shim June 24, 2016 at 10:38 am #
• Magoosh Test Prep Expert June 29, 2016 at 2:15 am #
Hi Shim 🙂
Good question! Because of the limited size of the PowerPrep software’s question pool, no, it is not really section-adaptive. If you take the same practice exam more than once, you’ll see the same questions, although the order of the questions (and which questions are in a given section) may vary. It’s also good to keep in mind that the PowerPrep exams use the same material as the CD that comes with the ETS GRE Official Guide.
Hope this helps 🙂
6. Izaak June 21, 2016 at 10:31 pm #
Hi Magoosh Team,
I’m pretty confused about the limits when one ends up with a lower difficulty (Easy, Med.) second section; strictly speaking quantitative.
Assume that I get the maximal score in the first section that limits me to the boundary of the second section (i.e, if the boundary to get 2nd:Easy is a score on 1st of < 10, and I get 9).
Further, lets say that on the second section I get all questions correct.
In such a case I get:
2nd: Hard – Upper bound is 170
2nd: Med – Upper bound is ?
2nd: Easy – Upper bound is ?
I understand that the first section limits my score, so, given I ended up with 2nd: Easy, I have to have gotten a bunch wrong on 1st. However, does a 20/20 score on 2nd:Hard contribute as many points as 20/20 score on 2nd:Easy?
• Magoosh Test Prep Expert June 29, 2016 at 6:43 am #
Hi Izaak,
This is a tough question! And only ETS would have a definite answer. Honestly, even if this were an easy question to answer, it would not help you to do any better on the test. Let’s take a look at why:
This brings up another point: students aren’t given “easy” sections or “hard” sections. It will be a sprinkling of different difficulty levels. There are not just three categories of difficulty on the test; it is more nuanced and complex than simply a “hard” section or “medium” section. Due to the adaptive nature of the test, each section will have a range of difficulties that are based on your performance on previous sections.
Lastly, you have no way to know for sure what questions you got right and what questions you got wrong. You can guess and estimate, but none of this is a guarantee for knowing. So even if I could answer your question, you would still have the added barrier of trying to determine how many questions you have answered correctly. Again, this is just a waste of your brain power. Use as much of your mental energy for answering questions—not trying to figure out how many questions you answered correctly. Ultimately, your study time will be better spent focusing on strategies and practice.
I hope this helps, at least a little!
7. Joanne April 15, 2016 at 1:24 pm #
Hi Chris,
Maybe a little off-topic, but is there a way to skip the multiple choice and do the numerical entry questions first since its much harder to “guess” on those?
I’d rather have 5 multiple choice questions left when I’m down to say 1 minute than 5 numerical entry questions with 1 minute left.
Thanks!
• Magoosh Test Prep Expert April 18, 2016 at 9:33 am #
Hi Joanne,
I haven’t personally used this strategy before, but the reasoning makes sense to me. If you want to focus on what feels like the more labor-intensive work and leave the guessable questions for the end, that could work! (Of course, ideally there will be no guessing involved.) 🙂
8. Sarah March 30, 2016 at 9:56 am #
I don’t really understand the purpose of the adaptive nature of the computerized test. Also, if someone takes the paper version, how does that compare regarding score since the paper version is static?
Thanks.
• Magoosh Test Prep Expert April 11, 2016 at 6:20 am #
The adaptive nature of the GRE is one of the stranger features of the exam, to be sure. The purpose relates to scoring. On the electronic version of the exam, scores are determined partly based on the difficulty level a student progresses to, instead of just being based on the amount of correct answers. The exact algorithm for adaptive scoring is a bit complicated, and ETS doesn’t reveal much specific information on how questions of different difficulty are factored in. Rachel Wisuri gives a little bit of insight into this here.
Since there’s no adaptive component to the paper test, GRE paper-based test scores have fewer adjustments for the relative difficulty of the questions you answer. There will still be some adjustments to your score based on difficulty, because different paper-based tests have a different mix of questions, and you may be randomly given some questions that are either easier or more difficult than average.
Also note that there is one significant format difference between the electronic and paper GREs. The paper GRE has 25 questions per Verbal and Quant section, while the electronic one has only 20 questions a section.
9. Karen March 11, 2016 at 7:10 pm #
Hi, I know this post is similar to many others’ questions, but I am still very unsure of the answer. I have been doing very well on the first math section of the test (generally getting 2-5 incorrect). The next section is much more difficult, and I end up doing the reverse, getting about 5 right! I feel much more rushed in that section, whereas for the first section I have about 7 extra minutes at the end to check my questions. Can you advise the best strategy for this situation?
Thank you for all your work at magoosh. The site have been a life saver!
• Magoosh Test Prep Expert March 15, 2016 at 4:29 am #
Hi Karen,
Thanks for reaching out! 🙂
Just to be clear–are you saying on the real GRE this is your experience? If so, that makes sense if you do very well on the first section that your second section will be harder. This is the direct result of that adaptive nature we are talking about. You will need to work on your understanding and efficiency related to those harder, less common concepts to combat the issue–both time and accuracy. Do you have any insight into which types of questions specifically cause you trouble? That could give you a starting point as you try to decide where to focus your energies!
I hope that helps a little. 🙂
10. Ray October 9, 2015 at 3:38 pm #
Hey,
I’m a little confused about order of difficulty on the Math section of the GRE. You say there is no order of difficulty within a section here.
http://magoosh.com/gre/2014/book-review-official-gre-quantitative-reasoning-practice-questions/
“Would #5 in the Quantitative Comparison actually show up as a #5, which is presumably in the medium range?”
How can you predict that #5 is in the medium range of difficulty if there is no established order of difficulty? Just want a clarification whether there is or isn’t order of difficulty within a section as this does effect my mentality when taking the exam in regards to time. Thanks in advance!
11. Kiana September 20, 2015 at 4:00 pm #
Hi!
So I’ve been searching everywhere trying to find an answer to this scoring question…
The score is from 130-170, right? which means 40 is for grabs.
And there are 40 questions for Verbal and quantitative sections.
So how is it that the second section, if harder, bears more points/scores??
If we say that each question is 1 point, and there are 40 points and 40 questions in total, how can the second section give you more points?
• Chris Lele September 23, 2015 at 5:13 pm #
Hi Kiana,
That’s a good question. The thing is there is not a 1:1 correspondence the number of questions you miss and the number of points, from 170, you drop. For example, you can miss two questions and still receive a perfect verbal score. As to how the tests weighs questions from the more difficult section, I am not sure. Indeed, I don’t think anybody is sure outside of ETS–it’s their secret formula.
You can play around with this algorithm by taking the powerprep test and then comparing your score with the number of questions you miss. Of course, you’d have to know the answers to these questions. You can find most of them in the paper-based practice test:
http://www.ets.org/s/gre/pdf/practice_book_GRE_pb_revised_general_test.pdf
Hope that helps 🙂
12. Ebin August 11, 2015 at 10:51 pm #
Hi,
I have been preparing for GRE since last month.But as I am working I am not able to completely focus on GRE. And will not be able to take up GRE in the next couple of months.Is it alright to write GRE in January 2016?
I would like to get admission in a German university.Kindly suggest some German universities that offer courses in embedded computing.
Thanks
13. Tushar July 25, 2015 at 9:33 am #
Going by the thread of discussions, does it mean that everyone gets an easy section to begin with and the 2nd section is adaptive?
14. Zachary Ervin July 23, 2015 at 2:41 pm #
Let’s say I get about 15/20 questions correct on the first medium level test right and a little more than half of the hard section questions right. What would my score be in the quantitative section if this were the case? Thanks!
15. Vatsal Bajpai May 22, 2015 at 10:37 am #
Hi ! Chris first of all I will like to thank you for excellent discussions that you do along with your post. They are extremely helpful. What I got from this discussion is that GRE adapts between section and not within a section. If I am getting this correct, once I start a section the set of questions which I have to answer will not change if I — (1) Get a question wrong (2) Skip a question .
Is it a good strategy to skip difficult or time consuming questions in order to attempt more question ?
16. Amy November 2, 2014 at 7:20 pm #
Hi Chris,
Assuming a person does well on the first section of verbal and therefore receives a harder section next, what happens if that person misses too many questions on the second section? Say if a person gets 18 out of 20 correct in the first section, and then 12 out of 20 correct in the second section. Will this person still receive a decent score because his/her excellent performance on the first section creates a floor? Meaning his/her score cannot fall under a certain score?
If this logic is true, I understand if a person doesn’t do so well on the first section and subsequently score improve on the next easy section wouldn’t be able to anticipate a stellar score since the mediocre performance in the first section would’ve created a ceiling, a score the applicant cannot surpass.
Of course, the bottom line is we should try our best on every single section but I just wanted to clarify that I’m understanding this correctly. Thank you!
• Chris Lele November 3, 2014 at 11:31 am #
Hi Amy,
That’s the gist of it. Not getting the harder section put a ceiling on your score. Apparently, there is also a medium section as the second section of math or verbal. So not getting the hard section does not mean you get the easy section; you’ll get a second medium section. The ceiling won’t be as low as it will be with the easy section.
Hope that helps!
• Simon August 16, 2015 at 2:22 am #
Hi Chris,
many thanks for that explanation. I have also been wondering what the section adaptiveness implies in terms of test strategy (have not found any clear recommendations on this at Magoosh or anywhere else).
Is there any general rule and what the score ceilings on the different section difficulties are? For example, if I get 15/20 correct on the first quantitative, medium section and based on that get a second quantiative, medium difficulty section: what would my maximum score be?
I am just wondering, if my goal is to get 165 on the quantitative, whether it would be a better strategy to get two medium sections (and e.g. score 15/20 on the first and 19/20 on the second); rather then aiming high on the first section and then failing on the difficult one (e.g. score 19/20 on the first and then 10/20 on the hard section)? Maybe the hard sections are only for people aiming for the 170 range?
Any insights on this?
Thanks
Simon
17. Samarth July 11, 2014 at 3:46 am #
Hi Chris.
I took my GRE Today and I really felt the adaptive feature makes it too hard.
I have been giving my practice tests for a while now.
I usually get 2-3 questions wrong in the first quant and 1 in the second. Today on my actual test I had 10 minutes left after first section so I had the time to make sure that everything was correct and most probably all of them are correct. When I reached the second section the difficulty increased like anything. I don’t knoa how it’s possible but at least 10 out of 20 questions were challenging. 3-4 being exceptionally hard. My practice test average was 168 ( Kaplan, Powerprep II , Manhattan Review ) and I ended up getting 164 today.
18. Joe June 17, 2014 at 9:05 pm #
Hi Chris,
How adaptive is the GRE? If, for example, I got every question right on the first math section, what would my average question look like on the second section?
I’ve been doing well on the paper ETS practice tests, but am worried I’m just not seeing the level of difficulty I’ll see on the exam.
Thanks!
19. swastik March 1, 2014 at 5:13 am #
hey chris 🙂
Just wanted to thank you for your all the good work you have put in:)
• Chris Lele March 3, 2014 at 1:29 pm #
You are welcome 🙂
20. Peter Tosh January 28, 2014 at 2:58 pm #
Does the GRE choose the second section based on the number you get right (say 17/20), or based which questions you get right? For example if a student answers 15 right including all of the difficult questions, is that the same as answering 15 right but getting all of the difficult questions wrong?
• Chris Lele January 29, 2014 at 12:04 pm #
Hi Peter,
I don’t think anyone–besides ETS–is completely sure how they figure out how the section adapts. But from what ETS has said and from my own tinkering with the Power Prep software, each question is worth the same. It is the number of questions you answer correctly that determines the following related section, math or verbal.
Hope that helps!
21. Nursultan September 11, 2013 at 5:54 am #
Hi Chris,
Do you think it would be a good strategy to intentionally do mediocre on the first section in order to get easier problems in the second section?
• Chris Lele September 11, 2013 at 1:35 pm #
Hi Nursultan,
Oh no! Don’t do that :). Your score on the GRE is based on your performance on one of the sections. If you end up getting the easier section, you put a ceiling on your score. In other words, even if you get every question right on the easy section you may not get over 150. Do your best on every section.
Hope that helps clear things up!
• Valentin September 10, 2014 at 9:53 pm #
I know this is an old post, but can you please clarify that? What do you mean by having a ceiling on my score if I get the easy section? That’s what happened to me yesterday(got the easy section), and I got a 150 even though I think I answered most questions in the easy(last) section right. How exactly is my final score determined by my performance on one section? What if I got all questions wrong on the easy section, what will happen to my score?
My plan was to get 15-17 questions right on each scored section, ending up with a total of 160-164. But looks like I’m really missing some important details about the scoring policy.
• Chris Lele September 15, 2014 at 11:33 am #
Hi Valentin,
The ceiling refers to the fact that even if you get every question right on the easy section, you can still only max out at a certain, somewhere in the low-150s, provided you don’t get everything wrong on the very first math section.
To get 160-164, you’d have to get at least 14 out of 20 right on the first section of math or verbal. The number may change a little, and there is also a medium section, so it can get kind of complicated. My advice: don’t overly fixate on the scoring nuances; just do your best on the first section of either math or verbal.
Hope that helps!
• Valentin September 15, 2014 at 8:40 pm #
Alright, thank you for the reply. I just don’t understand what went wrong that day. My practice test scores are always in the upper 150s to the lower 160s, but I got such a horrible score on the actual test. Probably went through the questions too fast.
And btw, I signed-up for Magoosh and I really like it. Hopefully I’ll get a better score next time.
• Chris Lele September 16, 2014 at 4:50 pm #
Yes, test day things can definitely get a little stressful so that we end up making careless mistakes we wouldn’t otherwise. I’m glad you’re enjoying Magoosh! Let me know if you have any questions along the way :).
• Scott October 6, 2014 at 6:48 pm #
Hi Chris!
I was aware that the first section dictates the difficulty of the future sections but was unaware that first section places your final score in a sort of grouping where the final score has a defined minimum and maximum. I was always under the impression, that if you did poorly on the first section that it was possible to “make up” in future sections. Thank you very much for clarifying this important point!
You mentioned in a previous post that in order to score above a 160 on quantitative or verbal, a person would need to score of at least 14 out of 20 on the first section. Is there a rubric for how many you have to get right on the first section in order to receive a 150-155 or a 155-160? I understand its good not get score fixated. But I am just curious as I am sure others are as well 🙂
• Chris Lele October 7, 2014 at 2:39 pm #
Hi Scott,
You know there isn’t an exact rubric. I gleaned these numbers from tinkering around with the PowerPrep software. Who knows, maybe ETS has even tinkered around with them a little. So it’s hard to say exactly what the cutoff would be for 160 but it may be as low as 12, provided you get most of the questions on the second section of the corresponding section–which seems unlikely, given that that section would be as hard (the medium section) or harder (hard section).
At the same time, I know it’s nice to have a sense of a cut off, so if you are going through questions at the end and you want to get as many right as possible, you better off going over a couple of answers rather than try to knock off that one really difficult question.
Hope that helps 🙂
22. Cait June 15, 2013 at 4:11 pm #
Hey Chris,
I understand that the test is adaptive. But I am wondering if it is best to guess on a question that you aren’t sure of or leave it blank? Is there a penalty for guessing?
• Chris Lele June 18, 2013 at 3:55 pm #
Hi Cait,
Yes, no matter what, guess. There is absolutely no penalty for guessing. I guess the big piece of advice is never leave a question unanswered.
Hope that helps!
23. Farah June 1, 2013 at 3:02 am #
hey Chris! well, you have mentioned here that each question carries 1 mark but i think its not entirely correct. I have taken couple of powerprep tests where I have got to experience something really confounding. I corrected around 15 questions in the verbal section and 7 in the next part of the same section, so I should have got a total of 152 in verbal section but i got 159 when I hit on ‘report scores’ ! then i corrected 26 maths questions but it showed that I got 154! When I asked an expertise like yourself, he said it depends on the difficulty level ! now, how on earth am I going to determine which question carries how much marks?
• Chris Lele June 3, 2013 at 11:17 am #
I think the issue here is that the scale is different for math and verbal. So you can miss the same number of questions in math and verbal but end up getting the same score. At an official level–meaning what ETS says–each question is worth the same. I too sometimes think that may be slightly misleading because if you get the “harder” section and end up missing more questions than someone who gets the “easier” section than do you get the same score?
I’ll have a look and play around with the PowerPrep test. I would be surprised if the tough questions were given more weight than the easy ones. Not sure why ETS would tell a flat out lie…also, I haven’t heard from anyone citing discrepancies in scores based on the number of questions answered correctly.
Thanks though for letting me know what’s going on, and I’ll get back to you via this thread :).
24. Vaz March 9, 2013 at 9:20 am #
Can I choose between the sections in the revised GRE?That is, can I select which section I should answer first and which one next, like that?
• Chris Lele March 11, 2013 at 4:45 pm #
Hi Vaz,
Actually the section you get depends on how well you do on the first section. For instance, if you miss more than half the questions you will get an easy section as your second section. Also of note, the first math section and the first verbal section will be of medium difficulty. So if you do well, you will never see an easy section on the GRE.
Hope that clears things up :).
25. Paola May 10, 2012 at 3:50 pm #
Hi Chris, so just to get this straight, what this is saying is that if I begin with the first section of the verbal and do awesome, the second section of the verbal will be “tougher”? Then if I do bad in the first section of the quantitative the second part of the quantitative will be “easier”?[and vice versa]… AND the analytical writing is obviously not adaptive.
• Chris Lele March 11, 2013 at 7:50 pm #
Hi Paola,
Yes, that is EXACTLY correct. Incidentally, there appears to be a medium-difficulty section as a second section. Meaning if you did average on the first section, the test adapts, and for the second section you get an average-difficulty section.
Hope that helps
• Raj October 4, 2013 at 8:40 am #
Hi Chris,
If I’ve understood correctly, the system determines the difficulty level for the second section based on how the first section was performed. If this is the case, what would be the procedure for paper-based test?
• Chris Lele October 4, 2013 at 1:50 pm #
Yes, that is correct, Raj. For the paper-based test, there is no such system. Your score is based on the number of questions you answer correctly.
