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aleksandr82 [10.1K]
3 years ago
5

Mrs. Post bought a carton of eggs containing 24 eggs to use for cookies. When she got home 3 were broken. What percent of the eg

gs were broken?
Mathematics
2 answers:
Kitty [74]3 years ago
8 0

Answer:

12.5%

Step-by-step explanation:

Take the number of eggs that were broken over the total number of eggs

3/24

1/8

As a decimal

.125

Change to percent form

12.5%

sattari [20]3 years ago
5 0

Answer: 12.5%

Explanation:

3/24, or 1/8 of Mrs. Post’s eggs broke,

1/8 as a decimal is 0.125

0.125 as a percent is 12.5%

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1. Suppose that a theater charges a school group $4.50 per student to show a special film. Suppose that the theater's operating
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The functions I(x) and E(x) of the theatre's income and expenses are illustrations of linear functions.

<h3>The equation of the theatre's income</h3>

The theatre charges $4.50 per student.

Assume the number of students is x, the equation of the theatre's income would be:

I(x) = 4.5x

<h3>The equation of the theatre's expenses</h3>

The theatre expense per student is $1.25, and the operating cost on the staff is $130

The equation of the theatre's expenses would be:

E(x) = 1.25x + 130

<h3>Complete the table</h3>

Using the formulas I(x) = 4.5x and E(x) = 1.25x + 130, the complete table is:

Students, x  0       10        20     30      40      50      60    70

Income, I      0      45        90     135     180    225    270   315

Expenses, E 130  142.5   155    167.5   180   192.5   205  217.5

<h3>The graph of the theatre's income and expenses</h3>

See attachment

<h3>The pattern by which theatre's income and expenses increase</h3>

The functions I(x) and E(x) are linear functions.

So, the pattern with which the functions increase is a linear pattern.

<h3>The number of students when the theatre's income and expenses are equal</h3>

This means that:

I(x) = E(x)

So, we have:

4.5x = 1.25x + 130

Subtract 1.25 from both sides

3.25x = 130

Divide both sides by 3.25

x = 40

Hence, the number of students is 40

<h3>The theatre profit</h3>

This is the difference between the theatre expenses and their income.

So, we have:

P(x) = E(x) - I(x)

This gives

P(x) = 1.25x + 130 - 4.5x

Simplify

P(x) = 130 - 3.25x

<h3>Solution to the inequalities</h3>

We have:

E(x) < 255

This gives

1.25x + 130 < 255

Subtract 130 from both sides and divide by 1.25

x < 100 students

Also, we have:

I(x) > 675

This gives

4.5x > 657

Solve for x

x > 146 students

Hence, the number of students for the inequalities are less than 100 and greater than 146

Read more about linear equations and inequalities at:

brainly.com/question/11234618

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