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$$2^{-9}$$-$$2^{-10}$$=
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 $$n$$?
Citing the corruption and intrigue that characterized politics in the city, my colleague ____________ the newspaper's trove of journalism prizes, declaring that finding exciting stories in the city must be effortless.
The commission's report is free of bureaucratic jargon and, for a document that must have been written by multiple authors, it is remarkably (i)____________ in style. In that respect, the document is an improbable literary triumph; its analysis and recommendations, however, are (ii)____________.
It can be inferred from the passage that members of "feminist consciousness-raising groups"
In the context of the passage, the highlighted portion serves primarily to
The author would likely agree with which of the following statements about the “black holes [the LHC] could conceivably form"?

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