The cost of a business is the amount of money spent to start the business and keep it in operation. The revenue is the amouunt of
money the business earns from the sale of goods or services.
An online business called Muffins A-plenty started on January 1 of a recent year. The lines in the graph represent the cost function and
the revenue function of the first six months that Muffins A-plenty has been in operation.
Part A
Write equations to represent the cost function and the revenue function for this business,
Parts
The profit of a business equals revenue minus cost. First write an equation that represents the profit function for Muffins replenty using
the functions for cost and revenue, Then, predict the profit after 10 months of operation, found your answer to the nearest dollar. Provide
valid mathematical reasoning and calculations to support your answer,

Answers

Answer 1

The profit function of the business is the difference between the revenue and the cost functions

The equations of the cost and the revenue functions are: [tex]y = \frac 43x[/tex] and [tex]y = 0.5x + 3.5[/tex]The profit function is [tex]y = \frac 56x - 3.5[/tex]The profit after 10 months of operation is 29/6

Part A: The equations to represent the functions

For the revenue function, we have the following points

(x,y) = (0,0) and (6,8.0)

Since the line passes through the origin, the equation of the line would be:

[tex]y = \frac{y_1}{x_1} * x[/tex]

So, we have:

[tex]y = \frac{8.0}{6} * x[/tex]

[tex]y = \frac 43x[/tex]

For the cost function, we have the following points

(x,y) = (0,3.5) and (9,36) for x > 5

The equation of the line would be:

[tex]y = \frac{y_1-y_2}{x_1-x_2} * (x - x_1) + y_1[/tex]

So, we have:

[tex]y = \frac{6.5-3.5}{6-0} * (x - 0) + 3.5[/tex]

[tex]y = 0.5x + 3.5[/tex]

Hence, the equations of the cost and the revenue functions are: [tex]y = 0.5x + 3.5[/tex] and [tex]y = \frac 43x[/tex]

Part B: The profit function

This is calculated as:

Profit = Revenue - Cost

So, we have:

[tex]y = \frac 43x - 0.5x - 3.5[/tex]

Evaluate the difference

[tex]y = \frac 56x - 3.5[/tex]

Part C: The profit after 10 months of operation

Substitute 10 for x in [tex]y = \frac 56x - 3.5[/tex]

[tex]y = \frac 56 * 10 - 3.5[/tex]

[tex]y = \frac {50}6 - 3.5[/tex]

Evaluate the difference

[tex]y = \frac {50-21}6[/tex]

[tex]y = \frac {29}6[/tex]

Hence, the profit after 10 months of operation is 29/6

Related Questions

Use the information below to answer 1–3.
Three students are playing a video game. Each player is randomly
assigned a character from a collection of characters that includes
5 blue, 6 green, and 3 red characters. After each character is picked,
it is not replaced in the collection.
1. What is the probability that the first player does not get a blue character?

Answers

Answer:

The probability the 1st player does not get a blue chracter is 9/14.

Step-by-step explanation:

So there is a total of 14 characters.

9 of them are not blue

9/14 = .642857 (~64%, not the answer since it's not asking for percents)

The probability the 1st player does not get a blue chracter is 9/14.

The population of Florida has increased, on average, at a rate of 8% per year since 1953. In 1993, the population of Florida was 13 million.

What was the population in 1953?

*show work & will give brainliest*

Answers

Answer:

598,402

Step-by-step explanation:

Let y = population at year x

x is the number of years since 1953, so for 1993, x = 40

a = population in 1953

y = a(1.08)^x

In 1993, the population is 13,000,000, so y = 13,000,0000 when x = 40.

13,000,000 = a(1.08)^40

13,000,000 = 21.7245a

a = 598,402

Answer: 598,402

Select the correct answer. What is the decimal form of 17%?A. 17B. 1. 7C. 0. 17D. 0. 17

Answers

Answer:

Step-by-step explanation:

You would move the decimal back only 2 places.

Answer:

0.17

Step-by-step explanation:

When we multiply the exponents with the same base, we add the exponents

x^(4/3+2/3)

x^(6/3)

x^2

What is an equation of the line that passes through the points (3,6) and (-1,-6)

Answers

Answer:

the slope is 3

Step-by-step explanation:

use the equation

y2 -y 1 / x2 - x1

to find the slope

6 - (-6) / 3 - (-1)

6 + 6 / 3 + 1

12 / 4

Anyone know? Someone said 120 but that’s obviously not an option!

