We are performing a one-sample z-test about mean. The sample size is 64, the sample mean 56.7, the sample standard deviation is 30, and the testing mean is 60. What is the value of the test statistic?

Answer:

a. The number of units which will minimize average cost is approximately 5,130 units.

b. The firm should produce 12,500 items, x, for maximum profit.

c. The number of items, x, that will produce a maximum profit is 60 items.

Step-by-step explanation:

Note: This question is not complete as there are some signs are omitted there. The complete question is therefore provided before answering the question as follows:

1. If the total cost function for a product is C(x) = 200(0.02x + 6)^3 dollars, where x represents the number of hundreds of units produced, producing how many units will minimize average cost?

2. A firm can produce only 3900 units per month. The monthly total cost is given by C(x) = 500 + 200x dollars, where x is the number produced. If the total venue is given by R(x) = 450x-1/100x^2 dollars, how many items, x, should the firm produce for maximum profit?

3. If the profit function for a product is P(x) = 3600x + 60x2 - x3 - 72,000 dollars, selling how many items, x, will produce a maximum profit?

The explanation to the answer is now given as follows:

1. If the total cost function for a product is C(x) = 200(0.02x + 6)3 dollars, where x represents the number of hundreds of units produced, producing how many units will minimize average cost?

Given;

C(x) = 200(0.02x + 6)^3 ……………………………………….. (1)

We first simplify (0.02x + 6)^3 as follows:

(0.02x + 6)^3 = (0.02x + 6)(0.02x + 6)(0.02x + 6)

First, we have:

(0.02x + 6)(0.02x + 6) = 0.004x^2 + 0.12x + 0.12x + 36 = 0.004x^2 + 0.24x + 36

Second, we have:

(0.02x + 6)^3 = 0.004x^2 + 0.24x + 36(0.02x + 6)

(0.02x + 6)^3 = 0.00008x^3 + 0.048x^2 + 7.20x + 0.0024x^2 + 1.44x + 216

(0.02x + 6)^3 = 0.00008x^3 + 0.048x^2 + 0.0024x^2 + 7.20x + 1.44x + 216

(0.02x + 6)^3 = 0.00008x^3 + 0.0504x^2 + 8.64x + 216

Therefore, we have:

C(x) = 200(0.02x + 6)^3 = 200(0.00008x^3 + 0.0504x^2 + 8.64x + 216)

C(x) = 0.016x^3 + 10.08x^2 + 1,728x + 43,200

Therefore, the average cost (AC) can be calculated as follows:

AC(x) = C(x) / x = (0.016x^3 + 10.08x^2 + 1,728x + 43,200) / x

AC(x) = (0.016x^3 + 10.08x^2 + 1,728x + 43,200)x^(-1)

AC(x) = 0.016x^2 + 10.08x + 1,728 + 43,200x^(-1) …………………………. (2)

Taking the derivative of equation (2) with respect to x, equating to 0 and solve for x, we have:

0.032x + 10.08 - (43,300 / x^2) = 0

0.032x + 10.08 = 43,300 / x^2

X^2 * 0.32x = 43,300 – 10.08

0.32x^3 = 43,189.92

x^3 = 43,189.92 / 0.32

x^3 = 134,968.50

x = 134,968.50^(1/3)

x = 51.30

Since it is stated in the question that x represents the number of hundreds of units produced, we simply multiply by 100 as follows:

x = 51.30 * 100 = 5,130

Therefore, the number of units which will minimize average cost is approximately 5,130 units.

2. A firm can produce only 3900 units per month. The monthly total cost is given by C(x) = 500 + 200x dollars, where x is the number produced. If the total revenue is given by R(x) = 450x-1/100x^2 dollars, how many items, x, should the firm produce for maximum profit?

P(x) = R(x) - C(x) ……………. (3)

Where;

P(x) = Profit = ?

R(x) = 450x-1/100x^2

C(x) = 500 + 200x

Substituting the equations into equation (3), we have:

P(x) = 450x - 1/100x^2 - (500 + 200x)

P(x) = 450x - 0.01x^2 - 500 - 200x

P(x) = 450x - 200x - 0.01x^2 - 500

P(x) = 250x - 0.01x^2 – 500 …………………………………. (4)

Taking the derivative of equation (4) with respect to x, equating to 0 and solve for x, we have:

250 - 0.02x = 0

250 = 0.02x

x = 250 / 0.02

x = 12,500 items

Therefore, the firm should produce 12,500 items, x, for maximum profit.

3. If the profit function for a product is P(x) = 3600x + 60x2 – x^3 - 72,000 dollars, selling how many items, x, will produce a maximum profit?

