In the figure shown, PQRSTU is a regular polygon with sides of length x. What is the perimeter of triangle PRT in terms of x ?
A window is in the shape of a regular hexagon with each side of length 80 centimeters.If a diagonal through the center of the hexagon is w centimeters long, then w =
The sequence a1, a2, . . . , an, . . . is such that an = 2an _ 1 - x for all positive integers n > 2 and for a certain number x. If a5 = 99 and a3 = 27, what is the value of x ?
The infinite sequence a1, a2, . . . , an, . . . is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an = an-4 for n > 4. What is the sum of the first 97 terms of the sequence?
A positive integer n is a perfect number provided that the sum of all the positive factors of n, including 1 and n, is equal to 2n. What is the sum of the reciprocals of all the positive factors of the perfect number 28 ?
The figure shown above consists of three identical circles that are tangent to each other.
If the area of the shaded region is 64~$\sqrt{3}$~-32π , what is the radius of each circle?
Two numbers differ by 2 and sum to S. Which of the following is the greater of the numbers in terms of S ?
A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-mile trip?
(Assume that the driver did not make any stops during the 40-mile trip.)
Andrew started saving at the beginning of the year and had saved $240 by the end of the year. He continued to save and by the end of 2 years had saved a total of $540. Which of the following is closest to the percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year?
A certain manufacturer sells its product to stores in 113 different regions worldwide, with an average (arithmetic mean) of 181 stores per region. If last year these stores sold an average of 51,752 units of the manufacturer's product per store, which of the following is closest to the total number of units of the manufacturer's product sold worldwide last year?
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