Answers

believe the answer is 11

I need help Solveing for X

Answers

The answer to X is 57

Answer:

x = 57°

Step-by-step explanation:

23° + 100° + x = 180°

123° + x = 180°

-123 -123

x = 57°

Hope this helps!

A hollow post is made out of a lightweight aluminum alloy that is 1.5 cm thick. The alloy is folded into the shape of a right rectangular prism measuring 9 cm by 9 cm by 28 cm. Find the total volume of alloy in the post. Round your answer to the nearest hundredth if necessary.

Answers

The total volume of alloy in the post is about 900 cm³

What is a volume?

Volume is the amount of space occupied by a three dimensional shape or object.

Volume = length * width * height

The right rectangular prism measuring 9 cm by 9 cm by 28 cm. The alloy is 1.5 cm thick.

Length = 9 - 1.5 - 1.5 = 6 cm, width = 9 - 1.5 - 1.5 = 6 cm, height = 28 - 1.5 - 1.5 = 25 cm. Hence:

Volume = 6 * 6 * 25 = 900 cm³

The total volume of alloy in the post is about 900 cm³

Find out more on volume at: https://brainly.com/question/12410983

Answer:

1837.5

Step-by-step explanation:

I jut did it

Can someone help with this math problem pleaseeee

Answers

Answer: Choice A

Explanation:

The square root undoes the squaring operation.

Think of a square that is 1 ft by 1 ft. Its area would be 1*1 = 1 sq ft.

Now imagine you told your friend "the area is 1 sq ft" and you didn't relay the side lengths. Your friend would use the square root to find the side length is 1 ft.

I'm not sure why your teacher is using plus minus notation when that is not correct. Saying [tex]\sqrt{1} = \pm 1[/tex] is not true. The result of a square root is simply one value only. If your teacher meant [tex]\pm \sqrt{1} = \pm 1[/tex], then it would be a true statement; however, there's no need to involve negative numbers for this problem.

James had $400 in his bank account. After
paying bills for 4 months, his balance is now
$160. What is his rate of change in dollars per month?

A.40
B.-40
C.60
D.-60

Answers

Answer:

Step-by-step explanation:

400-160=240

240/4=60

Enter your answer and show all the steps that you use to solve this problem in the space provided.

Find the values of x and y.

Answers

Step-by-step explanation:

The figure shows an isosceles triangle. The two sides of an isosceles triangle are equal and the two base angles are equal. Since line AD is the angular bisector of the top Angle of an isosceles triangle, AD is also the base midline and base perpendicular bisector of the triangle.

So x=90 degrees.

The angles of a triangle add up to 180 degrees. So ∠DAC=(180-90-47)=43 degrees

y=43 degrees.

Answer:

y = 43°

x = 90°

Step-by-step explanation:

x = 90°(right angle)

y + 47 + x = 180(base angles of isosceles are equal)(all angles of triangle are equal)

y + 47 + 90 = 180

y + 137 = 180

y = 180 - 137

y = 43°

A restaurant uses 4⁄5 ounce of gravy for each serving of meat loaf. If 45 people ordered meat loaf, how much gravy will the restaurant need in ounces?

Answers

Answer: 34 ounces of gravy

Step by step:
4/5 x 45 make 45 into a fraction
4/5 x 45/1 multiply
180/5 simplify
34 (ounces)

Answer:

The correct answer is 36 ounces

Step-by-step explanation:

simplify (6 - sqrt25)/4

Using proportions, it is found that the speed of the runners are of 16 mph and of 20 mph.

What is a proportion?

A proportion is a fraction of a total amount.

After 30 minutes, the runners are 2 miles apart, hence the second runner is 4 miles per hour faster than the second, that is:

[tex]v_2 = v_1 + 4[/tex].

