7. Determine the value of x for which ris if
m_1 = 80 - X; and
• m22 90 - 2x.

The given is that r║s while the angles are known.

m∠1 = 80 - x

m∠2 = 90 - 2x

m∠1 = m∠2 because of corresponding angles theorem.

So,

m∠1 = m∠2

80 - x = 90 - 2x

- x = 90 - 80 - 2x

- x = 10 - 2x

- x + 2x = 10

x = 10

The value of x is 10

44

step-by-step explanation:

the

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.