Charles has a circular carpet in his drawing room. He wants to put a circular table in the middle of the carpet. The diameter of the carpet is 12 meters and the diameter of the table is 4 meters. Calculate how much area of carpet is left after putting the table in place. Carpet Area=
Table Area=
Difference=

Give all possible names for the line shown.calculation tip: lines can be written with either point first.

Parabolas y=−2x^2 and y=2x^2 +k intersect at points a and b that are in the third and the fourth quadrants respectively. find k if length of the segment ab is 5.

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.