One yardstick for measuring how steadily—if slowly—athletic performance has improved is the mile run. In 1957, the local record for the running of a certain distance was 3 minutes, 59.2 seconds, or 239.2 seconds. In the half-century since then, the record has decreased by 0.4 seconds per year. a.) Express the record time for the mile run, M, as a function of the number of years after 1957, x.
b.) If this trend continues, in which year will someone run a 3-minute or 180-second, mile?

47 - 90 = 43

43 - 180 = x

x = 137

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.

4y - 6 + y^2 - 9 = y^2 + 4y - 15

y^2 term

terms

- terms

total of 3 terms when simplified

step-by-step explanation: