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题目内容
Five gift cards will be distributed among 10 people so that no person receives more than one gift card. The gift cards consist of one $100 gift card, one $50 gift card, one $25 gift card and two $10 gift cards. How many different distributions of the five gift cards among the 10 people are possible if the two $10 gift cards are considered to be identical?
Three coins—two $$10$$-cent coins and one $$5$$-cent coin—are to be flipped simultaneously. For each of the three coins, the probability that the coin will land heads up is $$\frac{1}{2}$$. What is the probability that the total value of the coins that will land heads up is $$15$$ cents?
Give your answer as a fraction.
A telephone system has $$n$$ telephone lines. For each of the $$n$$ lines, the event that the line will fail during a certain reliability test has probability $$0.3$$, and these $$n$$ events are independent. If the probability that at least one of the $$n$$ lines will not fail during the reliability test is greater than $$0.99$$, what is the minimum value of $$n$$?
When positive integer n is divided by 53, the remainder is 21, and when positive integer p is divided by 53, the remainder is 25. What is the remainder when the product np is divided by 53?
If $$p$$ is an prime number greater than $$5$$, and if $$5$$ is a factor of $$p+p^{2}$$,which of the following might be the remainder when $$p$$ is divided by $$5$$?

Indicate all such numbers.
If $$a$$, $$b$$, and $$c$$ are positive integers such that $$\frac{a}{c}=0.075$$, and $$\frac{b}{c}=0.09$$, What is the least possible value of $$c$$?
One day in 1997 at a gas station in the United States near the border of Canada, gasoline was selling for $1.20 per gallon (United States dollars). On that day, 1 United States dollar could be exchanged for 1.25 Canadian dollars. If gasoline was being sold at an equivalent rate at a gas station across the border in Canada, which of the following calculations gives an approximate price, in Canadian dollars, for a liter of gasoline at the Canadian gas station that day? (1 gallon is approximately 3.785 liters.)
A large pump and a small pump are available to fill a public fountain with 7,500 gallons of water. The pumps can be used alone or simultaneously. Working alone at their respective constant rates, the small pump would take 1.6 times as long as the large pump to fill the fountain. Working simultaneously at their respective constant rates, the two pumps would take 3 hours to fill the fountain. How long would the small pump take to fill the fountain, working alone at its constant rate?

_____hours
A certain charity is conducting a fund-raiser. For the first $9,000 raised by the charity, Company B will contribute $1 for every $3 collected by the charity. For any amount over $9,000 raised by the charity, Company B will contribute $2 for every $5 collected by the charity. How much money must the charity raise in order to reach a total of $68,000, including the contribution from Company B?
Which of the following is greatest?


Which of the following shaded regions represents the set of all points $$(a, b)$$ in the xy-plane above such that $$(a+1, b+1)$$ is in quadrant Ⅰ? (Note that a point lies on axis is not in any quadrant)
Of the following, which graph best represents a shaded region in which every point $$(x, y)$$ satisfies the inequality $$y ≤ |x|$$?


The figure above represents six straight city streets that will be repaved. The figure shows only the centerlines of the streets, and all the streets have the same width. Four of the streets are parallel, with centerlines that are 200 meters apart from each other. If the cost to repair each street is estimated as $72,000 per kilometer of the length of its centerline, what is the total estimated cost to repave the six streets?

$_____
A group of 10 couples plans to rent bayside summer houses on Island X from Realtor M for a certain week. The total rental cost for the houses will be evenly distributed among the 10 couples, and each couple will have their own bedroom. If Realtor M has at least three bayside summer houses of each type available that week, what is the least possible rental cost per couple?
Of customers 4, 6, 8, 9 and 10, which one was served by the customer service representative who served customer 1?
According to the recorded times, which customer had the greatest ratio of waiting time to service time?
What was the range of the recorded service times, in minutes, for the 15 customers?


Data set D consists of 35 values, all of which are integers. The frequency distribution of the values in D is shown in the histogram, where each interval shown contains values that are greater than or equal to the left endpoint but less than the right endpoint.

Quantity A

The average (arithmetic mean) of the values in D

Quantity B

The median of the values in D
Larry and Tony work for different companies. Larry's salary is the $$90^{th}$$ percentile of the salaries in his company, and Tony's salary is the $$70^{th}$$ percentile of the salaries in his company.

Which of the following statements individually provide(s) sufficient additional information to conclude that Larry's salary is higher than Tony's salary?

Indicate all such statements.
The probability distribution function $$f$$ of a continuous random variable $$x$$ is defined by $$f(x) = \frac{2}{13}|x|$$ for $$−3 \leq x \leq 2$$

Quantity A

The median of the distribution of $$x$$

Quantity B

-$$\frac{9}{5}$$

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