Given;

P(x) = 3600x + 60x2 – x^3 - 72,000 …………………………. (5)

Taking the derivative of equation (5) with respect to x, equating to 0 and solve for x, we have:

3600 + 120x - 3x^2 = 0

Divide through by 3, we have:

1200 + 40x – x^2 = 0

1200 + 60x – 20x – x^2 = 0

60(20 + x) – x(20 + x) = 0

(60 – x)(20 + x) = 0

Therefore,

x = 60, or x = - 20

The negative value of x (i.e. x = - 20) will be will be ignored because it has no economic significance. Therefore, the number of items, x, that will produce a maximum profit is 60 items.

Answer:

3 cm on the map represents 31.5 km in reality.

3cm : 31.5 km

1cm :  31.5/3 km

1cm : 10.5km

So the scale on the map is 1cm represents 10.5 km.

Answer:

what is the question

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The product of z and w is (-20+10i).

An imaginary number is a real number multiplied by the imaginary unit i.

Given is a coordinate plane showing imaginary and real numbers.

Coordinates of w = (-5, 5i)

Coordinates of z = (3,i)

w*z = (-5, 5i)* (3,i)

= -15-5i+15i-5

= -20+10i

Hence, The product of z and w is (-20+10i).

For more references on imaginary numbers, click;

https://brainly.com/question/6748860

#SPJ5

Answer:

Dividing

Step-by-step explanation:

I think you meant dividing instead of diving

Answer:

34.28 percent of the items in the bag are DVDs

Step-by-step explanation:

Given that he had following items

DVDs 12

MArbles 12

Books 11

Total items are: 11+12+12 = 35

In order to find the percentage of DVDs we have to divide the quantity of DVDs by total and multiply by 100

So,

Percentage of DVDs is:

[tex]=\frac{12}{35} *100\\= 0.3428*100\\= 34.28\%[/tex]

Hence,

34.28 percent of the items in the bag are DVDs

Answer:

200- 25d

Step-by-step explanation:

d equals number of days on the trip

Answer:

64 miles per gallon

27 feet per second

14 quarts in a barrel

Step-by-step explanation:

Answer:

810 min

Step-by-step explanation:

5+6+7=18

18x45=810

Answer: 105

Step-by-step explanation:

Answer: Salary is a fixed amount of money or compensation paid to an employee by an employer in return for work performed. Salary is commonly paid in fixed intervals, for example, monthly payments of one-twelfth of the annual salary.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

Following are the solution to this question:

Step-by-step explanation:

Please find the complete question and its solution file in the attachment.

Answer:

D

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

To give the same amount of stamps to each student you would divide 67 by 8. Dividing would give each students 8 stamps because you can only equally divide it to 64 (EX, 64/8=8). This leaves you with 3 stamps leftover, because we only used 64 equally and 67-64=3.

Answer:

He can give each of his students 8 stamps.

With 3 stamps left over.

Step-by-step explanation:

Hope this helps!

Answer:

1.5 goes in between the 0 and the first line (meaning 1) and 0.5 goes in between the left of the zero and the line before the zero

Answer:

4

Step-by-step explanation

hookes law gives the equation F=kx where F is the elastic force and k is the constant and x or small e is extension if we draw a graph you'll see that the graph increases by the same ratio every single time hence giving a straight line show that they are F and x are propotional to a certain limit

Answer:

The answer you're looking for is 40

Step-by-step explanation:

Answer:

|-8|=8

|10|=10

Step-by-step explanation:

any negative number between the two slashes '||' equals to always a positive number

and a positive number between the two slashes '||' remains the same

Answer:

answer is 1-8(87)

Step-by-step explanation:

Answer:

Yes there is a proportinal relationship because when I did 19 divided by 2 I got 9.5 and when I do 76 divided by 8 I got 9.5 so its proportinal. Yes I can find how much money 6 pounds is its 57. And yes I can do it without a table because all you have to do is divide the 19 and 2 and the other 2 numbers and if there the same then its proportinal.

Step-by-step explanation:

BRAINLIEST MAYBE???

Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(1−2)

Equation Form:

x= 1

y=−2

Step-by-step explanation:

Answer:

hehdhrhth

Step-by-step explanation:

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Answer:

#2) 30% of 400 is 120 and 120/6 = 2 so it took him 2 hours

#3) 2.5/3.2 = .78 and 1/1.2 =.83 so buying the bigger one you are paying less

Answer:

1. 0.5454

2. 8

3. 0.6785

4. 1.1428

5. 6

6. 1.5

7. 1.75

8. 1.6666

Step-by-step explanation:

calculator :)

the answer is c i got it on edge 2020

Answer:

c

Step-by-step explanation:

Answer:

5:8

Step-by-step explanation:

Answer:

8 to 5

Step-by-step explanation: