If
C(x) = 12000 + 400x − 2.6x2 + 0.004x3
is the cost function and
p(x) = 1600 − 8x
is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)

Answers

Answer 1

Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

How to find the production level that'll maximize profit?

The cost function, C(x) is given by 12000 + 400x − 2.6x² + 0.004x³ while the demand function, P(x) is given by 1600 − 8x.

Next, we would differentiate the cost function, C(x) to derive the marginal cost:

C(x) = 12000 + 400x − 2.6x² + 0.004x³

C'(x) = 400 − 5.2x + 0.012x².

Also, revenue, R(x) = x × P(x)

Revenue, R(x) = x(1600 − 8x)

Revenue, R(x) = 1600x − 8x²

Next, we would differentiate the revenue function to derive the marginal revenue:

R'(x) = 1600 - 8x

At maximum profit, the marginal revenue is equal to the marginal cost:

1600 - 8x = 400 − 5.2x + 0.012x

1600 - 8x - 400 + 5.2x - 0.012x² = 0

1200 - 2.8x - 0.012x² = 0

0.012x² + 2.8x - 1200 = 0

Solving by using the quadratic equation, we have:

x = 220.40 or x = -453.73.

Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.

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Related Questions

A recipe uses 5 cups of flour to 1-1/10 cups of milk. If you have two cups of flour, how much milk should you use.

Answers

The quantity of milk that should be used for the given amount of flour would be = 11/25

How to calculate the amount of milk to use for the recipe?

The following steps are being taken to calculate the amount of milk that would be needed for the recipe.

The number of cups of flour for 1⅒ of milk = 5

The quantity of milk needed for 2cups of flour= X

That is;

1⅒milk = 5 flour

X milk = 2 flour

cross multiply;

X milk = 2×1⅒/5

= 11/25

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You deposit $5000 in an account earning 6% interest compounded monthly. How much will you have in the
account in 15 years?

Answers

Answer:

$12270.46

----------------------

Use the compound interest formula:

[tex]A = P(1 + r/n)^{nt}[/tex]

Where:

A = final amount;P = initial deposit = $5000;r = annual interest rate = 6%;n = number of times the interest is compounded per year = 12;t = time period in years = 15.

Plugging in the values, we get:

A = 5000(1 + 0.06/12)¹²*¹⁵ A = 12270.46

What is 1/3 of 343???????????

Answers

The number that is one-third of 343 is 49.

1/3 of 343 can be found by multiplying 343 by 1/3:

1/3 x 343 = (1/3) x (343) = 343/3

To simplify the result, we can divide both the numerator and denominator by the greatest common factor (GCF) of 343 and 3, which is 7:

343/3 = (343 ÷ 7) / (3 ÷ 7) = 49/1

Therefore, 1/3 of 343 is 49.

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The scatterplot above displays the relationship between the amount of food hippopotamuses eat per day and their age. Describe and explain any associations and data features on the scatterplot. Then, use the variables on the graph to interpret the relationship that is shown.

Answers

The scatter plot shows a [positive linear] association.

How to determine the association of the scatterplot

From the question, we have the following parameters that can be used in our computation:

The image of the scatter plot

On the scatter plot, we can see that

The points appear to be on a straight line

Also, we can see that

As the x values increases the y values increases

This represents a positive linear association.

Hence, the association is a positive linear association.

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What is the total cost of 20 books at R25 each?

Answers

Answer:

R500

Step-by-step explanation:

20 books x R25 each = R500.

Please help me out on this question

Answers

The relative frequency distribution is:

Income ($) | Frequency Relative | Frequency200-300 | 51 | 18.82%301-400 | 58 | 21.40%401-500 | 74 | 27.30%501-600 | 69 | 25.46%More than 600 | 19 | 7.01%

The correct option is A.

What is a relative frequency?

A relative frequency is the proportion of the total number of outcomes to the number of times a certain value of the data happens in the set of all outcomes.

Relative frequency = frequency of given data/total frequency * 100%

The relative frequency distribution of the given data is constructed below:

Total number of students = 51 + 58 + 74 + 69 + 19

Total number of students = 271

The relative frequency of each class interval will be:

200-300; 51/271 * 100% = 18.82%

301-400; 58/271 * 100% = 21.40%

401-500; 74/271 * 100% = 27.30%

501-600; 69/271 * 100% = 25.46%

More than 600; 19/271 * 100% = 7.02%

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A TV station is going to air a movie marathon with 11 movies. It will consist of 6 science fiction movies and 5 horror movies. The horror movies will be aired later in the evening. So, all of the horror movies will be aired last (after all of the science fiction movies). In how many ways can the station air the movie marathon?

