Afunction f ( x ) is said to have a removable discontinuity at x = a if: 1. f is either not defined or not continuous at x = a . 2. f ( a ) could either be defined or redefined so that the new function is continuous at x = a . let f ( x ) = 2 x 2 + 4 x − 48 x − 4 show that f ( x ) has a removable discontinuity at x = 4 and determine what value for f ( 4 ) would make f ( x ) continuous at x = 4 . must define f ( 4 ) = .

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.