The dimensions x and y of an object are related to its volume v by the formula upper v equals 12 x squared y. a. how is startfraction dv over dt endfraction related to startfraction dy over dt endfraction if x is constant? b. how is startfraction dv over dt endfraction related tostartfraction dx over dt endfraction if y is constant? c. how is startfraction dv over dt endfraction related tostartfraction dx over dt endfraction and startfraction dy over dt endfraction if neither x nor y is constant?

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.