Hope that helps!
26. James March 16, 2012 at 1:09 pm #
Chris, what is the largest score increase you’ve ever seen for a student you’ve tutored?
• Chris March 16, 2012 at 1:40 pm #
Hi James,
With the new GRE, I’ve just started tutoring so the pool of students who’ve taken the test is very small.
On the old GRE, the largest point increase was from 800 (mock test to about 1350/60 (actual exam). So that’s almost 600 points!
Another student increased by 250 points on the Quant alone after only a handful of sessions.
Of course such successes are by no means solely attributable to me. Both students were very driven and focused.
Let me know if you have any more questions :).
27. Julia Campos February 20, 2012 at 3:08 pm #
The PhD program requires a 70 percentile or higher. What is the numerical score for a 70 percentile? Thank you so much for your info.
Julia
28. Julia Campos February 19, 2012 at 3:54 am #
Does that mean that if you do well in one section and they give you a more difficult section that you are not good for, that means you are doing worse becasue you did well in the ifrst? if they give you something more difficult your score is going down.
• Chris February 20, 2012 at 1:56 pm #
Hi Julia,
No one is 100% sure how it works – except ETS, of course. My guess is that you are given a harder section, there is some minimum score you cannot fall below. If that minimum score is greater than the score you would get if you answered every question on the easy section, I can’t say for sure.
It is also important to note that not every single question on the difficult section is difficult, and not every question on the easy section is easy. Each section will have a mix of difficulty-levels.
• Ashay July 25, 2013 at 8:58 pm #
Hi Chris,
This was the exact doubt which came to my mind when I read that the second section would be more difficult if you did well in the first one.
Currently my accuracy for ‘Hard’ questions (in Magoosh practice questions) in verbal is not good 🙁 Was wondering what should be the accuracy for ‘Hard’ questions to get 160 in verbal.
Thanks!
• Chris Lele July 26, 2013 at 1:32 pm #
Hi Ashay,
That’s a hard question to answer — and many Magoosh users who’ve recently taken the GRE (and scored really well) say that the Magoosh questions are even more difficult than those that they saw on the test. It seems that most of these students who went on to break 160 V were getting at least 60% of the Magoosh TC/RC right. There is, however, no breakdown between easy/medium/ and difficult questions. So even if you miss more than half of the difficult and very difficult Magoosh questions that doesn’t mean that you won’t be able to break 160.
I know that was not an exact answer to your question, but I hope that helps :).
• Ashay July 26, 2013 at 9:54 pm #
Thanks Chris ! I was just apprehensive as the predicted score currently says 151-156. But I do have a month to do. Hope I improve on that.
Thanks a lot though, you guys rock !
• Chris Lele July 30, 2013 at 12:11 pm #
Hi Ashay,
Keep up the studying and you should be able to inch towards 160. Let me know if you have any questions along the way :).
• Ashay July 26, 2013 at 9:57 pm #
Hi Chris,
I see what you are saying. I was just apprehensive because my current predicted score is 151-156. But I do have a month to go, so hope to improve on that 😀
Thanks a lot though ! You guys rock !
29. carol February 18, 2012 at 10:29 am #
the manhattan revised gre practice book says a big difference is that you can answer questions in any order, which, they say, is different than the old gre.
• Chris February 20, 2012 at 1:53 pm #
Hi Carol,
True, that is a big difference. I will add that to the text above. Thanks for the heads up!
30. soumya February 18, 2012 at 9:10 am #
Wow! you guys are quick!!
• Chris February 20, 2012 at 1:53 pm #
Thanks!
Magoosh blog comment policy: To create the best experience for our readers, we will only approve comments that are relevant to the article, general enough to be helpful to other students, concise, and well-written! 😄 Due to the high volume of comments across all of our blogs, we cannot promise that all comments will receive responses from our instructors.
We highly encourage students to help each other out and respond to other students' comments if you can!
If you are a Premium Magoosh student and would like more personalized service from our instructors, you can use the Help tab on the Magoosh dashboard. Thanks! | 8,163 | 34,890 | {"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-2016-44 | latest | en | 0.955173 |
https://prashantbarahi.com.np/docs/algorithms/contents/add-two-numbers | 1,702,194,635,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679101282.74/warc/CC-MAIN-20231210060949-20231210090949-00551.warc.gz | 522,215,329 | 10,882 | ``class ListNode: def __init__(self, x): self.val = x self.next = None def __str__(self): l = "" head = self while head is not None: l += str(head.val) head = head.next return lclass Solution: def addTwoNumbers(self, l1, l2): p = l1 q = l2 dummy = ListNode(0) head = dummy carry = 0 while p is not None or q is not None: sum = (0 if p is None else p.val) + (0 if q is None else q.val) + carry carry = int(sum / 10) head.next = ListNode(sum % 10) head = head.next print(head.val, carry) if p is not None: p = p.next if q is not None: q = q.next if carry > 0: head.next = ListNode(carry) return dummy.nextdef traverse(l1): res = "" head = l1 condition = True while condition: res += str(head.val) head = head.next condition = head is not None return resif __name__ == "__main__": l1 = ListNode(1) l2 = ListNode(2) l3 = ListNode(3) l1.next = l2 l2.next = l3 l3 = ListNode(7) l4 = ListNode(7) # l5 = ListNode(8) l3.next = l4 # l4.next = l5 print(l1) print(l3) s = Solution() print('sum', s.addTwoNumbers(l1, l3))`` | 377 | 1,335 | {"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-2023-50 | latest | en | 0.616002 |
http://mathhelpforum.com/differential-geometry/180589-darboux-sums-print.html | 1,524,394,747,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125945584.75/warc/CC-MAIN-20180422100104-20180422120104-00105.warc.gz | 206,424,603 | 2,978 | # Darboux Sums
• May 14th 2011, 03:36 PM
Conn
Darboux Sums
So we were doing Darboux sums in Analysis, and this was a given sample question and answer, but I don't really understand where part of this solution comes from:
"Suppose f is increasing on [0,1]. Show that f is integrable on [0,1]
Let P = $\displaystyle \left\{ x_{0},x_{1},...,x_{n} \right\}$ be a partition of [0,1] into n subintervals of the same length.
Since f(x) is increasing, we have
$\displaystyle \inf_{[x_{k+1},x_{k}]} f(x) = f(x_{k}) for 0 \leqslant k \leqslant n-1$
and this implies that
$\displaystyle S^{-}(f,P) = \sum_{k = 0}^{n-1} \inf_{[x_{k+1},x_{k}]} f(x).(x_{k+1}-x_{k})$
$\displaystyle = \frac{1}{n}(f(x_{0})+f(x_{1})+...+f(x_{n-1})$
But I don't understand how those last two statements are equal; for example, how is
$\displaystyle \sum_{k = 0}^{2} f(x).(x_{k+1}-x_{k})$
$\displaystyle = (f(x_{0})(x_{1}-x_{0})+f(x_{1})(x_{2}-x_{1})+f(x_{2})(x_{3}-x_{2}))$
equal to
$\displaystyle \frac{1}{3} (f(x_{0})+f(x_{1})+f(x_{2})?$
• May 14th 2011, 03:48 PM
TheEmptySet
Quote:
Originally Posted by Conn
So we were doing Darboux sums in Analysis, and this was a given sample question and answer, but I don't really understand where part of this solution comes from:
"Suppose f is increasing on [0,1]. Show that f is integrable on [0,1]
Let P = $\displaystyle \left\{ x_{0},x_{1},...,x_{n} \right\}$ be a partition of [0,1] into n subintervals of the same length.
Since f(x) is increasing, we have
$\displaystyle \inf_{[x_{k+1},x_{k}]} f(x) = f(x_{k}) for 0 \leqslant k \leqslant n-1$
and this implies that
$\displaystyle S^{-}(f,P) = \sum_{k = 0}^{n-1} \inf_{[x_{k+1},x_{k}]} f(x).(x_{k+1}-x_{k})$
$\displaystyle = \frac{1}{n}(f(x_{0})+f(x_{1})+...+f(x_{n-1})$
But I don't understand how those last two statements are equal; for example, how is
$\displaystyle \sum_{k = 0}^{2} f(x).(x_{k+1}-x_{k})$
$\displaystyle = (f(x_{0})(x_{1}-x_{0})+f(x_{1})(x_{2}-x_{1})+f(x_{2})(x_{3}-x_{2}))$
equal to
$\displaystyle \frac{1}{3} (f(x_{0})+f(x_{1})+f(x_{2})?$
It follows from the fact that
$\displaystyle (x_{k+1}-x_k)=\frac{1}{n}, \quad \forall \, k$
Then just factor it out of each term! | 855 | 2,176 | {"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} | 3.890625 | 4 | CC-MAIN-2018-17 | latest | en | 0.869361 |
https://www.learnamic.com/learning_resources/sas-math-stretch | 1,550,532,109,000,000,000 | text/html | crawl-data/CC-MAIN-2019-09/segments/1550247488490.40/warc/CC-MAIN-20190218220415-20190219002415-00186.warc.gz | 870,676,504 | 18,681 | # SAS Math Stretch
## Description
Free from SAS Curriculum Pathways, Math Stretch provides a suite of activities for developing elementary math skills and number sense. Specifically, activities target counting, number relations and operations, and telling and manipulating time. Math Stretch activities offer both practice and quiz modes. Settings allow students, parents, and teachers to control the level of difficulty of each activity independently. Practice sessions and completed quizzes can easily be shared with parents and teachers. Math Stretch now includes whole numbers, fractions, and decimals. Customize each activity to your students’ level with settings.
Activities
Place Picker – Build numbers by placing the correct value in each position. Ordering Numbers – Arrange numbers in order from lowest to highest. Largest or Smallest – Find the largest or smallest number among a collection. Skip Counter – Complete number patterns of varying difficulty. Number Bonds – Complete the number bond from a selection of numbers. Number Comparison – Compare numbers (both whole numbers and fractions). Even/Odd – Sort numbers into evens and odds. Number Line – Add and subtract using a number line. Find the Time – Manipulate the hour and minute hand to display the correct time. Time Conversion –Convert time measurements to hours, minutes, and seconds. Pi – Practice building pi and see how many places you can memorize. Hundred Chart –Identify missing numbers in a chart containing numbers from 1 to 100. Math Drag-and-Drop – Count, add, and subtract using number blocks, a virtual math manipulative. Ten Grid – Count in groups of 10. Math Grid – Add and subtract using number grids. Daily Numbers – View three new numbers every day. Practice writing the word form and take a photo of the number in action.
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Free
See all resources for Math | 1,798 | 8,449 | {"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} | 3.765625 | 4 | CC-MAIN-2019-09 | latest | en | 0.87976 |
https://discuss.leetcode.com/topic/12560/recursive-solution-in-java | 1,513,305,689,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948563083.64/warc/CC-MAIN-20171215021156-20171215041156-00603.warc.gz | 535,012,611 | 8,361 | # Recursive Solution in Java
• ``````public int findMin(int[] nums) {
return binary(nums, 0, nums.length - 1);
}
public int binary(int[] nums, int lo, int hi){
if(lo == hi)
return nums[lo];
int mid = (lo + hi) / 2;
if(nums[mid] > nums[hi])
return binary(nums, mid + 1, hi);
return binary(nums, lo, mid);
}
``````
Another one with iteration is:
``````public int findMin(int[] nums) {
int lo = 0, hi = nums.length - 1;
while(lo < hi){
int mid = (lo + hi) / 2;
if(nums[mid] > nums[hi])
lo = mid + 1;
else
hi = mid;
}
return nums[lo];
}``````
Looks like your connection to LeetCode Discuss was lost, please wait while we try to reconnect. | 202 | 642 | {"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-2017-51 | latest | en | 0.533103 |
https://artofproblemsolving.com/wiki/index.php?title=2022_USAMO_Problems&diff=prev&oldid=172934 | 1,656,488,618,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103624904.34/warc/CC-MAIN-20220629054527-20220629084527-00461.warc.gz | 159,404,391 | 12,904 | # Difference between revisions of "2022 USAMO Problems"
## Day 1
### Problem 1
Let $a$ and $b$ be positive integers. The cells of an $(a+b+1)\times (a+b+1)$ grid are colored amber and bronze such that there are at least $a^2+ab-b$ amber cells and at least $b^2+ab-a$ bronze cells. Prove that it is possible to choose $a$ amber cells and $b$ bronze cells such that no two of the $a+b$ chosen cells lie in the same row or column.
### Problem 2
Let $b\geq2$ and $w\geq2$ be fixed integers, and $n=b+w$. Given are $2b$ identical black rods and $2w$ identical white rods, each of side length 1.
We assemble a regular $2n-$gon using these rods so that parallel sides are the same color. Then, a convex $2b$-gon $B$ is formed by translating the black rods, and a convex $2w$-gon $W$ is formed by translating the white rods. An example of one way of doing the assembly when $b=3$ and $w=2$ is shown below, as well as the resulting polygons $B$ and $W$.
Prove that the difference of the areas of $B$ and $W$ depends only on the numbers $b$ and $w$, and not on how the $2n$-gon was assembled.
### Problem 3
Let $\mathbb{R}_{>0}$ be the set of all positive real numbers. Find all functions $f:\mathbb{R}_{>0} \to \mathbb{R}_{>0}$ such that for all $x,y\in \mathbb{R}_{>0}$ we have $$f(x) = f(f(f(x)) + y) + f(xf(y)) f(x+y).$$
## Day 2
### Problem 4
Find all pairs of primes $(p, q)$ for which $p-q$ and $pq-q$ are both perfect squares.
### Problem 5
A function $f: \mathbb{R}\to \mathbb{R}$ is essentially increasing if $f(s)\leq f(t)$ holds whenever $s\leq t$ are real numbers such that $f(s)\neq 0$ and $f(t)\neq 0$.
Find the smallest integer $k$ such that for any 2022 real numbers $x_1,x_2,\ldots , x_{2022},$ there exist $k$ essentially increasing functions $f_1,\ldots, f_k$ such that$$f_1(n) + f_2(n) + \cdots + f_k(n) = x_n\qquad \text{for every } n= 1,2,\ldots 2022.$$
### Problem 6
There are 2022 users on a social network called Mathbook, and some of them are Mathbook-friends. (On Mathbook, friendship is always mutual and permanent.)
Starting now, Mathbook will only allow a new friendship to be formed between two users if they have at least two friends in common. What is the minimum number of friendships that must already exist so that every user could eventually become friends with every other user?
2022 USAMO (Problems • Resources) Preceded by2021 USAMO Followed by2023 USAMO 1 • 2 • 3 • 4 • 5 • 6 All USAMO Problems and Solutions | 775 | 2,460 | {"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": 44, "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-2022-27 | latest | en | 0.836177 |
https://www.urionlinejudge.com.br/judge/en/profile/289648?amp%3Bdirection=desc&sort=Ranks.run_id&direction=asc | 1,596,564,039,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439735881.90/warc/CC-MAIN-20200804161521-20200804191521-00074.warc.gz | 881,537,299 | 6,194 | # PROFILE
Check out all the problems this user has already solved.
Problem Problem Name Ranking Submission Language Runtime Submission Date
1008 Salary 02257º 11772270 Java 0.056 9/27/18, 9:13:18 PM
1011 Sphere 00627º 11772751 Java 0.044 9/27/18, 9:44:12 PM
1012 Area 03880º 11777349 Java 0.068 9/27/18, 9:56:59 PM
1004 Simple Product 02139º 11831149 Java 0.044 9/27/18, 4:43:20 PM
1036 Bhaskara's Formula 02296º 11934723 Java 0.068 10/7/18, 7:17:29 PM
1044 Multiples 02484º 11936261 Java 0.056 10/11/18, 5:41:39 PM
1038 Snack 02654º 11938189 Java 0.056 10/11/18, 8:43:49 PM
1059 Even Numbers 02442º 11961615 Java 0.036 10/14/18, 7:34:15 PM
1168 LED 00446º 12024979 Java 0.096 10/19/18, 4:03:23 AM
1009 Salary with Bonus 00593º 12187133 Java 0.044 9/27/18, 9:21:17 PM
1010 Simple Calculate 00421º 12187165 Java 0.044 9/27/18, 9:35:03 PM
1015 Distance Between Two Points 00889º 12187210 Java 0.048 9/28/18, 4:10:39 AM
1003 Simple Sum 02353º 12187306 Java 0.044 9/27/18, 4:26:28 PM
1016 Distance 00194º 12187349 Java 0.036 9/28/18, 4:21:31 AM
1001 Extremely Basic 00201º 12187357 Java 8 0.032 9/25/18, 12:56:40 PM
1002 Area of a Circle 01012º 12187381 Java 0.044 9/27/18, 3:50:51 PM
1013 The Greatest 02808º 12187395 Java 0.052 9/28/18, 2:59:15 AM
1005 Average 1 00783º 12187463 Java 0.044 9/27/18, 5:10:16 PM
1006 Average 2 00740º 12187478 Java 0.044 9/27/18, 6:44:44 PM
1007 Difference 01103º 12187491 Java 0.040 9/27/18, 6:50:37 PM
1017 Fuel Spent 00306º 12187512 Java 0.040 9/28/18, 4:29:49 AM
1018 Banknotes 01402º 12187522 Java 0.048 9/28/18, 5:38:43 AM
1019 Time Conversion 00528º 12187537 Java 0.040 9/28/18, 4:45:21 AM
1020 Age in Days 00962º 12187559 Java 0.044 9/28/18, 4:51:35 AM
1035 Selection Test 1 00576º 12187601 Java 0.040 10/7/18, 6:09:09 PM
1041 Coordinates of a Point 00598º 12187604 Java 0.048 10/12/18, 12:51:14 PM
1048 Salary Increase 00422º 12187620 Java 0.048 10/14/18, 7:58:40 PM
1037 Interval 00119º 12187649 Java 0.040 10/11/18, 3:42:44 PM
1043 Triangle 00418º 12187668 Java 0.048 10/11/18, 6:54:24 PM
1042 Simple Sort 03258º 12221974 Java 0.060 10/11/18, 7:37:31 PM
1 of 2 | 999 | 2,102 | {"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} | 2.609375 | 3 | CC-MAIN-2020-34 | latest | en | 0.325333 |
https://www.physicsforums.com/threads/special-theory-of-relativity-velocity-of-airplane.757069/ | 1,624,040,559,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623487640324.35/warc/CC-MAIN-20210618165643-20210618195643-00357.warc.gz | 866,274,049 | 16,263 | Special theory of relativity: velocity of airplane
Homework Statement
If a clock in an airplane is found to slow down by 5 parts in 1013, (i.e. Δt/Δto = 1 + 5x10-13), at what speed is the airplane travelling? (Hint: You may need to use the binomial expansion for γ.)
