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Akimi4 [234]
3 years ago
13

Steven is starting a baseball hat printing business and plans on selling each hat for $20 with his cost being $8 per hat. The eq

uipment will cost $800. Steven orders 500 hats and determines that the profit for his new business is modeled by the function P = 12x-800. Which of the following is the domain of this function in this situation? A). x ≥ 20 B). all real numbers C). {0 ≤ x ≤ 500} D). {0 ≥ x ≥ 500}
Mathematics
2 answers:
vampirchik [111]3 years ago
5 0
Since Steven ordered 500 hats, he cannot sell more than 500 hats, therefore, the domain of the profit function is {0 ≤ x ≤ 500}

Option D is the correct answer.
Vikki [24]3 years ago
3 0

Answer:

D). {0 ≥ x ≥ 500}

Step-by-step explanation:

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(4x-9) times (4x+9)

Step-by-step explanation:

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A piecewise function is shown below
Greeley [361]

Answer:

p = 5/7

Step-by-step explanation:

The given function is:

g(x) = -3x^{2} - 2x + 8 for -4 ≦ x < 1

g(x) = -2x + 7p for 1 ≦ x ≦ 5

Part a)

A continuous function has no breaks, jumps or holes in it. So, in order for g(x) to be continuous, the point where g(x) stops during the first interval -4 ≦ x < 1 must be equal to the point where g(x) starts in the second interval 1 ≦ x ≦ 5

The point where, g(x) stops during the first interval is at x = 1, which will be:

-3(1)^{2}-2(1)+8=3

The point where g(x) starts during the second interval is:

-2(1)+7(p) = 7p - 2

For the function to be continuous, these two points must be equal. Setting them equal, we get:

3 = 7p - 2

3 + 2 = 7p

p = \frac{5}{7}

Thus the value of p for which g(x) will be continuous is \frac{5}{7}.

Part b)

We have to find p by setting the two pieces equal to each other. So, we get the equation as:

-3x^{2}-2x+8=-2x+7p\\\\ -3x^{2}+8=7p

Substituting the point identified in part (a) i.e. x=1, we get:

-3(1)^{2}+8=7p\\\\ 5=7p\\\\ p=\frac{5}{7}

This value agrees with the answer found in previous part.

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66 = 8W, so W = 8.25

W = 8.25, L = 24.75

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3 years ago
An inequality for a number exceeds 9
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We are asked to write an inequality that would represent a number exceeds 9. In the problem, we need to assign "n" variable to represent the number (any number) and we need to ">" symbol to represent "greater than" or "exceed". Thus, the inequality can be represented as:
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The answer is n > 9 and this would represent the phrase "a number that exceeds 9".
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