Suppose a Cobb-Douglas Production function is given by the function: P(L, K) = 18L0.5 K0.5 Furthermore, the cost function for a facility is given by the function:C(L, K) = 400L + 200K Suppose the monthly production goal of this facility is to produce 6,000 items. In this problem, we will assume L represents units of labor invested and K represents units of capital invested, and that you can invest in tenths of units for each of these. What allocation of labor and capital will minimize total production Costs? Units of Labor L = (Show your answer is exactly 1 decimal place) Units of Capital K = (Show your answer is exactly 1 decimal place) Also, what is the minimal cost to produce 6,000 units? (Use your rounded values for L and K from above to answer this question.) The minimal cost to produce 6,000 units is $

The p-value is 0.01, which means that it is very rare to observe a test statistic that is equal to or more extreme than the one that was actually observed. SO the option a is correct.

In the given question, in a hypothesis test for population proportion, we calculated the p-value is 0.01 for the test statistic, we have to find which statement of the p-value is correct.

The p-value is the probability of obtaining results as extreme as, or more extreme than, the observed results of a statistical hypothesis test, assuming that the null hypothesis is true. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

If the null hypothesis is correct, the p-value is the likelihood that a test statistic will be equal to or more extreme than the one that was actually observed. Given that the null hypothesis is correct in this situation, the p-value of 0.01 indicates that it is extremely unusual to see a test statistic as dramatic as the one that was actually seen. This shows that the alternative hypothesis is more likely to be correct and that the null hypothesis is probably not true.

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Answer:

a) Label the points given (give the ordered pair).

b) What is the unit rate?

c) Plot and label the point whose ordered pair represents the unit rate.

d) What are the coordinates of that point?

e) Explain what the point that you plotted means in this context of this problem.

f) Write an equation for this graph. ​

Answer:

x = - 1, y = 1

Step-by-step explanation:

Given the 2 equations

2y + 7x = - 5 → (1)

5y - 7x = 12 → (2)

Adding the2 equations term by term will eliminate the term in x, that is

7y = 7 ( divide both sides by 7 )

y = 1

Substitute y = 1 into either of the 2 equationsand solve for x

Substituting into (1)

2(1) + 7x = - 5

2 + 7x = - 5 ( subtract 2 from both sides )

7x = - 7 ( divide both sides by 7 )

x = - 1

solution is x = - 1, y = 1

The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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Answer:

QR=2x=16

Step-by-step explanation:

2x+8= 3x

8=3x-2x

8=x

QR=2x= 8*2=16

Answer:

3; 6; 6; 5

Step-by-step explanation:

15 / 5 = 3

18 / 3 = 6

12 / 2 = 6

25 / 5 = 5

Answer:

20 vegetable plants

Step-by-step explanation:

In order to figure this out, you need to find 40% of 50. You can solve that by doing 0.40 * 50, which gives you 20. I hope that helps!

Answer:

area =  452.39 square units

circumference = 75.40 square units

Step-by-step explanation:

area = \(\pi r^{2}\)

r = 12

452.389

circumference = \(\pi *d\)

d = 2r

r = 12

d = 24

75.398

Answer:

(See the attachment)

Step-by-step explanation:

None

The graph of the inequality 8x - 5y < 3 is given below.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

8x - 5y < 3

The graph of this inequality is given below.

Thus,

The graph is given below.

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The correct choice is within your skills and abilities.

Once you get to determine things you are capable of and things you are not capable of, you will be able to concentrate on your strengths more. This will in turn produce big results as compared to if you opted to concentrate on your weaknesses.

It will also result in no or less time wasted in doing what you are less capable of.

Its almost close to impossible to be able to do everything. Each person is gifted in a certain area or skill or capability. We are all different and that's okay.

Its so important to concentrate in the areas you are more comfortable with. This will help you much with improving your skills and abilities.

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Answer:

Step-by-step explanation:

a you just had to say a

Answer:

Step-by-step explanation:

Answer:

17 drops per minute

Step-by-step explanation:

To find the number of drops per minute, we can do 85 / 5 = 17 drops per minute

Hope that helps!

Answer:

first sub in (0,-2) to get

-2 = ab^0, but b^0 = 1

so a=-2

so far we have

y = -2b^x

now use the other point (2,-50)

-50 = -2(b^2)

b^2 = 25

b= ±5

however in exponentional equations the base is usually positve, so now you have

y = -2(5^x)

sub in x=-2 and you got it.

Step-by-step explanation:

hope it helps..

