Consider the following hypothesis test. H0: μ ≥ 10 Ha: μ < 10 The sample size is 120 and the population standard deviation is 5. Use α = 0.05. If the actual population mean is 7, the probability of a type II error is 0.2912. Suppose the researcher wants to reduce the probability of a type II error to 0.10 when the actual population mean is 8. What sample size is recommended? (Round your answer up to the nearest integer.)

Multiply. −2x(6x4−7x2+x−5) express the answer in standard form. enter your answer in the box.

List x1, x2, x3, x4 where xi is the midpoint endpoint of the five equal intervals used to estimate the area under the curve of f(x) between x = 0 and x = 10.

1. an economy consists of three workers: larry, moe, and curly. each works 10 hours a day and can produce two services: mowing lawns and washing cars. in an hour, larry can either mow one lawn or wash one car; moe can either mow one lawn or wash two cars; and curly can either mow two lawns or wash one car. a. calculate how much of each service is produced under the following circumstances: a. all three spend all their time mowing lawns. b. all three spend all their time washing cars. c. all three spend half their time on each activity d. larry spends half of his time on each activity, while moe only washes cars and curly only mows lawns b. using your answers to part a, draw a production possibilities frontier and label points a, b, c, and d on your graph. explain why the production possibilities frontier has the shape it does. c. are any of the allocations calculated in part a inefficient? explain.