[原创] 十月十六日 数学机井海外版 至101

findjuhl

92. In a certain day, a museum sold 30 tickets in every 5 minutes from 9:00(am) to 5:55 (pm), inclusive. Only two types tickets were sold, $10 value and $6value. If the number of $10 tickets sold is 3 times the number of the $6 tickets sold, what is the total revenue in the day?

93. Three quarts of chemical A contain 10% of hydrogen peroxide. A different chemical B, which contains 40% of hydrogen peroxide, will be mixed with the 3 quarts of A. How much B should be added to the A so that the resulting mixture contains 30% of hydrogen peroxide?

94. Is the standard deviation of a certain set greater than 15,000?
1). The range of the set is 25,000
2). The mean of the set is 150,000

95. Set S consists numbers arranged in ascending order. A new set is created as the follows: each elements of S is increased by a value equal to that number's place within the set. By how much is mean of new set greater than mean of the original set?
1). S consists of 10 elements.
2). The sum of the elements in the original set is 100

96. A jar contains 10 red balls and 10 green balls. If 3 balls are removed at random without replacement, what is the probability that all 3 balls removed from the jar are green?

97. Is R^2 + S^2 =0 ?
1). R+S=0
2). 3R^2 + 4R^2 =0

98. Of the 15 members in a club, 2/3 can speak English, 2/5 can speak French, 1/3 can speak Spain, and only one can speak all three languages. How many people can speak exactly two languages?

99. Does 8x=16+2x?
1). -3x is greater than or equal to -9
2). 2x is greater than or equal to 6

100. In 2002, Tony's earned more annual salary than Peter's. During each of the two following years, both them acquired 3% annual salary increasing. From 2002 to 2004, by what percent did their salary difference increase?
Answer:
Let the salaries in 2002 be x and y, respectively.
Then, the difference in 2002 is x-y
The difference in 2004 is x*1.03^2-y*1.03^2
The increase percent is (x*1.03^2-y*1.03^2)-(x-y)/(x-y)=(1.03)^2-1

101. A bus traveled to its destination at speed of 60km/h. On the return trip, the bus traveled the same distance, but had an average speed of 80km/h, making the trip 2 hours shorter. What is the total distance of the round trip?

specters

sofa, hohoho

米可可

以下是引用findjuhl在2006-10-16 10:42:00的发言：

92. In a certain day, a museum sold 30 tickets in every 5 minutes from 9:00(am) to 5:55 (pm), inclusive. Only two types tickets were sold, $10 value and $6value. If the number of $10 tickets sold is 3 times the number of the $6 tickets sold, what is the total revenue in the day?

28890

比较奇怪的是算出来的10元票和6元票卖出的张数不是一个整数。

93. Three quarts of chemical A contain 10% of hydrogen peroxide. A different chemical B, which contains 40% of hydrogen peroxide, will be mixed with the 3 quarts of A. How much B should be added to the A so that the resulting mixture contains 30% of hydrogen peroxide?

6

94. Is the standard deviation of a certain set greater than 15,000?
1). The range of the set is 25,000
2). The mean of the set is 150,000

E

这题很不确定

95. Set S consists numbers arranged in ascending order. A new set is created as the follows: each elements of S is increased by a value equal to that number's place within the set. By how much is mean of new set greater than mean of the original set?
1). S consists of 10 elements.
2). The sum of the elements in the original set is 100

E

96. A jar contains 10 red balls and 10 green balls. If 3 balls are removed at random without replacement, what is the probability that all 3 balls removed from the jar are green?

2/19

97. Is R^2 + S^2 =0 ?
1). R+S=0
2). 3R^2 + 4R^2 =0

B

98. Of the 15 members in a club, 2/3 can speak English, 2/5 can speak French, 1/3 can speak Spain, and only one can speak all three languages. How many people can speak exactly two languages?