Answer:

50 and the vertex is c ata 100

I don't know my answer if check or rong

Answer:

Ray DC and Ray DE

Step-by-step explanation:

Before performing a significance test about a population mean or proportion, the following conditions must be verified:

Sample Size: The sample size should be sufficiently large to allow the application of the normal distribution. A minimum sample size of 30 is required to meet this requirement.

Normality: The sample should be approximately normally distributed. When the sample size is greater than or equal to 30, the central limit theorem ensures normality. For sample sizes of less than 30, the data should be examined for normality. If the distribution is skewed or has outliers, nonparametric tests should be considered.

Independence: The observations in the sample should be independent of one another. This means that the response from one observation does not depend on the response from another observation.

Equal Variance: The variance of the population should be approximately equal to the variance of the sample. If the variances are unequal, a modified t-test should be used instead of the traditional t-test.

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Answer:

350

Step-by-step explanation:

629= A+S

A-71 = S

629 = A+A-71

700=2A

A=350

Answer:

\({ \tt{ = \frac{7}{9} \div \frac{1 }{3} }} \\ = { \bf{ \frac{7}{9} \times \frac{3}{1} }} \\ = \frac{7}{3} \)

Answer:

\(A\) ≈ \(78.54cm^2\)

Step-by-step explanation:

Using the formulas

A=π r^2

d=2 r

Solving for A

A=1/4πd^2=1/4·π·10^2≈78.53982cm²

Mr Yang needs to be aware of his legal position before opening his new company, given his history as a director and auditor. He should seek professional advice to ensure that he complies with all the legal requirements and regulations and avoids any potential legal consequences.

It is important for Mr Yang to understand his legal position before opening a new company, given his history as a director of previously wound-up companies and as an auditor of his wife's company. Mr Yang should take into account the Companies Act 2016, which outlines the legal responsibilities and obligations of company directors, as well as the potential consequences of breaching these obligations.
Under the Companies Act 2016, a director has a fiduciary duty to act in the best interests of the company and its shareholders. They are required to exercise due care, skill, and diligence in carrying out their duties, and to avoid conflicts of interest. If a director breaches these obligations, they can be held personally liable for any losses suffered by the company.Given that Mr Yang's previous companies were wound up, it is possible that he may have breached his legal obligations as a director. If this is the case, he could face legal action or be disqualified from acting as a director in the future. Furthermore, as an auditor of his wife's company, Mr Yang should ensure that he is fulfilling his legal responsibilities and carrying out his duties impartially and professionally.In terms of setting up a new company, Mr Yang should ensure that he complies with all the legal requirements and regulations governing the incorporation of a limited by shares company. This includes registering the company with the Companies Commission of Malaysia (SSM), obtaining the necessary licenses and permits, and adhering to the requirements of the Companies Act 2016.

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To find the surface area of the figure, we need to consider the individual surfaces and add them together.

First, let's identify the surfaces of the figure:

The lateral surface area of the larger prism (excluding the base)

The two bases of the larger prism

The lateral surface area of the smaller prism (excluding the base)

The two bases of the smaller prism

The lateral surface area of a prism is given by the formula: perimeter of the base multiplied by the height.

The bases of the prisms are rectangles, so their areas can be calculated by multiplying the length by the width.

To find the missing prism's surface area, we need to consider that it is a smaller prism nested inside the larger prism. The lateral surface area and bases of the missing prism should also be included.

Once we have calculated the individual surface areas, we add them together to find the total surface area of the figure.

Without specific measurements or dimensions of the figure, it is not possible to provide a numerical answer. Please provide the necessary measurements or dimensions to calculate the surface area.

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P(Y₁ < 3, Y₂ > 6) is 0.0108 by integrating the given joint density function. P(Y₁ + Y₂ = 7) is 0.4472by integrating the same joint density function over the appropriate region.

To find P(Y₁ < 3, Y₂ > 6), we need to integrate the joint density function over the region defined by Y₁ < 3 and Y₂ > 6

P(Y₁ < 3, Y₂ > 6) = ∫∫\(e^{-(Y_1 Y_2)}\) dY₁ dY₂, where the limits of integration are Y₁ from 0 to 3 and Y₂ from 6 to infinity.

