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.)

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

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

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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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

(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.

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

Answer: 10/9, 0

Step-by-step explanation:

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

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

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

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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Answer:

20cm

Step-by-step explanation:

Answer:24.1104189866

Step-by-step explanation:

the answer to What is 692837 divided by 28736 is 24.1104189866

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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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)

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:

The relative frequency distribution is:

The correct option is A.

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.

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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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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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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The volume of the stump is 7451.9 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 scatter plot shows a [positive linear] association.

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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The missing sides of the triangle are given as follows:

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:

For the angle of 30º, we have that:

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

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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Answer: Point P

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

Answer: M

Step-by-step explanation:

The highest common factor of 270 and 105 is 15.

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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Answer:

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

Use the compound interest formula:

Where:

Plugging in the values, we get:

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

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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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.

Answer:

R500

Step-by-step explanation:

20 books x R25 each = R500.

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