To be honest, I'm really confused about what this question's telling me. What's in the brackets?
Homework Equations
γ = 1/√(1-v2/c2)
That's the equation I used.
The Attempt at a Solution
When I rearranged the equation to find the velocity, I got v = √((1-(1/γ)2)(c2))
I subbed in 1 + 1.5x10-13 for γ but I keep getting 0 as my velocity and the answer's supposed to be 300 m/s. Am I even doing this right? Thanks in advance! I appreciate any help you can give me!
1st why did you sub 1 + 1.5x10-13 for γ instead of 1 + 5x10-13, as described in the problem.
2nd yes your method is correct but either you're misusing the calculator or the calculator can't handle the calculation. Yes, calculators don't always provide correct answers. That's why the problem said "You may need to use the binomial expansion for γ" by what they mean a Taylor expansion.
1 person
why did you sub 1 + 1.5x10-13 for γ
Oops! Sorry! I meant to write 5x10-13. I'm afraid I don't really know what a Taylor expansion is... How does this work?
Taylor's expansion is very important and useful but it takes more than a few lines to explain it. You should definitely learn it, but for right now I would try using a better calculator. Use the calculator that comes with Windows. It's very good.
vela
Staff Emeritus
$$(1+x)^m = 1 + \frac{m}{1!} x + \frac{m(m-1)}{2!}x^2 + \frac{m(m-1)(m-2)}{3!}x^3 + \cdots.$$ In particular, for ##m=-1/2##, you get
$$(1+x)^{-1/2} \cong 1 - \frac 12 x.$$ Therefore, you have
$$\gamma = \left[ 1 + \left(-\frac{v^2}{c^2}\right)\right]^{-1/2} \cong 1 + \frac 12 \frac{v^2}{c^2}.$$ | 586 | 1,857 | {"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": 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} | 3.984375 | 4 | CC-MAIN-2021-25 | latest | en | 0.935627 |
https://kijijitutor.com/2022/01/06/multiple-choice-2/ | 1,674,892,439,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499524.28/warc/CC-MAIN-20230128054815-20230128084815-00470.warc.gz | 351,877,283 | 17,644 | Multiple Choice
1. Question 1
4 PointsA(n) __________ variable is one in which values are determined by chance.Blank 1
2. Question 2
4 PointsThe following distribution is not a probability distribution because X21012P(X)0.160.20–0.120.450.31
3. Question 3
4 PointsA(n) __________ probability distribution consists of the finite number of values a random variable can assume and the corresponding probabilities of the values.Blank 1
4. Question 4
4 PointsThe sum of the probabilities of all the events in the sample space of a probability distribution must equal 1.
5. Question 5
4 PointsDiscrete variables have values that can be measured.
6. Question 6
4 PointsThe following distribution is not a probability distribution because X21012P(X)0.080.210.430.170.26
7. Question 7
4 PointsContinuous random variables are obtained from data that can be measured rather than counted.
8. Question 8
4 PointsFind the mean of the distribution shown.X46P(X)0.360.64
9. Question 9
4 PointsFind the mean of the distribution shown.X12P(X)0.320.68
10. Question 10
4 PointsThe number of cartoons watched on Saturday mornings by students in Mrs. Kelly’s first grade class is shown below. Number of cartoons watched X012345Probability P(X)0.150.200.300.100.200.05
What is the mean of the data?
11. Question 11
4 PointsGive the variance of the following distribution? X01234P(X)0.200.350.100.250.10
12. Question 12
4 PointsFind the mean of the distribution shown below. X234P(X)0.350.240.41
13. Question 13
4 PointsWhat is the standard deviation of the following probability distribution? X02468P(X)0.200.050.350.250.15
14. Question 14
4 PointsA pet supplier has a stock of parakeets of which 20% are blue parakeets. A pet store orders 3 parakeets from this supplier. If the supplier selects the parakeets at random, what is the chance that the pet store gets exactly one blue parakeet?
15. Question 15
4 PointsA coin is tossed five times. Find the probability of getting exactly three heads.
16. Question 16
4 PointsThe probability of a success remains the same for each trial in a binomial experiment.
17. Question 17
4 PointsA coin is tossed 72 times. Find the standard deviation for the number of heads that will be tossed.
18. Question 18
4 PointsA surgical technique is performed on twelve patients. You are told there is 70% chance of success. Find the probability that the surgery is successful for exactly 9 patients.
19. Question 19
4 PointsA surgical technique is performed on nine patients. You are told there is 70% chance of success. Find the probability that the surgery is successful for exactly 5 patients.
20. Question 20
4 PointsA surgical technique is performed on ten patients. You are told there is 85% chance of success. Find the probability that the surgery is successful for at least 8 patients
21. Question 21
4 PointsA surgical technique is performed on seven patients. You are told there is 70% chance of success. Find the probability that the surgery is successful for at least 5 patients
22. Question 22
4 PointsIf a student randomly guesses at 15 multiple-choice questions, find the probability that the student gets exactly seven correct. Each question has four possible choices.
23. Question 23
4 PointsIf a student randomly guesses at 10 multiple-choice questions, find the probability that the student gets exactly five correct. Each question has four possible choices.
24. Question 24
4 PointsFind the mean and the standard deviation of a Binomial Distribution with n= 124 and p= 0.26
25. Question 25
4 PointsFind the mean and the standard deviation of a Binomial Distribution with n= 316 and p= 0.72
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https://stats.stackexchange.com/questions/379292/would-it-be-more-appropriate-to-use-negative-binomial-regression-instead-of-pois | 1,716,591,537,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058751.45/warc/CC-MAIN-20240524214158-20240525004158-00685.warc.gz | 477,559,340 | 39,847 | # Would it be more appropriate to use negative Binomial regression instead of Poisson regression if my sample variance is greater than my sample mean?
My response variable $$y_i$$ denotes the number of articles produced by journalist $$i$$ in the last two years. It is a count variable with fixed exposure hence why I chose to use Poisson regression.
I have a dataset containing the number of articles produced by numerous different journalists and I also have values of other variables (my predictor variables).
I have calculated the sample mean and sample variance of the variable $$y$$, and the sample variance is nearly double (over-dispersion). Is this a good enough reason for me to use negative Binomial regression? Should I consider anything else? The deviance of the model also drops by a noticeable amount when I use NB over Poisson.
This is my first time considering using a negative Binomial regression so I apologise if the question is very basic.
• Welcome to our site. The sample variance is large because it incorporates variation among the predictor variables, too: thus, it is inappropriate for selecting the model. Consider applying what you initially thought was a good model and conducting diagnostic analyses on its residuals: that is what matters.
– whuber
Nov 28, 2018 at 22:30
• @whuber Thank you for your response but I am not convinced by that explanation. I am only looking at the sample variance and mean of the number of articles produced; I do not consider the predictors when I do this. Nov 28, 2018 at 22:34
• To expound on @whuber's point, over-dispersion in regression analysis refers to the distribution of the response within predictors- whereas it sounds like you've considered the distribution of the response across predictors.
– khol
Nov 28, 2018 at 22:35
• @khol Interesting. How could I correctly test for over-dispersion, given a glm? Nov 28, 2018 at 22:38
Formally, i don't think you can go off your raw sample variance and mean, because the distribution is conditional i.e. $$Y|X \thicksim P(\lambda)$$
I can be totally wrong on the first point, so someone correct me. But generally as a rule of thumb test for overdispersion is to fit your model and divide the residual deviance by the residual degrees of freedom; if it's much larger than 1 then it's probably overdispersed.
A more formal hypothesis test is to simply test if the negative binomial fits better. That is, the Poisson is the Negative Binomial when $$k \rightarrow 0$$. So, we are actually testing if
$$H_0: k = 0$$ and $$H_1: k > 0$$
This can be tested using the log likelihood ratio test:
$$LR=2(\ell_{NB}-\ell_p)$$ which is distributed $$\chi_p^2$$ where $$p$$ is the number of parameters. Only tricky thing is the cutoff is at $$\alpha=0.1$$ instead of $$0.05$$ because the distribution of LR has a mass of $$0.5$$ at $$k=0$$ and a half-$$\chi_p^2$$ distribution above zero. Basically just fit two models and use the log likelihood reatio test to compare their deviances.
In R, you can either compute it by hand using the logLik to pull out the loglikelihoods and substituting into the formmula and then looking up the chi squared criitical value at 0.1. Or, the pscl package has a odTest command to test this for you. See more here, but I haven't tried that one myself. | 781 | 3,297 | {"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": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 15, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.15625 | 3 | CC-MAIN-2024-22 | latest | en | 0.923286 |
https://livewell.com/finance/amount-realized-definition-example-calculation-formula/ | 1,726,695,956,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651941.8/warc/CC-MAIN-20240918201359-20240918231359-00357.warc.gz | 339,306,282 | 39,542 | Home>Finance>Amount Realized: Definition, Example, Calculation Formula
Finance
# Amount Realized: Definition, Example, Calculation Formula
Learn the definition and calculation formula for amount realized in finance, with an illustrative example. Master the concept of amount realized for better financial understanding.
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## Amount Realized: Definition, Example, Calculation Formula
As part of our ongoing commitment to providing valuable financial resources, we are excited to introduce a new addition to our FINANCE category: Amount Realized: Definition, Example, Calculation Formula. In this blog post, we will demystify the concept of amount realized and provide you with practical examples and a calculation formula to help you understand its significance in the world of finance.
## Key Takeaways:
• Amount realized is the total sum of money received or to be received from a financial transaction.
• It plays a crucial role in determining gains or losses and is essential for making informed investment decisions.
Now, let’s dive deeper into the concept of amount realized:
When engaging in financial transactions such as selling assets or investments, it is essential to understand the amount realized. Amount realized refers to the total sum of money received or to be received from the sale or disposition of an asset or investment. It takes into account the net proceeds, including any cash received, debts assumed by the buyer, fair market value of non-cash assets received, and other monetary considerations.
Calculating the amount realized involves considering several factors. Here’s a step-by-step guide to help you understand the calculation process:
1. Determine the cash received or to be received from the transaction. This can include the initial purchase price, additional payments, or any other monetary considerations.
2. Adjust the cash amount for any liabilities assumed by the buyer, such as outstanding debts or obligations.
3. Add the fair market value of any non-cash assets received as part of the transaction.
4. Subtract any transaction costs or expenses associated with the sale.
By following this calculation formula, you can arrive at the accurate amount realized from your financial transaction. Understanding the amount realized is crucial as it directly impacts the calculation of gains or losses. Tracking gains and losses helps you evaluate your investment performance and make informed decisions for future financial endeavors.
Let’s consider an example to further illustrate the concept of amount realized:
Suppose you sell a piece of real estate for \$500,000. The buyer assumes a mortgage of \$200,000, and as part of the transaction, you receive an additional \$50,000 in cash. The fair market value of non-cash assets received, such as furniture and fixtures, is estimated at \$30,000. Finally, you incur \$10,000 in transaction costs. To calculate the amount realized:
1. Cash received: \$50,000
2. Liabilities assumed by the buyer: -\$200,000
3. Fair market value of non-cash assets: +\$30,000
4. Transaction costs: -\$10,000
By adding and subtracting these amounts, the total amount realized from the transaction would be \$-130,000 (\$50,000 – \$200,000 + \$30,000 – \$10,000).
In conclusion, understanding the concept of amount realized is essential for anyone involved in financial transactions. It helps you determine the total sum of money received or to be received, considering various factors involved in the sale or disposition of assets or investments. By calculating the amount realized, you can accurately assess gains or losses and make informed decisions for your financial future.
We hope this blog post has shed light on the definition, calculation formula, and practical examples of amount realized. Stay tuned for more informative articles in our FINANCE category!
• https://livewell.com/finance/amount-realized-definition-example-calculation-formula/ | 807 | 4,142 | {"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} | 3.171875 | 3 | CC-MAIN-2024-38 | latest | en | 0.944558 |
https://en.academic.ru/dic.nsf/enwiki/559789 | 1,591,048,793,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347419639.53/warc/CC-MAIN-20200601211310-20200602001310-00397.warc.gz | 330,057,657 | 13,511 | # Inner model
Inner model
In mathematical logic, suppose "T" is a theory in the language
:$L = langle in angle$
of set theory.
If "M" is a model of $L$ describing a set theory and "N" is a class of "M" such that
:$langle N, in_M, cdots angle$
is a model of "T" containing all ordinals of "M" then we say that "N" is an inner model of "T" (in "M").
This term "inner model" is sometimes applied to models which are proper classes; the term set model is used for models which are sets.
A model of set theory is called standard if the element relation of the model is the actual element relation restricted to the model. A model is called transitive when it is standard and the base class is a transitive class of sets. A model of set theory is often assumed to be transitive unless it is explicitly stated that it is non-standard. Inner models are transitive, transitive models are standard, and standard models are well-founded.
The assumption that there exists a standard model of ZFC (in a given universe) is stronger then the assumption that there exists a model. In fact, if there is a standard model, then there is a smallest standard model called the minimal model contained in all standard models. It is countable and satisfies V=L. The minimal model contains no standard model (as it is minimal) but (assuming the consistence of ZFC) it containssome model of ZFC by the Godel completeness theorem. This model is necessarily not well founded otherwise its Mostowski collapse would be a standard model. (It is not well founded as a relation in the universe, though itsatisfies the axiom of foundation so is "internally" well founded. Being well founded is not an absolute property.)In particular in the minimal model there is a model of ZFC but there is no standard model of ZFC.
Use
Usually when one talks about inner models of a theory, the theory one is discussing is ZFC or some extension of ZFC (like ZFC+$exists$ a measurable cardinal). When no theory is mentioned, it is usually assumed that the model under discussion is an inner model of ZFC. However, it is not uncommon to talk about inner models of subtheories of ZFC (like ZF or KP) as well.
Related ideas
It was proved by Kurt Gödel that any model of ZF has a least inner model of ZF (which is also an inner model of ZFC + GCH), called the constructible universe, or L.
There is a branch of set theory called inner model theory which studies ways of constructing least inner models of theories extending ZF. Inner model theory has led to the discovery of the exact consistency strength of many important set theoretical properties.
ee also
*Countable transitive models and generic filters
Wikimedia Foundation. 2010.
### Look at other dictionaries:
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• Model (physical) — A physical model is a smaller or larger physical copy of an object. The object being modelled may be small (for example, an atom) or large (for example, the Solar System).The geometry of the model and the object it represents are often similar in … Wikipedia | 1,239 | 5,582 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "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-2020-24 | latest | en | 0.9542 |
http://www.jiskha.com/display.cgi?id=1294893478 | 1,462,445,496,000,000,000 | text/html | crawl-data/CC-MAIN-2016-18/segments/1461860126502.50/warc/CC-MAIN-20160428161526-00069-ip-10-239-7-51.ec2.internal.warc.gz | 594,738,439 | 4,132 | Thursday
May 5, 2016
# Homework Help: stats help!
Posted by ashley on Wednesday, January 12, 2011 at 11:37pm.
in a given year the college admissions office accepts applicants from students, who are then either accepted or not accepted. accepted students may or may not decide to attend college. suppose the scores on a certain entrance exam for applicants of murphy college follow the normal distribution with mean 1600 and standard deviation 300.
whats the probability that a given applicant has a score of more than 2050?
What is the probability that a given applicant has a score of between 1450 and 1900?
Suppose that top scoring applicants are award merit scholarship money based on their scores. Suppose that any student scoring above 1900 is awarded \$20,000 in scholarship money. If 1000 students apply to Murphy college in a given year, how much money does the college award in total?
How would college calculate the expected amount in \$ of merit scholarships dispersed in a given year?
• stats help! - PsyDAG, Thursday, January 13, 2011 at 11:08am
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to those Z scores. | 278 | 1,238 | {"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-2016-18 | longest | en | 0.951887 |
https://www.projectcubicle.com/pivot-table-add-column-adding-columns-to-your-excel-pivot-tables/ | 1,721,226,329,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514771.72/warc/CC-MAIN-20240717120911-20240717150911-00539.warc.gz | 815,970,778 | 49,945 | How do I add more columns to a PivotTable? Do I add columns to a PivotTable sheet? How do I add a new field PivotTable Analyze? How do I add more data to a PivotTable?
The Art of Adding a Custom Column: Unlocking a New Dimension of Analysis
The specific steps to add a column will vary slightly depending on your spreadsheet software (Excel, Google Sheets, etc.), but the core process remains consistent:
1. Unleashing the Field List: Navigate to the PivotTable Analyze tab (or its equivalent). Look for the option for Fields, Items, & Sets or Field List. This will display a treasure trove – a list of all the fields available in your data source. Think of it as a menu offering a variety of ingredients (your data fields) that you can use to cook up a brand new dish (your custom column).
2. Calculated Field Magic: Look for the option to create a Calculated Field. This is where the real fun begins! Here, you define the recipe for your new column. Think of it as a formula that combines existing ingredients (data fields) to create a brand new metric tailored to your specific needs. You can use mathematical operators, logical functions, and even combine fields from different parts of your data source.
3. Formula Fun: Here’s where your inner mathematician gets to shine! Build a formula that incorporates the fields you want to use. Let’s say you’re curious about “Profit Margin.” You could craft a formula like `[Price] - [Cost]`. This would calculate the profit margin for each data point in your pivot table. Imagine you have a dataset tracking sales figures and advertising spend for different marketing campaigns. You could create a calculated field for “Return on Ad Spend” using a formula like `[Sales] / [Ad Spend]`. This allows you to see which campaigns are generating the most revenue for your advertising investment.
