Part a: the area of a square is (4x2 - 12x + 9) square units. determine the length of each side of the square by factoring the area expression completely. show your work.
part b: the area of a rectangle is (16x2 - 9y2) square units. determine the dimensions of the rectangle by factoring the area expression completely. show your work.
part c: the volume of a rectangular box is (x3 - 7x2 - 4x + 28) cubic units. determine the dimensions of the rectangular box by factoring the volume expression completely. show your work.

explanation:

step-by-step explanation:

i believe a. 12x≥120 is the answer

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.