A music school offers its students 8 different classes each semester. 4 of the classes are in music theory, 3 of the classes are in music teaching, and 1 of the classes is in the instrument of the student's choice. Students are required to choose 3 classes. What is the probability that a randomly chosen student did not choose any music theory classes? Fill in the blanks for the answer below.

Problem fathi wants to print out a pdf document that is 48 pages long. to save paper, he decides to print on both sides of each sheet and to print two pages on each side of the sheet. how many sheets of paper will he need?

The median for the given set of six ordered data values is 29.5 9 12 25 __ 41 48 what is the missing value?

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.)