Carol and chick are counting calories ehile eating lunch at the school cafeteria in one week carol had 8 slices of pizza,5containers of skim milk and five cups of fruit salad. chick had 5 slices pf pizza,7 containers of fruit salad, and 7 containers of skim milk. chicks calorie count was 2500 and carols was 3070. if each container of skim milk is 40 calories how many calories did carol get from pizza

2320 calories

Step-by-step explanation:

We are given the following information;

Carol;

8 slices of pizza

5 containers of skim milk

5 cups of fruit salad

Chick;

5 slices pf pizza

7 containers of skim milk

7 containers of fruit salad

We let x denote the calories in each slice of pizza and y the calories in each cup or container of fruit salad. Chicks calorie count can thus be represented by the following expression;

5x + 7(40) + 7y

5x + 7y + 280

We are also informed that chicks calorie count was 2500 and thus the following equation is formed;

5x + 7y + 280 = 2500

5x + 7y =2220. This will be our first equation

On the other hand, Carols calorie count can be represented by the following expression;

8x + 5(40) + 5y

8x + 5y + 200

We are also informed that Carols calorie count was 3070 and thus the following equation is formed;

8x + 5y + 200 = 3070

8x + 5y = 2870. This will be our second equation

Now, we have two sets of equation;

5x + 7y =2220

8x + 5y = 2870

We solve these simultaneously to determine the values of x and y;

We multiply the first equation by 8 and the second by 5 in order to eliminate x and solve for y;

40x + 56y = 17760

40x + 25y = 14350

Subtracting the second equation from the first yields;

31y = 3410

y = 110

We substitute this value in the first equation and solve for x;

5x + 7(110) = 2220

5x = 2220 - 770

5x = 1450

x = 290

Therefore, each slice of pizza contains 290 calories. Carol had 8 slices of pizza implying that her total calories count from pizza was;

8 * 290 = 2320 calories

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.