An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 4.0 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 15 engines and the mean pressure was 4.3 pounds/square inch with a standard deviation of 0.7. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Water at a local bulk temperature of 24°C flows at 0.8 m/s through a smooth, 1.5-cm-ID tube that is kept at 30°C and the flow is fully developed.

a) The system is extremely clean and quiet; therefore, the flow stays laminar regardless of the magnitude of ReD, until a noisy air compressor is turned on in the laboratory. Then the flow suddenly goes turbulent. Calculate the ratio of turbulent to laminar heat transfer coefficients. Use the Gnielinski correlation for turbulent flow.

b) Air at 227°C flows across the pipe at 20 m/s. Find the pipe wall temperature assuming the water flow to be turbulent, h from part a). You may assume a thin-walled pipe. This calculation is performed at the local point where the bulk temperature is 24°C.

18. Consider the following closed economy:

C = 60 +0.8(Y-T)

I = 150-1000i

G = 250

T = 200

Ms/P = 100

Md/P = 40+0.1Y-1000i

a. Derive the IS and LM functions.

b. Find the equilibrium interest rate and the equilibrium level of income.

c. Suppose we change this model such that investment is assumed to be completely interest inelastic: that is, investment does not depend on the rate of interest or we have I=150. Write the new equations for the IS and LM schedules and illustrate them graphically. What is the new equilibrium value of income?

d. How would an increase in money stock affect equilibrium values of Y and i under (c) above? Illustrate and explain your answer.

Current average gasoline prices in the U.S. are about $2.26/gallon. A year ago, they were about $2.69/gallon. This represents a price decrease over the last year of about 17%. If the own price elasticity of gasoline is -0.2%, by what percentage would you expect the quantity demanded to change over this period?

In studying the insurance preferences of homeowners the following conclusions are made: A homeowner is three times as likely to purchase additional jewelry coverage as additional electronics coverage The purchase of one of these coverages is independent of the purchase of the other The probability a homeowner purchases both coverages is 0.2 Find the probability that a homeowner purchases exactly one coverage.

In a sample of 200 individuals, the frequency of the BB genotype is 0.4, the Bb genotype is 0.4, and the bb genotype is 0.2. Perform a Chi-square test to test whether this population is in Hardy-Weinberg equilibrium. For full credit, be sure to include the null hypothesis, Chi-square number, degrees of freedom, p-value, and conclusion.

Consider the following second-order ODE,

y"+1/4y=0

with y(0) = 1 and y'(0)=0.

Transform this unique equation into a system of two 1st-order ODEs.

Solve the obtained system for t in [0,0.6] with h = 0.2 by MATLAB using Euler Method or Improved Euler Method.

An 85 kg man is climbing a 30 kg ladder that is placed against a building at an angle of 15 degrees. The Coefficient of friction is between the ladder is and the ground is 0.2.

A) Find the force of friction.

B) What is the maximum height the man can climb before the ladder starts to slip?

Thorough solution is much appreciated!