In the figure shown, the triangle is inscribed in the semicircle.  If the length of line segment AB is 8 and the length of line segment BC is 6, what is the length of arc ABC?

The population of City X is 50 percent of the population of City Y.  The population of City X is what percent of the total population of City X and City Y?

If k is an integer and (0.0025)(0.025)(0.00025)×10^k is an integer, what is the least possible value of k?

In the rectangular solid above, the three sides shown have areas 12, 15, and 20, respectively.  What is the volume of the solid?

If b(a+1) = b, then ab =

In a stack of cards, 9 cards are blue and the rest are red.  If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 6/11.  What is the number of cards in the stack?

A certain company sold 800 units of its product for $8 each and 1,000 units of its product for $5 each.  If the company’s cost of producing each unit of its product was $6, what was the company’s profit or loss on the 1,800 units of its product?

The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3 : 2 : 2.  In terms of x, which of the following equals the height of the carton, in feet?

If n is a positive integer, what is the remainder when 3⁸ⁿ⁺³ + 2 is divided by 5?

2x + y = 12

~$\left | y \right |\leq 12$~

For how many ordered pairs (x , y) that are solutions of the system above are x and y both integers?