The first runner's speed is 4/5 of the speed of the second runner, hence:

[tex]v_1 = \frac{4}{5}v_2[/tex]

[tex]v_1 = \frac{4}{5}(v_1 + 4)[/tex]

[tex]\frac{1}{5}v_1 = \frac{16}{5}[/tex]

[tex]v_1 = 16[/tex]

[tex]v_2 = 16 + 4 = 20[/tex]

Hence, the speed of the runners are of 16 mph and of 20 mph.

More can be learned about proportions at https://brainly.com/question/24863377

Answer:

Using proportions, it is found that the speed of the runners are of 16 mphand of 20 mph.What is a proportion?A proportion is a fraction of a total amount.After 30 minutes, the runners are 2 miles apart, hence the second runner is 4 miles per hour faster than the second, that is:.The first runner's speed is 4/5 of the speed of the second runner, hence:Hence, the speed of the runners are of 16 mph and of 20 mph.

Step-by-step explanation:

∠A and
∠
B
∠B are supplementary angles. If m
∠
A
=
(
7
x
+
7
)
∘
∠A=(7x+7)
∘
and m
∠
B
=
(
4
x
−
14
)
∘
∠B=(4x−14)
∘
, then find the measure of
∠
B
∠B.

Answers

Supplementary angles mean that the angles add up to a measure of 180.

angle A+ angle B = 180
(7x+7)+(4x-14)=180

Combine like terms

11x-7=180
11x=187
x=187/11
x=17

Insert x value.

4(17)-14

68-14

54.

Measure of A would be
7(17)+7
126

54+126 is 180 so they are supplementary.

Again, measure of angle B is 54

The cost of an afternoon movie ticket was $4.00.
This year an afternoon movie ticket costs $5.00.
What is the percent increase of the ticket from last
year to this year?
A. 10%
B. 20%
C. 25%
D. 40%

Answers

Answer:

Step-by-step explanation:

25% of 4 or 4 divided by 4 is 1. 1+4 is 5

Hi there can anyone help
-42/x = 14/-2
what is x
thanks

Answers

Answer:

x=6

Step-by-step explanation:

14÷(-2)=-7

-42÷(-7)=6

If the sum of three consecutive number is 36,find the numbers?

Answers

x+x+x= 36 what about 3x you divide by the co_efficient of 3 which you will get 12.....(so 12-1 on your left and +1 on your right hand side....so the numbers are ( 11+12+13=36)

ASAP!

Emma invested $750 in an account paying an interest rate of 1. 9% compounded

quarterly. Assuming no deposits or withdrawals are made, how long would it take, to

the nearest tenth of a year, for the value of the account to reach $910?

Answers

Answer:

the answer is 2.6 show in the workings below

What is the factorization of 49b2 − 81? (7b – 9)(7b – 9) (7b – 9)(7b 9) (7b2 – 9)(7b2 – 9) (7b2 – 9)(7b2 9).

Answers

answer : (7b+9)(7b-9)

what’s 34 + 2x = 49??? I NEED HELP

Answers

34 + 2x = 49
minus 34 from both sides
2x = 15
divide both sides by 2
x = 7.5

(to confirm 2x = 15, 34 + 15 = 49)

Answer:

x = 7.5

Step-by-step explanation:

Use algebraic manipulation (and remember that anything you do to one side must be done to the other, in most cases):

34 + 2x = 49

-34 -34

2x = 49 - 34

2x = 15

x = 7.5

What is the solution of startroot negative 4 x endroot = 100? x = –2500 x = –50 x = –2.5 no solution

Answers

Hey there!

-√4x = 100

WELL….
-√4 = -2

NEW EQUATION:
-2x = 100

DIVIDE -2 to BOTH SIDES

-2x/-2 = 100/-2

CANCEL out: -2/-2 because it give you 1

KEEP: 100/-2 because it help solve for the x-value (mainly give you it)

NEW EQUATION: x = 100/-2

SIMPLIFY IT!

x = -50

Therefore, your answer is: x = -50

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

B-X=-50

Step-by-step explanation:

Need help ASAP (IMAGE ATTACHED)

Answers

Answer:

The answer is B

Step-by-step explanation:

It becomes 8y = -3x + 12.

Then divide by 8 on both sides.

y = -0.375+1.5

This you can turn it into a fraction which is y = -3/8 + 1.5

B or c . I think it’s b though I don’t know for sure

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