4. A Name Speaks a Thousand Numbers: Give your new column a clear and descriptive name that reflects the calculation you performed. This will make it easier for you (and anyone else who interacts with your pivot table) to understand the data it presents. For instance, instead of a cryptic “Column1,” opt for something like “Profit Margin” or “Return on Ad Spend” for easy comprehension.
There are two main ways to add a column to a pivot table:
1. Adding an Existing Field:
This is the simplest way to add a new column. You can simply drag and drop an existing field from the Field List to the Columns area of your pivot table. This will group your data by the values in that field.
For example, let’s say you have a pivot table that shows sales figures by product category. You could add a new column to show the sales figures by region as well. Just drag the “Region” field from the Field List to the Columns area.
1. Creating a Calculated Field:
A calculated field allows you to create a new column based on a formula. This can be useful for performing calculations on your existing data, such as creating a profit margin column or a percentage change column.
For example, let’s say you have a pivot table that shows sales figures and cost prices. You could create a calculated field to show the profit margin for each product category. The formula for this calculated field would be `Sales - Cost Price`.
Here are the steps on how to create a calculated field in Excel:
1. Click any cell in your pivot table.
2. Go to the Analyze tab (or Options tab in older versions of Excel).
3. Click Fields, Items, & Sets.
4. Select Calculated Field.
5. In the Name field, type a name for your new column.
6. In the Formula field, type the formula for your calculation.
7. Click OK.
The Benefits of Adding Columns: A Data Analyst’s Toolkit Expansion
The ability to add columns unlocks a treasure trove of benefits for your data exploration adventures:
• Deeper Insights Beyond the Surface: Go beyond basic summaries and see additional metrics alongside your existing data. This allows you to gain a more comprehensive understanding of the story your data tells. Imagine a pivot table showing website traffic by source. Adding a “Conversion Rate” column alongside “Visits” provides a much richer picture, helping you identify which traffic sources are most effective at converting visitors into customers. You could also add a “Bounce Rate” column (percentage of visitors who leave immediately) to see which sources are sending low-quality traffic.
• Profit Margin Power: As the example above demonstrates, you can create custom columns to calculate important metrics like profit margin. This empowers you to identify the most profitable areas of your business, allowing you to optimize your resources and focus on high-performing products, regions, or customer segments. Imagine a pivot table showing sales figures for different product categories. Adding a “Profit Margin” column allows you to see which categories are not only generating the most sales but also contributing the most to your bottom line.
• Comparative Analysis Made Easy: Effortlessly compare different data points within the same pivot table. This allows you to see how metrics like profit margin, conversion rates, or average order value vary across different categories in your data. Imagine comparing sales figures and profit margins for different product categories within a single pivot table.
Why Profit Margin Matters in Your Pivot Tables
Imagine your pivot table reveals Region X as the undisputed sales leader. Fantastic news! But hold on a second. Is Region X truly your profit champion? Adding a “Profit Margin” column sheds light on the true profitability picture. Perhaps Region Y, with slightly lower sales, boasts a significantly higher profit margin. This newfound knowledge could completely change your strategic focus. Region Y might be a more strategic area for investment, allowing you to maximize profits while potentially growing sales further.
Unearthing Hidden Gems: Low Sales, High Margin Products
Ever come across a product with seemingly low sales figures in your reports? Don’t dismiss it just yet! Your pivot table’s “Profit Margin” column might reveal a hidden gem – a product with a surprisingly high profit margin. This could be an under-promoted goldmine with significant potential waiting to be unleashed. Imagine a scenario where a particular product line consistently shows low sales figures. Traditionally, this might lead to decreased production or marketing efforts. However, the “Profit Margin” column in your pivot table analysis reveals a surprisingly high profit margin for this product line. This could indicate a need to investigate further. Perhaps the product is simply under-marketed or not positioned correctly. By uncovering this hidden gem, you can develop a targeted marketing strategy to boost sales without sacrificing profitability.
Mastering Pivot Chart in Excel: Pivot Chart in Excel (In Simple Steps)
Smarter Inventory Management Decisions: Optimizing for Profit, Not Just Sales Volume
Not all products are created equal. Knowing which products deliver the highest profit margins within specific regions empowers you to optimize inventory allocation in a way that prioritizes profitability over just sales volume. Focus on stocking profitable products in high-demand areas, ensuring you maximize return on investment. This strategic approach can lead to a more efficient and streamlined inventory management system. Imagine a situation where your pivot table analysis reveals that a particular product category has high sales volume in Region A, but the “Profit Margin” column shows a low margin. On the other hand, a different product category might have lower sales volume in Region A but boasts a significantly higher profit margin. With this knowledge, you can make informed decisions about inventory allocation. You might choose to decrease stock of the high-volume, low-margin product category in Region A and prioritize stocking the lower-volume, high-margin product category instead.
What are Pivot Tables and Why Add Columns?
Pivot tables are the workhorses of data analysis in Excel. They transform raw data into insightful summaries, allowing you to categorize information and calculate various metrics. But what if you crave a more granular understanding of your data? Adding columns to your pivot table is the key to unlocking a new level of detail.
For example, imagine a pivot table showing product sales by region. Valuable, yes, but wouldn’t it be even better to see the profit margin alongside those sales figures? Adding a “Profit Margin” column lets you analyze not just sales volume but also profitability across different regions. This extra layer of detail empowers you to make data-driven decisions, like prioritizing high-profit regions for marketing campaigns.
Step-by-Step Guide: Adding Columns to Your Pivot Table
How to Add Columns:
There are two primary methods to add columns and enrich your pivot table with additional data:
1. Leverage Existing Data Fields:
• Click anywhere within your pivot table to activate the PivotTable Analyze tab.
• Find the desired field (e.g., “Profit”) in the PivotTable Fields pane.
• Simply drag and drop this field into the Columns area.
This effortlessly adds a new column displaying the chosen data alongside your existing information.
Pivot Table Power Up: Your Questions Answered (FAQs)
Ever felt limited by the columns in your Excel Pivot Table? Fear not! This FAQ guide equips you with the knowledge to unlock the full potential of your pivot tables.
• Q: How do I add more columns to a PivotTable?
• A: There are two ways to add new columns (or fields) to your pivot table:
1. Using Existing Data Fields:
• Click anywhere within your pivot table to activate the PivotTable Analyze tab.
• Locate the desired field (e.g., “Profit”) in the PivotTable Fields pane.
• Drag and drop this field into the Columns area.
2. Creating Calculated Fields for New Metrics (Custom Columns):
• Go to the PivotTable Analyze tab and click Fields, Items, & Sets > Calculated Field.
• In the Formula window, craft your calculation using field names and operators (e.g., Profit / Sales * 100 for profit margin).
• Assign a name to your calculated field and click OK.
• Q: How do I add a new field in a PivotTable?
• A: See the answer above for “How do I add more columns to a PivotTable?” Adding a new field is essentially the same process as adding more columns using existing data fields.
• Q: Can I add a custom column to a pivot table?
• A: Absolutely! You can create custom columns using calculated fields. This allows you to define new metrics not directly present in your data source and then add them to the Columns area for analysis.
Adding More Data (New Rows):
• Q: How do I add more data to a PivotTable?
• A: Pivot tables themselves can’t directly include new data additions. To include fresh data:
1. Ensure your pivot table source data range includes the new information.
2. Click anywhere within your pivot table.
3. In the PivotTable Analyze tab, locate the Refresh button and click it.
Modifying and Reorganizing:
• Q: Where do I modify PivotTable fields?
• A: The PivotTable Fields pane allows you to modify existing fields, add/remove fields, and explore filtering options. You can access this pane by clicking anywhere within your pivot table and going to the PivotTable Analyze tab.
• Q: How do you edit existing PivotTable fields?
• A: While you can’t directly edit existing fields within the PivotTable Fields pane, you can remove them and add them back with any desired changes to their formatting or calculations (if applicable).
• Q: How do I add a field to a pivot table more than once?
• A: While not directly adding multiple columns, you can place the same field in both the Rows and Columns sections to create a matrix view of your data. This allows you to analyze your data from different perspectives (e.g., showing sales figures by region and product category).
• Q: How do I reorder columns?
• A: Existing columns can be easily reordered by dragging them within the Columns area.
• Q: How do I expand the range of a PivotTable?
• A: If your pivot table doesn’t display all the data you want, you might need to expand the source data range. This can be done by selecting the pivot table and then adjusting the range in the formula bar.
By mastering these techniques, you can transform your pivot tables into powerful data analysis tools (PivotTable Analyze), unlocking deeper insights and creating informative reports.
Craft Calculated Fields for New Metrics (Optional)
What are Calculated Fields?
While the previous method leverages existing data, calculated fields allow you to create new metrics not directly present in your data source.
For example, you might want to see the average order value in your pivot table. Since this calculation isn’t inherently available, you can create a calculated field.
How to Create Calculated Fields:
• Head to the PivotTable Analyze tab and navigate to Fields, Items, & Sets > Calculated Field.
• In the Formula window, craft your calculation using field names and operators (e.g., [Total Sales] / [Number of Orders] for average order value).
• Assign a name to your calculated field and click OK.
This method empowers you to create new metrics and then drag the newly created field to the Columns area for seamless integration.
Bonus Tips: Mastering Your Pivot Table Columns
• Effortless Reordering: Existing columns can be easily reordered by dragging them within the Columns area.
• Refresh for New Data: Pivot tables can’t directly include new data additions. To include new data, you’ll need to refresh the pivot table using the updated data source. Remember, refresh is key!
• Unlock Complex Calculations: For intricate calculations, explore the power of Excel formulas within calculated fields. You can even use them to combine multiple Excel columns into one or separate pivot table row labels into separate columns.
By following these steps and mastering these tips, you can effortlessly add columns to your pivot tables, unlocking a wealth of insights hidden within your data.
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Start promoting your Excel content today! | 3,065 | 14,974 | {"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} | 3.09375 | 3 | CC-MAIN-2024-30 | latest | en | 0.853977 |
https://au.mathworks.com/matlabcentral/cody/problems/3056-chess-probability/solutions/1702199 | 1,597,229,113,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738888.13/warc/CC-MAIN-20200812083025-20200812113025-00414.warc.gz | 214,114,060 | 16,042 | Cody
# Problem 3056. Chess probability
Solution 1702199
Submitted on 4 Jan 2019 by HH
• Size: 9
• This is the leading solution.
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 = 1800; y = 1800; assert(isequal(expected_score(x,y),0.5))
[Warning: Function assert has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In unix (line 32) In expected_score (line 2) In ScoringEngineTestPoint1 (line 3) In solutionTest (line 3)]
2 Pass
x = 1900; y = 1800; assert(isequal(expected_score(x,y),0.64))
[Warning: Function assert has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In unix (line 32) In expected_score (line 2) In ScoringEngineTestPoint2 (line 3) In solutionTest (line 5)]
3 Pass
x = 1900; y = 2000; assert(isequal(expected_score(x,y),0.36))
[Warning: Function assert has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In unix (line 32) In expected_score (line 2) In ScoringEngineTestPoint3 (line 3) In solutionTest (line 7)]
4 Pass
x = 1900; y = 2100; assert(isequal(expected_score(x,y),0.24))
[Warning: Function assert has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In unix (line 32) In expected_score (line 2) In ScoringEngineTestPoint4 (line 3) In solutionTest (line 9)]
5 Pass
x = 1800; y = 2775; assert(isequal(expected_score(x,y),0.004))
[Warning: Function assert has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In unix (line 32) In expected_score (line 2) In ScoringEngineTestPoint5 (line 3) In solutionTest (line 11)]
6 Pass
x = 1800; y = 2865; assert(isequal(expected_score(x,y),0.002))
[Warning: Function assert has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In unix (line 32) In expected_score (line 2) In ScoringEngineTestPoint6 (line 3) In solutionTest (line 13)]
7 Pass
x = 2865; y = 2775; assert(isequal(expected_score(x,y),0.627))
[Warning: Function assert has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In unix (line 32) In expected_score (line 2) In ScoringEngineTestPoint7 (line 3) In solutionTest (line 15)]
8 Pass
x = 2865; y = 2851; assert(isequal(expected_score(x,y),0.52))
[Warning: Function assert has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In unix (line 32) In expected_score (line 2) In ScoringEngineTestPoint8 (line 3) In solutionTest (line 17)]
9 Pass
x = 2865; y = 2844; assert(isequal(expected_score(x,y),0.53))
[Warning: Function assert has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In unix (line 32) In expected_score (line 2) In ScoringEngineTestPoint9 (line 3) In solutionTest (line 19)]
10 Pass
x = 2785; y = 2865; assert(isequal(expected_score(x,y),0.387))
[Warning: Function assert has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In unix (line 32) In expected_score (line 2) In ScoringEngineTestPoint10 (line 3) In solutionTest (line 21)]
11 Pass
x = 2785; y = 1800; assert(isequal(expected_score(x,y),0.997))
[Warning: Function assert has the same name as a MATLAB builtin. We suggest you rename the function to avoid a potential name conflict.] [> In unix (line 32) In expected_score (line 2) In ScoringEngineTestPoint11 (line 3) In solutionTest (line 23)] | 1,100 | 3,823 | {"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-2020-34 | latest | en | 0.843096 |
https://calculatorsonline.org/roman-numeral-date-converter/august-25-2010 | 1,721,646,189,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517846.73/warc/CC-MAIN-20240722095039-20240722125039-00387.warc.gz | 122,884,440 | 5,303 | # August 25, 2010 in roman numeral
Here you will see step by step solution to convert August 25, 2010 date to roman numeral. How to write August 25, 2010 as a roman numeral? August 25, 2010 as a roman numeral written as VIII.XXV.MMX (MM.DD.YYYY), please check the explanation that how to convert 25 August, 2010 in roman number.
## Answer: August 25, 2010 in roman numeral
VIII.XXV.MMX
### How to convert August 25, 2010 in roman number?
To convert the August 25, 2010 in roman number simply expand the each number from month, date and year from hindu-arabic number to roman numerals, then replace the all numbers of expanded form of date, month and year with respective roman numerals.
#### Solution for August 25, 2010 to roman numeral
Given date is => 25-08-2010
After expanding number from Month, Date and year, this table provides a simple and explanation of how to convert the date 'August 25, 2010' to its Roman number:
MonthDayYear
Date 08 [Aug] 25 2010
Expanded Number Values 5 + 1 + 1 + 1 10 + 10 + 5 1000 + 1000 + 10
Roman Numeral Values V + I + I + I X + X + V M + M + X
Result = VIII XXV MMX
Hence, in order to correct roman numerals date combination of Month, Day and Year of August 25, 2010 is written as VIII.XXV.MMX or in 25/August/2010 [DD/MM/YYYY] format it is written as XXV/VIII/MMX. | 391 | 1,314 | {"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} | 3.28125 | 3 | CC-MAIN-2024-30 | latest | en | 0.822983 |
https://www.queryhome.com/puzzle/1961/can-you-tell-how-many-females-are-there | 1,601,273,460,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600401585213.82/warc/CC-MAIN-20200928041630-20200928071630-00622.warc.gz | 977,903,091 | 32,558 | # Can you tell how many females are there?
168 views
A is the father of two children - B and D who are of different sexes.
C is B's spouse.
E is the same sex as D.
B and C have the two children - F who is the same sex as B and G who is the same sex as C.
E's mother, H who is married to L, is the sister of D's mother, M.
E and E's spouse, I have two children - J and K who are the same sex as I.
Note that no persons have married more than once. Also, there are more number of females than males.
Can you tell how many females are there?
posted Jul 16, 2014
There are seven females
The name of A's first child has got to be a girl and Cs spouse has got to be a woman
Similar Puzzles
Out of the 70 employees working with ABC Inc., 30 are females. Also,
24 employees are above 30 years of age
19, amongst the promoted employees are over 30 years, of which 7 are males
12 males are above 30 years of age
15 males have received a promotion
How many un-promoted females are there and how many of them are older than 30 years?
You are given 100 rs to buy 100 sponges.
Now, you may buy no more or less than 100 sponges and also, the total price must be 100 rs.
There are three types of sponges: Red sponges costing Rs. 6, Yellow Sponges costing Rs. 3 and Blue Sponges costing Rs. 0.10.
If there is no sales tax applied, how many of each can you buy?
+1 vote
Bea Smith , Vera Bennett, Franky Doyle and Doreen Anderson were in Wentworth Prison for murder. But their behavior on the jails is appreciated by the warden and the warden decided to give all these 4 prisoners 11 cupcakes.They all like cupcakes and they had all cupcakes in no matter of time but they do not know how many cupcake each individual had.Therefore Bea started the conversation Bea : "Hey T-Vera, did you had more cupcakes than I had ?"Vera : "I do not know girl, Hey Franky, did you had more cupcakes than I had ?".Franky: "I do not know"Doreen replied instantlyDoreen: "I know how exactly how many cupcakes each of you had?"
So can you tell how many cupcakes each of them had ? | 538 | 2,053 | {"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} | 3.453125 | 3 | CC-MAIN-2020-40 | longest | en | 0.985487 |
https://www.ato.gov.au/individuals-and-families/your-tax-return/instructions-to-complete-your-tax-return/mytax-instructions/2018/deductions/work-related-expenses/self-education-expenses/calculated-total | 1,701,297,389,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100146.5/warc/CC-MAIN-20231129204528-20231129234528-00192.warc.gz | 756,078,629 | 94,437 | # Calculated total
Last updated 27 June 2018
myTax works out the total amount you can claim for your work-related self-education expenses from the information you provide. If you would like to see how myTax works this out, use this worksheet.
The worksheet adds up your self-education expenses under the following categories because, in working out what you can claim, certain costs are reduced by \$250.
Worksheet
Row
Category type
Explanation
Amount
A
General expenses
and
Car expenses where Calculation method is 'Logbook'
General expenses that are deductible, including textbooks, stationery, student union fees, student services and amenities fees, course fees and public transport fares.
