Please answer asap I will mark the brainly. Can you please explain step by step​

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 sample proportion who prefer balancing the budget is 0.59

The sample proportion is the ratio of a sample's number of successes to its overall sample size. A single dataset may contain many sample proportions, some of which may or may not be equal; yet, the sample proportion is roughly normally distributed because it is a random variable.

P=X/N, where X represents the number of successes and N represents the sample size, yields the sample proportion.

How to calculate Sample Space?

Count the total number of successes in the sample as well as its size to determine the sample proportion. This could entail resolving challenging combinatorial puzzles. After that, calculate the sample size to the total number of successes. This is a sample percentage.

So, our sample proportion will be 702/1190 = 0.59

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We can deduce that X + 4 = 8 by looking at the top row & second column. The X value is therefore 4.

an arrangement of written or printed items on a page that are vertical. a vertical part of a printed page divided into two or more equal columns of numbers.

X + 4 corresponds to a value in the second column and top row.

The third row's value is equal to the first column's value plus two.

(Third row, second column) The value is 12 at the bottom right corner.

First row and the first column, top left, represents value as B.

It reads 8, first row, second column, in the upper right corner.

C is the value located on the bottom left (third row, first column).

We can deduce that X + 4 equals 8 from top row & second column. Hence, we can find X:

X plus 4 = 8

When we take 4 away from both sides, you get:

X = 4

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When a predictive model is made overly complex to fit in the quirks of given sample data, it is called overfitting.

Overfitting occurs when a model is too complex and tries to fit the data too closely. This can result in a model that performs well on the training data but performs poorly on new, unseen data.

Overfitting can be prevented by simplifying the model or using a larger training dataset. It is important to strike a balance between complexity and simplicity in order to create a model that generalizes well to new data.

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An economist's use of experiments and real-world data to test a theory is an example of empirical research, which involves gathering data through observation and experimentation to support or refute a hypothesis.

Empirical research is a cornerstone of the scientific method and is used in a wide range of disciplines to explore, understand, and predict natural and social phenomena. In the case of an economist, this might involve conducting a controlled experiment in a laboratory setting or analyzing data from real-world economic transactions to test a hypothesis or theory.

The use of empirical research in economics is important because it provides a way to test and refine economic theories and models, as well as to gain insight into complex economic phenomena. By combining theoretical models with real-world data, economists can develop more accurate and nuanced understandings of economic systems and make informed predictions about future trends. This, in turn, can inform policy decisions and help guide the development of effective economic strategies.

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Answer:

Evaluate.

15.91828182 = 289.47

The slope intercept form of the line is ,

> y = mx + c

where ,

Example :-

> y = 2x + 5

Answer:

A and B.

Step-by-step explanation:

The definition of parallel lines is: "Parallel lines are straight lines that are always the same distance apart from each other. Parallel lines never meet no matter how much they are extended in either direction." So, in conclusion, your answer is: A and B.

Hope this helped!

Answer:

A&B because they are not intersecting.

Answer:

37.5

Step-by-step explanation:

18/48 = x/100

18 x 100 = 48 x x

1800 = 48x

1800/48 = x

x = 37.5

Based on the information given regarding the percentage, the correct option is 37.5%.

It should be noted that in order to calculate the percentage, the following should be done.

= 18/48 × 100

= 3/8 × 100

= 37.5%

Therefore, based on the information given, it can be seen that the answer is 37.5%.

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We have that, if all the diagonal entries are positive, then all the eigenvalues have a positive real part, where the proof is based on the transpose and the hermetic matrix

Since \($A$\) is an \($n \times n$\) matrix, and all diagonal entries of \($A$\) are positive. Let the eigenvalue of \($A$\) be \($\lambda$\) and the eigenvector of \($A$\) be \($x$\). So

\($$Ax = \lambda x$$ $$\Rightarrow x^{*}Ax = \lambda x^{*}x$$\)

Here, \($x^{*}$\) It is the transpose of \($x$\). We know that\($A$\) is a Hermitian matrix, so\($A = A^{*}$\). Therefore

\($x^{*}Ax = x^{*}A^{*}x = (Ax)^{*} x = (\lambda x)^{*}x = \lambda^{*}x^{* }x$\)

Now we have

\($$x^{*}Ax = \lambda^{*}x^{* }x \geq 0$$\)

Therefore, we can conclude that

\($\lambda^{*} \geq 0$\) \($\text{Re}(\lambda) \geq 0$\)

Thus, we have proved that if all the diagonals are positive, then all the eigenvalues have a positive real part.

