Mr. Vestas sells electricity from a wind turbine to his local utility. He receives 3¢ per kilowatt hour for the first 500 kilowatt hours, 2¢ per kilowatt hour for the next 1000 kilowatt hours, and 1¢ per kilowatt hour for each kilowatt hour thereafter. Mr. Vestas sold 1800 kilowatt hours last month. What was the average price per kilowatt hour the utility paid to Mr. Vestas last month, rounded to the nearest hundredth of a cent?

Step-by-step explanation:

We are expected to solve the weighted average price per kilowatt hour.

Step one:

The formula is  

W =∑wX/∑w

W=weighted average  

w=weights applied to x values

X=data values to be averaged

Step two:

given the total killowatt hour is 1800

the 1st = 500 at 3¢

2nd= 1000 at 2¢

3rd = (1800-1000+500) at 1¢ =(1800-1500) at 1¢ = (300) at 1¢

Step two:

Substituting into the expression we have

W =(500*3)+(1000*2)+(300*1)/500+1000+300

W=1500+2000+300/1800

W=3800/1800

W=2.11¢

The average price per kilowatt hour the utility paid to Mr. Vestas last month is 2.11¢

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!

what do you mean by fog

step-by-step explanation: