An unstable nucleus of mass 1.7 ✕ 10−26 kg, initially at rest at the origin of a coordinate system, disintegrates into three particles. One particle, having a mass of m1 = 1.0 ✕ 10−27 kg, moves in the positive y-direction with speed v1 = 5.8 ✕ 106 m/s. Another particle, of mass m2 = 9.0 ✕ 10−27 kg, moves in the positive x-direction with speed v2 = 3.8 ✕ 106 m/s. Find the magnitude and direction of the velocity of the third particle. (Assume that the +x-axis is to the right and the +y-axis is up along the page.) magnitude m/s direction ° counterclockwise from the +x-axis

“Minister of labour, Thulas Nxesi, has gazetted South Africa’s new minimum wage which will take effect from 1 March 2020. The gazette states that the new national minimum wage is R20.76 – an increase of 3.8%”. Adapted from:

https://businesstech.co.za/news/government/374920/6-planned-laws-that-government-hasjust-announced-for-south-africa/ Accessed: 21/02/2020

Provide a discussion on the welfare effect of the above, that illustrates the case for when the above results in unemployment in the market for domestic workers as well as a case for when the above has no effect on the market for domestic workers. Use a diagram to support your discussion.

The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.8 years and a standard deviation of 0.6 years. He then randomly selects records on 16 laptops sold in the past.

What is the distribution of ¯xx¯? ¯xx¯ ~ N( )

What is the probability that one randomly selected laptop is replaced less than 3.7 years?

For 16 laptops, find the probability that the average replacement time is less than 3.7 year.

For part d), is the assumption of normal necessary? No or Yes

Problem 4-51 (LO. 6, 7)

Julio sold his corporation to a competitor, Exeter LLC, for $100,000,000. Julio incorporated his business 17 years ago by investing $500,000 plus his proprietary know-how. There have been no other corporate shareholders.

Compute Julio's after-tax cash flow from the sale, assuming he is in the 35% tax bracket (20% long-term capital gain rate) and has no other property sales during the year. Assume the 3.8 percent Net Investment Income Tax applies.

Julio's after-tax cash flow from the sale is $.

You are considering the risk-return of two mutual funds for investment. The relatively risky fund promises an expected return of 14.7% with a standard of 15.6%. The relatively less risky fund promises an expected return and standard deviation of 6.4% and 3.8%, respectively. Assume that the returns are approximately normally distributed. Using normal probability calculations and complete sentences, give your assessment of the likelihood of getting, on one hand, a negative return and on the other, a return above 10% with these funds. You may choose to use excel normal distribution formulas, but if you do, give the explicit formulas. Offer some remarks about your possible investment approach.

A data set is given below. ​(a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. ​(b) Given that x̅ = 3.6667, sx = 2.0656​, ŷ = 4.2000​, sy = 1.4805, and r = −0.9287​, determine the​ least-squares regression line. ​(c) Graph the​ least-squares regression line on the scatter diagram drawn in part​ (a).

x   y
1   5.2
2   5.8
3   5.4
4   3.8
6   2.4
6   2.6

​(a) Choose the correct graph below.

Graph B

There appears to be a linear, negative relationship.

​(b)

ŷ =__?__x+(__?__)

​(Round to three decimal places as​ needed.)

The following data represent the calories and​ sugar, in​ grams, of various breakfast cereals.

Use the data above to complete parts​ (a) through​ (d).

Compute the covariance.

b. Compute the coefficient of correlation.

c. Which do you think is more valuable in expressing the relationship between calories and

sugarlong dash—the

covariance or the coefficient of correlation? Explain.

d. What conclusions can you reach about the relationship between calories and sugar?

Write the equation (formula) for a residual and then calculate its value “by hand” for the observation in the data set whose distance between the fire and nearest fire station (in miles) is 3.0; show your work. Based on this value, was the observation overestimated (below average) or underestimated (above average) by the regression? Explain. See page 191 in the course text.

(a) Starting from today, every month you save $200 into a bank account which earns interest at annual rate of 3.8%.

How much money do you have in the account at the end of 8 years?

(b) What is the modified duration of an 6% bond with 11 years to maturity that is trading at a yield of 6%?

Assume that coupon is paid semi-annually.

(c) Suppose that the 6-month US Treasury bill rate is equal to 5.98%, and the forward rate on a 6-month Treasury bill 6 months from now is 7.88%. (Both are in yearly terms).

What is the 1-year bill rate?