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Answer:

3

Step-by-step explanation:

If the stock of Company A lost $5. 31 throughout the day and ended at a value of $112. 69. The stock of Company A declined by 4.5% throughout the day.

The percentage decline in stock price is calculated by dividing the loss in value by the original value of the stock. To find out the percentage loss of stock A, we can use the formula:

(Loss in value / Original value) x 100%

Let us substitute the values we know:

Loss in value = $5.31

Original value = $118.00

Percent change = (5.31 / 118.00) x 100%

Percent change = 0.045 or 4.5%

Therefore, the stock of Company A declined by 4.5% throughout the day.

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Answer:

A

Step-by-step explanation:

The solution we're looking at here is a set of all the points between two parallel lines. Let's see what we can find out about those lines from the inequality, and use that the pick the correct option.

We can start by splitting the inequality at the top into two seperate inequalities:

\(7\leq y-3x<11\\y-3x\geq7\\y-3x<11\)

From here, we can put each inequality into slope-intercept form:

\(y\geq3x+7\\y<3x+11\)

Our slope for both lines is positive, so we can immediately eliminate B and D. A and C both display lines with slopes of 3 and y-intercepts of 7 and 11; the only difference is in which line is dashed and which line is solid.

As a reminder, a dashed line means that the line itself is not included in the solution, a solid line means that it is. Dotted lines always pop up when you see the symbols < and >, while solid lines pop up when you see ≤ and ≥.

\(y\geq3x+7\) (Solid)

\(y<3x+11\) (Dashed)

This matches up very nicely with the graph in A, our solution.

The coordinates of point g of the pre-image is (-2, 1).

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

The coordinates of the image are given as:

d' = (-8,8)

e' = (-3,8)

f' = (-5,4)

g' = (-8,4)

The dilation rule is given as:

(x,y) -> 4(x,y)

So, we have:

(-8,4) = 4 x g

g = (-2,1)

Hence, the coordinates of point g of the pre-image is (-2, 1)

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If the original numbers, let's call them x and y, multiply to give a result of 864, and we double both numbers and multiply them, the new result can be calculated as (2x)(2y) = 4xy.

Given that the original product is 864, we can substitute xy = 864 into the equation: 4xy = 4 * 864 = 3456.Therefore, if we double both original numbers and multiply them, the result would be 3456. Hence, the correct answer is d) 3456. To understand why the other options are not correct: a) 864: This is the original product, not the result of doubling both original numbers and multiplying them. b) 868: This is not the correct result. Doubling both original numbers would lead to a larger result. c) 1728: This is the result of cubing 12, not the result of doubling both original numbers and multiplying them.

Thus, the correct answer is d) 3456.

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Answer:

V = 1/3 * π * 80² * 150

Step-by-step explanation:

The formula for the volume of a cone:

V = ⅓ * π * r² * h

r = 80cm

h = 150cm

V = ⅓ * π * 80² * 150

Answer:

-3/2

Step-by-step explanation:

The slope of a line is calculated by dividing the difference in the y-coordinates by the difference in the x-coordinates.

Here, the given ordered pairs are (-6, -8) and (-14, 4), so the slope is:

slope = m = (4 - (-8)) / (-14 - (-6)) = 12 / (-8) = -3/2

The answer is thus -3/2.

~ an aesthetics lover

Answer:

m= -3/2

I hope this helps.

The sample size should be of 105 patients so as to have maximum sampling error of 10%, if population is normally distributed.

