Questions
Starting with a spring index of C = 10, design a compression coil spring of 302...
Starting with a spring index of C = 10, design a compression coil spring of 302 stainless wire with squared ends. The spring is to deflect y = 50 mm, for an applied force of F = 90 N and to close solid when ys = 60 mm. At closure, use a design factor of 1.2 guarding against yielding. Select the smallest diameter wire where wire diameters are available in 0.2-mm increments between 0.2 to 3.2 mm. For the design, specify the wire diameter, the inside and outside diameters of the coil, the spring rate, the total number of coils, the free length of the spring, the final factor of safety, and stability conditions.
In: Mechanical Engineering
Assume a market portfolio consisting of two securities, i = 1,2. Further, assume that the weight...
Assume a market portfolio consisting of two securities, i = 1,2. Further, assume that the weight of security 1 in the market portfolio is W1 = 0.5 and that the covariance matrix is given below.
a) Compute the variance of the market portfolio, ?M2 when the standard deviations for i = 1,2 are 5 and 8 percent respectively .
| R1 | R2 | |
| R1 | 0.2 | 0.1 |
| R2 | 0.1 | 0.2 |
b) Compute the CAPM-betas of security 1 and security 2, i.e. 1 and 2. [4]
c) Assume that E[rM] = 0.05 (i.e., 5%) and rf = 0.01 (i.e., 1%). Compute the expected return of both securities and their Sharpe ratios.
In: Finance
A biotech company produces a therapeutic drug whose concentration has a standard deviation of 0.2 g/l(gram...
A biotech company produces a therapeutic drug whose concentration has a standard deviation of 0.2 g/l(gram per liter). A new method of producing this drug has been proposed, although some additional cost is involved. Management will authorize a change in production technique only if the standard deviation of the concentration in the new process is less than 0.2 g/l. With the data of sample size n = 10 in the table below, conduct a hypothesis testing analysis to determine whether this new process can be implemented.
16.628 16.622 16.627 16.623 16.618 16.630 16.631 16.624 16.622 16.626 (unit: g/l)
In: Statistics and Probability
Question 1. Consider the following time series data. Week 1 2 3 4 5 6 Value...
Question 1. Consider the following time series data.
|
Week |
1 |
2 |
3 |
4 |
5 |
6 |
|
Value |
118 |
113 |
116 |
111 |
117 |
114 |
-
Construct a time series plot. What type of pattern exists in the data?
-
Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7.
-
Use a =0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7.
Compare the three-week moving average forecast with the exponential smoothing forecast using =0.2. Which appears to provide the better forecast based on MSE? explain.
In: Operations Management
1. The weights in ounces of a sample of rats in a lab are given below....
1. The weights in ounces of a sample of rats in a lab are given below.
4, 4, 2, 5, 5, 3, 4, 7, 9, 5
a. Construct a frequency distribution using five classes.
b. Construct a histogram for the above distribution.
c. Find the Mean
d. Find the Median & Mode
e. Find the sample variance and standard deviation (5 points)
2. The probability that a part will malfunction is 0, 1, 2, 3, or 4 or more times in a decade is 0.4, 0.2, 0.2, 0.1 and 0.1 respectively.
a. Construct a probability distribution.
b. Find the mean.
c. Find the variance and standard deviation.
d. Graph ()
In: Statistics and Probability
beta numbers (1.1 for Apple and 0.8 for Microsoft), would you give me the "fake" return...
beta numbers (1.1 for Apple and 0.8 for Microsoft), would you give me the "fake" return values for these stocks. And using those return values, would you please calculate the "fake" Portfolio Return.
