The Watson Family is going on a road trip. The data in the table shows the relationship between speed and fuel economy for their car. The data can be modeled by the quadratic function y=-0.0075x^2 +0.575x + 11.5, where x represents the speed in miles per hour and y represents the fuel economy in miles per gallon (MPG). Which speed rounded to the nearest whole number will give them the best fuel economy? A. 40 mph

B. 23 mph

C. 32 mph

D. 38 mph

It keeps saying image is to big so I'll type
Table:
Speed (miles per hour)
30
40
50
Fuel economy (miles per gallon)
22.0
22.5
21.5

66.666666667%

step-by-step explanation:

divide 150 by 100

divide 100 by 1.5

there you go!

decreased by 33.333333334%

step-by-step explanation:

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.