The work of a student to solve a set of equations is shown: Equation 1: m = 8 + 2n Equation 2: 3m = 4 + 4n Step 1:−3(m) = −3(8 + 2n) [Equation 1 is multiplied by −3.] 3m = 4 + 4n [Equation 2] Step 2:−3m = −24 − 6n [Equation 1 in Step 1 is simplified.] 3m = 4 + 4n [Equation 2] Step 3: −3m + 3m = −24 − 6n + 4n [Equations in Step 2 are added.] Step 4:0 = −24 − 2n Step 5:n = −12 In which step did the student first make an error?

15.36 per mile

but forgot to round

i am pretty sure

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.

(−$11) ⋅ 12

deductions are subtracted and there are 12 months in a year