| Amt Invested | Portfolio Weights | Expected Portfolio Return | Total Portfolio Value | Portfolio Beta | |
| Microsoft | $333,000.00 | 0.33 | 1.60% | 0.8 | |
| Apple | $670,000.00 | 0.67 | 1.90% | 1.1 | |
| Both | $1,000,000.00 |
| Yearly Stock Return | |||
| Year | Market | Microsoft | Apple |
| 1 | 14.93% | -0.34% | 3.86% |
| 2 | 2.06% | -0.37% | 2.09% |
| 3 | 15.84% | 0.40% | 2.87% |
| 4 | 32.21% | 2.81% | 0.38% |
| 5 | 13.53% | 1.91% | 3.05% |
| 6 | 1.34% | 1.75% | -0.45% |
| 7 | 11.80% | 1.37% | 1.24% |
| 8 | 21.69% | 2.72% | 3.41% |
| 9 | -4.45% | 1.41% | -0.33% |
| 10 | 31.29% | 4.06% | 5.89% |
In: Finance
In the Keynesian cross model, assume that the consumption function is given by C=120+0.8(Y-T)
solve the following:
a. In the Keynesian cross model, assume that the consumption function is given by
C=120+0.8(Y-T).
Planned investment is 200; government purchases and taxes are both 400. Y, C, I G&T are all in billions.
i Graph planned expenditure as a function of income.
ii. What is equilibrium income?
iii. If government purchases increase to 420, what is the new equilibrium income? What is the multiplier for government purchases?
iv. What level of government purchases is needed to achieve an income of 2,400? (Taxes remain at 400.)
v. What level of taxes is needed to achieve an income of 2,400? (Government purchases remain at 400.)
vi. If you were the economic adviser to the president and the government's goal is to stimulate the economy by increasing GDP by $2,400 billion, which one
will you recommend to achieved this GDP target? Government spending or tax cut? Why?
In: Economics
A stationary bicycle wheel of radius 0.8 m is mounted in the vertical plane (see figure below)
A stationary bicycle wheel of radius 0.8 m is mounted in the vertical plane (see figure below). The axle is held up by supports that are not shown, and the wheel is free to rotate on the nearly frictionless axle. The wheel has mass 4.2 kg, all concentrated in the rim (the spokes have negligible mass). A lump of clay with mass 0.5 kg falls and sticks to the outer edge of the wheel at the location shown. Just before the impact the clay has speed 7 m/s, and the wheel is rotating clockwise with angular speed 0.27 rad/s. (Assume +x is to the right, +y is upward, and +z is out of the page. Assume the line connecting the center to the point of impact is at an angle of 45° from the horizontal.)
(a) Just before the impact, what is the angular momentum (magnitude
and direction) of the combined system of wheel plus clay about the
center C?
(b) Just after the impact, what is the angular momentum (magnitude
and direction) of the combined system of wheel plus clay about the
center C?
(c) Just after the impact, what is the angular velocity (magnitude
and direction) of the wheel?
(d) Qualitatively, what happens to the linear momentum of the
combined system? Why?
| Some of the linear momentum is changed into energy. |
| There is no change because linear momentum is always conserved. |
| Some of the linear momentum is changed into angular momentum. |
| The downward linear momentum decreases because the axle exerts an upward force. |
In: Physics
Consider the closed-economy market-clearing model. Assume that the marginal propensity to consume is 0.8. The economy's...
Consider the closed-economy market-clearing model. Assume that the marginal propensity to consume is 0.8. The economy's output increases by $10 billion, tax revenue decreases by $6 billion, and the government budget deficit increases by $2 billion.
(a) Calculate the dollar change in government spending. (b) Calculate the dollar change in public saving. (c) Calculate the dollar change in private saving. (d) Calculate the dollar change in national saving. (e) Would the equilibrium real interest rate increase, decrease, or stay the same?
In: Economics
A biologist estimates that the chance of germination for a type of bean seed is 0.8. A student was given 10 seeds.
A biologist estimates that the chance of germination for a type of bean seed is 0.8. A student was given 10 seeds. Let Xbe the number of seeds germinated from 10 seeds.
a) Assuming that the germination of seeds is independent, explain why the distribution of Xis binomial.
b) What are the values of nand p?
c) What is the mean and standard deviation of the number of seeds that germinate?
d) What is the probability that all seeds germinate?
e) What is the probability that only one seed does not germinate?
f) What is the probability that at most four seeds germinate?
g) Suppose that a group of students plant 200 seeds. What is the mean and standard deviation of the number that germinate?
h) What is the probability that at least 150 of the seeds germinate?
In: Statistics and Probability