Lving equations of the form ax + b = cx + d 2 3 questions 1 2 3 question 3 the cost of maintaining car a is $300 per year plus $.014 per mile driven. the cost of maintaining car b is $200 per year plus $.025 per mile driven. how many miles are driven in the first year in order for the total costs between car a and b to be equal? car a = 300 + .014x car b = 200 + .025x solve the following equation to determine when costs are equal 300 + .014x = 200 + .025x .011x=100

she will travel a distance in the range of 3 - 11 miles

m∠a is 90°

m∠b is 40°

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.