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题目内容
Consider all the permutations of the letters in the word $$MISSISSIPPI$$, where $$I$$ is a vowel and the other letters are consonants.

Quantity A

The number of permutations in which all the vowels are next to each other

Quantity B

The number of permutations in which all the consonants are next to each other
Two balls are to be randomly selected from a bag, one at a time and without replacement. The probability that the first ball selected will be red is $$\frac{5}{8}$$. If the first ball selected is not red, the probability that the second ball selected will be red is $$\frac{2}{3}$$. What is the probability that the first or the second ball selected will be red (that is, one red ball either in the first attempt, or in the second attempt, but not both)?

Give your answer as a $$\underline{fraction}$$.


Each morning Betty walks from intersection P to intersection R, always walking along streets shown in the figure above and always going east or north. If she varies her walks as much as possible, taking every different path in turn before repeating the sequence of paths, on how many mornings in 48 consecutive mornings will Betty walk through intersection Q?
One cup of a certain type of yogurt contains 9 grams of protein, which is equal to x percent of the recommended daily consumption of protein. How many grams is the recommended daily consumption of protein in terms of x?
What is the least positive integer n for which $$\frac{n}{2}$$, $$\frac{n}{3}$$, $$\frac{n}{4}$$, $$\frac{n}{5}$$, $$\frac{n}{6}$$, $$\frac{n}{8}$$ and $$\frac{n}{9}$$ are integers?
List S: 21, 22, 23, 25, 27, 32

List T: 221, 222, 223, 225, 227, 232

If the standard deviation of the numbers in list S is x, what is the standard deviation of the numbers in list T?
0 < a < b < c

a, b, and c are positive integers and the average (arithmetic mean) of a and c is 15. Which of the following could be the value of b?

Indicate all such values.
Rhonda has 2 different jackets, 3 different skirts, 2 different blouses, and 4 different scarfs that can be worn as part of an outfit. If an outfit consists of a jacket, a skirt, and a blouse with or without a scarf, how many different outfits can Rhonda wear?
If P is the product of all of the 100 different numbers of the form $$\frac{m+1}{m}$$, where m is an integer and 1 ≤ m ≤ 100, which of the following statements about P is true?
n is the least possible integer such that 108n is the square of an integer.

Quantity A

n

Quantity B

9
Each copy of a certain textbook in a college bookstore is classified as new or used. The bookstore sells each new copy for $90 and each used copy for another fixed price. For all the copies sold last week, the total revenue from the sales of new copies was equal to the total revenue from the sales of used copies, and the average (arithmetic mean) price per copy was $60. What is the price of each used copy？
The positive numbers a, b, c, d, e, and f are different from each other.

Quantity A

The range of the numbers a, b, c, d, e, and f

Quantity B

The range of the numbers $$a^{2}$$, $$b^{2}$$, $$c^{2}$$, $$d^{2}$$, $$e^{2}$$ and $$f^{2}$$
x and y are different positive integers

$$x^{2}y$$=180

Quantity A

x

Quantity B

y
In the xy-plane, lines l and m, with equations y+x+r=0 and y-x+s=0, respectively, intersect at the point (1, 2).

Quantity A

r+s

Quantity B

0
$$\frac{x}{x-2}$$=$$\frac{x-1}{x+1}$$

Quantity A

x

Quantity B

1

Quantity A

The area of a rectangle with a perimeter of 32

Quantity B

The area of a rectangle with a perimeter of 52
Amy wants to build a fence around her level, circular garden. If the maximum distance between any two points in the garden is 6 feet, what length of fence, in feet, will form the border of the garden?
Solution A contains x percent alcohol by volume. Solution B contains y percent alcohol by volume. If 3 liters of solution A are mixed with 5 liters of solution B to yield 8 liters of solution C, what percent of the volume of solution C is alcohol?
If $$8^{x}=16$$, then $$x$$=
z > 0

Quantity A

20% of z

Quantity B

10% of 2z

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