Jorge is building a train set for his cousin. He has a piece of plywood that measures 49.5 inches in length, and he needs 2.25 inch pieces for the tracks. How many pieces can he cut from his piece of plywood?

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.)

What is the value of the discrimination for the quadratic equation 0=×2+2+×2

If angle ase measures 168 degrees, find the measure of angle dse. the figure mag not be drawn to scale