Using the formula for the integral of exponential functions, we have:

P(Y₁ < 3, Y₂ > 6) =\(\int\limits^6_\infty\)\(\int\limits^0_3\) \(e^{-(Y_1 Y_2)}\)  dY₁ dY₂

=\(\int\limits^6_\infty\) [-1/Y₂ \(e^{-(Y_1 Y_2)}\) ] from 0 to 3 dY₂

=\(\int\limits^6_\infty\) [(-1/3Y₂) + (1/Y₂\(e^{3Y_2}\))] dY₂

= [(-1/3) ln(Y₂) - (1/9)\(e^{3Y_2}\)] from 6 to infinity

= (1/3) ln(6) + (1/9)e¹⁸

≈ 0.0108

Therefore, P(Y₁ < 3, Y₂ > 6) ≈ 0.0108.

To find P(Y₁ + Y₂ = 7), we need to first determine the range of values for Y₂ that satisfy the equation. If we set Y₂ = 7 - Y₁, then Y₁ + Y₂ = 7, so we have:

P(Y₁ + Y₂ = 7) = P(Y₂ = 7 - Y₁)

We can then integrate the joint density function over the region defined by this range of values for Y₁ and Y₂:

P(Y₁ + Y₂ = 7) = ∫∫\(e^{-(Y_1 Y_2)}\) dY₁ dY₂, where the limits of integration are Y₁ from 0 to 7 and Y₂ from 7 - Y₁ to infinity.

Using the substitution Y₂ = 7 - Y₁ and the formula for the integral of , we have

P(Y₁ + Y₂ = 7) = \(\int\limits^0_7\) \(\int\limits^{ \infty} _{7-Y_1\) \(e^{-(Y_1(7- Y_1)}\)) dY₂ dY₁

= \(\int\limits^0_7\) \(e^{7Y_1}\)/49 - 1/7 dY₁

= (7/6)(e⁷/49 - 1)

≈ 0.4472

Therefore, P(Y₁ + Y₂ = 7) ≈ 0.4472.

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--The given question is incomplete, the complete question is given below " Let Y₁ and Y₂ have the joint density function

f(y₁,y₂) = {e^-(Y₁ Y₂)   Y₁ > 0, Y₂> 0

             {0,  elsewhere_

What is P(Y₁ < 3, Y₂>  6)? (Round your answer to four decimal places:) (b) What is P(Y₁+ Y₂= 7)? (Round your answer to four decimal places:)"--

Answer: Sweets needs to sell to cover its fixed and variable costs.

Let x be the number of dozens of milk fritters that Royal Sweets needs to sell to break even.

Revenue from selling x dozens of milk fritters = price per dozen x number of dozens sold = $3.50x

Total cost = fixed cost + variable cost

Total cost = $15,000 + ($2.00 x)

At break-even point, revenue = total cost, so:

$3.50x = $15,000 + ($2.00 x)

$1.50x = $15,000

x = 10,000/1.5

x = 6,666.67

Therefore, Royal Sweets needs to sell approximately 6,667 dozens of milk fritters to break even.

Answer:

x = -4 + √15 and x = -4 - √15.

Step-by-step explanation:

To solve for x in the equation (x + 4)^2 = 15 using square roots, we can take the square root of both sides of the equation, remembering to include both the positive and negative square root:

(x + 4)^2 = 15

Taking the square root of both sides:

±(x + 4) = √15

Now we can isolate x by subtracting 4 from both sides of the equation:

x + 4 = ±√15

x = -4 ±√15

Therefore, the solutions to the equation (x + 4)^2 = 15 are x = -4 + √15 and x = -4 - √15.

Answer:

I exactly don't have or know the answer

The absolute value of the test statistic when testing the claim that the proportion of women who voted for the proposition is greater than the proportion of men who voted for the proposition is approximately 1.86.

To test the claim that the proportion of women who voted for the proposition is greater than the proportion of men who voted for the proposition, we can use the two-sample z-test for proportions.

Let p1 be the proportion of women who voted for the proposition and p2 be the proportion of men who voted for the proposition.

The test statistic is calculated as:

z = (p1 - p2) / sqrt((p1(1 - p1) / n1) + (p2(1 - p2) / n2))

In this case, p1 = 20/50 = 0.4 (proportion of women who voted for the proposition), p2 = 11/54 ≈ 0.204 (proportion of men who voted for the proposition), n1 = 50 (sample size of women), and n2 = 54 (sample size of men).

Substituting these values into the formula, we have:

z = (0.4 - 0.204) / sqrt((0.4(1 - 0.4) / 50) + (0.204(1 - 0.204) / 54))

Calculating this expression, we find that the absolute value of the test statistic is approximately 1.86 (rounded to the nearest hundredth).

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Answer:

ITS C

Step-by-step explanation:

MULTIPLIED BY THE NUMBER TO THE LEFT LOL