Thirty-eight cities were researched to determine whether they had a professional sports team, a symphony, or a children's museum. of these cities, 21 had a professional sports team, 20 had a symphony, 17 had a children's museum, 14 had a professional sports team and a symphony, 10 had a professional sports team and a children's museum, 10 had a symphony and a children's museum, and 6 had all three activities. How many of the cities surveyed had only a professional sports team?

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.

Find the area of the region that is inside r=3cos(theta) and outside r=2-cos(theta). sketch the curves.

What unit of been sure would be appropriate for the volume of a sphere with a radius of 2 meters