The marginal revenue function is MR = R’(x) = 15 – 6x + 3 x2 and the marginal cost function MC = C’(x) = 9 = 4x where x is the output. If the fixed cost is 20, find the profit function and the profit when the output is x + 5.​

Use the graph of the sine function y=2sinθ shown below

F(n + 1) = f(n) – 8. if f(1) = 100, what is f(6)?

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e. g. 98.76543).