House of Mohammed sells packaged lunches, where their finance department has established a
weekly relationship between its Revenue R, in dollars and the number of lunches x, as R=x(82−x)
(a) Write the revenue R, in the form R=ax2+bx+c (b) What is the revenue when 35 lunches are sold? (c) Explain why the graph of R has a maximum.
(d) Write R in the form a(x−h)2+k
(e) How many lunches must be sold for them to achieve their maximum revenue?
(f) State the company's maximum revenue.
(2 marks) (2 marks) (2 marks)
(5 marks)
(2 marks) (2 marks)
(g) Complete the following table of values and graph the Revenue equation using the ordered pairs
(x , R). Label the coordinates of the vertex.
x
10
20
30
40
50
60
70
80
90
R
( 10 marks)

Answers

Answer 1

The revenue function is a quadratic equation and the graph of the function

has the shape of a parabola that is concave downwards.

The correct responses are;

(a) R = -x² + 82·x(b) $1,645(c) The graph of R has a maximum because the leading coefficient of the quadratic function for R is negative.(d)  R = -1·(x - 41)² + 1,681(e) 41(f) $1,681

Reasons:

The given function that gives the weekly revenue is; R = x·(82 - x)

Where;

R = The revenue in dollars

x = The number of lunches

(a) The revenue can be written in the form R = a·x² + b·x + c by expansion of the given function as follows;

R = x·(82 - x) = 82·x - x²

Which gives;

R = -x² + 82·x

Where, the constant term, c = 0

(b) When 35 launches are sold, we have;

x = 35

Which by plugging in the value of x = 35, gives;

R = 35 × (82 - 35) = 1,645

The revenue when 35 lunches are sold, R = $1,645

(c) The given function for R is R = x·(82 - x) = -x² + 82·x

Given that the leading coefficient is negative, the shape of graph of the

function R is concave downward, and therefore, the graph has only a

maximum point.

(d) The form a·(x - h)² + k is the vertex form of quadratic equation, where;

(h, k) = The vertex of the equation

a = The leading coefficient

The function, R = x·(82 - x), can be expressed in the form a·(x - h)² + k, as follows;

R = x·(82 - x) = -x² + 82·x

At the vertex, of the equation; f(x) = a·x² + b·x + c,  we have;

[tex]\displaystyle x = \mathbf{-\frac{b}{2 \cdot a}}[/tex]

Therefore, for the revenue function, the x-value of the vertex, is; [tex]\displaystyle x = -\frac{82}{2 \times (-1)} = \mathbf{41}[/tex]

The revenue at the vertex is; [tex]R_{max}[/tex] = 41×(82 - 41) = 1,681

Which gives;

(h, k) = (41, 1,681)

a = -1 (The coefficient of x² in -x² + 82·x)

The revenue equation in the form, a·(x - h)² + k is; R = -1·(x - 41)² + 1,681

(e) The number of lunches that must be sold to achieve the maximum revenue is given by the x-value at the vertex, which is; x = 41

Therefore;

The number of lunches that must be sold for the maximum revenue to be achieved is 41 lunches

(f) The maximum revenue is given by the revenue at the vertex point where x = 41, which is; R = $1,681

The maximum revenue of the company is $1,681

Learn more about the quadratic function here:

https://brainly.com/question/2814100


Related Questions

Please see all the screenshots. I have included multiply problems in this one question.

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Answer:

so basacilly the answer to all of the question is a

Step-by-step explanation: you welcome!

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Answer:

in my class just say the (x) mean number 1

NEED HELP ASAP! WHOEVER EXPLAINS FIRST GETS BRAINLIEST!!


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


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Answers

x = -99/4

GIMMIE brother

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Answers

The y-intercepts are points where the graph of a function or an equation crosses or “touches” the y-axis of the Cartesian Plane.

Choose the true statement about virtue-based ethics.
i. According to the principles of virtue-based ethics, character is more important than actions.
ii. According to the principles of virtue-based ethics, right and wrong are assessed using culture as a guide.
iii. According to the principles of virtue-based ethics, the consequences of actions are very important.
iv. According to the principles of virtue-based ethics, rules are used to evaluate actions.

Answers

Virtue based ethics holds that character is more important than actions.

Virtue based ethics is the aspect of ethics that holds that the moral character of a person if of more paramount importance than the person's actions and its consequences.

Hence, the true statement about virtue based ethics from the options is that; "according to the principles of virtue-based ethics, character is more important than actions."

Learn more about ethics: https://brainly.com/question/25784680

Plz help me NOW I will mark u brainliest

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[tex]m\% \: \: of \: \: p\% \: \: of \: \: n \\ = \frac{m}{100} \times \frac{p}{100} \times n \\ = \frac{m \times p \times n}{100 \times 100} \\ = \frac{mnp}{10000} [/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

Rapid Rental Car charges a $40 rental fee, $15 for gas, and $0.25 per mile driven. For the same car,
Capital Cars charges $45 for rental and gas and $0.35 per mile. For bow many miles is the rental cost at
both companies the same?

Answers

Answer:

Step-by-step explanation:

40 + 15 + 0.25m = 45 + 0.35m

       55 + 0.25m = 45 + 0.35m

                       10 = 0.10m

                        m = 100 miles

                     

Can someone please help me

Answers

Answer: B

Step-by-step explanation: I beilieve it's B but, don't take my word.

which is the least per pound 5 pounds of chicken for 9.45,3 pounds for 5.97, or 1 pound for 2.05

Answers

5 pounds - 1.89

3 pounds - 1.99

1 pound - 2.05

In this case, the 5 pounds of chicken is the cheapest by exactly one dime.

What is the standard form of the parabola whose vertex form is y= 2(x+4)^2+5
A. y = 2x2 +16x - 37
B. y=-2x² + 4x - 25
C. y = 2x° +16x +37
D. y = 2x² + 4x - 25

Answers

[tex]y = 2(x+4)^2+5\implies y = 2(x+4)(x+4)+5 \\\\\\ y = 2(\stackrel{\mathbb{USING~FOIL}}{x^2+8x+16})+5\implies y= 2x^2+16x+32+5 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y = 2x^2+16x+37~\hfill[/tex]

Jay works as a waiter at a restaurant.
He works 12 hours each weekend. Jay makes $5.50 per
hour and he gets to keep 60% of his tips.
If Jay wants to earn $150 before taxes, how much tip
money should he get during the weekend?
PLEASE HURRY

Answers

Answer:

67.33.

Step-by-step explanation:

To figure out the tip, you need to find 20% of $52.60.

0.2×52.6=10.52

You should leave $10.52 for the waiter if you want to leave him exactly 20%.

To figure the tax, you need to find 8% of $52.60.

0.08×52.6=4.208

Next, add them up:

52.6+10.52+4.208=67.328

The total bill, including tax and tip, will be $67.33.

Graph the solution to the following system of inequalities.
-7x + 5y < -10
5x + 4y > 8
Then give the coordinates of one point in the solution set.

Answers

Graph attached

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Matt has 5 cookies Addie eats 3. How old is Addie?

Answers

old enough for Matt to seek vengeance against her

Answer:

old enough to eat a cookie

HELP ME ASAP!!!
Question 3(Multiple Choice Worth 5 points)
(04.04 MC)

If a sprinkler waters 1 over 15 of a lawn in 1 over 3 hour, how much time will it take to water the entire lawn?

5 hours
15 hours
18 hours
45 hours

Answers

It would take 5 hours.

1/15 of the lawn in 1/3 hours means it takes 1 hour to water 3/15 of the lawn aka 1/5

1/5 of the lawn in 1 hour would mean it takes 5 hours to finish watering the entire lawn.

1.) Write .378 as a fraction in simplest form

Answers

Here you go! I hope this helps! It looks like your math is hard but it will get easier

A fair coin is tossed four times. What is the probability of obtaining at least three tails?

Answers

The probability of obtaining at least three tails is; 5/16

When tossing a coin four times, the number of possibilities since one is either a tail or head is;

Total number of possibilities = 2⁴ = 16

Now, various ways of getting at least three tails are;

TTTH, TTHT, THTT, HTTT, and TTTT.

This is a total of 5 different ways.

Thus;

P(obtaining at least 3 tails) = 5/16

Read more about probability when a coin is tossed at; https://brainly.com/question/1334780


Please help!!!!
check for understanding:

Answers

Answer:i thinks is 115.9 maybe im not sure because its in my HW

Step-by-step explanation:

Answer:

x=7.245

Step-by-step explanation:

pythagoras theorem says:

c=√a^2+b^2

so:

c=a2+b2=3.22+6.52≈7.245

Please help

Find the mean
of the data.
Data: 46 22 46 49 45 39 40 42 41 39 40 36

Answers

Answer:

40.083

Step-by-step explanation:

The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.

Pls help me
Given the following data pairs (x, y): (1, 1.24), (2, 5.23), (3, 7.24), (4, 7.60), (5, 9.97), (6, 14.31), (7, 13.99),(8, 14.88), (9, 18.04), (10, 20.70) obtain a prediction for x = 4.5​

Answers

Answer:

(5.33) the answer but I am not sure

(-3,5) (3,7)
What is the slope of AB ?

Answers

The slope is : 1/3
Ok done. Thank to me:>

A car is traveling at a constant speed of 65 miles per hour. Drag each list or statement below to show whether it describes the independent quantity or the dependent quantity.

Answers

Answer:

dependent quantity.

Step-by-step explanation:

The sum of two numbers is 58.25. The second number is 14 less than 2 times the first number. What are the two numbers?
plz fast

Answers

Answer:

The first number is 24.08 and the second number is 34.17

There is a cookie jar in Julio's kitchen filled with 7 cookies. His mother bakes some more cookies. Now there are 14 cookies. How many cookies did Julio's mother bake.

Answers

The Answer is 7 cookies because she had 7 cookies filled in the jar and after making 7 more it becomes 14 so
Also 7+7=14

What would be the total cost of
Software M over time?
Satisfaction 55%. $0
$[?]
Not Satisfied
$6,000
Software X
45% - $18,000
Software M.
$12,000
95% - $0
Satisfaction
Not Satisfied
5% • $2,000
Entor

Answers

1. The total cost of Software M over time is $10,000.

2. The total cost of Software X over time is $4,000.

Data and Calculations:

Cost of Software M = $12,000

Satisfaction rate with Software M = 95%

Cost of satisfaction level = $0

Cost of dissatisfaction level = $2,000

Percentage of not satisfied = 5%

The total cost of Software M over time is $10,000 {($12,000 x 95% - $0) + ($12,000 x 5% - $2,000)}.

Cost of Software X = $6,000

Satisfaction rate with Software X = 55%

Cost of satisfaction level = $0

Cost of dissatisfaction level = $18,000

Percentage of not satisfied = 45%

The total cost of Software M over time is $4,000 {($6,000 x 55% - $0) + ($6,000 x 45% - $2,000)}.

Learn more about total cost based on satisfaction ratio here: https://brainly.com/question/25940131


mZLOM= 3x – 15°
mZMON = 5x – 23°
Find mZMON:

Answers

Answer:

57

Step-by-step explanation:

Together both angles equal 90

(3x - 15) + (5x -23) = 90

Combine like terms

8x - 38 = 90

Add 38 to both sides

8x = 128

Divide by 8

x = 16

You can check by replacing x with 16 and seeing if it still equals 90.

To find angle MON... replace x with 16

5(16) - 23

Angle MON = 57

I hope this helps!!

Together, Mike and Bill have $50 more than Joe has. Mike has $26 more than Bill. The three boys have a total $506. How much money does each boy have.

Answers

i wish i had that much money

Answer:

Step-by-step explanation:

1. 84

2. 96

Answer: Divisible by 2, 3, 6

3. 896

4. 942

Answer: Divisible by 2, 3, 6

5. 22,335

6. 39,075

Answer: Divisible by 3, 5

Find Prime Factorizations and Least Common Multiples In the following exercises, find the

prime factorization.

7. 86

8. 78

Answer: 2 3 13 ⋅ ⋅

9. 455

10. 400

Answer: 222255 ⋅⋅⋅⋅⋅

11. 432

12. 627

Answer: 3 11 19 ⋅ ⋅

In the following exercises, find the least common multiple of each pair of numbers using the

prime factors method.

13. 8, 12

hope that help mark me brinliylist

as an estimation we are told 5 miles is 8km convert 60km to miles

Answers

Answer:

60km is 37 Miles

it is a decimal- 37.2 Miles

Step-by-step explanation:

divide 60 by 1.609

Answer: using this we can say that 60km is 37.5 miles

Step-by-step explanation:

first you divide 60 and 8 which gives us 7.5

using this we multiply 7.5*5=37.5

what is the answer to this question

Answers

Answer:

a) 32km

b) 40 miles

Step-by-step explanation:

Find the value of the expression

Answers

Answer:

20

Step-by-step explanation:

t=1

u=2

t+8+u+8+1=1+8+2+8+1=20

What is the slope of the line (-5,-7) and (4,-1)

Answers

Answer:

2/3

Step-by-step explanation:

slope = change in y / change in x = (-7-(-1))/(-5-4) = (-6)/(-9) = 2/3

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