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题目内容
$$r$$ and $$t$$ are consecutive even integers, and $$r \lt t$$.

Quantity A

$$\frac{1}{3}(t-r)^5$$

Quantity B

$$10$$
Set K consists of 6 consecutive odd integers. What is the range of the integers in K?
If the average (arithmetic mean) of 4 consecutive odd integers is $$m$$, what is the greatest of these integers?
If the sum of five consecutive even integers is $$y$$, what is the least of the five integers, in terms of $$y$$?
Set S consists of the consecutive even integers from 2 to 30, inclusive.

Quantity A

The number of prime numbers in set S

Quantity B

1
If $$x$$ and $$y$$ are prime numbers, each greater than $$10$$, which of the following must be an even integer?
$$p$$ is a prime number greater than $$2$$.

Quantity A

The number of prime factors of $$p-1$$

Quantity B

$$2$$
If $$n$$ is an integer greater than $$2$$, which of the following could be a prime number?
A number is to be randomly selected from the integers 4 through 15, inclusive. What is the probability that the number selected will not be a prime number?
A survey was given to a sample of residents in a certain town to determine the level of interest in creating a new park. Of those residents in the sample, 50 percent responded they were in favor of the park and 30 percent responded they were not in favor of the park. The remaining 20 percent of the sample did not respond to the survey.

Which of the following statements individually provide(s) sufficient additional information to determine the number of residents in the sample?

Indicate all such statements
Of all the applicants for jobs at a certain company last year, $$\frac{1}{3}$$ received a first interview. Of the applicants who received a first interview, $$\frac{1}{4}$$ received a second interview, The applicants who received no interview or only a first interview were not hired. Of the applicants who received a second interview, $$\frac{1}{5}$$ were hired and the rest were not hired. The applicants who received at least one interview and were not hired were what fraction of all the applicants for the jobs?
The pieces of art in a certain collection are classified as either ancient or modern. All pieces in the collection are on display in one of two wings of a museum, C or D. Of the pieces in the collection on display in C, $$\frac{1}{3}$$ are ancient pieces, and of the pieces in the collection on display in D, $$\frac{1}{4}$$ are ancient pieces. The number of modern pieces on display in C is equal to the number of modern pieces on display in D. Of all the ancient pieces in the collection, what fraction are on display in wing C?
The faces of a cube are numbered 1, 2, 3, 4, 5, and 6, respectively. Whenever the cube is rolled, each number is equally likely to appear on the top face after the roll. The cube is to be rolled twice. What is the probability that the number appearing on the top face after the second roll will be different from the number appearing on the top face after the first roll?

Give your answer as a fraction.
One student is to be selected at random from a class. The probability that the student selected will be male is equal to the probability that the student selected will be an English major. The probability that the student selected will be both male and an English major is 0.35. The probability that the student selected will be neither male nor an English major is 0.15. What is the probability that the student selected will be an English major?
Marina's total monthly salary consists of a base monthly salary of $400 plus a commission equal to 10 percent of her sales up to a certain amount and a commission of 20 percent on any additional sales in excess of that amount. Last month Marina's sales were $12,000, and her total monthly salary was $2,000. What is the amount of sales at which the commission rate changes from 10 percent to 20 percent?
A certain teacher determines the grade on an assignment by first finding the percent of questions that are answered correctly and then, if the assignment was handed in late, deducting 7 percentage points from the grade for each day that the assignment was late. If Tim answered 3 of the 25 questions incorrectly and handed the assignment in to this teacher 2 days late, what grade did he receive on the assignment?
Each salesperson in a retail store is paid a commission based on the amount of his or her daily sales. For daily sales up to and including $200, the commission is $$r$$ percent of the daily sales. For daily sales over $200, the commission is $$2r$$ percent of the daily sales. On Friday, Amanda had daily sales of $300 and Bill had daily sales of $200. If the total of Amanda' s and Bill' s commissions on Friday was $40, what is the value of $$r$$?
Nancy has a job where she is paid at a regular hourly rate for the first 40 hours that she works each week. For each hour that Nancy works each week in excess of the first 40 hours, she is paid 1.5 times her regular hourly rate. Nancy worked 35 hours during the first week of last month and 50 hours during the second week of last month. If Nancy was paid $270.00 more during the second week than during the first week, what is her regular hourly rate?
Each time a certain coin is tossed, the coin lands either heads up or tails up. For any given toss, the probability that the coin will land heads up is equal to the probability that the coin will land tails up. The coin is to be tossed $$n$$ times. What is the least possible value of $$n$$ such that the probability of the coin landing heads up $$n$$ times in a row is less than $$0.05$$?
In a legislature with 360 members, each member is in one of two political parties, either A or B. Party A has 110 members, and Party B has 250 members. In order for a certain bill to pass in the legislature, at least two-thirds of all the members must vote in favor of the bill. If 50 percent of the members of Party A and $$p$$ percent of the members of Party B will vote in favor of the bill, what is the least value of $$p$$ for which the bill will pass?

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