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To conduct a review, the manager of Corporation R restaurants in the northwest region must form a group of Corporation R restaurants by choosing one restaurant from each of the 3 city population categories in the northwest region. Which of the following represents the number of different groups of restaurants that can possibly be chosen for the review?
$$2^{-9}$$-$$2^{-10}$$=
If x is the average (arithmetic mean) of 10 and y, and y is the average of x and 22, which of the following statements are true?

Indicate all such statements.
A certain data set consists of n values, and the mean of the values is positive. If an additional value equal to 70 percent of the mean is included in the data set to create a new data set, then the mean of the values in the new data set will be 2 percent less than the mean of the values in the original data set. What is the value of n?
A candy shop owner decides to create a mixed assortment of candies by mixing two kinds of candies. One kind costs the owner 90 cents per pound, while another costs the owner 70 cents per pound. If the mixed assortment of candies costs the owner 85 cents per pound, and 30 pounds of 90 cents kind is used in the process, then what is the total pounds of mixed candies that can be created?
x > y > z

Quantity A

xy

Quantity B

yz
z > 140



Quantity A

y-x

Quantity B

10
There is an octahedral (8-faces) die whose faces each have one different number from the set {1, 2, 3, 4, 5, 6, 7, 8}. The die is rolled twice, and the number appearing on top after the first roll is recorded as the x-coordinate of a point A, while the number appearing on top after the second roll is recorded as the y-coordinate of the point A. What is the total number of all the possible points A that can be created?
Last week painter A started a job on Tuesday, completing $$\frac{1}{5}$$ of the job that day, and on Wednesday another printer B completed $$\frac{1}{6}$$ of the job that remained.

Quantity A

The fraction of the job that was not completed by the end of the day last Wednesday

Quantity B

$$\frac{2}{3}$$
0 < s < t

Quantity A

$$\frac{s}{t}$$+0.4

Quantity B

$$\frac{5s+2t}{5t}$$
The average (arithmetic mean) of the 4 integers q, r, s, and t is 0.

Quantity A

The average of the 4 integers q+10, r, s, and t

Quantity B

The average of the 5 integers q, r, s, t, and 10


Point O and point X are the centers of the two circles in the figure. If the length of arc PSX is 6π, what is the circumference of the circle with center O?


The design shown in the figure consists of squares and is created in several steps. In the first step, a square measuring 1 inch on each side is drawn. In the second step, a 1-inch-wide border is drawn around the square, creating a larger square. In each subsequent step, a 1-inch-wide border is drawn around the largest existing square. What is the number of steps that will be needed in order to create a design in which the largest existing square measures 47 inches on each side?

_____ steps
If $$n$$, $$k$$, and $$r$$ are positive integers such that $$n^{k}=10r+3$$, which of the following could be the value of $$n$$?
$$x^{3}$$ > $$x^{5}$$

Quantity A

x

Quantity B

$$x^{3}$$

Quantity A

$$(\frac{2^{3}}{3^{2}})^{4}$$

Quantity B

$$(\frac{2^{-3}}{3^{-2}})^{-4}$$
x + 2y = 12 and 2y > 7

Quantity A

x

Quantity B

y
The length of a line segment connecting two points on circle C is 1.

Quantity A

The area of circle C

Quantity B

π
a < 0

b < 0

Quantity A

In the xy -plane, the slope of the line containing the points (a, b) and (0, 2)

Quantity B

In the xy -plane, the slope of the line containing the points (a, b) and (2, 0)
There are n different values of x that satisfy the equation (x-1)(x+5)=-9.

Quantity A

n

Quantity B

1

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