Suppose that the production function is given by Y=K^(1/2)L^(1/2)

a. Derive the steady state levels of capital per worker and output per worker in terms of the saving rate, s, and the depreciation rate, δ.

b. Suppose δ = 0.05 and s = 0.2. Find out the steady state output per worker.

c. Suppose δ = 0.05 but s increases to 0.5. Find out the steady state output per worker and compare your result with your answer in part b. Explain the intuition behind your results.

1) After taking an aliquot of your cells and diluting them with Trypan Blue in a 1:1 dilution, you load the cell/Trypan mixture onto a hemocytometer to count the cells.

You obtain the following counts:

What is the average number of Trypan-diluted cells per quadrant?

2) Now, take into consideration the Trypan Blue dilution. What is the more concentrated number of cells per quadrant?

3) What is the volume in each quadrant of a hemocytometer?

4) What is the cell density (concentration) of the cells (cells/mL)?

5) If your original cell culture (the one you took an aliquot from to count) has 13 mL of cell suspension, what is the total number of cells you have in culture?

) Use functions and arrays to complete the following programs. Requirements: • You should use the divide-and-conquer strategy and write multiple functions. • You should always use arrays for the data sequences. • You should always use const int to define the sizes of your arrays. a. Write a C++ program. The program first asks the user to enter 4 numbers to form Sequence 1. Then the program asks the user to enter 8 numbers to form Sequence 2. Finally, the program shall tell which sequence has a larger average. For example, if the user enters 3 4 5 6 for Sequence 1, and 0 1 2 3 4 5 6 7 for Sequence 2. Your program should know the average of Sequence 1 is 4.5, and the average of Sequence 2 is 3.5. Therefore, your program should conclude that Sequence 1 has a larger average.

Suppose your firm is considering investing in a project with the cash flows shown below. The required rate of return is 8%. What is the Net Present Value (NPV) of the project? Should the project be accepted or rejected based on the NPV criteria? Choose 1,2,3, or 4

1 - NPV = $19,916.62, accept the project since NPV > 0;

2 - NPV = $19,916.62, reject the project since NPV < initial cost of $96,000;

3 - NPV = $116,916.62, reject the project since NPV > initial cost of $96,000;

4 - NPV = $115,916.62, accept the project since NPV > 0.

Refering to the above question, what is the Internal Rate of Return (IRR)? Should the project be accepted or rejected based on the IRR criteria? Choose 1,2,3, or 4

1 - 15.82% , accept the project since IRR > the discount rate;

2 - 15.82%, reject the project since IRR > the discount rate;

3 - 7.91%, accept the project since IRR < the discount rate;

4 - 7.91%, reject the project since IRR < the discount rate.

Refering to the above question, assume the maximum allowable Discounted Payback (DPB) period is 4 years. What is the discount payback period? Should the project be accepted or rejected based on the DPB criteria? Choose 1,2,3, or 4

1 - 4.13 years, reject the project since DPB > 4 years

2 - 4.13 years, accept the project since DPB > 4 years

3 - 4.87 years, reject the project since DPB > 4 years

4 - 4.87 years, accept the project since DPB > 4 years

*****************PLEASE GIVE THE CODE IN RACKET PROGRAMMING ONLY AND MAKE SURE THE CODE RUNS ON WESCHEME IDE***************

Write a recursive Racket function "sum-diff" that takes two lists of integers that are the same length and evaluates to an integer. The resulting integer should be the sum of the absolute value of the differences between each pair of integers with the same index in the two lists. For example (sum-diff '(-1 -2 -3) '(1 2 3)) should evaluate to 12 because the absolute value of the differences between (-1 and 1), (-2 and 2) and (-3 and 3) are 2, 4, and 6, and 2+4+6=12. Note: (abs n) evaluates to the absolute value of n. Also, if the lists are empty the sum should be 0

Complete the following four hypotheses, using α = 0.05 for each.

a. Mean sales per week exceeds 41.5 per salesperson

b. Proportion receiving online training is less than 55%

c. Mean calls made among those with no training is less than 145

d. Mean time per call is greater than 15 minutes

1. Using the same data set from part A, perform the hypothesis test for each speculation in order to see if there is evidence to support the manager's belief. Use the Seven Elements of a Test of Hypothesis from Section 7.1 of your text book, as well as the p-value calculation from Section 7.3, and explain your conclusion in simple terms.