Also includes car expenses (other than 'Decline in value' amounts) worked out under the 'Logbook' method.
\$
B
Decline in value
Deductions for the decline in value of depreciating assets used for self-education, including computers.
Also includes 'Decline in value' amounts for car expenses worked out under the Logbook method.
\$
C
Repair expenses
Expenses for repairs to items of equipment used for self-education.
\$
D
Car expenses where Calculation method is 'Cents per kilometre'
Car expenses related to your self-education for which you are claiming deductions under the 'Cents per kilometre' method.
If you have included deductions for the decline in value of or repairs to your car under Category type 'Decline in value' or 'Repair expenses', you cannot claim car expenses under this category.
\$
E
Non-deductible expenses
Self-education expenses that are not deductible, which are:
• private costs, including non-deductible travel and childcare costs, and
• capital costs, like the purchase price of a desk or computer.
Do not include contributions you made under HECS-HELP or repayments under HELP, SFSS, SSL or TSL.
\$
Step 1
If you had any row A expenses, go to step 2. Otherwise, read on.
Row
Calculation
Amount
F
Add rows B, C and D.
\$
The amount at row F is the total amount you can claim for your work-related self-education expenses.
Step 2
Row
Calculation
Amount
G
Add rows C, D and E.
\$
If the amount at row G is less than \$250, go to step 3. Otherwise, read on.
Row
Calculation
Amount
H
Add rows A, B, C and D.
\$
The amount at row H is the total amount you can claim for your work-related self-education expenses.
Step 3
Row
Calculation
Amount
I
Take the amount at row G away from \$250.
\$
J
Take the amount at row I away from your category A amount. If the result is zero or less, write 0
\$
K
Add rows B, C and D.
\$
L | 619 | 2,612 | {"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} | 2.609375 | 3 | CC-MAIN-2023-50 | latest | en | 0.939805 |
https://en.wikipedia.org/wiki/Computable_topology | 1,472,270,013,000,000,000 | text/html | crawl-data/CC-MAIN-2016-36/segments/1471982297699.43/warc/CC-MAIN-20160823195817-00094-ip-10-153-172-175.ec2.internal.warc.gz | 837,870,963 | 25,480 | # Computable topology
Computable topology is a discipline in mathematics that studies the topological and algebraic structure of computation. Computable topology is not to be confused with algorithmic or computational topology, which studies the application of computation to topology.
## Topology of lambda calculus
As shown by Alan Turing and Alonzo Church, the λ-calculus is strong enough to describe all mechanically computable functions (see Church–Turing thesis).[1][2][3] Lambda-calculus is thus effectively a programming language, from which other languages can be built. For this reason when considering the topology of computation it is common to focus on the topology of λ-calculus. Note that this is not necessarily a complete description of the topology of computation, since functions which are equivalent in the Church-Turing sense may still have different topologies.
The topology of λ-calculus is the Scott topology, and when restricted to continuous functions the type free λ-calculus amounts to a topological space reliant on the tree topology. Both the Scott and Tree topologies exhibit continuity with respect to the binary operators of application ( f applied to a = fa ) and abstraction ((λx.t(x))a = t(a)) with a modular equivalence relation based on a congruency. The λ-algebra desribing the algebraic structure of the lambda-calculus is found to be an extension of the combinatory algebra, with an element introduced to accommodate abstraction.
Type free λ-calculus treats functions as rules and does not differentiate functions and the objects which they are applied to, meaning λ-calculus is type free. A by-product of type free λ-calculus is an effective computability equivalent to general recursion and Turing machines.[4] The set of λ-terms can be considered a functional topology in which a function space can be embedded, meaning λ mappings within the space X are such that λ:X → X.[4][5] Introduced November 1969, Dana Scott's untyped set theoretic model constructed a proper topology for any λ-calculus model whose function space is limited to continuous functions.[4][5] The result of a Scott continuous λ-calculus topology is a function space built upon a programming semantic allowing fixed point combinatorics, such as the Y combinator, and data types.[6][7] By 1971, λ-calculus was equipped to define any sequential computation and could be easily adapted to parallel computations.[8] The reducibility of all computations to λ-calculus allows these λ-topological properties to become adopted by all programming languages.[4]
## Computational algebra from λ-calculus algebra
Based on the operators within lambda calculus, application and abstraction, it is possible to develop an algebra whose group structure uses application and abstraction as binary operators. Application is defined as an operation between lambda terms producing a λ-term, e.g. the application of λ onto the lambda term a produces the lambda term λa. Abstraction incorporates undefined variables by denoting λx.t(x) as the function assigning the variable a to the lambda term with value t(a) via the operation ((λ x.t(x))a = t(a)). Lastly, an equivalence relation emerges which identifies λ-terms modulo convertible terms, an example being beta normal form.
## Scott topology
The Scott topology is essential in understanding the topological structure of computation as expressed through the λ-calculus. Scott found that after constructing a function space using λ-calculus one obtains a Kolmogorov space, a ${\displaystyle T_{o}}$ topological space which exhibits pointwise convergence, in short the product topology.[9] It is the ability of self homeomorphism as well as the ability to embed every space into such a space, denoted Scott continuous, as previously described which allows Scott's topology to be applicable to logic and recursive function theory. Scott approaches his derivation using a complete lattice, resulting in a topology dependent on the lattice structure. It is possible to generalise Scott's theory with the use of complete partial orders. For this reason a more general understanding of the computational topology is provided through complete partial orders. We will re-iterate to familiarize ourselves with the notation to be used during the discussion of Scott topology.
Complete partial orders are defined as follows:
First, given the partially ordered set D=(D,≤), a nonempty subset X ${\displaystyle \subseteq }$ D is directed if ${\displaystyle \forall }$ x,yX ${\displaystyle \exists }$ zX where xz & yz.
D is a complete partial order (cpo) if:
${\displaystyle \cdot }$ Every directed X ${\displaystyle \subseteq }$D has a supremum, and:
${\displaystyle \exists }$ bottom element ${\displaystyle \perp }$ such that ${\displaystyle \perp }$D & ${\displaystyle \forall }$ xD ${\displaystyle \perp }$x.
We are now able to define the Scott topology over a cpo (D, ≤ ).
O ${\displaystyle \subseteq }$ D is open if:
(1) for x ∈ O, and x ≤ y, then y ∈ O, i.e. O is an upper set.
(2) for a directed set X ${\displaystyle \subseteq }$ D, and supremum(X) ∈ O, then X ${\displaystyle \cap }$ O ${\displaystyle \neq }$ ${\displaystyle \emptyset }$.
Using the Scott topological definition of open it is apparent that all topological properties are met.
${\displaystyle \cdot }$${\displaystyle \emptyset }$ and D, i.e. the empty set and whole space, are open.
${\displaystyle \cdot }$Arbitrary unions of open sets are open:
Proof: Assume ${\displaystyle U_{i}}$ is open where i ∈ I, I being the index set. We define U = ${\displaystyle \cup }${ ${\displaystyle U_{i}}$ ; i ∈ I}. Take b as an element of the upper set of U, therefore a ≤ b for some a ∈ U It must be that a${\displaystyle U_{i}}$ for some i, likewise b ∈ upset(${\displaystyle U_{i}}$). U must therefore be upper as well since ${\displaystyle U_{i}}$ ∈ U.
Likewise, if D is a directed set with a supremum in U, then by assumption sup(D) ∈ ${\displaystyle U_{i}}$where ${\displaystyle U_{i}}$is open. Thus there is a b ∈ D where b ∈ ${\displaystyle U_{i}\cap D\subseteq U\cap D}$. The union of open sets ${\displaystyle U_{i}}$is therefore open.
${\displaystyle \cdot }$Open sets under intersection are open:
Proof: Given two open sets, U and V, we define W = U${\displaystyle \cap }$V. If W${\displaystyle =\emptyset }$ then W is open. If non-empty say b ∈ upset(W) (the upper set of W), then for some aW, ab. Since aU${\displaystyle \cap }$V, and b an element of the upper set of both U and V, then bW.
Finally, if D is a directed set with a supremum in W, then by assumption sup(D) ∈ ${\displaystyle U\cap V}$. So there is a${\displaystyle U\cap D}$ and b${\displaystyle V\cap D}$. Since D is directed there is cD with ${\displaystyle a\leq c,b\leq c}$; and since U and V are upper sets, c${\displaystyle U\cap V}$ as well.
Though not shown here, it is the case that the map ${\displaystyle f:D\rightarrow D^{'}}$ is continuous if and only if f(sup(X)) = sup(f(X)) for all directed X${\displaystyle \subseteq }$D, where f(X) = {f(x) | xX} and the second supremum in ${\displaystyle D^{'}}$.[4]
Before we begin explaining that application as common to λ-calculus is continuous within the Scott topology we require a certain understanding of the behavior of supremums over continuous functions as well as the conditions necessary for the product of spaces to be continuous namely
(1) With ${\displaystyle {f_{i}}_{i}\subseteq [D\rightarrow D^{'}]}$ be a directed family of maps, then ${\displaystyle f(x)=\cup _{i}f_{i}(x)}$ if well defined and continuous.
(2) If F ${\displaystyle \subseteq [D\rightarrow D^{'}]}$ is directed and cpo and ${\displaystyle [D\rightarrow D^{'}]}$ a cpo where sup({f(x) | fF).
We now show the continuity of application. Using the definition of application as follows:
Ap: ${\displaystyle [D\rightarrow D^{'}]\times D\rightarrow D^{'}}$ where Ap(f,x) = f(x).
Ap is continuous with respect to the Scott topology on the product (${\displaystyle [D\rightarrow D^{'}]\times D\rightarrow D^{'}}$) :
Proof: λx.f(x) = f is continuous. Let h = λ f.f(x). For directed F${\displaystyle \subseteq [D\rightarrow D^{'}]}$
h(sup(F)) = sup(F)(x)
= sup( {f(x) | fF} )
= sup( {h(f) | fF} )
= sup( h(F) )
By definition of Scott continuity h has been shown continuous. All that is now required to prove is that application is continuous when it's separate arguments are continuous, i.e. ${\displaystyle [D\rightarrow D^{'}]}$and ${\displaystyle D\rightarrow D^{'}}$are continuous, in our case f and h.
Now abstracting our argument to show ${\displaystyle f:D\times D^{'}\rightarrow D^{''}}$ with ${\displaystyle g=\lambda x.f(x,x_{0})}$ and ${\displaystyle d=\lambda x^{'}.f(x_{0},x^{'})}$ as the arguments for D and ${\displaystyle D^{'}}$ respectively, then for a directed X ${\displaystyle \subseteq }$ D
${\displaystyle g(\sup(X))=f(\sup(X),x_{0}^{'}))}$
= f( sup( (x,${\displaystyle x_{0}^{'}}$) | x ∈ X} ))
(since f is continuous and {(x,${\displaystyle x_{0}^{'}}$) | x ∈ X}) is directed):
= sup( {f(x,${\displaystyle x_{0}^{'}}$) | x ∈ X} )
= sup(g(X))
g is therefore continuous. The same process can be taken to show d is continuous.
It has now been shown application is continuous under the Scott topology.
In order to demonstrate the Scott topology is a suitable fit for λ-calculus it is necessary to prove abstraction remains continuous over the Scott topology. Once completed it will have been shown that the mathematical foundation of λ-calculus is a well defined and suitable candidate functional paradigm for the Scott topology.
With ${\displaystyle f\in [D\times D^{'}\rightarrow D^{''}]}$ we define ${\displaystyle {\check {f}}}$ (x) =λ y ∈ ${\displaystyle D^{'}}$f(x,y)We will show:
(i) ${\displaystyle {\check {f}}}$ is continuous, meaning ${\displaystyle {\check {f}}}$${\displaystyle [D\rightarrow [D^{'}\rightarrow D^{''}]}$
(ii) λ ${\displaystyle f.{\check {f}}:[D\times D^{'}\rightarrow D^{''}]\rightarrow [D\rightarrow [D^{'}\rightarrow D^{''}]}$ is continuous.
Proof (i): Let X ${\displaystyle \subseteq }$ D be directed, then
${\displaystyle {\check {f}}}$(sup(X)) = λ y.f( sup(X),y )
= λ y.${\displaystyle \sup _{x\in X}}$( f(x,y) )
= ${\displaystyle \sup _{x\in X}}$( λy.f(x,y) )
= sup(${\displaystyle {\check {f}}}$(X))
Proof (ii): Defining L = λ ${\displaystyle f.{\check {f}}}$ then for F ${\displaystyle \subseteq [D\times D^{'}\rightarrow D^{''}]}$ directed
L(sup(F)) = λ x λ y. (sup(F))(x,y))
= λ x λ y. ${\displaystyle \sup _{y\in F}}$f(x,y)
= ${\displaystyle \sup _{y\in F}}$λx λy.f(x,y)
= sup(L(F))
It has not been demonstrated how and why the λ-calculus defines the Scott topology.
## Böhm trees and computational topology
Böhm trees, easily represented graphically, express the computational behavior of a lambda term. It is possible to predict the functionality of a given lambda expression from reference to its correlating Böhm tree.[4] Böhm trees can be seen somewhat analogous to ${\displaystyle \mathbb {R} }$ where the Böhm tree of a given set is similar to the continued fraction of a real number, and what is more, the Böhm tree corresponding to a sequence in normal form is finite, similar to the rational subset of the Reals.
Böhm trees are defined by a mapping of elements within a sequence of numbers with ordering (≤, lh) and a binary operator * to a set of symbols. The Böhm tree is then a relation among a set of symbols through a partial mapping ${\displaystyle \psi }$.
Informally Böhm trees may be conceptualized as follows:
Given: ${\displaystyle \Sigma }$ = ${\displaystyle \perp \cup }$ { λ x_{1} ${\displaystyle \cdots }$x_{n} . y | n ∈ ${\displaystyle \mathbb {N} ,x_{1}...x_{n}}$y are variables and denoting BT(M) as the Böhm tree for a lambda term M we then have:
BT(M) = ${\displaystyle \perp }$ if M is unsolvable (therefore a single node)
BT(M) = λ${\displaystyle {\vec {x}}}$.y
/ \
BT(${\displaystyle M_{1})}$ BT(${\displaystyle M_{m}}$ ) ; if M is solvable
More formally:
${\displaystyle \Sigma }$ is defined as a set of symbols. The Böhm tree of a λ term M, denoted BT(M), is the ${\displaystyle \Sigma }$ labelled tree defined as follows:
If M is unsolvable:
${\displaystyle BT(M)(\langle \ \rangle )=\perp ,}$
BT(M)(${\displaystyle \langle k\rangle *\alpha }$) is unsolvable ${\displaystyle \forall k,\alpha }$
If M is solvable, where M = λ x_{1}${\displaystyle \cdots x_{n}.yM_{0}\cdots M_{m-1}}$:
BT(M)(< >) = λ x_{1} ${\displaystyle \cdots x_{n}.y}$
BT(M)(${\displaystyle \langle k\rangle *\alpha }$) = BT(M_k)(${\displaystyle \alpha }$) ${\displaystyle \forall \alpha }$ and k < m
= undefined ${\displaystyle \forall \alpha }$ and k ${\displaystyle \geq }$ m
We may now move on to show that Böhm trees act as suitable mappings from the tree topology to the scott topology. Allowing one to see computational constructs, be it within the Scott or tree topology, as Böhm tree formations.
### Böhm tree and tree topology
It is found that Böhm tree's allow for a continuous mapping from the tree topology to the Scott topology. More specifically:
We begin with the cpo B = (B,${\displaystyle \subseteq }$) on the Scott topology, with ordering of Böhm tree's denoted M${\displaystyle \subseteq }$ N, meaning M, N are trees and M results from N. The tree topology on the set ${\displaystyle \Gamma }$ is the smallest set allowing for a continuous map
BT:${\displaystyle \Gamma \rightarrow }$B.
An equivalent definition would be to say the open sets of ${\displaystyle \Gamma }$ are the image of the inverse Böhm tree ${\displaystyle BT^{-1}}$ (O) where O is Scott open in B.
The applicability of the Bömh trees and the tree topology has many interesting consequences to λ-terms expressed topologically:
Normal forms are found to exist as isolated points.
Unsolvable λ-terms are compactification points.
Application and abstraction, similar to the Scott topology, are continuous on the tree topology.
## Algebraic structure of computation
New methods of interpretation of the λ-calculus are not only interesting in themselves but allow new modes of thought concerning the behaviors of computer science. The binary operator within the λ-algebra A is application. Application is denoted ${\displaystyle \cdot }$ and is said to give structure ${\displaystyle A=(X,\cdot )}$. A combinatory algebra allows for the application operator and acts as a useful starting point but remains insufficient for the λ-calculus in being unable to express abstraction. The λ algebra becomes a combinatory algebra M combined with a syntactic operator λ* that transforms a term B(x,y), with constants in M, into C(${\displaystyle {\hat {y}}}$)${\displaystyle \equiv }$ λ* x.B(x,${\displaystyle {\hat {y}}}$). It is also possible to define an extension model to circumvent the need of the λ* operator by allowing ${\displaystyle \forall }$x (fx =gx) ${\displaystyle \rightarrow }$ f =g . The construction of the λ-algebra through the introduction of an abstraction operator proceeds as follows:
We must construct an algebra which allows for solutions to equations such as axy = xyy such that a = λ xy.xyy there is need for the combinatory algebra. Relevant attributes of the combinatory algebra are:
Within combinatory algebra there exists applicative structures. An applicative structure W is a combinatory algebra provided:
${\displaystyle \cdot }$W is non-trival, meaning W has cardinality > 1
${\displaystyle \cdot }$W exhibits combinatory completeness (see completeness of the S-K basis). More specifically: for every term A ∈ the set of terms of W, and ${\displaystyle x_{1},...,x_{n}}$ with the free variables of A within ${\displaystyle {x_{1},...,x_{n}}}$ then:
${\displaystyle \exists f\forall x_{1}\cdot \cdot \cdot x_{n}}$ where ${\displaystyle fx_{1}\cdot \cdot \cdot x_{n}=A}$
The combiniatory algebra is:
${\displaystyle \cdot }$Never commutative
${\displaystyle \cdot }$Not associative.
