Hi, can you help me to solve this exercise, please!!

The long-run cost function is C(q) = 2w(sqrt[rw(q^3)]). The profit-maximizing output can be found by minimizing this cost function with respect to q.

Part a: Deriving the long-run cost function C(q):

To derive the long-run cost function, we need to find the minimum cost of producing a given output level q using the given production function.

Given the production function q = F(L, K) = (KL)^(1/3), we can rewrite it as K = (q^3)/L.

Now, let's express the cost function C(q) in terms of q. We have the cost function as C(q) = wL + rK, where w is the wage rate and r is the rental rate.

Substituting the expression for K in terms of q, we get C(q) = wL + r[(q^3)/L].

To minimize the cost function, we can take the derivative of C(q) with respect to L and set it equal to zero:

dC(q)/dL = w - r[(q^3)/(L^2)] = 0.

Simplifying the equation, we have w = r[(q^3)/(L^2)].

Solving for L, we get L^2 = r(q^3)/w.

Taking the square root, we have L = sqrt[(r(q^3))/w].

Substituting this value of L back into the cost function equation, we get:

C(q) = w(sqrt[(r(q^3))/w]) + r[(q^3)/sqrt[(r(q^3))/w]].

Simplifying further, we have:

C(q) = 2w(sqrt[rw(q^3)]).

So, the long-run cost function C(q) is given by C(q) = 2w(sqrt[rw(q^3)]).

Part b: Solving the long-run profit maximization problem directly:

To solve the profit maximization problem directly, we need to maximize the expression:

max K, L [F(L, K) - wL - rK].

Taking the derivative of the expression with respect to L and K, and setting them equal to zero, we can solve for the optimal values of L and K.

The first-order conditions are:

dF(L, K)/dL - w = 0, and

dF(L, K)/dK - r = 0.

Differentiating the production function F(L, K) = (KL)^(1/3) with respect to L and K, we get:

(1/3)(KL)^(-2/3)K - w = 0, and

(1/3)(KL)^(-2/3)L - r = 0.

Simplifying the equations, we have:

K^(-2/3)L^(1/3) - (3/2)w = 0, and

K^(1/3)L^(-2/3) - (3/2)r = 0.

Solving these two equations simultaneously will give us the optimal values of L and K.

Part c: Using the derived long-run cost function:

In Part a, we derived the long-run cost function as C(q) = 2w(sqrt[rw(q^3)]).

To find the profit-maximizing output, we can minimize the long-run cost function C(q) with respect to q.

Taking the derivative of C(q) with respect to q and setting it equal to zero, we can solve for the optimal value of q.

dC(q)/dq = w(sqrt[rw(q^3)]) + (3/2)w(q^2)/(sqrt[rw(q^3)]) = 0.

Simplifying the equation, we have:

(sqrt[rw(q^3)])^2 + (3/2)(q^2) =

0.

Solving this equation will give us the profit-maximizing output q.

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The angle in radians between the vectors a = (-3, 3, 10) and b = (3, -10, 4) is 1.89 radians (rounded to two decimal places) which is calculated using the dot product formula.

To find the angle between two vectors, we can use the dot product formula which is given by: a · b = ||a|| ||b|| cosθwhere a and b are the vectors, ||a|| and ||b|| are the magnitudes of vectors a and b respectively, and θ is the angle between them.

In order to find the angle between the given vectors, we need to calculate the dot product of vectors a and b and their magnitudes. The magnitudes can be found using the formula:||a|| = √(a1² + a2² + a3²)||b|| = √(b1² + b2² + b3²)where a1, a2, a3 are the components of vector a and b1, b2, b3 are the components of vector b.

Using the formulas above, we get: ||a|| = √((-3)² + 3² + 10²) = √118||b|| = √(3² + (-10)² + 4²) = √125. To calculate the dot product, we need to multiply corresponding components of the two vectors and then add them up: a · b = (-3)(3) + (3)(-10) + (10)(4) = -9 - 30 + 40 = 1

Finally, we can substitute the values we calculated into the dot product formula to get:1 = √118 √125 cosθcosθ = 1 / (√118 √125)θ = cos⁻¹(1 / (√118 √125)) = 1.89 radians (rounded to two decimal places). Therefore, the angle in radians between the vectors a = (-3, 3, 10) and b = (3, -10, 4) is 1.89 radians.

