Solve the given differential equation by undetermined coefficients. y'' − y' + (1/4) y = 6 + e^(x/2)

What are the four emergent properties of water? Give an example of how each supports life.

1.

2.

3.

4.

Can anyone solve this?

You are given the following information:
• The 1-year interest rate is 4.5% (with continuous compounding).
• The 2-year swap rate is 5.11% (with simple compounding).
• A 3-year, 7% coupon bond is priced at $104.30.
• A 4-year, 3% coupon bond is priced at $90.80.
Assume that all swaps and bonds have annual payment frequency. Bond prices are given as $ and ¢ per $100 par (not in “32nds” as customary in US bond markets).
(a)What are the spot rates (with continuous compounding) for 2, 3, and 4 years’ maturity? What are the implied discount factors?
(b) What are the implied forward rates (continuous compounding) for “1-into- 2”, “2-into-3”, and “3-into-4” years? What do these forward rates tell us about market participants’ expectations about future spot rates?
Consider a 4-year swap, in which one party will pay fixed annual interest at a rate of 6%, whilst receiving floating interest (also annually), both on a principal of $1 million.
(c) Given the rates you have calculated in parts a) and b) above, what (to the nearest $1) is the “fair” value of the swap (to the payer of fixed)? (Hint: don’t forget to convert the forward rates from part b) into simple compounding!)
(d) For the swap considered in part c), what is the “swap rate”? Confirm your result by re-valuing the swap, using the swap rate for the “fixed leg”. Why is the swap rate higher / lower than that of the 2-year swap?

Suppose that the prices of zero-coupon bonds with various maturities are given in the following table. The face value of each bond is $1,000.

a. Calculate the forward rate of interest for each year. (Round your answers to 2 decimal places.)

b. How could you construct a 1-year forward loan beginning in year 3? (Round your Rate of synthetic loan answer to 1 decimal place.)

c. How could you construct a 1-year forward loan beginning in year 4?

Question 2: Use the following information to complete Exercises 3 – 5: A political scientist took a pool of the political attitudes of the students in one of his classes. Students were asked to rate, on a scale from 1 to 11, “What is your overall political attitude?”, where 1 = extremely liberal and 11 = extremely conservative. The following frequency analysis resulted: (1.5 points)

4. Compute the values that define the following percentiles:

a. 25^th             b. 50^th             c. 57^th             d. 75^th    

What is the interquartile range of the data in #4?

6. Compute the exact percentile ranks that correspond to the following scores:

a. 3            b. 5            c. 7            d. 9

Two independent methods of forecasting based on judgment and experience have been prepared each month for the past 10 months.

The forecasts and actual sales are as follows:

Month Sales Forecast 1 Forecast 2

1 771 774 772

2 790 789 791

3 794 792 792

4 776 776 775

5 772 773 772

6 770 771 772

7 761 761 765

8 774 778 778

9 792 792 794

10 794 798 797

a. Compute a tracking signal for the 10th month for each forecast using the cumulative error for months 1 to 10. Use action limits of ± 4. Is there bias present? (Do not round your intermediate calculations. Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

Forecast Tracking Signal Bias Method 1 Method 2

b. Compute 2s control limits for each forecast. (Do not round your intermediate calculations. Round your answers to 2 decimal places.)

Forecast Control Limits Method 1 Method 2

Please open “LIFE” data. The data is related to results of a survey that asks people to grade themselves in terms of Conscientiousness and Life satisfaction. Conscientiousness grading scale is from 1 to 10 whereas Life satisfaction criteria was graded from 1 to 80. And each person, surveyed grade himself by own for both criteria. Gender information is included in data as well. The objective of survey is whether life satisfaction can be explained with conscientiousness and gender. So, the dependent variable is defined as life satisfaction and the independent variables are gender and conscientiousness. Please do the following steps:

1) Test if conscientiousness has no significant effect on life satisfaction at alpha=0.05 significance level.

2) Give a complete interpretation of the slope coefficient of conscientiousness.

3) Find Adjusted R^2 and give a complete interpretation.

4) Create a plot that shows how residuals vary by predicted values (ZRESID vs ZPREDIC)

  LIFE DATA

15-11 Equity Method for Stock Investment

On January 4, Year 1, Ferguson Company purchased 72,000 shares of Silva Company directly from one of the founders for a price of $48 per share. Silva has 200,000 shares outstanding, including the Daniels shares. On July 2, Year 1, Silva paid $194,000 in total dividends to its shareholders. On December 31, Year 1, Silva reported a net income of $647,000 for the year. Ferguson uses the equity method in accounting for its investment in Silva.

a. Provide the Ferguson Company journal entries for the transactions involving its investment in Silva Company during Year 1.

b. Determine the December 31, Year 1, balance of Investment in Silva Company Stock.

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In Regression Analysis, you are given the following information:

Y = 21.33 + 9.67x

SSE = 573 SSR = 4498

1. Predict the value of y if X = 4    . (2 decimal places)

2. Calculate the coefficient of determination  . (2 decimal places)

3. Is the following statement true or false?

The coefficient of determination is the proportion of the variation in y that is not explained by the variation in x.   

4. Based upon the Coefficient of Determination, if this regression equation represented data for a safety issue, what would you recommend be done to improve the equation results?

5. y = 21.33 + 9.67x - 10.02w

Predict the value of y if x = 3 and w = -2      (2 decimal places)

Please do not ignore part 3 and 4.

Thanks