Due to yet another road construction project in her city, Sarah must take a detour to get from work to her house. Not convinced the detour is the shortest route, Sarah decided to perform an experiment. On each trip, she flips a coin to decide which way to go; if the coin flip is heads, she takes the detour and if it's tails, she takes her alternative route. For each trip, she records the time it takes to drive from work to her house in minutes. She repeats this procedure 13 times. Sarah wants to know if the mean driving time for the alternative route is different from the mean driving time for the detour. Based on the p-value there was moderate evidence against the null hypothesis. Select the appropriate statement for this hypothesis test.

a. There is little to no evidence to conclude the mean driving time for the alternative route is the same as the mean driving time of the detour.
b. There is little to no evidence to conclude the mean driving time for the alternative route is different from the mean driving time of the detour.
c. There is moderate evidence to conclude the mean driving time for the alternative route is the same as the mean driving time of the detour.
d. There is moderate evidence to conclude the mean driving time for the alternative route is different from the mean driving time of the detour.

b). There is little to no evidence to conclude the mean driving time for the alternative route is different from the mean driving time of the detour.

Step-by-step explanation:

The most adequate statement to examine the proposition is that 'there is lack of adequate evidence to substantiate the claim that the mean time taken for driving through the detour and the alternative route is distinct.' This will help in testing that there is a lack of evidence to establish the validity or truth of the proposition that if the detour is actually shorter than the alternative route or not. No data has been provided to clarify that the mean driving time in both routes traveled by Sarah was varied. Hence, option b is the correct answer.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3