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Answer:1/8, 2/5 3/4

Step-by-step explanation: you can turn each into decimal

0.125, 0.4 and 0.75

Answer:

\(\dfrac{1}{8} < \dfrac{2}{5} < \dfrac{3}{4}\)

Step-by-step explanation:

\(\text{You can rewrite the fractions as}\\\\\dfrac 18=\dfrac{5}{40}\\\\\\\dfrac 25 = \dfrac{16}{40}\\\\\\\dfrac 34 = \dfrac{30}{40}\\\\\\\text{So,} ~\dfrac{5}{40} < \dfrac{16}{40} < \dfrac{30}{40}\)

Answer:

Danielle burns calories at a higher rate

Step-by-step explanation:

Alex: 650/75=8 2/3 calories per minute

Danielle: 420/45=9 1/3 calories per minute

Answer:

80

Step-by-step explanation:

10(n-6)

10(14-6)

10(8)

80

Answer:

80

Step-by-step explanation:

10(n-6)            Expression

10 ( 14 - 6 )      Replacing n with 14

10 ( 8 )            Solving the expression in the brackets

80                   Removing parenthesis

80!

The probability of 5 people of different ages are sitting in age order is 1/12.

Let the youngest individual take a seat first. If the seats are not designated, this person may occupy any of the five available seats, and each one is equally valuable.

The next senior citizen must then be placed. For this reason, there are two possible placements for the second person: either to the left of the first person or to the first person's right. The two options, ascending order and descending order, are matched by this.

We are unable to place the additional individuals after the second person is set because there is only one spot available adjacent to the first person.

There are only two methods to arrange five persons of different ages sitting at a round table in ascending or descending order.

The number of ways in which we can arrange are 5 people at a round table without any restriction is  4!.

Probability of 5 people in  around table is 2/4! = 1/12.

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Answer:

a = -1

b = 1

Step-by-step explanation:

Step 1: Isolate x's

x² + 2x = -2

Step 2: Complete the Square

x² + 2x + 1 = -2 + 1

(x + 1)² = -1

Step 3: Move everything to 1 side

(x + 1)² + 1 = 0

And we have our answer.

Answer:

A=1 and b=1

Step-by-step explanation:

Answer: 70

Step-by-step explanation:

Note that we can find the number of ways to choose 4 numbers out of the 8 to represent the unordered triple \((a,b,c,d)\). The other 4 numbers will represent the unordered triple \((e,f,g,h)\). For each of these triples, there is only one allowed permutation because the numbers need to be in sequential order.

So, the final answer is \(\binom{8}{4}=70\).

Answer: 51

Step-by-step explanation:

By adding the color frequency of each color, you can find that the spinner was originally spun a total of 70 times. Now you can use this to create an equality equation to find how many times you may land on purple. It would look something like this:

\(\frac{12}{70}=\frac{x}{300}\)

Now, with this, you can calculate what the answer would be by solving the inequality. You can cross multiply the equality and turn it into this:

\(12\cdot300=70\cdot x\)

Now you can divide out the 12 from both sides, and you are given this:

\(\frac{\left(12\cdot300\right)}{12}=\frac{\left(70\cdot x\right)}{12}\)

Which gives you this when simplified:

\(300=\left(\frac{70}{12}\right)\cdot x\)

You can simplify 70/12 to be 35/6

and you are given this:

\(300=\left(\frac{35}{6}\right)\cdot x\)

Now you can remove the parenthesis

\(300=\frac{35}{6}\cdot x\)

Multiply both sides by 6:

\(300\cdot6=\frac{35}{6}\cdot6\cdot x\)

Simplify to this:

\(1800=35\cdot x\)

Now, the final step is to divide both sides by 35:

\(\frac{1800}{35}=\frac{\left(x\cdot35\right)}{35}\)

And the final answer is

\(51.4285714286=x\)

and since you are rounding to the nearest whole number, you can turn it into this: 51=x

Answer:

  See attached

Step-by-step explanation:

You want a graph of triangle ABC after dilation by a factor of 1/2 about the origin.

Each coordinate is multiplied by the scale factor when dilation is about the origin:

  (x, y) ⇒ (x/2, y/2) . . . . . . dilation by a factor of 1/2

  A(4, -2) ⇒ A"(2, -1)

  B(-2, -2) ⇒ B"(-1, -1)

  C(-2, 2) ⇒ C"(-1, 1)

The graph is shown in the attachment.

The speed on the third day was 3.5 mph.

To determine the speed on the third day, we need to find the total time Mr. Walker spent walking and the total distance he covered.

On the first day, he worked for 6 hours at a speed of 4 mph. Therefore, the distance covered on the first day is:

Distance = Speed * Time = 4 mph * 6 hours = 24 miles.