2. Compute 99% confidence intervals for each of the variables described in a.-d., and interpret these intervals.

3. Write a report about the results, distilling down the results in a way that would be understandable to someone who does not know statistics. Clear explanations and interpretations are critical.

- Summary Report (about one paragraph on each of the speculations a.- d.)

- Appendix with the calculations of the Seven Elements of a Test of Hypothesis, the p-values, and the confidence intervals. Include the Excel formulas used in the calculations.

For planning purposes, senior executives at a large national clothing maker and retailer need to understand and forecast quarterly sales revenue. The available data are contained in the table attached below. The data is in units of hundreds of millions of dollars ($100M).

You have been tasked with describing the historical data and with developing preliminary forecasts for 2018 based on the historical data from the first quarter of 2011 (quarter 1) through the last quarter of 2017 (quarter 28).

a. Perform a linear time series regression (“Trend Analysis” in Minitab or “Trendline” in Excel) of the historical data using excel or minitab

b.   State the equation of the fitted regression line.

c. On the basis of this regression analysis, calculate and state the sales revenue forecasts for all four quarters of 2018.

d. Calculate and state the RMSE of this simple linear regression. [Hint: Different from forecasting, for regression RMSE = ?SSE/?(n-2).]

e. Calculate and state the forecast values for all four quarters of 2018 by the following time series decompositions. Perform the time series decompositions in Minitab. (Go to Stat > Time Series > Decomposition; for all decompositions, set the seasonal length)

e1.   Additive with seasonal only.

e2.   Additive with trend plus seasonal.

e3.   Multiplicative with seasonal only.

e4.   Multiplicative with trend plus seasonal.

e5.   On the basis of the Minitab time series decomposition plots, do you recommend forecasting with the trend component alone (as you were asked to do in part d above), the seasonal component alone (parts e(1) and e(3), or with both the trend and seasonal components together (parts e(2) and e(4). Briefly state why.

f. Calculate and state the accuracy of each of the forecasting methods in part e using the RMSE as the measure. (Note: MSE is stated on the Minitab graphs as “MSD.” RMSE is the square root of this value.)

f1. Which is the most accurate method of the decomposition methods used in part e? Briefly state why.

   f2. What are the most accurate forecasts? Briefly state why

Use the Spearman's rank correlation coefficient at the 0.05 CI to investigate the relation between two variables X and Y below.

A study was performed to test whether cars get better fuel consumption on premium petrol than on regular petrol. Each of ten 6-cylinder cars was first filled with either regular or premium, decided by a coin toss, and the fuel consumption for that tank was recorded. The consumption was recorded again for the same cars using the other kind of petrol. A lower fuel consumption figure in litres/100km is better fuel consumption

A second test was conducted using ten 4-cylinder cars and the difference between Regular and Premium fuel consumption for 4 cylinder cars is included in the table below.

Part 1. Consider the information given about the experimental design, and test if fuel consumption in litres/100km is better (ie lower) using premium instead of regular for 6cyl cars?

Define the parameter(s) involved (1 mark)

Parameter is the proportion of 6 cylinder cars/fuel consumption

State the Null and Alternate hypotheses

Ho:

What assumption(s) is/are required to perform this test? (You can assume any required assumptions have been met) (1 mark)

Consider the two charts below. Using the appropriate chart for your test, what is i) the range of the p-value, ii) your decision regarding H₀, and iii) your conclusion about fuel consumption?

Calculate and Interpret a 95% Confidence Interval for the population parameter. The relevant critical value is 2.262

write a python program that include a function named activity_selection() and take in two arguments, first one would be the number of tasks and the second argument would be a list of activities. Each activity would have an activity number, start time and finish time.

Example activity_selection input and output:

activity_selection (11, [[1, 1, 4 ], [2, 3, 5], [3, 0, 6], [4, 5, 7], [5, 3, 9], [6, 5, 9],[7, 6, 10], [ 8, 8, 11], [ 9, 8, 12], [10, 2, 14], [11, 12, 16] ]

In the above example the first activity set contains 11 activities with activity 1 starting at time 1 and finishing at time 4, activity 2 starting at time 3 and finishing at time 5, etc. The activities are not in any sorted order. Your results including the number of activities selected and their order should be outputted to the terminal. For the above example the results are: Number of activities selected = 4 Activities: 2 4 9 11

Note: There can be multiple optimal solutions.

please comments the program.