What is the area of the sign?Darren made a display board in the shape of a trapezoid. Part A The height of the trapezoid is half the length of the shorter base, and the longer base is twice the length of the shorter base. What are the lengths of the height and the longer base? Enter your answers in the boxes.

Height = 2 yards

Longer base = 8 yards

Step-by-step explanation:

From the figure attached :

The length of the shorter base of the Trapezoid = 4 yards

Hence, if height of Trapezoid is half the length of the shorter base ;

Then ;

Height of Trapezoid = shorter base/2 = 4 /2 = 2 yards

Longer base is twice the length of shorter base :

Longer base = 2 * shorter base = 2 * 4 = 8 yards

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.