Consider the optimization problem of maximizing Cobb–Douglas production function: Q = 20 K1/2 L1/2, subject to cost constraint: K + 4L = 64. a/ Use the method of Lagrange multipliers to find the maximum value of the production function;
b/ Estimate the change in the optimal value of Q if the cost constraint is changed to K + 4L = 65, and state the new maximum value of the production function.

Answers

Answer 1

Answer:

Answer:

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Translate the English phrase into an algebraic expression: the sum of 17y² and 19.

Julio is planning activities for a trip that lasts from Thursday to Sunday. He is interested in visiting a museum, hiking the trails, attending the food festival, riding a jet ski, exploring a famous park, or going shopping. each activity takes a full day, and he will not do any activity twice. Julio wants to either visit a museum or explore the park on Thursday, and he is definitely attending the food festival on Saturday. How many different ways can he plan activities for his trip?A)24
B)30
C)40
D)120

Answers

Thursday: 2 choices {museum, park}

Friday: 4 choices {shopping, jet ski, hiking, and the choice not chosen for Thu}

Saturday: 1 choice {food}

Sunday: 3 choices {the remaining 3 after Friday's choice}

The total number of ways these choices can be arranged is 2×4×1×3 = 24

The apprpropriate selection is A) 24.

A grandmother is 12 times as old as her grandson, and the grandson is 55 years younger than his grandmother. How old is each now?

Answers

Answer:

5 & 60

Step-by-step explanation:

s * 12 = g

s + 55 = g

12s = s + 55

11s = 55

s = 5

10x² - 43x+28

How do you factor this

Answers

Keep your head up.

Trying to spread positivity

Sophia earned $240 at her brother's store. If she worked for 8 days and earned the same amount of money each day, how much did she earn per day?

Answers

Answer:

$30

Step-by-step explanation:

$240 divided by 8

She earns $30 each day

8x=240

Where 8 is the amount of days, 240 is the total pay, and x represents the pay per day.

8x=240
—- ——
8 8

In this step, you are dividing both sides by 8 to isolate the x

x=30

Therefore, she was paid $30 each day. You can check this by inserting back into your equation.

8(30)=240
240=240

Hope this helps!

(6)and-
The terms of an expression 4x² – 3xy are:
(a) 4x and -3xy (b) 4x² and 3xy
(c) 4x² and -xy
(d) x

Answers

Answer:

(b) 4x² and 3xy

Step-by-step explanation:

The terms of an expression 4x² – 3xy are:

The terms are the factors of the expression, which are 4x² and -3xy. The signal is not counted as a term. So the correct answer is given by option b.

In a climate survey, it was determined that in a random sample of 15 days, the average temperature in Kalamazoo at 2:00 PM in the months of July and August is 73.38 degrees with a standard deviation of 3.798 degrees. Using this information, a 95% confidence interval for the average is (71.28, 75.48). Which of the following is the appropriate interpretation of this interval?1)

We are certain that 95% of the days in the months of August and July will have a temperature at 2:00 PM between 71.28 and 75.48.
2)

We cannot determine the proper interpretation of this interval.
3)

We are 95% confident that the average daily temperature for the months of July and August at 2:00 PM for the days recorded is between 71.28 and 75.48.
4)

We are 95% confident that the proportion of all days' temperatures will fall between 71.28 and 75.48.
5)

We are 95% confident that the average daily temperature for the months of July and August at 2:00 PM is between 71.28 and 75.48.

Answers

Answer:

$73.38-1.76(3.798)/(√(15))=71.65$

$73.38+1.76(3.798)/(√(15))=75.11$

So on this case the 95% confidence interval would be given by (71.65;75.11)

The interval given for this case by the problem is:

(71.28, 75.48)

And the best conclusion is given by:

4) We are 95% confident that the average daily temperature for the months of July and August at 2:00 PM is between 71.28 and 75.48.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=73.78$ represent the sample mean

$\mu$ population mean (variable of interest)

$s=3.798$ represent the sample standard deviation

n=15 represent the sample size

95% confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_(\alpha/2)(s)/(√(n))$ (1)

The degrees of freedom are given:

$df= n-1 = 15-1=14$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabele to find the critical value. The excel command would be: "=-T.INV(0.05,14)".And we see that $t_(\alpha/2)=1.76$

Now we have everything in order to replace into formula (1):

$73.38-1.76(3.798)/(√(15))=71.65$

$73.38+1.76(3.798)/(√(15))=75.11$

So on this case the 95% confidence interval would be given by (71.65;75.11)

The interval given for this case by the problem is:

(71.28, 75.48)

And the best conclusion is given by:

4) We are 95% confident that the average daily temperature for the months of July and August at 2:00 PM is between 71.28 and 75.48.

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