Answers

The solution is: In 86400 ways can the station air the movie marathon.

Given:

Number of total movies = 11

Number of science fiction movie = 6

Number of horror movie = 5

Computation:

Number of science fiction movies way air = 6!

so, we get,

Number of science fiction movies way air = 720

Number of horror movies way air = 5!

so, we have,

Number of horror movies way air = 120

The number of ways the station air the movie marathon is:

720 * 120

=86400

so, we get,

Final answer is 86400 ways.

Hence, The solution is: In 86400 ways can the station air the movie marathon.

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Intro
Nautilus Clothing's stock has a 50% chance of producing a 15% return, a 20%
chance of producing a 21% return, and a 30% chance of producing a -13% return.
Part 1
What is the stock's expected return?

Answers

To calculate the stock's expected return, we need to multiply the probability of each return by its corresponding percentage return, and then sum up the results.

Let's calculate it step by step:

Return 1: 15% * 50% = 0.15 * 0.5 = 0.075 (or 7.5%)
Return 2: 21% * 20% = 0.21 * 0.2 = 0.042 (or 4.2%)
Return 3: -13% * 30% = -0.13 * 0.3 = -0.039 (or -3.9%)

Now, let's sum up the results:

Expected return = 0.075 + 0.042 - 0.039 = 0.078 (or 7.8%)

Therefore, the stock's expected return is 7.8%.

Harper recorded the heights of plants, in inches, as shown in the table.
nd the mean of the data.
11 12 13 14 15 16 17 18 19 20 21
Heights of Plants (in.)

Answers

The mean height of the plants whose heights are shown by the data set is 16 in.

Calculation of mean

To find the mean:

Sum of the values = 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 = 176

Total number of values = 11 (since there are 11 values in the data set)

Mean = Sum of the values / Total number of values

          = 176 / 11

          = 16

In other words, the mean of the given data set is 16 in and thus, the mean height of the plant is 16 in.

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Find the solution set for the equation. |9x-5|+3=8

Answers

Answer: 10/9, 0

Step-by-step explanation:

14. The graph below represents the number of books checked out at a library. What
is the constant of proportionality (unit rate per hour)?

Answers

The required constant of proportionality is 5.

A graph is shown, we have to find out the constant of proportionality.
In the given case, the constant of proportionality is given by the slope of the curve.

So, the slope is given as,
m = rise/run

From the graph put the value  for any point, we choose (2, 10)

So,
m = 10/2
m = 5

Thus, the required constant of proportionality is 5.

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Can someone help me? The velocity of a sound in air is given by the equation v=20 radical273+t where v is the velocity in meters per second and t is the temperature in degrees Celsius find the temperature when the velocity is 348 meters per second round the answer to the nearest degree

Answers

when the velocity is 348 meters per second, the approximate temperature is 18 degrees Celsius.

How to find the temperature when the velocity is 348 meters per second

To find the temperature when the velocity is 348 meters per second, we can substitute the given velocity into the equation v = 20√273 + t and solve for t.

Given: v = 348 meters per second

Substituting this value into the equation:

348 = 20√273 + t

Now, let's solve for t. We can start by isolating the term with t:

t = 348 - 20√273

Calculating the value:

t ≈ 348 - 20 * 16.523

t ≈ 348 - 330.46

t ≈ 17.54

Rounding the answer to the nearest degree, we have:

t ≈ 18 degrees Celsius

Therefore, when the velocity is 348 meters per second, the approximate temperature is 18 degrees Celsius.

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What is 692837 divided by 28736

Answers

Answer:24.1104189866

Step-by-step explanation:

the answer to What is 692837 divided by 28736 is 24.1104189866

Find the percentage and round to the nearest hundredth

7.2% of $ 8,650,00

Answers

The percentage is given by the expression A = ( 7.2 % ) ( 8650.00 ) and the value of A = $ 622.80

Given data ,

Let the initial amount be represented as P

Now , the value of P is

P = $ 8,650.00

On simplifying the equation , we get

Let the percentage value be d = 7.2 %

On simplifying the percentage , we get d = 0.072

So , A = 0.072 ( 8,650.00 )

Multiplying the expression , we get

A = $ 622.80

Therefore , the value of A is A = $ 622.80

Hence , the expression is A = $ 622.80

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c) Mrs. Chamling earns Rs 6,000 in a week. She spends Rs 250 for food Rs 75 for transportation everyday. (i) Write a mathematical expression to show this information. (ii) How much money does she save in a week? Cl LC and she divided the In this way, whole prime and compos of numbers, set of are the subset of 3.2 Prime and Prime numbe​

Answers

(i) The mathematical expression to show Mrs. Chamling's earnings and expenses can be written as:

Weekly earnings = Rs 6,000

Daily food expenses = Rs 250

Daily transportation expenses = Rs 75

Total weekly expenses = (Rs 250 + Rs 75) x 7 = Rs 2,275

Total weekly savings = Weekly earnings - Total weekly expenses

= Rs 6,000 - Rs 2,275

= Rs 3,725

(ii) Mrs. Chamling saves Rs 3,725 in a week.

As for the second part of the question, I am not sure what is being asked. The sentence is incomplete and unclear. Please provide more information or context so I can assist you better.

Which point is located at 2,1

Answers

Answer: Point P

Step-by-step explanation: over 2 up 1 (2,1)

Answer: M

Step-by-step explanation:

The sum of Jerry's and Carrie's ages is 52. Jerry is 4 years older than Carrie. What is Jerry's age?

Answers

X = Jerry’s age
4 + x = 52
X = 52-4 = 48
I hope it helps :)

Answer:

28

Step-by-step explanation:

let's assumed that

x = Jerry's age

y = Carrie's age

if Jerry 4 years older that Carrie

x = y + 4

x + y = 52

(y + 4) + y = 52

2y + 4 = 52

2y = 48

y = 24

x = y + 4

x = 24 + 4

x = 28

#CMIIW

I NEED HELP WITH STATISCTICS

Answers

Answer:

20cm

Step-by-step explanation:

four students are trying to find the rule that translates point N(-2,-4) to N'(2,4)

Answers

The student that gets the rule of the transformation correctly is Raheem

How to determine the student that gets the rule correctly

From the question, we have the following parameters that can be used in our computation:

Point N = (-2, -4)

Image of the point N = (2, 4)

This means that

N = (-2, -4)

N' = (2, 4)

From the above, we can see that

N' = -1 * N

This means that

N' = (-2, -4) * -1

So, we have

N' = (-2* -1 , -4 * -1)

So, the rule is (x * -1, y * 1)

Hence, the student that gets the rule correctly is Raheem

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Question

Four students are trying to find the rule that translates point N(-2,-4) to N'(2,4). Each student’s reasoning is shown below.

Raheem: The rule is (x * -1, y * -1)

Casey: The rule is (x + 2, y + 4)

Andrew: The rule is (x + 4, y + 0)

Lo: The rule is (x + 4, y + 8)

Which student is correct?

Raheem

Casey

Andrew

p, q and r are prime numbers such that pqr3=270.
Work out the values of p, q and r.
b. Work out the highest common factor of 270 and 105.

Answers

The highest common factor of 270 and 105 is 15.

How to find the highest common factor

finding the prime factorization of 270.

The prime factorization of 270 can be written as:

270 = 2 * 3^3 * 5

From the equation pqr^3 = 270, we can see that p, q, and r are prime numbers. Therefore, p must be 2, q must be 3, and r must be 5.

So the values of p, q, and r are:

p = 2

q = 3

r = 5

Moving on to part B, let's work out the highest common factor (HCF) of 270 and 105.

The prime factorization of 270 is:

270 = 2 * 3^3 * 5

The prime factorization of 105 is:

105 = 3 * 5 * 7

To find the HCF, we need to find the common factors and choose the highest one.

The common factors of 270 and 105 are 3 and 5.

The highest common factor of 270 and 105 is 3 * 5 = 15.

Therefore, the highest common factor of 270 and 105 is 15.

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Xavior took a total of 124 quarters and dimes to trade in for cash at the bank. He got exactly $25 back. How many quarters did he have?

A.
40

B.
62

C.
84

D.
100

Answers

C. 84 he had 84 quarters

The volume of a tree stump can be modeled by considering it as a right cylinder. Xavier measures its height as 2.1 ft and its circumference as 61 in. Find the volume of the stump in cubic inches. Round your answer to the nearest tenth if necessary.

Answers

The volume of the stump is 7451.9 cubic inches.

How to find the volume of the stump in cubic inches?