On the second day, he also worked for 6 hours at a speed of 3 mph. Therefore, the distance covered on the second day is:

Distance = Speed * Time = 3 mph * 6 hours = 18 miles.

To find the distance remaining after the first two days, we subtract the distances covered from the total distance:

Remaining distance = 70 miles - 24 miles - 18 miles = 28 miles.

On the third day, Mr. Walker worked for 8 hours to cover the remaining distance of 28 miles. Therefore, the speed on the third day is:

Speed = Distance / Time = 28 miles / 8 hours = 3.5 mph.

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If each person eat one quarte (1/4) of the cake, this means that only 4 people can eat from one cake, as:

Each person eats 2 pieces of 1/8 of the cake, as 2*1/8=2/8=1/4.

Answer: 4 people can eat cake.

Answer:

b=10mm

Step-by-step explanation:

6x10=60÷2=30

(base x height)÷2

1 standard deviation =  8 inches. the answer is OPTION E

We know that 99.7% of American men have heights between 5'0" and 7'0". Since height is normally distributed, we can use the empirical rule to estimate the standard deviation.

According to the empirical rule, 99.7% of the data falls within 3 standard deviations of the mean. Therefore, we can say that the range of heights from 5'0" to 7'0" is 3 standard deviations.

We can use this information to estimate the standard deviation as follows:

Range of heights = 7'0" - 5'0" = 2 feet

3 standard deviations = 2 feet

1 standard deviation = 2/3 feet

1 foot = 12 inches

Therefore, 1 standard deviation = 2/3 * 12 inches = 8 inches

So, our estimate of the standard deviation of the height of American men is 8 inches. Therefore, the answer is OPTION E in the given options.

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Complete question

If the heights of 99.7% of American men are between 5'0"

and 7'0", what is your estimate of the standard deviation of

the height of American men? (Assume the heights of

American Men are Normally Distributed).

A.) 1"

B.) 2"

C.) 4"

D.) 6"

E.) 8"

Answer:

  (a)  seventy-three and three fifths square inches

Step-by-step explanation:

You want to know the area of the quilt block shape shown.

The shape can be considered to be composed of a rectangle 10.6 inches long, together with a right triangle with side lengths 4 and 5 inches.

The relevant area formulas are ...

  triangle: A = 1/2bh

  rectangle: A = bh

The area of the triangle is ...

  A = 1/2(5 in)(4 in) = 10 in²

The area of the rectangle is ...

  A = (10.6 in)(6 in) = 63.6 in²

The total area is ...

  10 in² +63.6 in² = 73.6 in²

The area of the shape is 73 3/5 square inches.

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The probability that the number drawn is a multiple of 2 or 3 is 8/15 or 0.53.

This can be easily found by finding the number of multiples of 2 and 3 between 1 and 15 and adding them together. The multiples of three go from 3 to 15 and therefore there are 5 such numbers. The multiples of two go from 2 to 14 and hence there are 7 such numbers. Therefore, when we add these two numbers together, we get 12.

This is the total number of multiples of 2 or 3 between 1 and 15. We divide this by the total number of elements in the box, which is 15, to get the probability that the number drawn is a multiple of 2 or 3. This comes out to be 8/15 or 0.53.

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Answer:

18 cups of sugar

Step-by-step explanation:

Step 1:

120 ÷  6 = 20

Step 2:

360 ÷ 20

Answer:

18

Hope This Helps :)

Answer:

the answer to your question is 18 brownies

Step-by-step explanation:

lets say the number of cups of sugar used to make 360 brownies is x

6 = 120

x = 360

cross multiply

120x = 2160

x = 2160/120

x = 18

Answer:

dm me for help

Step-by-step explanation:

Using the calculus rule, we can rewrite the total derivative (dx/dz) at constant y as the sum of two partial derivatives.

The total derivative (dx/dz) at constant y can be rewritten as the sum of two partial derivatives:
(dx/dz) = (∂x/∂y)*(∂y/∂z) + (∂x/∂z) at constant y

Apply the chain rule
The chain rule in calculus allows us to find the derivative of a function with respect to another variable, by considering how the intermediate variables change.

In this case, we want to find (dx/dz) at constant y.

