If a series of rigid transformations maps ∠E onto ∠B where ∠E is congruent to ∠B, then which of the following statements is true? triangles ABC and FDE, in which angles A and D are right angles

ΔABC ~ ΔFDE because of the definition of similarity in terms of similarity transformations

segment DE ~ segment AB because corresponding parts of similar triangles are similar

ΔABC ~ ΔFDE because of the AA similarity postulate

segment DE ~ segment AB because of the definition of similarity in terms of similarity transformations

5y

step-by-step explanation:

its an acute right triangle

step-by-step explanation:

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.