To calculate the sample size needed to achieve a maximum sampling error of 10% with a population of 300 patients that is normally distributed, you need to use the formula for calculating sample size.

Sample size = (Zscore)^2 * StdDev*(1-StdDev) / (margin of error)^2

In this case, Zscore = 1.645, StdDev = 0.5 and Margin of Error = 0.1.

Using the formula, Sample size = (1.645)^2 * 0.5*(1-0.5) / (0.1)^2

Therefore, the Sample size = 104.9, or 105 patients.

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An example of a commutative ring R with 1, a prime ideal P, and no zero divisors but R is not an integral domain is the ring R = Z/6Z, where Z is the set of integers and 6Z is the ideal generated by 6.

The ring R = Z/6Z consists of the residue classes of integers modulo 6. The elements of R are [0], [1], [2], [3], [4], and [5], where [a] denotes the residue class of a modulo 6.

In this ring, addition and multiplication are performed modulo 6. For example, [2] + [3] = [5] and [2] * [3] = [0].

R has a multiplicative identity, which is the residue class [1]. It is commutative since addition and multiplication are performed modulo 6.

The ideal P = 2R consists of the elements [0] and [2]. P is a prime ideal since R/P is an integral domain, which means there are no zero divisors in R/P. However, R itself is not an integral domain because [2] * [3] = [0] in R, showing that zero divisors exist in R.

Therefore, the ring R = Z/6Z, with the prime ideal P = 2R, satisfies the given conditions.

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The answers are:

a) The z-score for a light bulb that lasts 500 hours is -10.

b) For a sample of 20 light bulbs, the probability that the average lifespan will be less than 980 hours is approximately 0.0367, or 3.67%.

c) The z-score for a light bulb that lasts 400 hours is -12. This is even more unusual than a lifespan of 500 hours.

d) Given the lifespan follows a normal distribution with a mean of 1000 hours, 50% of the light bulbs will have a lifespan less than 1000 hours.

a) The z-score is calculated as:

z = (X - μ) / σ

Where X is the data point, μ is the mean, and σ is the standard deviation. Here, X = 500 hours, μ = 1000 hours, and σ = 50 hours. So,

z = (500 - 1000) / 50 = -10.

The z-score for a bulb that lasts 500 hours is -10. This is far from the mean, indicating that a bulb lasting only 500 hours is very unusual for this brand of bulbs.

b) If a customer buys 20 of these light bulbs, we're now interested in the average lifespan of these bulbs. . In this case, n = 20, so the standard error is

50/√20

≈ 11.18 hours.

z = (980 - 1000) / 11.18 ≈ -1.79.

The probability that z is less than -1.79 is approximately 0.0367, or 3.67%.

c) The z-score for a bulb with a lifespan of 400 hours can be calculated as:

z = (400 - 1000) / 50 = -12.

The probability associated with z = -12 is virtually zero. So the probability of getting a bulb with a mean lifespan of 400 hours is virtually zero.

d) The mean lifespan is 1000 hours, so half of the light bulbs will have a lifespan less than 1000 hours. Since the lifespan follows a normal distribution, the mean, median, and mode are the same. So, 50% of light bulbs will have a lifespan less than 1000 hours.

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Answer:

\(f(-1)=-11\\f(0)=16\\f(2)=22\)

Step-by-step explanation:

\(\displaystyle f(-1)=3(-1)-8=-3-8=-11\\f(0)=3(0)+16=16\\f(2)=3(2)+16=6+16=22\)

Antionette can purchase a maximum of 56 adult-sized t-shirts.

What is algebraic ?

Algebraic refers to anything that pertains to algebra, which is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. Algebraic concepts include using variables (such as x or y) to represent unknown values, using operations such as addition, subtraction, multiplication and division.

Let x be the number of adult-sized t-shirts that Antionette purchases.

