You will build two identical rectangular enclosures next to a each other, sharing a side. You have a total of 324 324 feet of fence to use. Find the dimensions of each pen such that you can enclose the maximum possible area. One approach is to let x represent the length of fencing that the two pens share, and write a formula for a function of x that outputs the total area of the enclosures. Then find its vertex and interpret it. (Use ft for feet, and ft^2 for square feet.)

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.