Rex, Lassie, and Beethoven eat their dog foods at different rates, though each gets the same amount. Rex can finish his bowl in 4 minutes, Lassie can finish in 3 minutes, and it only takes Beethoven 2 minutes. They got their food at the same time and they started chowing down. As soon asBeethoven finished, he started eating out of Rex’s bowl (Rex didn’t mind). Same with Lassie. Each dog always ate at the same rate, no matter which bowl. What fraction of the total amount of dog food did Beethoven eat?Please give the answer as a fraction in the simplest form.

Elizabeth claims that the fourth root of 2 can be expressed as 2^m since (2^m)^n = 2. find the values of m and n for the case where elizabeth's claim is true.

If 30 lb of rice and 30 lb of potatoes cost ? $27.60? , and 20 lb of rice and 12 lb of potatoes cost ? $15.04? , how much will 10 lb of rice and 50 lb of potatoes? cost?

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i.e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)