THIS IS WORTH 15 POINTS BECAUSE OF IMPROPER ANWSERS FOR POINTS BUT WILL GIVE BRAINLIEST IF CORRECT Henry and Amy provide the following proofs for vertical angles to be equal:

A line PQ is shown cut by a transversal t. 1, 2, 3, 4 are marked clockwise as the four angles formed by the transversal on the

Henry's proof: angle 2 + angle 3=180° (t is a straight line)

angle 1 + angle 2 = 180° (PQ is a straight line)

Therefore, angle 1 + angle 2 = angle 2 + angle 3 (Transitive Property of Equality)

Hence, angle 1 = angle 3 (Subtraction Property of Equality)

Amy's proof: angle 1 + angle 2 + angle 3 + angle 4 = 360°

Therefore, angle 1 + angle 4 = 180° (t is a straight line)

Hence, angle 4 = angle 2 (Transitive Property of Equality)

Which statement is correct? (6 points)

A. Both Henry's and Amy's proofs are incorrect.

B. Only Amy's proof is correct.

C. Only Henry's proof is correct.

D. Both Henry's and Amy's proofs are correct.

step-by-step explanation:

ddd

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)

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.