Madelyn needs to lease out a music studio to record her new album. The studio charges an initial studio-use fee plus an hourly fee for each hour in the studio. The fixed fee to use the studio is $250 and the total cost charged for 5 hours is $500. Write an equation for P, P, in terms of t, t, representing the amount of money Madelyn would have to pay to use the studio for t hours.

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.