${\displaystyle \cdot }$Never finite.
${\displaystyle \cdot }$Never recursive.
Combinatory algebras remain unable to act as the algebraic structure for λ-calculus, the lack of recursion being a major disadvantage. However the existence of an applicative term ${\displaystyle A(x,{\vec {y}}}$) provides a good starting point to build a λ-calculus algebra. What is needed is the introduction of a lambda term, i.e. include λx.A(x, ${\displaystyle {\vec {y}}}$).
We begin by exploiting the fact that within a combinatory algebra M, with A(x, ${\displaystyle {\vec {y}}}$) within the set of terms, then:
${\displaystyle \forall {\vec {y}}}$ ${\displaystyle \exists b}$ s.t. bx = A(x, ${\displaystyle {\vec {y}}}$).
We then require b have a dependence on ${\displaystyle {\vec {y}}}$ resulting in:
${\displaystyle \forall x}$ B(${\displaystyle {\vec {y}}}$)x = A(x, ${\displaystyle {\vec {y}}}$).
B(${\displaystyle {\vec {y}}}$) becomes equivalent to a λ term, and is therefore suitably defined as follows: B(${\displaystyle {\vec {y}})\equiv }$ λ*.
A pre-λ-algebra (pλA) can now be defined.
pλA is an applicative structure W = (X,${\displaystyle \cdot }$) such that for each term A within the set of terms within W and for every x there is a term λ*x.A ∈ T(W) (T(W) ${\displaystyle \equiv }$ the terms of W) where (the set of free variables of λ*x.A) = (the set of free variables of A) - {x}. W must also demonstrate:
${\displaystyle (\beta )}$ (λ*x.A)x = A
${\displaystyle \alpha _{1}}$λ*x.A${\displaystyle \equiv }$ λ*x.A[x:=y] provided y is not a free variable of A
${\displaystyle \alpha _{2}}$(λ*x.A)[y:=z]${\displaystyle \equiv }$λ*x.A[x:=y] provided y,z ≠ x and z is not a free variable of A
Before defining the full λ-algebra we must introduce the following definition for the set of λ-terms within W denoted ${\displaystyle \Gamma (W)}$ with the following requirements:
a ∈ W ${\displaystyle \Rightarrow c_{a}\in \Gamma (W)}$
x ∈ ${\displaystyle \Gamma (W)}$ for x ∈ (${\displaystyle v_{0},v_{1},...}$)
M,N ∈ ${\displaystyle \Gamma (W)\Rightarrow }$ (MN) ∈ ${\displaystyle \Gamma (W)}$
M ∈ ${\displaystyle \Gamma (W)\Rightarrow }$ (λx.M) ∈ ${\displaystyle \Gamma (W)}$
A mapping from the terms within ${\displaystyle \Gamma (W)}$ to all λ terms within W, denoted * : ${\displaystyle \Gamma (W)\rightarrow \mathrm {T} (W)}$, can then be designed as follows:
${\displaystyle v_{i}^{*}=w_{i},c_{a}^{*}=c_{a}}$
(MN)* = M* N*
(λx.M)* = λ* x*.M*
We now define λ(M) to denote the extension after evaluating the terms within ${\displaystyle \Gamma (W)}$.
λx.(λy.yx)${\displaystyle c_{a}}$ = λx.${\displaystyle c_{a}}$x in λ(W).
Finally we obtain the full λ-algebra through the following definition:
(1) A λ-algebra is a pλA W such that for M,N ∈ ${\displaystyle \Gamma }$(W):
λ(W) ${\displaystyle \vdash }$ M = N ${\displaystyle \Rightarrow }$ W ${\displaystyle \vDash }$ M = N.
Though arduous, the foundation has been set for a proper algebraic framework for which the λ-calculus, and therefore computation, may be investigated in a group theoretic manner.
## References
1. ^ Church 1934:90 footnote in Davis 1952
2. ^ Turing 1936–7 in Davis 1952:149
3. ^ Barendregt, H.P., The Lambda Calculus Syntax and Semantics. North-Holland Publishing Company. 1981
4. Barendregt, H.P., The Lambda Calculus Syntax and Semantics. North-Holland Publishing Company. 1981.
5. ^ a b D. S. Scott. Models for the λ-calculus. Informally distributed, 1969. Notes, December 1969, Oxford Univ.
6. ^ Gordon, M.J.C., The Denotational Description of Programming Languages. Springer Verlag, Berlin. 1979.
7. ^ Scott, D. S. and Strachey, C. Toward a Mathematical Semantics for Computer Languages, Proc. Symp. on Computers and Automata, Polytechnic Institute of Brooklyn, 21, pp. 19 46. 1971.
8. ^ G. Berry, Sequential algorithms on concrete data structures, Theoretical Computer Science 20, 265 321 (1982).
9. ^ D. S. Scott. “Continuous Lattices.” Oxford University Computing Laboratory August, 1971. | 5,373 | 19,906 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 157, "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-2016-36 | longest | en | 0.906802 |
https://www.cfd-online.com/W/index.php?title=Wall_shear_stress&diff=16165&oldid=9497 | 1,487,785,893,000,000,000 | text/html | crawl-data/CC-MAIN-2017-09/segments/1487501171004.85/warc/CC-MAIN-20170219104611-00018-ip-10-171-10-108.ec2.internal.warc.gz | 807,257,613 | 10,535 | Wall shear stress
(Difference between revisions)
Revision as of 13:47, 18 December 2008 (view source) (riclazelnoda)← Older edit Latest revision as of 10:21, 5 December 2012 (view source)Zonder (Talk | contribs) (Unit) (3 intermediate revisions not shown) Line 1: Line 1: - liormo The wall shear stress, $\tau_w$, is given by: The wall shear stress, $\tau_w$, is given by: :$\tau_w = \mu \left(\frac{\partial u}{\partial y} \right)_{y=0}$ :$\tau_w = \mu \left(\frac{\partial u}{\partial y} \right)_{y=0}$ - Where $\mu$ is the [[Dynamic viscosity|dynamic viscosity]], $u$ is the flow velocity parallell to the wall and $y$ is the distance to the wall. + Where $\mu$ is the [[Dynamic viscosity|dynamic viscosity]], $u$ is the flow velocity parallel to the wall and $y$ is the distance to the wall. + + The SI unit of wall shear stress is pascal ($Pa$), which is identical to $\frac{kg}{m\cdot s^2}$.
Latest revision as of 10:21, 5 December 2012
The wall shear stress, $\tau_w$, is given by:
$\tau_w = \mu \left(\frac{\partial u}{\partial y} \right)_{y=0}$
Where $\mu$ is the dynamic viscosity, $u$ is the flow velocity parallel to the wall and $y$ is the distance to the wall.
The SI unit of wall shear stress is pascal ($Pa$), which is identical to $\frac{kg}{m\cdot s^2}$. | 391 | 1,280 | {"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": 7, "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} | 2.875 | 3 | CC-MAIN-2017-09 | longest | en | 0.870714 |
https://www.jiskha.com/display.cgi?id=1302643637 | 1,503,310,335,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886108264.79/warc/CC-MAIN-20170821095257-20170821115257-00144.warc.gz | 782,169,175 | 3,517 | # chemistry
posted by .
given the following info for water specfic heat capacity of ice 2.06j/gdegrees calculate the total quanity of heat evolved when 10.0g of steam is condensed,cooled,and frozen to ice at -50 degrees
• chemistry -
## Similar Questions
1. ### chemistry
Given that the specific heat capacities of ice and steam are 2.06 J/g°C and 2.03 J/g°C, the molar heats of fusion and vaporization for water are 6.02 kJ/mol and 40.6 kJ/mol, respectively, and the specific heat capacity of water is …
2. ### CHEMISTRY
Given that the specific heat capacities of ice and steam are 2.06 J/g°C and 2.03 J/g°C, the molar heats of fusion and vaporization for water are 6.02 kJ/mol and 40.6 kJ/mol, respectively, and the specific heat capacity of water is …
3. ### chemistry
given the following info for water molar heat of fusion 6.02kj/mol calculate the total quanity of heat evolved when 10.0g of steam is condensed,cooled,and frozen to ice at -50 degrees
4. ### chemistry
given the following info for water molar heat of vaporization 40.6kj/mol calculate the total quanity of heat evolved when 10.0g of steam is condensed,cooled,and frozen to ice at -50 degrees
5. ### chemistry
given the following info for water molar heat of specific heat capacity of liquid water 4.18 j/g degrees calculate the total quanity of heat evolved when 10.0g of steam is condensed,cooled,and frozen to ice at -50 degrees
6. ### chemistry
given the following info for water specific heat capacity of steam 2.03 j/g degrees calculate the total quanity of heat evolved when 10.0g of steam is condensed,cooled,and frozen to ice at -50 degrees
7. ### Chemistry
Given that the specific heat capacities of ice and steam are 2.06 J/g degrees C and 2.03 J/g degrees C, respectively, calculate the total quantity of heat evolved when 10.0 g of steam at 200 degrees C is condensed, cooled, and frozen …
8. ### Chemistry
Given that the specific heat capacities of ice and steam are 2.06 J/g degrees celsius, respectively, and considering the information about water given in exercise 16, calculate the total quantity of heat evolved when 10.0g of steam …
9. ### chemistry
Given that the specific heat capacities of ice and steam are 2.06 J/g degrees celsius and 2.03 J/g degrees celsius, respectively, and considering the information about water given, calculate the total quantity of heat evolved when …
10. ### Chemistry
22.) The molar heats of fusion and vaporization for water are 6.02 kJ/mol and 40.6 kJ/mol, respectively, and the specific heat capacity of liquid water is 4.18 J/gC. (1) What quantity of heat is required to melt 25.0 g of ice at 0C?
More Similar Questions | 678 | 2,663 | {"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-2017-34 | latest | en | 0.836489 |
http://slideplayer.com/slide/1507484/ | 1,529,534,977,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267863939.76/warc/CC-MAIN-20180620221657-20180621001657-00227.warc.gz | 291,953,115 | 22,096 | # 1.02 M Timetables 1.02M Timetables.
## Presentation on theme: "1.02 M Timetables 1.02M Timetables."— Presentation transcript:
1.02 M Timetables 1.02M Timetables
Why is a timetable important?
The timing of tasks is important to ensure the completion of recipes in food lab or at home. A timetable is implemented by preparing a sheet into five categories : 1.02M Timetables
Such as setting the table. Gathering food and equipment. Pre-preparation: opening packages and measuring ingredients are examples. These tasks can all be Dovetailed. 1.02M Timetables
Pre-Preparation and Preparation
2. List Pre-preparation time: Time needed to get ready for lab experience 3. List Preparation time: The estimation of time to complete the preparation task(s). Estimate preparation times of each task. It is better to allow too much time than too little. 1.02M Timetables
List Cooking Time 4. List Cooking time: Always record the time that each dish needs to cook. 1.02M Timetables
Calculate Total time: The addition of the pre-preparation, preparation and cooking time. If the pre-preparation is 3 minutes, preparation time is 3 minutes and cooking time is 10 minutes then the total time is 16 minutes for the dish. Calculate Starting Time: The subtracting of the total time from the desired serving time. If the meal needs to served at 6:00. Subtract 16 minutes from 6:00, this means the dish needs to be started by 5:44 to be ready on time. 1.02M TimeTables
Let’s make a timetable! Let’s make a timetable for the brownies.
If class is 60 minutes long, use this as a guide. If class is 90 minutes long, use this as a guide. If class starts a 8:00 a.m. Remember the steps? List each: List tasks List pre-preparation time List preparation time List cooking time Calculate total time Calculate starting time 1.02M TimeTables
Brownie Pre-Preparation
Task Preparation Time Cooking Time Total Time Starting Time Brownie Pre-Preparation Wash Hands, restrain hair and put on apron 5 min 8:00 a.m. Preheat Oven 10 min 8:05 a.m. Set Table Gather ingredients/ equipment Grease Pan Measure dry ingredients 2 min 8:35 a.m. Measure liquid ingredients Cream sugar and butter, Add eggs and vanilla 8:37 a.m. Combine dry ingredients in separate bowl. 8:39 a.m. Fold in chips and place batter in greased pan 8:41 a.m. Bake Brownies and cool 35 min + 10 min 9:16 a.m. Mix frosting ingredients 9:00 a.m. Frost, Cut, Serve 9:18 Final Clean Up 9:23 a.m.
Let’s Evaluate! Take note of the way the brownie recipe was broken down into brownie pre-preparation brownie preparation. Also notice that the time that is estimated for preparation time is added to the running start time of the next task. 1.02M Timetables
Brownie Pre-Preparation
Task Preparation Time Cooking Time Total Time Starting Time Brownie Pre-Preparation Wash Hands, restrain hair and put on apron 5 min 8:00 a.m. Preheat Oven 10 min 8:05 a.m. Set Table Gather ingredients/ equipment Grease Pan Measure dry ingredients 2 min 8:35 a.m. Measure liquid ingredients Cream sugar and butter, Add eggs and vanilla 8:37 a.m. Combine dry ingredients in separate bowl. 8:39 a.m. Fold in chips and place batter in greased pan 8:41 a.m. Bake Brownies and cool 35 min + 10 min 9:16 a.m. Mix frosting ingredients 9:00 a.m. Frost, Cut, Serve 9:18 Final Clean Up 9:23 a.m. Pre-preparation steps. Preparation steps The Preparation time is added to the running starting time Pre-preparation steps. Preparation steps The Preparation time is added to the running starting time
Now It’s Your Turn! Choose a recipe from a cookbook or the internet to devise a timetable. Remember the Steps… List tasks List pre-preparation time List preparation time List cooking time Calculate total time Calculate starting time 1.02M Timetables
Similar presentations | 951 | 3,773 | {"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} | 3.015625 | 3 | CC-MAIN-2018-26 | latest | en | 0.869846 |
https://git.enlightenment.org/core/efl.git/commit/?h=devs/lauromoura/cv-finalize-csharp&id=b6d5ee9745cc3a71dc8529f8028aa8cfcd8e6c2a | 1,604,002,695,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107905777.48/warc/CC-MAIN-20201029184716-20201029214716-00604.warc.gz | 335,661,839 | 8,609 | summaryrefslogtreecommitdiff log msg author committer range
diff options
context: 12345678910152025303540 space: includeignore mode: unifiedssdiffstat only
author committer Jaehyun Cho 2019-09-09 14:46:01 +0900 Jaehyun Cho 2019-09-09 14:47:10 +0900 b6d5ee9745cc3a71dc8529f8028aa8cfcd8e6c2a (patch) a72c871ac81ce58470e9364bdd74bc999af733f6 1ecaf6fa025137771ac05ca97b4f78c0b281d3d5 (diff)
elm perf_test: fix warning of implicit conversion of floating point
The result of integral division is converted into floating point. To fix the warning by assigning the result to Evas_Coord variable, type cast is done.
-rw-r--r--src/bin/elementary/perf_test_01.c4
-rw-r--r--src/bin/elementary/perf_test_02.c4
-rw-r--r--src/bin/elementary/perf_test_03.c4
3 files changed, 6 insertions, 6 deletions
diff --git a/src/bin/elementary/perf_test_01.c b/src/bin/elementary/perf_test_01.cindex adb849fb80..d29f84813b 100644--- a/src/bin/elementary/perf_test_01.c+++ b/src/bin/elementary/perf_test_01.c @@ -36,9 +36,9 @@ TST(01, tick) (Evas *e EINA_UNUSED, double f, Evas_Coord win_w, Evas_Coord win_h 36 w = 5 + ((1.0 + cos((double)((f * 30.0) + (i * 10)))) * w0 * 2); 36 w = 5 + ((1.0 + cos((double)((f * 30.0) + (i * 10)))) * w0 * 2); 37 h = 5 + ((1.0 + sin((double)((f * 40.0) + (i * 19)))) * h0 * 2); 37 h = 5 + ((1.0 + sin((double)((f * 40.0) + (i * 19)))) * h0 * 2); 38 x = (win_w / 2) - (w / 2); 38 x = (win_w / 2) - (w / 2); 39 x += sin((double)((f * 50.0) + (i * 13))) * (w0 / 2); 39 x += (Evas_Coord)(sin((double)((f * 50.0) + (i * 13))) * (w0 / 2)); 40 y = (win_h / 2) - (h / 2); 40 y = (win_h / 2) - (h / 2); 41 y += cos((double)((f * 45.0) + (i * 28))) * (h0 / 2); 41 y += (Evas_Coord)(cos((double)((f * 45.0) + (i * 28))) * (h0 / 2)); 42 evas_object_geometry_set(o, x, y, w, h); 42 evas_object_geometry_set(o, x, y, w, h); 43 } 43 } 44 } 44 } diff --git a/src/bin/elementary/perf_test_02.c b/src/bin/elementary/perf_test_02.cindex 2683cd116d..ac381c732a 100644--- a/src/bin/elementary/perf_test_02.c+++ b/src/bin/elementary/perf_test_02.c @@ -36,9 +36,9 @@ TST(02, tick) (Evas *e EINA_UNUSED, double f, Evas_Coord win_w, Evas_Coord win_h 36 w = 5 + ((1.0 + cos((double)((f * 30.0) + (i * 10)))) * w0 * 2); 36 w = 5 + ((1.0 + cos((double)((f * 30.0) + (i * 10)))) * w0 * 2); 37 h = 5 + ((1.0 + sin((double)((f * 40.0) + (i * 19)))) * h0 * 2); 37 h = 5 + ((1.0 + sin((double)((f * 40.0) + (i * 19)))) * h0 * 2); 38 x = (win_w / 2) - (w / 2); 38 x = (win_w / 2) - (w / 2); 39 x += sin((double)((f * 50.0) + (i * 13))) * (w0 / 2); 39 x += (Evas_Coord)(sin((double)((f * 50.0) + (i * 13))) * (w0 / 2)); 40 y = (win_h / 2) - (h / 2); 40 y = (win_h / 2) - (h / 2); 41 y += cos((double)((f * 45.0) + (i * 28))) * (h0 / 2); 41 y += (Evas_Coord)(cos((double)((f * 45.0) + (i * 28))) * (h0 / 2)); 42 evas_object_geometry_set(o, x, y, w, h); 42 evas_object_geometry_set(o, x, y, w, h); 43 } 43 } 44 } 44 } diff --git a/src/bin/elementary/perf_test_03.c b/src/bin/elementary/perf_test_03.cindex 065bd6d984..6737bedac5 100644--- a/src/bin/elementary/perf_test_03.c+++ b/src/bin/elementary/perf_test_03.c @@ -36,9 +36,9 @@ TST(03, tick) (Evas *e EINA_UNUSED, double f, Evas_Coord win_w, Evas_Coord win_h 36 w = 5 + ((1.0 + cos((double)((f * 30.0) + (i * 10)))) * w0 * 2); 36 w = 5 + ((1.0 + cos((double)((f * 30.0) + (i * 10)))) * w0 * 2); 37 h = 5 + ((1.0 + sin((double)((f * 40.0) + (i * 19)))) * h0 * 2); 37 h = 5 + ((1.0 + sin((double)((f * 40.0) + (i * 19)))) * h0 * 2); 38 x = (win_w / 2) - (w / 2); 38 x = (win_w / 2) - (w / 2); 39 x += sin((double)((f * 50.0) + (i * 13))) * (w0 / 2); 39 x += (Evas_Coord)(sin((double)((f * 50.0) + (i * 13))) * (w0 / 2)); 40 y = (win_h / 2) - (h / 2); 40 y = (win_h / 2) - (h / 2); 41 y += cos((double)((f * 45.0) + (i * 28))) * (h0 / 2); 41 y += (Evas_Coord)(cos((double)((f * 45.0) + (i * 28))) * (h0 / 2)); 42 evas_object_geometry_set(o, x, y, w, h); 42 evas_object_geometry_set(o, x, y, w, h); 43 } 43 } 44 } 44 } | 1,800 | 3,939 | {"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} | 2.5625 | 3 | CC-MAIN-2020-45 | latest | en | 0.392098 |
https://nrich.maths.org/public/topic.php?code=-334&cl=2&cldcmpid=840 | 1,596,943,519,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738380.22/warc/CC-MAIN-20200809013812-20200809043812-00044.warc.gz | 424,944,330 | 9,081 | # Resources tagged with: Games
Filter by: Content type:
Age range:
Challenge level:
### There are 153 results
Broad Topics > Thinking Mathematically > Games
### Counters
##### Age 7 to 11 Challenge Level:
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
### Seeing Squares
##### Age 5 to 11 Challenge Level:
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
### Dominoes
##### Age 7 to 16 Challenge Level:
Everthing you have always wanted to do with dominoes! Some of these games are good for practising your mental calculation skills, and some are good for your reasoning skills.
