For the cube shown above, what is the degree measure of  ~$\angle PQR$~?

If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?

If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2ⁱ3^k5^m7^p, then i + k + m + p =

A wire that weighs 24 kilograms is cut into two pieces so that one of the pieces weighs 16 kilograms and is 34 meters long.  If the weight of each piece is proportional to its length, how many meters long is the other piece of wire?

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.)

If  ~$\frac{7x}{3}+a=8$~ and a > 8, then, in terms of a,  ~$\frac{3x}{7}=$~

The surface of a certain planet reflects 80 percent of the light that strikes it.  The clouds around the planet then absorb 40 percent of the reflected light.  What percent of the light that strikes the planet is reflected from the surface and passes through the clouds without being absorbed?

Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours.  S and T, working together at their respective constant rates, can do the same job in 5 hours.  How many hours would it take R, working alone at its constant rate, to do the same job?

If x < 0 and 0 < y < 1, which of the following has the greatest value?

This year Henry will save a certain amount of his income, and he will spend the rest.  Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend.  In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?