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Flauer [41]
3 years ago
9

**!!WILL GIVE BRAINLIEST I NEED AN ANSWER ASAP!!** Maria earns $4.76 an hour at the local supermarket. each week, 25% of her tot

al pay is deducted for taxes. In addition, she pays $25 a week, after taxes, in union dues. If she wants her take-home pay to be at least $100 a week, how many hours must she work? (From Merrill Algebra Chapter 5)
Please give an answer with work shown; I can't use it otherwise. Happy to give brainliest to the best answer! :)
Mathematics
1 answer:
Fofino [41]3 years ago
6 0
About 35 Hours, 35.0140056 to be exact.

1. I wrote out the word problem to have Maria’s pay hourly, then the percentage of tax from that pay, and finally the 25$ after taxes they pay.
2. I went ahead and deducted the percentage of taxes, 25%, from the hourly pay to see how much Maria really takes home.
2.5. I subtracted the tax amount, 1.19$, from Maria’s hourly pay to show how much they take home.
3. I wrote out an equation of the amount Maria takes home multiplied by the hours they work, X, and minus the 25, to finally equal the amount Maria wants to take home. Solved the equation.
4. X is the amount of hours Maria has to work to take home 100 dollars with tax and the union fee.

I hope this is correct!! And that it helped!! :)

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The volume (in cubic inches) of a shipping box is modeled by V =2x³ -19x² +39x, where x is the length (in inches). Determine the
yawa3891 [41]

Answer:

The values of x for which the model is 0 ≤ x ≤ 3

Step-by-step explanation:

The given function for the volume of the shipping box is given as follows;

V = 2·x³ - 19·x² + 39·x

The function will make sense when V ≥ 0, which is given as follows

When V = 0, x = 0

Which gives;

0 = 2·x³ - 19·x² + 39·x

0 = 2·x² - 19·x + 39

0 = x² - 9.5·x + 19.5

From an hint obtained by plotting the function, we have;

0 = (x - 3)·(x - 6.5)

We check for the local maximum as follows;

dV/dx = d(2·x³ - 19·x² + 39·x)/dx = 0

6·x² - 38·x + 39 = 0

x² - 19/3·x + 6.5 = 0

x = (19/3 ±√((19/3)² - 4 × 1 × 6.5))/2

∴ x = 1.288, or 5.045

At x = 1.288, we have;

V = 2·1.288³ - 19·1.288² + 39·1.288 ≈ 22.99

V ≈ 22.99 in.³

When x = 5.045, we have;

V = 2·5.045³ - 19·5.045² + 39·5.045≈ -30.023

Therefore;

V > 0 for 0 < x < 3 and V < 0 for 3 < x < 6.5

The values of x for which the model makes sense and V ≥ 0 is 0 ≤ x ≤ 3.

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Answer:

The answer is "7".

Step-by-step explanation:

Given values:

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