If a 30 -meter pine tree casts a shadow of 30 meters, how far is the tip of the shadow from the top of the tree?

55 bridesmaids want to make 325 325 decorations for a wedding. each decoration takes about 212 2 1 2 minutes to make. which response gives the best estimate for the amount of time each bridesmaid will spend making decorations?

One of the same side angles of two parallel lines is 20° smaller than the other one. find the measures of these two angles.

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.)