Given the complex number z1 = 24√3(cos(7π/6)+i sin(7π/6)) and z2 = 4( cos(2π/3)+ i sin(2π/3)), express the result of z1/z2 in rectangular form with fully simplified fractions and radicals.

The isosceles triangle has two sides of equal length, a, that sre longer than the length of the base ,b. the equation 2a+b=15.7 can be used to find the sides length. if one of the longer sides is 6.3 centimeters what is the length of the base

The width of a rectangle is 20 units. can the perimeter p of the rectangle be 64 units when its length x is 11 units? no, because p = 2x + 2(20) no, because p ≠ 2x + 2(20) yes, because p ≠ 2x + 2(20) yes, because p = 2x + 2(20)

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.