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a poll is taken at a concession stand to discover the customers’ favorite item to buy. the results are displayed in the table. this situation can be approximately modeled by rolling a die.

  see below

Step-by-step explanation:

Popcorn is preferred by about 1/2 of the folks, so 3 of the 6 outcomes from a die roll will model this well. Only the 1st and 3rd choices show 3 outcomes representing Popcorn.

Hotdogs are preferred by about 1/6 of the folks, so 1 of the 6 outcomes from a die roll will model this well. Only the 1st and 2nd choices show 1 outcome representing Hotdogs.

Only the 1st choice models the preferences appropriately.

Popcorn: die roll is greater than 3

Pizza: die roll is 2 or 3

Hot dogs: die role is a 1

Step-by-step explanation:

A poll is taken at a concession stand to discover the customers’ favorite item to buy. The results are displayed in the table given.

The following situation can be approximately modeled by rolling a die.

Popcorn: die roll is greater than 3

Pizza: die roll is 2 or 3

Hot dogs: die role is a 1

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!

x^6

step-by-step explanation:

this is correct because:

x-6=0

0*x=0

so

x^6