### Counter Roundup
##### Age 7 to 11 Challenge Level:
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
### Low Go
##### Age 7 to 16 Challenge Level:
A game for 2 players. Take turns to place a counter so that it occupies one of the lowest possible positions in the grid. The first player to complete a line of 4 wins.
### Spiralling Decimals for Two
##### Age 7 to 14 Challenge Level:
Spiralling Decimals game for an adult and child. Can you get three decimals next to each other on the spiral before your partner?
### Squayles
##### Age 11 to 14 Challenge Level:
A game for 2 players. Given an arrangement of matchsticks, players take it is turns to remove a matchstick, along with all of the matchsticks that touch it.
### Lambs and Tigers
##### Age 11 to 14 Challenge Level:
Investigations based on an Indian game.
### Making Maths: Happy Families
##### Age 5 to 11 Challenge Level:
Here is a version of the game 'Happy Families' for you to make and play.
### Part the Piles
##### Age 7 to 11 Challenge Level:
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
### Using Games in the Classroom
##### Age 7 to 16
Gillian Hatch analyses what goes on when mathematical games are used as a pedagogic device.
### Seeing Squares for Two
##### Age 5 to 11 Challenge Level:
Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?
### Learning Mathematics Through Games Series: 1. Why Games?
##### Age 5 to 14
This article supplies teachers with information that may be useful in better understanding the nature of games and their role in teaching and learning mathematics.
### Learning Mathematics Through Games Series: 2.types of Games
##### Age 5 to 14
This article, the second in the series, looks at some different types of games and the sort of mathematical thinking they can develop.
### 18 Hole Light Golf
##### Age 5 to 16 Challenge Level:
The computer starts with all the lights off, but then clicks 3, 4 or 5 times at random, leaving some lights on. Can you switch them off again?
### Play to 37
##### Age 7 to 11 Challenge Level:
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
### Patience
##### Age 11 to 14 Challenge Level:
A simple game of patience which often comes out. Can you explain why?
##### Age 7 to 11 Challenge Level:
This is a game for 2 players. Each player has 4 counters each, and wins by blocking their opponent's counters. A good follow-on from two stones.
### Winning Lines
##### Age 7 to 16
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
### First Connect Three for Two
##### Age 7 to 11 Challenge Level:
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
### Dicey Perimeter, Dicey Area
##### Age 7 to 11 Challenge Level:
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
### How Long Does it Take?
##### Age 7 to 11 Challenge Level:
How long does it take to brush your teeth? Can you find the matching length of time?
### Countdown
##### Age 7 to 14 Challenge Level:
Here is a chance to play a version of the classic Countdown Game.
### Traffic Lights
##### Age 7 to 11 Challenge Level:
The game uses a 3x3 square board. 2 players take turns to play, either placing a red on an empty square, or changing a red to orange, or orange to green. The player who forms 3 of 1 colour in a line. . . .
### Down to Nothing
##### Age 7 to 11 Challenge Level:
A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.
### Jumping Reindeer
##### Age 7 to 11 Challenge Level:
A game for 1 person to develop stategy and shape and space awareness. 12 counters are placed on a board. Counters are removed one at a time. The aim is to be left with only 1 counter.
### Got it for Two
##### Age 7 to 14 Challenge Level:
Got It game for an adult and child. How can you play so that you know you will always win?
### Go Moku
##### Age 7 to 11 Challenge Level:
A game for two players on a large squared space.
### Online
##### Age 7 to 11 Challenge Level:
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
### Factors and Multiples Game for Two
##### Age 7 to 14 Challenge Level:
Factors and Multiples game for an adult and child. How can you make sure you win this game?
### Ratio Pairs 2
##### Age 7 to 11 Challenge Level:
A card pairing game involving knowledge of simple ratio.
### Got a Strategy for Last Biscuit?
##### Age 11 to 16 Challenge Level:
Can you beat the computer in the challenging strategy game?
### Train Tactics for Two
##### Age 7 to 11 Challenge Level:
Train game for an adult and child. Who will be the first to make the train?
### Tac-tickle
##### Age 5 to 11 Challenge Level:
This is a challenging game of strategy for two players with many interesting variations.
### Making Maths: Snake Pits
##### Age 5 to 14 Challenge Level:
A game to make and play based on the number line.
### Spiralling Decimals
##### Age 7 to 14 Challenge Level:
Take turns to place a decimal number on the spiral. Can you get three consecutive numbers?
##### Age 11 to 16 Challenge Level:
Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.
### Developing Logical Thinking: the Place of Strategy Games
##### Age 5 to 11
This article outlines how strategy games can help children develop logical thinking, using examples from the NRICH website.
### Less Is More
##### Age 5 to 11 Challenge Level:
Use your knowledge of place value to try to win this game. How will you maximise your score?
##### Age 3 to 11
What might your first lesson with a new class look like? In this article, Cherri Moseley makes some suggestions for primary teachers.
### Tangram Pictures
##### Age 5 to 14 Challenge Level:
Use the tangram pieces to make our pictures, or to design some of your own!
### Going for Games
##### Age 5 to 11
In this article for teachers, Liz Woodham describes the criteria she uses to choose mathematical games for the classroom and shares some examples from NRICH.
### Strike it Out
##### Age 5 to 11 Challenge Level:
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
### Dicey Operations
##### Age 11 to 14 Challenge Level:
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
### Twin Corresponding Sudoku III
##### Age 11 to 16 Challenge Level:
Two sudokus in one. Challenge yourself to make the necessary connections.
### More Upper Primary Strategy Games
##### Age 7 to 11
Here are some more upper primary strategy games for you to play.
### Making Maths: Birds from an Egg
##### Age 7 to 11 Challenge Level:
Can you make the birds from the egg tangram?
### Twin Corresponding Sudokus II
##### Age 11 to 16 Challenge Level:
Two sudokus in one. Challenge yourself to make the necessary connections.
### Intersection Sudoku 1
##### Age 11 to 16 Challenge Level:
A Sudoku with a twist.
### Fifteen
##### Age 7 to 14 Challenge Level:
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15. | 2,040 | 8,640 | {"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-2020-34 | latest | en | 0.895144 |
http://scienceblogs.com/builtonfacts/2010/06/01/zero-point-free-lunches/ | 1,498,498,512,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320841.35/warc/CC-MAIN-20170626170406-20170626190406-00534.warc.gz | 346,206,138 | 14,580 | # Zero-point free lunches
Grab a particle and put it in a box.
According to elementary quantum mechanics, that particle isn’t described by the classical model in which it can have any value of energy as it bounces around. Instead, the possible energy levels of that particle are described by a discrete set. When you measure the energy of that particle in the box, it will always have one of those specific energy levels and nothing else. Exactly which level it will occupy depends on the details of how you put it into the box, but whatever you do you’re constrained to having the particle in those levels or at least a superposition thereof. The possible energy levels are:
Where each n is a positive integer, L is the length of the sides of the box, and m is the mass of the particle. However, the smallest the energy can possibly be is where all three n values are equal to 1. This is the famous zero-point energy, and for this particular system the energy of the particle cannot possibly be any less than exactly
Occasionally you’ll hear some intrepid thinker propose to use this as a source of power. If the particle always has that minimum energy, why can’t we bleed off energy from the particle as nature constantly replenishes it to keep it at the zero-point value? Unfortunately it doesn’t work. As weird as quantum mechanics is, it still doesn’t give us away around thermodynamics. Imagine we put a particle into a large box with large L and thus small E, then squashed the box down to decrease L and increase E. Then we plan to open the box and extract the power from our newly-energetic particle.
Here’s the problem – changing the energy of a system by changing its volume requires doing work. Pressure by definition is the change in energy with respect to volume (with a minus sign because pressure is pushing in the opposite direction as the change in volume):
With V = L^3, of course. So as you adiabatically compress the box, you have to do work against the pressure. The work you have to do is equal to the increasing zero-point energy. This isn’t a proof – it could have been that the energy/volume relationship doesn’t hold in quantum mechanics – but it’s what thermodynamics predicts, it’s pretty easily testable, and it has in fact been experimentally demonstrated to work. For that matter, the fact that it does work underlies the description of all kinds of phenomena from the bulk modulus of metals to the pressure holding up neutron stars .
Those two equations above also give us a chance to take a look at why zero-point energy isn’t something we notice in everyday life. An electron in a 1 mm box has a zero point energy of about 6×10-32 J, which is pretty darn tiny even by electron standards. It’s well under a trillionth of an electron volt. The associated pressure is about 4×10 -23 pascals, and atmospheric pressure is about a hundred thousand pascals. This is also pretty tiny.
Big or tiny though, it’s not going to give us a free lunch of any size.
1. #1 Joseph Smidt
June 1, 2010
Really well put. Every once and a while I am asked why we can’t extract zero point energy and now I will have to use this as a helpful explanation.
2. #2 Peeter Joot
June 1, 2010
Shouldn’t that be hbar squared?
3. #3 Matt Springer
June 1, 2010
Yes, in all three cases. This is when I wish ScienceBlogs had a LaTeX editor instead of me having to redo all the equation imaged by hand…
4. #4 NickBMorgan
June 1, 2010
Now I thought it was because Mother Nature had a very large dog that would bite you if you tried to steal her energy.
5. #5 John S. Wilkins
June 2, 2010
I thought it was because Maxwell’s demon needed to use more energy to get the energy than he got.
6. #6 Uncle Al
June 2, 2010
A collapsing Casimir etalon extracts zero point energy, F(dot)d. A 100 nm gap gives 130 dyne/cm^2. That is 33 times the weight of aluminum foil/cm^2. Aside from fabrication energy pre-debt… only 1/2 cycle obtains, and it doesn’t have much throw before Casimir becomes van der Waals. Vacuum propeller proposals, even sober ones (arxiv:0912.1031), are similarly modest. Here is what we need to do,
2) ?
3) Energy independence!
7. #7 rob
June 4, 2010
Uncle Al:
i thought step 1 was steal underwear.
8. #8 Nathan Myers
June 4, 2010
Nah, that’s only if you’re after Profit(!!!). Energy independence(!) definitely needs the moon thing.
9. #9 Marc
June 4, 2010
I think the last line of this post deserves to be put into a list of great quotes!
10. #10 ball valves
March 27, 2011 | 1,084 | 4,509 | {"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} | 3.453125 | 3 | CC-MAIN-2017-26 | longest | en | 0.95867 |
https://www.consumerfinance.gov/rules-policy/regulations/1026/2023-05-15/interp-k/ | 1,726,466,605,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651676.3/warc/CC-MAIN-20240916044225-20240916074225-00861.warc.gz | 663,428,965 | 36,386 | An official website of the United States government
# Comment for Appendix K - Total Annual Loan Cost Rate Computations for Reverse Mortgage Transactions
This version is not the current regulation.
You are viewing a previous version of this regulation with amendments that went into effect on May 15, 2023.
### General.
1. The calculation of total annual loan cost rates under appendix K is based on the principles set forth and the estimation or “iteration” procedure used to compute annual percentage rates under appendix J. Rather than restate this iteration process in full, the regulation cross-references the procedures found in appendix J. In other aspects the appendix reflects the special nature of reverse mortgage transactions. Special definitions and instructions are included where appropriate.
(b) Instructions and equations for the total annual loan cost rate
(b)(5) Number of unit-periods between two given dates
1. Assumption as to when transaction begins. The computation of the total annual loan cost rate is based on the assumption that the reverse mortgage transaction begins on the first day of the month in which consummation is estimated to occur. Therefore, fractional unit-periods (used under appendix J for calculating annual percentage rates) are not used.
(b)(9) Assumption for discretionary cash advances
1. Amount of credit. Creditors should compute the total annual loan cost rates for transactions involving discretionary cash advances by assuming that 50 percent of the initial amount of the credit available under the transaction is advanced at closing or, in an open-end transaction, when the consumer becomes obligated under the plan. (For the purposes of this assumption, the initial amount of the credit is the principal loan amount less any costs to the consumer under § 1026.33(c)(1).)
(b)(10) Assumption for variable-rate reverse mortgage transactions
1. Initial discount or premium rate. Where a variable-rate reverse mortgage transaction includes an initial discount or premium rate, the creditor should apply the same rules for calculating the total annual loan cost rate as are applied when calculating the annual percentage rate for a loan with an initial discount or premium rate (see the commentary to § 1026.17(c)).
(d) Reverse mortgage model form and sample form
(d)(2) Sample form
1. General. The “clear and conspicuous” standard for reverse mortgage disclosures does not require disclosures to be printed in any particular type size. Disclosures may be made on more than one page, and use both the front and the reverse sides, as long as the pages constitute an integrated document and the table disclosing the total annual loan cost rates is on a single page. | 524 | 2,727 | {"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} | 2.890625 | 3 | CC-MAIN-2024-38 | latest | en | 0.918677 |
http://economicshelpdesk.com/micro/demand-function.php | 1,553,374,536,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912203021.14/warc/CC-MAIN-20190323201804-20190323223804-00068.warc.gz | 64,136,578 | 6,384 | Demand Function
# Demand Function Assignment Help
Home / Microeconomics Assignment Help / Demand Function
# Demand Function
Demand function shows the relationship between the quantity demanded of a good and the various factors that affect interact or influence the determination of quantity demanded.
All the factors influencing the demand for a good can be briefly expressed in the following functional relationship:
Qxd = f(Px, Py, Pz ,….. Pn, Y , T)
Where,
Qxd shows the quantity of a good X demanded,
Px stands for the price of good X,
Py , Pz , .. Pn stands for prices of all other goods (other than good X) which may be substitutes
Of or complementary to good X,
Y stands for income of the households,
T stands for tastes and preferences of the households,
And f shows the functional relationship between the demand for good X and the other Variable, uiz., Py , . . Pn , Y and T , etc. in simple words, this functional relationship Shows that the demand for a good X depends upon the price of X, the prices of Other goods Py , P , .. The income of the consumers and their tastes and preferences.
The demand function is just a shorthand expression of the relationship between the quantity demanded of a commodity (left hand side) and the variables that determine it (right hand side). The tern ‘function’ is indicator of this precise quantitative relationship between variables on the right side of the equation and the variable on the left side.
Since, quantity demanded of a good is dependent upon so many variables (factors), we usually pick up one such variable and study its impact on quantity demanded, assuming that all other variables remain unchanged or are constant. Thus, we can examine the impact of an increase in the price of good X on quantity demanded of X on the assumption that prices of all other goods, consumers’ income, their tastes and preferences, etc., remain constant or unchanged. Thus we can examine the impact of change of each individual variable on demand on this assumption that other factors or influences remain unchanged.
### Submit Homework
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### Can't Judge a Powder B
Posted: August 10th, 2014, 10:46 am
### Can't Judge a Powder
Posted: November 6th, 2014, 4:00 pm
I don't know how to find the density of a powder. Can anyone help me?
(This post was moved to the Can't Judge a Powder event forum - Mod)
### Re: Can't Judge a Powder
Posted: November 7th, 2014, 3:39 pm
Kahler wrote:I don't know how to find the density of a powder. Can anyone help me?
