1. The following table presents shear strengths (in kN/mm) and weld diameters (in mm) for a sample of spot welds.

1. Construct a scatterplot of strength (y) versus diameter (x). Verify that a linear model is appropriate.
2. Compute the correlation coefficient.
3. Compute the least-squares line for predicting strength from diameter.
4. Compute the fitted value and the residual for each point.
5. If the diameter is increased by 0.3 mm, by how much would you predict the strength to increase or decrease?
6. Predict the strength for a diameter of 5.5 mm.

How do you solve this?

A thin-wall pressure vessel is shown below. Internal diameter=d, wall thickness=t.

In addition to the internal pressure p (p=100 psi), a torque T is applied. Assume d=20 inch (r=10 in), t=0.1 inch, T=502,640 in-lb. Determine the wall stress components. Assume that the longitudinal direction is labeled as x and the circumferential (hoop) direction is label as y.

Use Mohr's circle to determine the principle strains and maximum shear strain. Assume that E=10,000 ksi and Poisson's ratio v=0.3 and plane stress case.

Find epsilon x, y, and z. Find gamma xy

A block has mass M=2kg and is initially at rest, then slides a distance L = 1.25m down a theta = 30degrees frictionless incline plane until it is momentarily brought to rest by a spring. The spring is compressed a distance X= 3cm .

a) Write down expressions for the initial and final energy of the system

b) Find an expression for the spring constant K in terms of L, X, theta and M and calculate K

c)The experiment is repeated but the spring is removed. This time the block slides a distance L = 1.4m to the bottom of the frictionless incline and at the bottom of the incline the block slides an additional distance d along a horizontal surface with coefficient of kinetic friction = 0.3, before coming to rest. Use Work and energy to find d.

A machine is designed to fill containers with 16 ounces of coffee. A consumer suspects that the machine is not filling the containers completely and the amount of coffee is less than 16 ounces when filled. A sample of 8 containers has a mean of 15.6 ounces of coffee and a standard deviation of 0.3 ounces of coffee.  Assume that the distribution of data is normal. At 10% significance level, is there enough evidence to support the consumer’s suspicion that the machine is not filling the containers completely and the amount of coffee in a container is less than 16 ounces when filled?

Question: Which of the following is the correct calculator command to use?

2-SampTTest

2-SampTInt

ANOVA

Z-Test

2-SampZTest

T-Interval

Z-Interval

2-SampZint

T-Test

A battery pack used in a medical device needs to be recharged about every 5 hours. A random sample of 20 battery packs is selected and subjected to a life test. The average life of these batteries is 5.05 hours with standard deviation ? = 0.3 hours. Assume that battery life is normally distributed. Is there evidence to support the claim that mean battery life is more than 5 hours? Use ? = 0.01.

a. Write the appropriate hypothesis.

b. Use P-value approach to test the hypothesis.

c. Use t-test to test the hypothesis.

d. Use confidence interval to test the hypothesis.

e. What is your conclusion?

f. If the true mean life is 5.1 hours, what is the type II error?

Assume firm A wants to borrow float while firm B wants to borrow fixed. Firm A is offered 10% fixed borrowing cost and LIBOR + 0.3% float borrowing cost while firm B is offered 11.2% fixed borrowing cost and LIBOR + 1% float borrowing cost.

1. Show how the two firms can reduce their borrowing costs equally by entering into an interest rate plain vanilla swap? Use a table to demonstrate your solution
2. If the agreed-upon notional amount is $100m (no need to know the swap tenor), how much each party annually pays the other in absolute amounts? (assume that the LIBOR = 5%). Show your answer in a table similar to that in (a) solution

Assume firm A wants to borrow float while firm B wants to borrow fixed. Firm A is offered 10% fixed borrowing cost and LIBOR + 0.3% float borrowing cost while firm B is offered 11.2% fixed borrowing cost and LIBOR + 1% float borrowing cost.

(a) Show how the two firms can reduce their borrowing costs equally by entering into an interest rate plain vanilla swap? Use a table to demonstrate your solution

(b) If the agreed-upon notional amount is $100m (no need to know the swap tenor), how much each party annually pays the other in absolute amounts? (assume that the LIBOR = 5%).

Show your answer in a table

Oil from a specific type of marine microalgae can be converted into biodiesel that may serve as an alternate transportable fuel for automobiles and trucks. If lined ponds are used to grow the algae, the construction cost is $13 million and the M&O cost is estimated at $1.8 million per year. Alternatively, if long plastic tubes are used for growing the algae, the initial cost will be higher at $25 million, but less contamination will render the M&O cost lower at $0.3 million per year. At an interest rate of 15% per year and a 5-year project period, which system is better—ponds or tubes? Use a present worth analysis. The present worth of lined ponds is $ and that of plastic tubes is $ . are used to grow algae.

The accompanying data table show the percentage of tax returns filed electronically in a city from 2000 to 2009. Complete parts a through e below.

Year   Percentage
2000   25
2001   33
2002   37
2003   38
2004   48
2005   50
2006   55
2007   59
2008   62
2009   64

a) Forecast the percentage of tax returns that will be electronically filed for 2010 using exponential smoothing with alpha= 0.1.

​b) Calculate the MAD for the forecast in part a.

c) Forecast the percentage of tax returns that will be electronically filed for 2010 using exponential smoothing with trend adjustment. Set alpha= 0.3 and beta= 0.4.

​d) Calculate the MAD for the forecast in part c.

A 6 meter tall concrete column 40 cm square is supporting a 4 MN compressive load. The concrete has an elastic modulus of 30 GPa, compressive strength of 28 MPa, tensile strength of 3.5 MPa and Poisson’s Ratio 0.3. The concrete is reinforced by 16 #8 W40 axial rebar (200 GPa elastic modulus, 275 MPa compressive strength), spaced 8 cm apart on each side, 8 cm from the surface of the column.

What is the compressive stress on the column?

What is the axial modulus of the reinforced concrete column?

What is the axial deflection (change in length) of the column?

What is the transverse change in dimension (change in width)?

Will this column fail? Why?