Explain why these two are not the same: -|x| and |-x|

Rectangle pqrs has length a and width 4b. the x-axis bisects ps and qr what are the coordinates of the vertices

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.

If you have 12 feet of string and you cut it into equal length of 5 inches each how much string will be left