Suppose that 40 students have done a test; here are the results obtained. the grade mean of the entire school population is 90. we would like to check if there is a statistically significant difference (with a confidence level of 90%) between the means of the sample and the population, assuming that the population variance is known and equal to 15. (65, 78, 88, 55, 48, 95, 66, 57, 79, 81 75, 58, 18, 35, 58, 96, 61, 52, 39, 44 61, 38, 68, 65, 88, 75, 46, 97, 72, 82 62, 78, 87, 50, 55, 99, 65, 53, 70, 84) use a one sample z-test, to solve the problem, and discuss if you accept the null hypothesis and why. z. test(x = ? , mu = ? , sd = ? )

What power can you write to represent the volume of the cube shown? write the power as an expression with a base and an exponent and then find the volume of the cube

Find an bif a = {3, 6, 9, 12) and b = {2, 4, 6, 8, 10).

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.)