We know that ,

The cost of each adult-sized t-shirt is $6.25

The cost of each youth-sized t-shirt is $4.50

Antionette has $550 to purchase both adult-sized and youth-sized t-shirts

Antionette purchases 45 youth-sized t-shirts

We can set up the equation to represent the total cost of all the t-shirts and the money Antionette has ,

(x6.25) + (454.50) = 550

To solve for x, we can simplify the equation by multiplying the number of adult-sized t-shirts by the cost per t-shirt and the number of youth-sized t-shirts by the cost per t-shirt, and then set it equal to the total money Antionette has ,

x*6.25 + 202.5 = 550

then we can subtract 202.5 from both sides , x*6.25 = 347.5

then divide both sides by 6.25 to get ,  x = 56

So, Antionette can purchase a maximum of 56 adult-sized t-shirts.

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The cost of each adult-sized t-shirt is $6.25

The cost of each youth-sized t-shirt is $4.50

Antionette has $550 to purchase both adult-sized and youth-sized t-shirts

Antionette purchases 45 youth-sized t-shirts

(x*6.25) + (454.50) = 550

x*6.25 + 202.5 = 550

then we can subtract 202.5 from both sides , x*6.25 = 347.5

then divide both sides by 6.25 to get ,  x = 56

So, Antionette can purchase a maximum of 56 adult-sized t-shirts.

Answer:help with what

Step-by-step explanation:

You need to say

The probability that one of the events Franco worked last year, selected at random, was a wedding is equals to the \( \frac{4}{17} \).

Franco is a professional DJ and he was very busy in work during Last year. Number of events where he worked = 26

Number of wedding where he worked

= 8

So, total events where he played his DJ

= 26 + 8 = 34

We have to determine probability that one of the events Franco worked last year, selected at random, was a wedding.

Now, one of event is Randomly selected from all of above events. Number of favourable outcomes for worked on wedding events = 8

So, probability of selected a wedding event \( = \frac{8}{34} \)

\( = \frac{4}{17} \). Hence the required probability value is \( \frac{4}{17} \).

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Answer: How you can isolate the term f/3 is to

subtract 22 from both sides.

Explanation:

When going from A(-2,-3) to A '(-6,-9), we multiplied both coordinates by the scale factor 3. In other words, we tripled the coordinates.

Do the same thing to the coordinates of point B.

Therefore we arrive at (12, 0) as the final answer. This is choice C.

4 ounces left

75%=3/4

so 3/4 of 16oz is 4.

Kashloopski Iardatsky Fartucci

The polynomials 1, 1-t, \(2-4t+t^2\) and \(6-18t+9t^2-t^3\) are linear independent and span \(P_3\). So the first four Laguerre polynomials forms a basis of \(P_3\).

We have the first four Laguerre polynomials. Here \(P_3\) is the space of all polynomials of degree at most 3.

i.e., \(P_3= \{ a+bx+cx^2+dx^3| a,b,c,d \in R\}\)

So the dimension of \(P_3\) is 4. Also there are 4 Laguerre polynomials.

Now to show that the first four Laguerre polynomials forms a basis, it remains to show that they are linear independent.

Consider the polynomials 1, 1-t, \(2-4t+t^2\) and \(6-18t+9t^2-t^3\). Write them into a matrix with the co-efficient of 1, t, \(t^2\) and \(t^3\) in each row.

\(\left[\begin{array}{cccc}1&1&2&6\\0&-1&-4&-18\\0&0&1&9\\0&0&0&-1\end{array}\right]\)

This matrix is already in its echelon form with all its pivots occupied. The pivot of first row is 1. The pivot of 2nd row is -1. The pivot of 3rd row is 1 and the pivot of 4th row is -1.

Hence the polynomials are linearly independent since the columns of the above matrix are linearly independent.

In conclusion, the first four Laguerre polynomials 1, 1-t, \(2-4t+t^2\) and \(6-18t+9t^2-t^3\)  forms a basis for \(P_3\).

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Answer:

4/5

Step-by-step explanation:

32/40 is how often he has come so far. You would need to simplify that fraction down to the lowest, which is 4/5.