An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used yy ( in cubic feet) to heat the home and outside temperature xx (in degree-days, where a day's degree-days are the number of degrees its average temperature falls below 65 oFoF) over a 23-month period. He then computed the least-squares regression line for predicting y from x and found it to be: yˆ=y^=89 + 19x. How much, on average, does gas used increase for each additional degree-day?

19

Step-by-step explanation:

The estimated least square regression line is

y^=89+19x

Here, dependent variable y is the amount of gas and independent variable is temperature.

The intercept and slope of the estimated regression line are 89 and 19 respectively.

The slope of the regression line shows that how the dependent variable varies when independent variable increased by 1 unit.

We can say that for additional degree day on average gas used increased by 19 units.

So, on average, gas used increased by 19 for each additional degree-day.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

a. she will receive a refund of $278.

step-by-step explanation: