Fall came early in Piney Orchard, and the community swimming pool was still full of water when the first frost occurred. The outside temperature hovered at 30° F. Maintenance quickly turned off the heat so that energy would not be wasted heating a pool that nobody would be swimming in for at least six months. As Tess walked by the pool each day on her way to school, she would peer through the fence at the slowly cooling pool. She could just make out the thermometer across the deck that displays the water’s temperature. On the first day, she noted that the water temperature was 68° F. Four days later, the temperature reading was 58° F. If the outside temperature remains at 30° F, and the pool is allowed to continue to cool, how long before it freezes (32 oF)? Write an equation that models this situation. Heating and cooling problems are typical application problems that use exponential equations of the form .

step-by-step explanation:

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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.

my computer is slow i can not see it sorry

hi there

the slope is 1/3.

this is because from the y-intercept, you go up one, and you go to the right three, to get to the next exact point on the graph. this is known at the “rise over run.”

p.s. (if you need it).your y-intercept is -2, because that is the point on the graph where the line crosses the y-axis.

hope that : )