Mark bought a new car and wanted to see the accuracy of the highway and city mileage. he recorded the average mpg for nine different trips on the highway and in the city and created the graph shown to analyze the distribution.

which statement correctly compares the distributions?
a) at one time he got 50 more mpg in the city than on the highway.

b) when driving on the highway he gets 22 mpg more than when driving in the city.

c) on average the gas mileage in the city was about 4 mpg less than that on the highway.
d) on average, the gas mileage in the city was about 4 mpg better than that on the highway.

C

On average the gas mileage in the city was about 4 mpg less than that on the highway.  

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

1/3

step-by-step explanation:

to find this, you can divide 12 by 4 which is 3 or you can multiply 4 until you reach 12 (4x3=12). both should give you 3, meaning theres three times less bananas than there are oranges.