The points R, T, and U lie on a circle that has radius 4.  If the length of arc RTU is  ~$\frac{4\pi }{3}$~, what is the length of line segment RU?

A company has assigned a distinct 3-digit code number to each of its 330 employees.  Each code number was formed from the digits

$$2, 3, 4, 5, 6, 7, 8, 9$$

and no digit appears more than once in any one code number.  How many unassigned code numbers are there?

Which of the following is equal to ~$5^{17}\times 4^{9}$~ ?

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 an automobile averaged 22.5 miles per gallon of gasoline, approximately how many kilometers per liter of gasoline did the automobile average?  (1 mile = 1.6 kilometers and 1 gallon = 3.8 liters, both rounded to the nearest tenth.)

The operation Δ is defined for all nonzero x and y by x Δ y ~$=x+\frac{x}{y}$~ .  If a > o, then 1 Δ (1 Δ a) =

A teacher gave the same test to three history classes:  A, B, and C.  The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively.  The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively.  What was the average score for the three classes combined?

The numbers x and y are three-digit positive integers, and x + y is a four-digit integer.  The tens digit of x equals 7 and the tens digit of y equals 5.  If x < y, which of the following must be true?

I.  The units digit of x + y is greater than the units digit of either x or y.
II.  The tens digit of x + y equals 2.
III.  The hundreds digit of y is at least 5.

In the figure above, O is the center of the circle.  If the area of the shaded region is 2π, what is the value of x?

A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour.  At what speed, in kilometers per hour, is the car traveling?