Is there any relationship between returns to scale and economies of scale? Assume a production function q = 100(K^0.7*L^0.3), where K is capital and L is labor. Derive the marginal product of labor and the marginal product of capital. Show that the marginal product of labor is decreasing (hint: beginning with K = 2, and L = 50)

Below are percentages for annual sales growth and net sales attributed to loyalty card usage at 74 Noodles & Company restaurants.

(b) Find the correlation coefficient. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.)
  
r            ___________

(c-1) To test the correlation coefficient for significance at α = 0.05, fill in the following. (Use the rounded value of the correlation coefficient from part b in all calculations. For final answers, round t_calc to 3 decimal places and the p-value to 4 decimal places. Negative values should be indicated by a minus sign.)
  

Can the italicized portion of the problem be explained? I understand up until the 0.015 moles of protonated acetic acid remained and I understand the HH portion of the problem after but I would like some clarity on how this number was concluded.

2. The following question has two parts.
a) What is the final pH of a solution obtained by mixing 250 ml of 0.3 M acetic acid with 300 ml

of 0.2 M KOH? (pKb of acetate = 9.24). (Show your work!)

Moles of acetic acid = 0.25 l X 0.3 M = 0.075 moles
Adding 0.3 l X 0.2 M = 0.06 moles of OH- to this solution will convert 0.06 moles of acetic

acid to 0.06 moles of acetate, 0.015 moles of protonated acetic acid will remain. pKa = 14 - pKb = 14 - 9.24 = 4.76

pH = pKa + log [CH3CO2-][CH3CO2H]

= 4.76 + log 0.06 moles / 0.55 l 0.015 moles / 0.55 l

= 4.76 + log 0.06 moles0.015 moles

= 5.36

pH = 5.36

1. I need to fuel my car every week. Based on my observation, the price of gas really follows a Markov Chain. The price can be 3.2 dollars, 3.3 dollars or 3.4 dollars for one gallon. If the price for this week is 3.2 dollars, the price of next week will be 3.2, 3.3 and 3.4 with the probability of 0.4, 0.4 and 0.2 respectively. If the price for this week is 3.3 dollars, the price of next week will be 3.2, 3.3 and 3.4 with the probability for 0.2, 0.5 and 0.3 respectively. If the price for this week is 3.4 dollars, the price of next week will be 3.2, 3.3 and 3.4 with probability 0.3, 0.3 and 0.4 respectively.
   1. Please give out the transition matrix.
   2. For one year, how much should I pay for the gas for my car? (Assume 52 weeks/year and I use 10 gallons every week).
   3. If the price of this week is 3.2 dollars, what is the probability that I will observe 3.3 dollars price after 2 weeks?

If the price of this week is 3.2 dollars, I will observe 3.3 dollars price for the first time after how many weeks in average?

While fuel taxes and fuel economy standards can both be effective in increasing the number of miles per gallon in new vehicles, clearly explain why fuel taxes are superior means of reducing emissions from automobiles.

Discuss one reason why a cap and trade market is more difficult to implement for water versus air emissions

Discuss one reason why economists prefer a gas tax to a standard on miles per gallon of vehicles

Calculate the conjugate base to acid ratio in Solution D (10 mL of 0.2 M acetic acid and 1 mL of 0.1 M sodium hydroxide, and 9 mL distilled water). Then calculate the theoretical pH.

Initial pH: 3.47

Molarity of HCl: 0.0992        about 0.3 mL added               pH after HCl addition: 3.09

Molarity of added NaOH: 0.0997M         about 0.2 mL added           pH after NaOH addition: 3.54

Intro

We know the following expected returns for stocks A and B, given different states of the economy:

The expected return on the market portfolio is 0.09 and the risk-free rate is 0.02.

Attempt 3/10 for 8 pts.

Part 1

What is the standard deviation of returns for stock A?

Use the data set named Store_Visits located in the folder Data Files for HW Assignment (outside of Minitab folder) in the K-drive. The response variable y is the number of visits of a customer to a particular food store in a large suburban area within the period of a month, and the independent variable x is the distance (in miles) of the customer’s home to the store.

Fit a simple linear regression model to the data, and answer the following questions.

a) Give the proportion of the variation in the number of visits per month of a customer explained by the distance of the customer’s home to the store.

b) Submit the residual plot. ^ It appears from the plot that there is a problem with one of the model assumptions. Which one is it, and what would you suggest to remedy the problem?

2. c) Carry out your suggestion to fix the problem of part (b) and submit a new residual plot. Does your suggested remedy work? ^

3. d) Based on your new model, what is the proportion of the variation in the number of visits per month of a customer explained by the distance of the customer’s home to the store? How does it compare to that of the original model?

4. e) Based on your new model, construct a 95% prediction interval for y, the number of visits to the store for a customer who lives 2.5 miles from the store. Interpret the P.I.

K-Drive data. -Minitab

y   x
12   0.8
5   1.2
6   2.3
8   1.5
3   3.2
2   6.3
1   7.9
2   5.3
6   1.5
3   1.9
10   1.7
5   2.6
3   2.9
6   4.2
2   3.9
4   3.1
3   5.8
6   1.7
7   2.2
2   4.5
1   6.1
1   5.8
1   7.4
3   6.4
2   4.7
2   3.9
3   4
4   4.6

Use the data set named Store_Visits located in the folder Data Files for HW Assignment (outside of Minitab folder) in the K-drive. The response variable y is the number of visits of a customer to a particular food store in a large suburban area within the period of a month, and the independent variable x is the distance (in miles) of the customer’s home to the store.

Fit a simple linear regression model to the data, and answer the following questions.

a) Give the proportion of the variation in the number of visits per month of a customer explained by the distance of the customer’s home to the store.

b) Submit the residual plot. ^ It appears from the plot that there is a problem with one of the model assumptions. Which one is it, and what would you suggest to remedy the problem?

2. c) Carry out your suggestion to fix the problem of part (b) and submit a new residual plot. Does your suggested remedy work? ^

3. d) Based on your new model, what is the proportion of the variation in the number of visits per month of a customer explained by the distance of the customer’s home to the store? How does it compare to that of the original model?

4. e) Based on your new model, construct a 95% prediction interval for y, the number of visits to the store for a customer who lives 2.5 miles from the store. Interpret the P.I.

K-Drive data. -Minitab

y   x
12   0.8
5   1.2
6   2.3
8   1.5
3   3.2
2   6.3
1   7.9
2   5.3
6   1.5
3   1.9
10   1.7
5   2.6
3   2.9
6   4.2
2   3.9
4   3.1
3   5.8
6   1.7
7   2.2
2   4.5
1   6.1
1   5.8
1   7.4
3   6.4
2   4.7
2   3.9
3   4
4   4.6