4

99. Does 8x=16+2x?
1). -3x is greater than or equal to -9
2). 2x is greater than or equal to 6

B

100. In 2002, Tony's earned more annual salary than Peter's. During each of the two following years, both them acquired 3% annual salary increasing. From 2002 to 2004, by what percent did their salary difference increase?
Answer:
Let the salaries in 2002 be x and y, respectively.
Then, the difference in 2002 is x-y
The difference in 2004 is x*1.03^2-y*1.03^2
The increase percent is (x*1.03^2-y*1.03^2)-(x-y)/(x-y)=(1.03)^2-1

6.09%

101. A bus traveled to its destination at speed of 60km/h. On the return trip, the bus traveled the same distance, but had an average speed of 80km/h, making the trip 2 hours shorter. What is the total distance of the round trip?

480km

不知道跟大家算得一样不，尤其是DS题94。

[此贴子已经被作者于2006-10-16 11:57:00编辑过]

dot_deng

不同意见的题：

95. Set S consists numbers arranged in ascending order. A new set is created as the follows: each elements of S is increased by a value equal to that number's place within the set. By how much is mean of new set greater than mean of the original set?
1). S consists of 10 elements.
2). The sum of the elements in the original set is 100

A

假设原有有a1,a2....an个数且和为sn,那么新的集合的数就是a1＋1,a2＋2....an＋n，新集合的平均数＝[sn+n(n+1)/2]/n=sn/n+(n+1)/2.所以新集合的平均数比原集合的平均数大（n+1）/2.所以由1）可以知道n，因此也就知道结果了。但是2）不能。

97. Is R^2 + S^2 =0 ?
1). R+S=0
2). 3R^2 + 4R^2 =0

C

此题首先我觉得2）是不是有误，都是R的平方吗，还是第二项是S的平方？

要是题没有错的话，由1）可以推出R=S=0,或者R=-S不等于0。由2）可以知道7R^2=0,则R=0。结合1）2）可以得到R^2 + S^2 =0

米可可

以下是引用dot_deng在2006-10-16 12:29:00的发言：

不同意见的题：

97. Is R^2 + S^2 =0 ?
1). R+S=0
2). 3R^2 + 4R^2 =0

C

此题首先我觉得2）是不是有误，都是R的平方吗，还是第二项是S的平方？

要是题没有错的话，由1）可以推出R=S=0,或者R=-S不等于0。由2）可以知道7R^2=0,则R=0。结合1）2）可以得到R^2 + S^2 =0

嗯，我是把第二个条件当作3R^2 + 4S^2 =0做的，要不没意义这么表达吧。

2000zlj

95. Set S consists numbers arranged in ascending order. A new set is created as the follows: each elements of S is increased by a value equal to that number's place within the set. By how much is mean of new set greater than mean of the original set?
1). S consists of 10 elements.
2). The sum of the elements in the original set is 100

E

请教nn这道题如何解？

米可可

以下是引用dot_deng在2006-10-16 12:29:00的发言：

不同意见的题：

95. Set S consists numbers arranged in ascending order. A new set is created as the follows: each elements of S is increased by a value equal to that number's place within the set. By how much is mean of new set greater than mean of the original set?
1). S consists of 10 elements.
2). The sum of the elements in the original set is 100

A

假设原有有a1,a2....an个数且和为sn,那么新的集合的数就是a1＋1,a2＋2....an＋n，新集合的平均数＝[sn+n(n+1)/2]/n=sn/n+(n+1)/2.所以新集合的平均数比原集合的平均数大（n+1）/2.所以由1）可以知道n，因此也就知道结果了。但是2）不能。

哦，我理解成乘法了，唉……

dot_deng

动作真快啊，呵呵这样讨论才有效率的哦

yaomao

大家动作的都很快的说
94题该选A吧，
standard deviation<range/2

2000zlj

再请教一下

[sn+n(n+1)/2]/n

当中的n(n+1)/2是一个公式吗？想不起来了