The factor tree for 1,764 is shown. A factor tree starts with 1,764 on the top. 1,764 branches down to 2 on the left and 882 on the right. 882 branches down to 2 on the left and 441 on the right. 441 branches down to 9 on the left and 49 on the right. 9 branches down to 3 on the left and 3 on the right. 49 branches down to 7 on the left and 7 on the right. What is the simplest form of StartRoot 1,764 EndRoot? 21 42 32(72) 22(32)(72)

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)

Liz had 140 pens and inna had 100 pens. after inna gave liz some pens, liz had 3 times as many pens as inna. how many pens did inna give liz?

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.