Problem 2: Concrete beams can fail in flexural mode or shear mode. A structural lab has 15 failed concrete beam - 9 of which failed in flexural mode, 6 of which failed in shear mode. • How many ways are there to randomly select 6 of these beams for a thorough inspection (without worrying about the order)? (2 points) • In how many ways can a sample of 6 beams can be randomly selected, so that exactly 5 of them failed in shear mode? (2 points) • If a random sample of 6 beams is selected, determine the probability that atleast 5 of them failed in shear mode? (3 points)

The square root of 9x plus 7 plus the square rot of 2x equall to 7

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.)

Robert is replacing sod in two square shaped areas of his backyard.one side of the first area is 7.5 feet.one side of the other is 5.7 feet.the sod costs y dollars per square foot.