(This post was moved to the Can't Judge a Powder event forum - Mod)
The density of a powder is mass/volume. So far in the event (I did this event last year too), I haven't actually had to find the density of anything. Just be ready to answer questions about relative density, such as "Is the powder more dense/less dense than ____ (name of reagent)?" In that case, you could stick in as an answer something like- "Observation ##: The powder sinks in/floats in ____ (same name of reagent) , therefore, the powder is more dense/less dense than ____(reagent)"
HIH,
~asthedeer~
### Re: Can't Judge a Powder
Posted: November 11th, 2014, 7:32 am
Kahler wrote:I don't know how to find the density of a powder. Can anyone help me?
(This post was moved to the Can't Judge a Powder event forum - Mod)
If they give you a balance and a graduated cylinder, then you can find it. This explains it nicely:
It's a pretty rare question (like asthedeer said), but I have seen it before. Good luck!
### Re: Can't Judge a Powder
Posted: November 13th, 2014, 11:58 am
Kahler wrote:I don't know how to find the density of a powder. Can anyone help me?
(This post was moved to the Can't Judge a Powder event forum - Mod)
Basically you need to start by taking the mass of the sample. I recommend taking the mass of the sample and the container first, then pouring it into a different container to mass the original container. You can subtract the two to get the mass of the sample, and that counts as another observation. (WARNING: Do not only give the mass of the sample. That is an inference.) Then, find the volume of the sample by measuring the volume in a beaker. As another observation, divide the mass by the volume. I recommend rounding to 2 decimal places. The SI unit is g/cm^3 or g/mL. Be certain that this is how you measure everything.
### Re: Can't Judge a Powder
Posted: November 15th, 2014, 5:35 pm
cupcakegirl wrote:
Kahler wrote:I don't know how to find the density of a powder. Can anyone help me?
(This post was moved to the Can't Judge a Powder event forum - Mod)
If they give you a balance and a graduated cylinder, then you can find it. This explains it nicely:
It's a pretty rare question (like asthedeer said), but I have seen it before. Good luck!
Unless I'm mistaken, you aren't allowed to bring graduated cylinders in competitions tho....
### Re: Can't Judge a Powder B
Posted: November 27th, 2014, 8:14 am
Unless I'm mistaken, you aren't allowed to bring graduated cylinders in competitions tho....
She means if they give you a graduated cylinder. You're right, you can't bring one yourself, which is why it's not always asked about.
### Re: Can't Judge a Powder B
Posted: November 27th, 2014, 9:22 am
Ah I see. I didn't notice the "if they give" part.
### Re: Can't Judge a Powder B
Posted: December 2nd, 2014, 2:33 pm
asthedeer wrote:Ah I see. I didn't notice the "if they give" part.
Ya Suuurreeeeeee
### Re: Can't Judge a Powder B
Posted: December 15th, 2014, 7:13 pm
Hello, I was just wondering if any of you had any specific suggestions on how to make observations. Also, should we keep referring back to the solution on every observation after or not?
Thanks!
### Re: Can't Judge a Powder B
Posted: December 16th, 2014, 9:15 am
No specific way as far as I know. I do believe though, that they like organized observations. For example, I wouldn't do an observation about the color of the powder for #1, then have another observation such as "The HCl conducts electricity" for #2, but instead put all the observations about the powder in, say, the first 10 observations.
I'm not sure what you mean by "referring back to the solution". Does it mean looking at the solution for everything you write?
### Re: Can't Judge a Powder B
Posted: December 16th, 2014, 10:34 am
A few suggestions from one that has run this event for several years:
* Each observation should stand on it's own... don't assume that because the observation prior was with an aqueous solution, that I will assume that this is as well... I won't.
* Pronouns are rarely a good thing in this event... Better to take the extra few seconds and write it out.
* This event boils down to giving a better observation than your competition... Look at it as being graded on a curve... Try to structure your observations to be both quantitative as well as qualitative
* Find ways to make your observations just a little better than the competitions by using adjectives that better describe what you observed
* Yes, abbreviations theoretically are allowed, if defined somewhere on the page, but is it worth the risk? If we are grading 50 tests in as little as an hour, it is very easy to miss the abbreviation key... I would not risk it
* The intent means nothing if I can't read what you've written... I'll give you every possible benefit, but if I can't read it, I can't give you credit. Decide if you or your partner have the neatest hand writing, and have that one do the recording
* In every test, there will probably be at least 1 question that you did not record an observation for - Yes, you are allowed to write in an answer, but it should be in form of an observation; complete and whole (i.e substance was soluble in
water...not "yes")
### Re: Can't Judge a Powder B
Posted: December 18th, 2014, 11:00 am
To any coaches out there: we got our school's CJAP tests back from an invitational, and our teams lost points because they answered questions with more than 3 observations. When I competed in this event in B division, there was no such rule. Did the proctors goof, or is this a legitimate rule now that I missed when reading the rules?
### Re: Can't Judge a Powder B
Posted: January 2nd, 2015, 12:52 pm
does anyone know what a "pure substance" is
### Re: Can't Judge a Powder B
Posted: January 3rd, 2015, 5:25 pm
samlan16 wrote:To any coaches out there: we got our school's CJAP tests back from an invitational, and our teams lost points because they answered questions with more than 3 observations. When I competed in this event in B division, there was no such rule. Did the proctors goof, or is this a legitimate rule now that I missed when reading the rules?
It's not an official rule, but some proctors (especially at invitationals) do place a limit on the number of observations you can answer a question with. They're supposed to tell the teams if they do that though. It's best not to put down more than 3 observations unless absolutely necessary.I think the nats proctor also had that same limit, but correct me if I'm wrong. | 1,760 | 6,981 | {"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} | 2.96875 | 3 | CC-MAIN-2019-35 | latest | en | 0.963408 |
https://stuvera.com/ebooks/applied-statistics-and-probability-for-engineers-6th-edition-solutions/ | 1,607,155,924,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141747323.98/warc/CC-MAIN-20201205074417-20201205104417-00252.warc.gz | 508,766,044 | 35,410 | ## Applied statistics and probability for engineers 6th edition solutions
You can download solutions manual forapplied statistics and probability for engineers 6th edition solutions
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So you can try downloading solutions manual forapplied statistics and probability for engineers 3rd edition pdf at stuvera.com.
## ABOUT applied statistics and probability for engineers 6th edition solutions
The text provides a practical approach oriented to engineering as well as chemical and physical sciences. Students learn how the material will be relevant in their careers through the integration throughout of unique problem sets that reflect realistic applications and situations. Applied Statistics, 6th Edition is suitable for either a one- or two-term course in probability and statistics.
Chapter 1 The Role of Statistics in Engineering
Chapter 2 Probability
Chapter 3 Discrete Random Variables and Probability Distributions
Chapter 4 Continuous Random Variables and Probability Distributions
Chapter 5 Joint Probability Distributions
Chapter 6 Descriptive Statistics
Chapter 7 Sampling Distributions and Point Estimation of Parameters
Chapter 8 Statistical Intervals for a Single Sample
Chapter 9 Tests of Hypotheses for a Single Sample
Chapter 10 Statistical Inference for Two Samples
Chapter 11 Simple Linear Regression and Correlation
Chapter 12 Multiple Linear Regression
Chapter 13 Design and Analysis of Single-Factor Experiments: The Analysis of Variance
Chapter 14 Design of Experiments with Several Factors
Chapter 15 Statistical Quality Control
Appendices
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# Professor: Members of most species are able to communicate
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Professor: Members of most species are able to communicate [#permalink]
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14. Professor: Members of most species are able to communicate with other members of the same species, but it is not true that all communication can be called “language.â€
If you have any questions
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03 Jun 2005, 08:04
Looks D to me.
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03 Jun 2005, 08:35
riteshgupta1 wrote:
Looks D to me.
Agreed.
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03 Jun 2005, 10:40
D it is.
GA
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04 Jun 2005, 06:00
The OA is D.
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### Show Tags
04 Jun 2005, 06:07
WinWinMBA wrote:
The OA is D.
I too vote for D.
HMTG.
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Display posts from previous: Sort by | 808 | 2,637 | {"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-2017-04 | latest | en | 0.868546 |
www.ms-legit.com.ng | 1,709,587,490,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476532.70/warc/CC-MAIN-20240304200958-20240304230958-00516.warc.gz | 880,836,144 | 52,382 | Have you been searching for 2022/2023 jamb Syllabus for Mathematics? Do you wish to download the 2022/2023 Jamb Mathematics syllabus ? Then this post is for you. Sit back and enjoy your reading.
Jamb Mathematics Syllabus 2022/2023
JAMB Mathematics Syllabus is to prepare candidates for JAMB Examination. It contains topics as well as subtopics which students are to study for their JAMB Examination. The aim of this syllabus is to help student prepare for their examination and to test the achievement of the course objectives. The course objectives include:
1. Acquire computational and manipulative skills;
2. Develop precise, logical, and formal reasoning skills;
3. Develop deductive skills in interpretation of graphs, diagrams, and data;
4. Apply mathematical concepts to resolve issues in daily living
Jamb Syllabus for Mathematics 2022/2023
Jamb syllabus for mathematics is divided into five section.
Section A: Number and Numeration
1. Number Base:
• Operations in different number bases from 2 to 10;
• Conversion from one base to another including fractional parts.
2. Fractions, Decimals, Approximation, and Percentage:
• Fractions and decimals;
• Significant figures;
• Decimal places;
• Percentage errors;
• Simple interest;
• Profit and loss percent;
• Ratio, proportion, and rate;
• Shares and value-added tax (VAT).
3. Indices, Logarithm, and Surds:
• Laws of indices;
• Standard form;
• Laws of logarithm;
• Logarithm of any positive number to a given base;
• Change of bases in logarithm and application;
• Relationship between indices and logarithm;
• Surds.
4. Sets:
• Types of sets
• Algebra of sets
• Venn diagrams and their applications.
Section B: Algebra
1. Polynomials;
• Change of subject of the formula
• Factor and remainder theorems
• Factorization of polynomials of degree not exceeding 3.
• Multiplication and division of polynomials
• Roots of polynomials not exceeding degree 3
• Simultaneous equations including one linear one quadratic;
• Graphs of polynomials of degree not greater than 3.
2. Variation;
• Direct
• Inverse
• Joint
• Partial
• Percentage increase and decrease.
3. Inequalities;
• Analytical and graphical solutions of linear inequalities;
• Quadratic inequalities with integral roots only.
4. Progression;
• nth term of a progression
• sum of A. P. and G. P.
5. Binary Operations;
• Properties of closure, commutativity, associativity, and distributivity;
• Identity and inverse elements (simple cases only).
6. Matrices and Determinants;
• Algebra of matrices not exceeding 3 x 3;
• Determinants of matrices not exceeding 3 x 3;
• Inverses of 2 x 2 matrices [excluding quadratic and higher degree equations].
Section C: Geometry and Trigonometry
1. Euclidean Geometry;
• Properties of angles and lines
• Polygons: triangles, quadrilaterals and general polygons;
• Circles: angle properties, cyclic quadrilaterals and intersecting chords;
• Construction.
2. Mensuration;
• Lengths and areas of plane geometrical figures;
• Lengths of arcs and chords of a circle;
• Perimeters and areas of sectors and segments of circles;
• Surface areas and volumes of simple solids and composite figures;
• The earth as a sphere:- longitudes and latitudes.
3. Locus;
• Locus in 2 dimensions based on geometric
• Principles relating to lines and curves.
4. Coordinate Geometry;
• Midpoint and gradient of a line segment;
• Distance between two points;
• Parallel and perpendicular lines;
• Equations of straight lines.
5. Trigonometry;
• Trigonometrical ratios of angels;
• Angles of elevation and depression;
• Bearings;
• Areas and solutions of triangle;
• Graphs of sine and cosine;
• Sine and cosine formulae.
Section D: Calculus
1. Differentiation;
• Limit of a function
• Differentiation of explicit algebraic and simple trigonometrical functions – sine, cosine and tangent.
2. Application of Differentiation;
• Rate of change;
• Maxima and minima.
3. Integration;
• Integration of explicit algebraic and simple trigonometrical functions;
• Area under the curve.
1. Representation of Data;
• Frequency distribution;
• Histogram, bar chart, and pie chart.
2. Measures of Location;
• Mean, mode, and median of ungrouped and grouped data – (simple cases only);
• Cumulative frequency.
3. Measures of Dispersion;
• Range, mean deviation, variance and standard deviation.
4. Permutation and Combination;
• Linear and circular arrangements;
• Arrangements involving repeated objects.
5. Probability;
• Experimental probability (tossing of coin, throwing of a dice etc);
• Addition and multiplication of probabilities (mutual and independent cases).
The Mathematics syllabus PDF File has all you need to know about JAMB Syllabus For Mathematics 2022. Kindly click the below link to download.
Mathematics Syllabus
• Adelodun A. A (2000) Distinction in Mathematics: Comprehensive Revision Text, (3rd Edition) Ado -Ekiti: FNPL.
• Anyebe, J. A. B (1998) Basic Mathematics for Senior Secondary Schools and Remedial Students in Higher/ institutions, Lagos: Kenny Moore.
• Channon, J. B. Smith, A. M (2001) New General Mathematics for West Africa SSS 1 to 3, Lagos: Longman.
• David -Osuagwu, M. et al (2000) New School Mathematics for Senior Secondary Schools, Onitsha: Africana – FIRST Publishers.
• Egbe. E et al (2000) Further Mathematics, Onitsha: Africana – FIRST Publishers
• Ibude, S. O. et al (2003) Agebra and Calculus for Schools and Colleges: LINCEL Publishers.
• Tuttuh – Adegun M. R. et al (1997), Further Mathematics Project Books 1 to 3, Ibadan: NPS Educational
• Wisdomline Pass at Once JAMB.
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Subscribe to our website ms-legit.com.ng to get more updates as they come. | 1,354 | 5,664 | {"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} | 3.984375 | 4 | CC-MAIN-2024-10 | longest | en | 0.875127 |
https://www.bartleby.com/questions-and-answers/6.6-worksheet-exercise-6.6.1-selecting-students-for-jobs.-a-a-teacher-selects-4-students-from-her-cl/7466d0d4-1190-4e63-b0ec-b04c079e6e9a | 1,582,838,447,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875146809.98/warc/CC-MAIN-20200227191150-20200227221150-00353.warc.gz | 636,039,464 | 32,047 | # 6.6 WorksheetExercise 6.6.1: Selecting students for jobs.(a) A teacher selects 4 students from her class of 37 to work together on a project. How many ways are therefor her to select the students?(b)A teacher selects students from her class of 37 students to do 4 different jobs in the classroom: pick uphomework, hand out permission slips, staple worksheets, and organize the classroom library. Each job isperformed by exactly one student in the class and no student can get more than one job. How many ways arethere for her to select students and assign them to the jobs?Exercise 6.6.2: Results of a piano competition.120 pianists compete in a piano competition.(a) In the first round, 30 of the 120 are selected to go on to the next round. How many different outcomes arethere for the first round?wordOwynom(b) In the second round, the judges select the first, second, third, fourth and fifth place winners of thecompetition from among the 30 pianists who advanced to the second round. How many outcomes are therefor the second round of the competition?26GAGH2Exercise 6.6.3: Choosing a lineup for a traveling basketball team.There are 20 members of a basketball team.(a) The coach must select 12 players to travel to an away game. How many ways are there to select the playerswho will travel?Page 1 of 3 6.6 Worksheet(b) From the 12 players who will travel, the coach must select her starting line-up. She will select a player foreach of the five positions: center, power forward, small forward, shooting guard and point guard. How manyways are there for her to select the starting line-up?(b) :parorc(c) From the 12 players who will travel, the coach must select her starting line-up. She will select a player foreach of the five positions: center, power forward, small forward, shooting guard and point guard. However,there are only three of the 12 players who can play center. Otherwise, there are no restrictions. How manyways are there for her to select the starting line-up?Exercise 6.6.4: Hiring a software engineer.A search committee is formed to find a new software engineer.(a)lf 100 applicants apply for the job, how many ways are there to select a subset of 9 for a short list?(b) If 6 of the 9 are selected for an interview, how many ways are there to pick the set of people who areinterviewed? (You can assume that the short list is already decided).29gbul(d)(c) Based on the interview, the committee will rank the top three candidates and submit the list to their bosswho will make the final decision. (You can assume that the interviewees are already decided.) How many waysare there to select the list from the 6 interviewees?812001)Exercise 6.6.5: Counting orders at a restaurant.A group of five friends go to a restaurant for dinner. The restaurant offers 20 different main dishes.a) Suppose that the group collectively orders five different dishes to share. The waiter just needs to place allve dishes in the center of the table. How many different possible orders are there for the group?Page 2 of 3
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Tagged in | 835 | 3,612 | {"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-2020-10 | latest | en | 0.960133 |
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A010145 Continued fraction for sqrt(61). 5
7, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET 0,1 LINKS Harry J. Smith, Table of n, a(n) for n = 0..20000 A. J. van der Poorten, An introduction to continued fractions, Unpublished. A. J. van der Poorten, An introduction to continued fractions, Unpublished [Cached copy] G. Xiao, Contfrac Index entries for continued fractions for constants Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1). EXAMPLE 7.810249675906654394129722735... = 7 + 1/(1 + 1/(4 + 1/(3 + 1/(1 + ...)))). - Harry J. Smith, Jun 07 2009 MATHEMATICA ContinuedFraction[Sqrt[61], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 08 2011 *) PadRight[{7}, 120, {14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1}] (* Harvey P. Dale, Mar 27 2013 *) PROG (PARI) { allocatemem(932245000); default(realprecision, 18000); x=contfrac(sqrt(61)); for (n=0, 20000, write("b010145.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 07 2009 CROSSREFS Cf. A010514 Decimal expansion. - Harry J. Smith, Jun 07 2009 Sequence in context: A231015 A183031 A021018 * A199388 A201750 A198825 Adjacent sequences: A010142 A010143 A010144 * A010146 A010147 A010148 KEYWORD nonn,cofr AUTHOR N. J. A. Sloane STATUS approved
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Last modified June 20 22:36 EDT 2024. Contains 373532 sequences. (Running on oeis4.) | 802 | 1,983 | {"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-2024-26 | latest | en | 0.591824 |
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