The volume of a cylinder can be calculated using formula below:

V = πr²h

where r is the radius and h is the height of the cylinder

We have circumference (C) = 61 in.

Let's find the radius (r) using the formula:

C = 2πr

61 = 2 * 22/7 * r

r = 9.70 in

h = 2.1 ft  = 2.1 * 12 = 25.2 in

Substituting into V = πr²h:

V = 22/7 * 9.70² * 25.2

V = 7451.9 cubic inches

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The table shows ordered pairs of the function y=8-2x. What is the value of y when x=8?
0-20
X
-3
-1
-
1
4
8
10
Mark this and return
y
14
10
6
0
?
-12
Save and Exit
Next
Submit

Answers

Answer:

The Value of Y is -8

Step-by-step explanation:

I believe it is -8 because giving the function, y = 8 - 2x, given that x = 8, we can replace the value into a function. y = 8 - 2(8) = 8 - 16 = -8.

So therefore, the value of y is -8. Hopes this helps :p

HELP PLS DUE IN 5 MINUTES!!!!!!!!!!

Answers

Answer:

Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.

Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.

Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.

Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.

Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.

Consider the following claim: Group behavior can increase the chances for an individual and a species to survive and reproduce.

Step-by-step explanation:

Please help. Any unnecessary answers will be reported.

You are in a competition that involves building card towers. The quickest person to reach 100 stories wins the competition. After reaching 5 stories of cards as shown in the picture below, you needed to use 40 cards.
How many cards will be necessary to build , in a similar way, a tower with 100 stories. Make sure you include work.

Answers

Answer:

To determine the number of cards necessary to build a tower with 100 stories, let's analyze the pattern observed in the given information.

From the information provided, we know that building 5 stories of cards required 40 cards. Now, let's examine the relationship between the number of stories and the number of cards used:

Number of stories: 5

Number of cards used: 40

To find the number of cards needed for 100 stories, we can calculate the ratio of the number of stories to the number of cards used for the 5-story tower and then apply that ratio to the target number of stories (100).

Ratio = Number of stories / Number of cards used

Ratio = 5 / 40

Now, we can use this ratio to calculate the number of cards needed for 100 stories:

Number of cards for 100 stories = Ratio * Number of stories

Number of cards for 100 stories = (5 / 40) * 100

Calculating the result:

Number of cards for 100 stories = (0.125) * 100

Number of cards for 100 stories = 12.5

Since it is not possible to use a fraction of a card, we need to round up to the nearest whole number. Therefore, we would need a minimum of 13 cards to build a tower with 100 stories using a similar pattern.

Please note that the actual number of cards required may vary depending on the specific construction technique and stability of the tower.

Graph

<
0
x<0x, is less than, 0.

Answers

The graph of the inequality is x < 0 and is plotted

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

A = x is less than 0

So , on simplifying , we get

x < 0

Hence , the inequality of x is all numbers less than 0 without including 0

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PLS HELP ME, WILL GIVE BRAINLIEST!!!!!!!!!!!!!

Answers

sorry i was going to show work but my water spill on the paper. so answer is 556.05cm^2

helpppppppppp meeeeee please ​

Answers

The missing sides of the triangle are given as follows:

[tex]SX = 4\sqrt{3}[/tex]RS = 12.

What are the trigonometric ratios?

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

Sine = length of opposite side to the angle/length of hypotenuse of the triangle.Cosine = length of adjacent side to the angle/length of hypotenuse of the triangle.Tangent = length of opposite side to the angle/length of adjacent side to the angle = sine/cosine.

For the angle of 30º, we have that:

6 is the opposite side.RS is the hypotenuse.

Hence the hypotenuse RS is obtained as follows:

sin(30º) = 6/RS

1/2 = 6/RS

RS = 6 x 2

RS = 12.

Applying the cosine, we have that:

cos(30º) = 6/SX

[tex]\frac{\sqrt{3}}{2} = \frac{6}{SX}[/tex]

[tex]SX = \frac{12}{\sqrt{3}}[/tex]

[tex]SX = 4\sqrt{3}[/tex]

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Select the correct answer. Consider this quadratic equation. x2 + 1 = 2x – 3 Which expression correctly sets up the quadratic formula? A. B. C. D.

Answers

The expression x = (2 ± √(-12)) / 2 is negative, this quadratic equation does not have real solutions.

The quadratic formula, we need the quadratic equation in the form ax^2 + bx + c = 0. The given equation is x^2 + 1 = 2x - 3. To set it up correctly, we need to move all terms to one side of the equation to have a zero on the other side.

