When spoke of a wheel reaches from the center of the wheel to its rim. if the circumference of the rim of the wheel is 42 inches, how long is each spoke? round your answer to the nearest hundredth

Janet is mixing a 15% glucose solution with a 35% glucose solution. this mixture produces 35 liters of a 19% glucose solution. how many liters of the 15% solution is januet using in the mixture? a. 25 liters c. 28 liters b. 7 liters d. 10 liters

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.)

Find the probability that -0.3203 < = z < = -0.0287 find the probability that -0.5156 < = z < = 1.4215 find the probability that 0.1269 < = z < = 0.6772