Lightbulbs of a certain type are advertised as have an average lifetime of 750 hours. a random sample of 50 bulbs was selected and the lifetime of each bulb was determined. the sample mean lifetime was 738.44 hours with a standard deviation of 38.2 hours. based on this data, can you conclude that the true average lifetime of these bulbs is less than what advertised? test using = .05.

Aline has a slope of 1/4 and passes through point (0.4,-1/2). what is the value of the y-intercept?

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

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.