Question Dennis contributed business assets to a new business in exchange for stock in the company. The exchange did not qualify as a tax-deferred exchange. The fair market value of these assets was $298,000 on the contribution date. Dennis’s original basis in the assets he contributed was $163,000, and the accumulated depreciation on the assets was $102,250. What is the business's basis in the assets it received from Dennis? What would be the business's basis if the transaction qualified as a tax-deferred exchange?

8. Get the data on eruption times and waiting times between eruptions of the Old Faithful geyser from the website. Estimate the mean waiting time and give a standard error for the estimate. Also, give a 90 percent confidence interval for the mean waiting time. Now estimate the median waiting time. In the next chapter we will see how to get the standard error for the median10. In 1975, an experiment was conducted to see if cloud seeding produced rainfall. 26 clouds were seeded with silver nitrate and 26 were not. The decision to seed or not was made at random. Get the data from http://lib.stat.cmu.edu/DASL/Stories/CloudSeeding.html Let ? be the difference in the mean precipitation from the two groups. Estimate ?. Estimate the standard error of the estimate and produce a 95 percent confidence interval.

The circuit below shows a filter commonly used as the output stage of a power supply. In this application, Vin(t) is switched between 0 and a DC input supply voltage (12V in this case). The filter smooths the switched input so that it is close some desired output from 0-12V. In this exercise, you are interested in determining the start-up behaviour of the system. To this end, do the following: a) Find the transfer function Vout(s) . You may assume that the capacitor and inductor are initially de- Vin(s) energised. b) Att = 0, Vin(t) is switched to 12 V (i.e. Vin(t) = 12u(t)). Find the time response Vout(t) = [-{Vout(s)}. Please use partial fraction expansion and the Laplace Transform table to conduct the inversion(s), showing all of your work and explaining your logic clearly to receive full credit. c) How long will it take for vout (t) to reach 6V? You may use computer tools here, but please clearly explain your logic for full credit. d) Sketch (by hand) the Bode plot for G(s) with the parameter values from part b. As a part of this, please carefully compute and label: i. All asymptotes (e.g. low-frequency & high frequency) All corner frequencies iii. The frequency and magnitude (in dB) of any resonances (if they exist) 50 x 10-3 H 000m 0.25 12 Vin(t) 0.2F 112 Vout(t) Figure 2: System for Question 3

The circuit below shows a filter commonly used as the output stage of a power supply. In this application, Vin(t) is switched between 0 and a DC input supply voltage (12V in this case). The filter smooths the switched input so that it is close some desired output from 0-12V. In this exercise, you are interested in determining the start-up behaviour of the system. To this end, do the following: a) Find the transfer function Your C). You may assume that the capacitor and inductor are initially de- Vin) energised. b) Att = 0, Vin(t) is switched to 12 V (i.e. Vin(t) = 12u(t) ). Find the time response Vout(t) = [-!{Vout($)}. Please use partial fraction expansion and the Laplace Transform table to conduct the inversion(s), showing all of your work and explaining your logic clearly to receive full credit. c) How long will it take for Vout(t) to reach 6V? You may use computer tools here, but please clearly explain your logic for full credit. d) Sketch (by hand) the Bode plot for G(s) with the parameter values from part b. As a part of this, please carefully compute and label: i. All asymptotes (e.g. low-frequency & high frequency) ii. All corner frequencies ii. The frequency and magnitude (in dB) of any resonances (if they exist) 50 x 10-3H 000 0.252 Vin(t) 0.2F 11 Vout(t) Figure 2: System for Question 3

the worst case. 4: Show that there are at most [n/2h+1] nodes of height h in an n-element heap

Receivables amount to P150,000. Receivable turnover is \( 10 \mathrm{x} \) and inventory is maintained at a level equal to 15 days' sales. Selling price per unit is P100 and has gross profit ratio of \( 40 \% \). A proposal has been made to change the term credit to \( \mathrm{n} / 60 \) to result to an increase in sales volume by one-third or by 5,000 units. Under this proposal, bad debts losses are estimated at \( 1 \% \) to \( 3 \% \) of sales but inventory turnover shall remain the same. How much is the increased accounts receivable? How much is the increased inventory? Compute for the increased operating income.

Vibrations Homework 1 1. (15 pts) A system consists of two cantilever beams (with an equivalent spring constant k1 and k2, respectively) and k1 two springs (k3 and k4) combined in the configuration shown. For k1-k2-k3 k4-100 N/m, calculate the equivalent spring constant of the system with respect to the xcoordinate. k3 k2 Ka 2. (15 pts) In the figure, for a Vibrations Homework 1 1. (15 pts) A system consists of two cantilever beams (with an equivalent spring constant k1 and k2, respectively) and k1 two springs (k3 and k4) combined in the configuration shown. For k1-k2-k3 k4-100 N/m, calculate the equivalent spring constant of the system with respect to the xcoordinate. k3 k2 Ka 2. (15 pts) In the figure, for a 10 cm, b 20 cm, m1- m2 10 Kg, and Jo 10 Kg-m2, calculate the equivalent mass with respect to the x coordinate.