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题目内容

The figure shows a smaller square with sides of length y inscribed in a larger square with sides of length x. Which of the following relationships between x, y, and z must be true ?
The functions f and g are defined by f (x) = |2x +1| and g(x)=3 for all numbers x. What is the least value of c for which f (c) = g (c)?
The area of a circular region is 5π

Quantity A

The diameter of the circular region

Quantity B

$$\sqrt{20}$$
The reciprocal of x - 2 is x +2.

Quantity A

x

Quantity B

3
x > 0

Quantity A

The area of a square region with diagonal of length $$\sqrt{2}x$$

Quantity B

The area of a circular region with diameter of length x
$$\frac{1}{2}$$ < r < 1

Quantity A

2r

Quantity B

$$\frac{1}{r}$$
In a data set of 10,000 numbers varying from 20 to 80, the number 62 is the 60th percentile and the number 74 is the nth percentile..

Quantity A: n
Quantity B: 70
A historian asserts that at the beginning of 1852, the population of a certain mining town was 16,000. The historian also asserts that for each of the years from 1849 through 1853, the town`s population at the beginning of the year was twice that of the preceding year. According to the historian, what was the range of the town`s populations at the beginning of each year from 1848 through 1853?
Line l in the xy-plane contains points A and B with coordinates (-4,5) and (6,-1), respectively. Line k is perpendicular to l and contains the midpoint of line segment AB. Which of the following statements are true?

Indicate all such statements.
If x < y, which of the following must be true?
A rectangular solid P has height 2c and a base of width a and length b. Two other rectangular solids, Q and R, each have height c and bases of width a and length b. Which of the following represents the amount by which the sum of the surface areas of Q and R exceeds the surface areas of P?
A survey of 550 male managers and 650 female managers was conducted. All 1,200 managers identified whether, for each of six characteristics, the characteristic is important to consider when hiring a new employee. For each of the six characteristics, the percent of managers surveyed who identified that characteristic as important to consider is given in the following table.
On his trip to the airport, Grant drove a total of 9 miles. His average speed on the trip was x miles per hour, where 30 ≤ x ≤ 35. Which of the following could be the total number of minutes that Grant took to make the trip?
Indicate all such numbers of minutes.
If n is an integer, what is the least possible value of $$3^{n}+(3)(3^{-n})$$
At a certain elementary school, 10 percent of the fifth-grade students are members of the school band. If 12 percent of the fifth-grade boys and 8 percent of the fifth-grade girls are members of the band, what percent of the fifth-grade students at the school are boys?
s, t, and u are integers, and 10 ≤ s < t < u ≤ 20

Quantity A

s+$$\frac{t}{u}$$

Quantity B

11

In square ABCD, point P is the midpoint of side BC and point Q is the midpoint of side AD. Point E (not shown) is located on line l and triangle BCE is equilateral.

Quantity A

The length of PQ

Quantity B

The length of PE
$$z*10^{k} = 6*10^{m}$$
$$m=k+2$$

Quantity A

$$z$$

Quantity B

60
A certain bag contains red balls, green balls, and blue balls and no other balls. The ratio of the number of red balls to the number of blue balls is 2:3, and the ratio of the number of blue balls to the number of green balls is 4:3. The number of blue balls in the bag is what fraction of the total number of balls in the bag?
Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the minimum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color?

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