The chain rule states:
(dx/dz) = (dx/dy)*(dy/dz) + (dx/dz) at constant y
Identify the partial derivatives:
Since we want to rewrite (dx/dz) as a sum of two partial derivatives, we will keep the terms (dx/dy) and (dy/dz) as partial derivatives:
(dx/dz) = (∂x/∂y)*(∂y/∂z) + (∂x/∂z) at constant y
Final answer
The total derivative (dx/dz) at constant y can be rewritten as the sum of two partial derivatives:
(dx/dz) = (∂x/∂y)*(∂y/∂z) + (∂x/∂z) at constant y.

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The given statement "An algorithm is a calculation that determines how long it will take to solve a problem." is False.

An algorithm is not just a calculation that determines how long it will take to solve a problem. An algorithm is a step-by-step set of instructions or a process used to solve a problem or perform a specific task. It is a systematic approach that allows a computer or human to break down a problem into smaller, manageable parts and reach a solution effectively.

Algorithms are the foundation of computer programming and can be applied in various fields such as mathematics, data processing, and problem-solving. They can be simple, like finding the largest number in a list, or complex, like solving a Rubik's Cube.

Efficiency is a key factor in evaluating algorithms. The time and resources required for an algorithm to solve a problem can vary greatly depending on the method used. However, the primary purpose of an algorithm is to provide a clear and concise procedure to reach a solution, rather than just estimating the time needed to solve a problem.

In summary, an algorithm is a well-defined process designed to perform a specific task or solve a problem, rather than just calculating the time required to do so. Its effectiveness depends on its efficiency, accuracy, and the simplicity of the steps involved.

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After losing 4 Kg ,the weight of Artur is 14 Kg .

In the question ,

it is given that ,

the ratio of weight of Max : Artur is 5 : 9 .

So the weights of Max and Artur before dieting is 5x and 9x .

Now Artur goes on dieting and lose 4 Kg weight and

the ratio of weight of Max and Artur becomes 5:7  .

and the weights of Max and Artur after dieting is  5x and 7x .

Present weight of Artur = 7x .

As we can see that the change in Artur weight is 9x - 7x = 2x

According to the question

2x = 4

x = 2

hence Artur now weighs 7*(2) = 14 Kg

Therefore , after losing, 4 Kg the weight of Artur is 14 Kg .

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By comparing the responses across the three groups, the researcher can identify potential variations in opinions based on educational background. This information can provide valuable insights into how different types of schooling may shape perspectives on civic policies like curfews.

That's an interesting research approach!  By gathering opinions from different groups of children, specifically home-schooled, private school attendees, and public school attendees, the researcher can gain insights into how various educational backgrounds might influence their opinions on the new town curfew.

Collecting a simple random sample from each group ensures that every child within the respective groups has an equal chance of being selected for the survey. This helps in minimizing bias and increasing the generalizability of the findings to the larger population of home-schooled, private school, and public school children.

Once the samples are obtained, the researcher can administer a survey or questionnaire to collect the children's opinions on the new town curfew. The survey may include questions related to their awareness of the curfew, their understanding of its purpose, and their personal opinions on whether they support or oppose it.

By comparing the responses across the three groups, the researcher can identify potential variations in opinions based on educational background. This information can provide valuable insights into how different types of schooling may shape perspectives on civic policies like curfews.

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Answer:

Carlos Got more votes.

Step-by-step explanation:

If you do the math and find out what 38% of 150 is then you will have your answer

The set of integers is not closed under the operation of division because when an integer is divided by another, the results are not limited to only integers i.e. zero and decimals are possibilities

Integers are numbers without decimal points

When integers are divided, the possible results are:

The decimal and the zero possibilities imply that the set of integers is not closed under the operation of division

This is so because when an integer is divided by another, the results are not limited to only integers i.e. zero and decimals are possibilities

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Answer:

D

Step-by-step explanation:

she made a sign error when multiplying and should have had 256 as an answer

Answer:

the answer is D

Step-by-step explanation:

I'm taking the test now

ANSWER:

10 units

EXPLAINATION:

The measure of the indicated side would be 10 units because the triangle shown here is a equilateral triangle this can be seen by the picture in which all the angles of the triangle are equal.

Answer:

\(17x-23=1/2\times81\)

\(17x-23=40.5\)

\(17x=40.5+23\)

\(17x=63.5\)

\(x=63.5/17\)

\(x=3.73\)

OAmalOHopeO

Answer:

c

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

\(\frac{AD}{WZ}\) = \(\frac{CD}{YZ}\) , substitute values

\(\frac{10}{46}\) = \(\frac{5}{YZ}\) ( cross- multiply )

10YZ = 230 ( divide both sides by 10 )

YZ = 23 → c