Rearranging the equation, we get x^2 - 2x + 4 = 0. Now we can identify the coefficients a, b, and c.

The correct expression to set up the quadratic formula is:

B) x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation x^2 - 2x + 4 = 0, we have:

a = 1

b = -2

c = 4

Plugging these values into the quadratic formula, we have:

x = (-(-2) ± √((-2)^2 - 4 * 1 * 4)) / (2 * 1)

Simplifying further, we get:

x = (2 ± √(4 - 16)) / 2

x = (2 ± √(-12)) / 2

Since the expression inside the square root is negative, this quadratic equation does not have real solutions.

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Note the full question may be :

Consider the quadratic equation 2x^2 + 5x - 3 = 0. Which expression correctly sets up the quadratic formula?

A) x = (-b ± √(b^2 - 4ac)) / (2a)

B) x = (-b ± √(b^2 + 4ac)) / (2a)

C) x = (-b ± √(4ac - b^2)) / (2a)

D) x = (b ± √(b^2 - 4ac)) / (2a)

STRUCTURE Gustavo sets up tables for a caterer on weekends. Each round table can seat 8 people. Each rectangular table can seat 10 people. One weekend, his boss asked him to set up tables for 124 people. He uses 2 more round tables than rectangular tables. Write a system of equations to find the number of round tables and rectangular tables Gustavo used. Then graph the system on a separate sheet of paper to solve the system. Let x = the number of round tables and let y = the number of rectangular tables. y = x+ x+ y= WHAT DO I PUT IN THE BOXES ​

Answers

The system of equation of the tables used is 8x + 10y = 124 and x = y + 2

He used 8 round tables and 6 rectangular tables

How to determine the system of equation of the tables used

From the question, we have the following parameters that can be used in our computation:

Each round table = 8 peopleEach rectangular table = 10 peopleTotal number of table = 124

Using the above as a guide, we have the following:

8x + 10y = 124

Where

x = round tables

y = rectangular tables

We understand that

He uses 2 more round tables than rectangular tables

This means that

x = y + 2

So, the system of equations is 8x + 10y = 124 and x = y + 2

The graph of the system is attached, where we have x = 8 and y = 6  

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The doubleVal function is supposed to be passed a pointer to an integer, and it doubles the value of the number. Which of the options below is the correct implementation of the doubleVal function?void doubleVal(int &ptr){ &ptr *= 2;void doubleVal(int *ptr){ ptr = 2; }void doubleVal(int &ptr){ ptr = 2; }void doubleVal(int *ptr){ &ptr *= 2; } what is the 40ar/40k ratio of the sample 1.65 million years after its formation? Some economists argue that private firms will not undertake the efficient amount of basic scientific research.a. Explain why this might be so. In your answer, classify basic research in one of the categories shown in Figure 1.RivalNon-RivalExcludablePrivate GoodClub GoodNon-ExcludableCommon ResourcesPublic Goodsb. What sort of policy has the United States adopted in response to this problem?c. It is often argued that this policy increases the technological capability of American producers relative to that of foreign firms. Is this argument consistent with your classification of basic research in part (a)? (Hint: Can excludability apply to some potential beneficiaries of a public good and not others?) how many times more intense was the loma prieta earthquake than an earthquake with a magnitude of ? round to the nearest whole unit. an automatic external defibrillator (aed) delivers 135 j of energy at a voltage of 725 v. what is the capacitance of this device? under private inheritance what will properties/methods visibility be in the child class?Public:Protected:private: Suppose X1, . . . , X64 are independent and identically distributed continuous uniform random variables on the interval (0,12). Recall that if X Unif (0,12), then f(x) = 1/12 for 0 < x < 12 (and otherwise), = E(X) = 6, and ^2 = Var(X) = 12 (there is no need to verify this). Approximate the probability that the sample mean X is less than 5.5. i.e. approximate P(X < 5.5). a. 0.1251 b. 0.0548 c. 0.1446d. 0.2420 Curzon is a victim of prejudice. He deals with it by remembering something that his father once told him:""a lot of white people have twisted hearts. It prevents them from seeing the world properly and turns them into tools of the Devil.""(Page 54) Who has the most twisted heart in Curzons company? How does he spread ""poison"" about Curzon? At what point does Curzon begin doubting Ebens loyalty? What does it take for Curzon and Eben to become friends again?