Use the Euler method to solve the following differential equation for the domain [2,2.5]. Use the step-size ℎ = 0.1. ?′=?ln?/? ;?(2)=?¹
b) Use the third order Taylor series method to find ?(0.1) and ?(0.2),
where ?′=1+2?? ;?(0)=0. Use the step-size ℎ=0.1.
c) Solve the problem in part (ii) using the fourth order Runge – Kutta method.
d) Solve the problem in part (ii) using the Predictor – Corrector method.

130 kg of uniform spherical particles with a diameter of 60 mm and particle density 1500 kg/m³ are fludised by water (density 1000 kg/m³, viscosity 0.001 Pa s) in a circular bed of cross-sectional area 0.2 m². The single particle terminal velocity of the particles is 0.98 mm/s and the voidage at incipient fludisation is known to be 0.47. Determine:

a. The minimum fludised velocity            

b. height when the liquid flow rate is 2x10^-5 m³/s.  

A counterflow, concentric tube heat exchanger is used to cool the lubricating oil for a large industrial gas turbine engine. The flow rate of cooling water through the inner tube (Di = 25 mm) is 0.2 kg/s, while the flow rate of oil through the outer annulus (Do = 45 mm) is 0.1 kg/s. The oil and water enter at temperatures of 100 and 30 C, respectively. How long must the tube be made if the outlet temperature of the oil is to be 60 C?

4. A uniformly charged dielectric solid sphere of radius a = 8 cm carries a total charge Q = 5 μC. Let the potential be zero an infinite distance away.

5. a) [26.6] What is the potential at the surface of the sphere?

6. b) [26.9] Sketch the graph of the potential due to the sphere from r = 0 to r = 20 cm.

7. c) [26.3] What work must be done to bring a 0.2 μC point charge from infinity to a point 16 cm from the center of the sphere?

B. Using the table below, create the balance sheet of MaineBank assuming the following information (in millions $$): Reserves = $360, Loans = $1,240, Deposits = $1,800, Debt = $150, Securities = $400, Capital (owner’s equity) = $50. What is the reserve-deposit ratio assuming all reserves are required reserves? What is the leverage ratio? Show your work/calculations. (10 points)

MaineBank Balance Sheet

Reserve deposit ratio =

Leverage ratio =

C.        The monetary base of Moneyland is $700 million. The current-deposit ratio (cr) is 0.2 and reserve-deposit ratio (rr) is 0.2. Calculate the money multiplier and money supply. Show your work. (5 points each)

            Money Multiplier =

            Money Supply =   

D.        The Federal Reserve's tools to control the money supply include: open-market operations, the reserve-deposit ratio, the discount rate, and interest payments on reserves. How should each instrument be changed if the Fed wishes to increase the money supply? An example is provided. (6 points)

This is a Matlab Exercise problem. Please create the Matlab code and figure for the following problem using problem specifications:

Plot x vs y when y=sin(x), y=cos(x), y=sin (2*x), and y=2*sin(x) when x = 1:0.1:10. Use 2 by 2 subplot, sin(x) is in location 1, cos(x) is in location 2, sin(2*x) is in location 3 and 2*sin(x) is in location 4.

The plot should have:

(1) x label = ‘x value’, y label = ‘y value’, legend ‘y=sin(x)’,’ y=cos(x)’,’ y=sin (2*x)’, ‘y= y=2*sin(x)’ and title = ‘x Vs. y’ under Font Name of Times New Roman, and Font Size of 14 pt. for all subplot location.

(2) For sine(x) use red solid line, for cos(x) use blue dashed line, for sin(2*x) use green dash-dot line, and for 2*sin(x) use solid line and RGB [0.5 0.2 0.2]

(3) Create minor grid for all subplot location.

Please attach editor code and the figure in your answer. Thank You!

A 2010 Pew Research poll asked 1,306 Americans "From what you've read and heard, is there solid evidence that the average temperature on earth has been getting warmer over the past few decades, or not?". The table below shows the distribution of responses by party and ideology, where the counts have been replaced with relative frequencies.

b) What is the probability that a randomly chosen respondent believes the earth is warming or is a liberal Democrat?  (please round to four decimal places)

c) What is the probability that a randomly chosen respondent believes the earth is warming given that he is a liberal Democrat?  (please round to four decimal places)

d) What is the probability that a randomly chosen respondent believes the earth is warming given that he is a conservative Republican?  (please round to four decimal places)

f) What is the probability that a randomly chosen respondent is a moderate/liberal Republican given that he does not believe that the earth is warming?  (please round to four decimal places)

A Fair Isaac Corporation (FICO) score is used by credit agencies such as banks to determine whether to lend money and the interest rate to charge. Its value ranges from 300 to 850 and if you have a score over 700, you are considered to be a "quality" credit risk. The mean credit score of average income earners in California is estimated by Fair Isaac to be 664. A recent survey of 47 high income earners in California had a mean FICO score of 677 and a standard deviation of s=60. Use a 0.05 significance level to test the claim that the mean FICO score of high income earners in California is equal to 664, the mean score of average income earners in California.

The test statistic is?: ["3.24", "2.88", "1.87", "2.27", "1.49"]           

Identify the range of the p-value: ["0.01 < P-value < 0.02", "0.1 < P-value < 0.2", "0.2 < P-value", "0.02 < P-value < 0.05", "P-value < 0.01", "0.05 < P-value < 0.1"]           

Based on this we?: ["Reject the null hypothesis", "Fail to reject the null hypothesis"]           

Conclusion: There ["does not", "does"] appear to be enough evidence to support the claim that the mean FICO score of high income earners in California is equal to 664, the mean score of average income earners in California.

**NOTE the values inside " " are possible answer choices

Problem 16-01 (Algorithmic)

The management of Brinkley Corporation is interested in using simulation to estimate the profit per unit for a new product. The selling price for the product will be $45 per unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated as follows:

1. Compute profit per unit for the base-case, worst-case, and best-case.
   
   Profit per unit for the base-case: $  
   
   Profit per unit for the worst-case: $  
   
   Profit per unit for the best-case: $  
   
2. Construct a simulation model to estimate the mean profit per unit. If required, round your answer to the nearest cent.
   
   Mean profit per unit = $  
   
3. Why is the simulation approach to risk analysis preferable to generating a variety of what-if scenarios?
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
   
4. Management believes the project may not be sustainable if the profit per unit is less than $4. Use simulation to estimate the probability the profit per unit will be less than $4. If required, round your answer to one decimal place.
   
   %

Suppose the inflation rate is expected to be 6.3% next year, 4.15% the following year, and 3.65% thereafter. Assume that the real risk-free rate, r*, will remain at 2.3% and that maturity risk premiums on Treasury securities rise from zero on very short-term bonds (those that mature in a few days) to 0.2% for 1-year securities. Furthermore, maturity risk premiums increase 0.2% for each year to maturity, up to a limit of 1.0% on 5-year or longer-term T-bonds.

a.

Calculate the interest rate on 1-year Treasury securities. Round your answer to two decimal places.

Calculate the interest rate on 2-year Treasury securities. Round your answer to two decimal places.

Calculate the interest rate on 3-year Treasury securities. Round your answer to two decimal places.

Calculate the interest rate on 4-year Treasury securities. Round your answer to two decimal places.

Calculate the interest rate on 5-year Treasury securities. Round your answer to two decimal places.

Calculate the interest rate on 10-year Treasury securities. Round your answer to two decimal places.

Calculate the interest rate on 20-year Treasury securities. Round your answer to two decimal places.