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wolverine [178]
3 years ago
7

A pyramid with a square base with dimensions 12 by 7 is shown. A cone is cut out of the center of the pyramid. The cone has a he

ight of 10 and a diameter of 6. Which expressions represent the volume of the composite figure (the shaded figure)? Check all that apply. (7)(12)(10) – π(32)(10) One-third(7)(12)(10) – One-thirdπ(32)(10) One-third(7)(12)(10) + One-thirdπ(32)(10) 280 – 30π 280 + 30π 840 – 90π
Mathematics
1 answer:
maks197457 [2]3 years ago
4 0

Answer:

2 and 4

2) One-third(7)(12)(10) – One-thirdπ(32)(10)

4) 280 – 30π

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1. C(n) = 2.25n + 120

2. R(n) = 3.51n

3. P(n) = 1.26n - 120

1. 96 frozen bananas must be sold in order to make a positive profit.

2. In order to make a profit, I have to sell a minimum of <u>96 frozen bananas</u>.

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1. Write a function, C(n), to represent your total costs for the week if you sell n frozen bananas.

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C(n) = 2.25n + 120

Where 2.25n is the total variable cost while 120 is the total fixed cost.

2. Write a function, R(n), to represent the revenue from the sale of n frozen bananas during the week.

Revenue is equal to selling price per unit multiplied by the number of units sold. Therefore, the function is as follows:

R(n) = 3.51 * n

R(n) = 3.51n

Where 3.51 is the selling price per unit while n the number of units sold.

3. Write a function, P(n), that represents the profits for selling n frozen bananas in a given week.

Profit is equal to total revenue minus total cost. Therefore, the function can be derived as follows:

P(n) = R(n) - C(n)

P(n) = 3.51n - 2.25n + 120

P(n) = 1.26n - 120

1. How many frozen bananas must you sell in order to make a positive profit? Write your answer as a whole number.

This can be obtained by equating the profit function to zero and solve for n as follows:

P(n) = 0 => 1.26n - 120 = 0

Therefore, we have:

1.26n = 120

n = 120 / 1.26

n = 95.2380952380952 frozen bananas

Writing it as a whole number, we have:

n = 95 frozen bananas

However, using this whole number will result in a negative profit by substituting it into the profit function as follows:

P(n) = (1.26 * 95) - 120 = -$0.30

Therefore, n has to be increased by one to 96 which is also a whole number to have a positive profit as follows:

P(n) = (1.26 * 96) - 120 = $0.96

Therefore, 96 frozen bananas must be sold in order to make a positive profit.

2. Complete the following sentence to explain the meaning of #1:

In order to make a profit, I have to sell a minimum of <u>96 frozen bananas</u>.

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