本人数学太弱了，请教几道PREP里的

self346959851 · 发表于 2011-3-27 22:59:32

先谢过大家了~

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At a dinner party, 5 people are to be seated around a circular table.Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?

答案24

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A certain company has 18 equally qualified applicants for 4 open positions.How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter?

【答案3060

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A thin piece of wire 40 meters long is cut into two pieces.One piece is used to form a circle with radius r, and the other is used to form a square.No wire is left over.Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r ?

(E)πr² + (10 – 1/2πr)^{2

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Alice's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month.The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save.If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?

sdcar2010 · 发表于 2011-3-27 23:21:18

At a dinner party, 5 people are to be seated around a circular table.Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?

答案24

For circular arrangement quesitions, you just reduce the total number by one. 5 people on a circle is the same as 4 people on a line. 4! = 24. Basically you let one guy sit on the table, then arrange the other 4 guys on the remaining 4 spots, similar to 4 guys on a line.

sdcar2010 · 发表于 2011-3-27 23:24:34

A thin piece of wire 40 meters long is cut into two pieces.One piece is used to form a circle with radius r, and the other is used to form a square.No wire is left over.Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r ?

(E)πr2 + (10 – 1/2πr)2

For a circle with radius r, its circumference is 2*pai*r. So the the total length of the string for the square is 40 - 2* pair*r. So the length of the side of the square is 10 - pai*r/2.

Plug in the number for the area equations for a circle and a square, you will have the right answer.

sdcar2010 · 发表于 2011-3-27 23:25:38

A certain company has 18 equally qualified applicants for 4 open positions.How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter?

(18*17*16*15)/(4*3*2)

sdcar2010 · 发表于 2011-3-27 23:29:43

Alice's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month.The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save.If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?

Salary each month = a
Salary saved each month = b
Salary not saved each month = a-b
12*b = 3*(a-b)
So 3a = 9b
So the fraction she saves each mont = b/a = 1/3

self346959851 · 发表于 2011-3-28 16:15:21

Alice's take-home pay last year was the same each month, and she saved the same fraction of her take-home pay each month.The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save.If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?

Salary each month = a
Salary saved each month = b
Salary not saved each month = a-b
12*b = 3*(a-b)
So 3a = 9b
So the fraction she saves each mont = b/a = 1/3

-- by 会员 sdcar2010 (2011/3/27 23:29:43)

谢谢美女sdcar哦~
前面几题都懂了·
这一题的题目看不懂。。。
能不能帮我翻译下呀~
麻烦了嘻嘻~~

lastjuly · 发表于 2011-7-16 12:59:54

THX~

helenwolfy · 发表于 2011-7-16 14:58:48

Alice's take-home pay last year was the same each month去年一年爱丽丝同学的可支配收入每个月是不变的,
and she saved the same fraction of her take-home pay each month她每月存同样的一个比例
The total amount of money that she had saved at the end of the year 到年底她存的总钱数
was 3 times the amount of that portion of her monthly take-home pay that she did not save 是她每个月花掉的钱数的3倍
.If all the money that she saved last year was from her take-home pay, what fraction of her take-home pay did she save each month?如果她的存款都是从可支配收入来的，那么她每月存钱的比例？

为啥这道题我算出来是1／5？
设她每月存a，月收入是b

12a = 3(b-a) ==> 15a = 3b
4楼看看咱俩谁算错了？是不是我脑子短路了？

sdcar2010 · 发表于 2011-7-16 19:50:50

No. My calculation was wrong.

永远爱koma62 · 发表于 2012-1-7 16:25:27

解释的好啊~~~~~~~~~~

本人数学太弱了，请教几道PREP里的

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