A buck converter is operated from the rectified 230 V ac mains,
such that the converter de input voltage
IS
V8 = 325 v ± 20%
A control circuit automatically adjusts the converter duty cycleD,
to maintain a constant de output voltage
of V = 240 V de. The de load current I can vary over a 10: 1
range:
lOA::;J:s;lA
The MOSFET has an on-resistance ofO.S Q. The diode conduction loss
can be modeled by a 0.7 V
source in series with a 0.2 Q resistor. All other losses can be
neglected.
(a) Derive an equivalent circuit that models the converter input
and output ports, as well as the loss
elements described above.
(b) Given the range of variation of V8 and I described above, over
what range will the duty cycle
vary?
(c) At what operating point (i.e., at what value of V8 and I) is
the converter power loss the largest?
What is the value of the efficiency at this operating point?
In: Electrical Engineering
Examine the following book-value balance sheet for University Products Inc. The preferred stock currently sells for $15 per share and pays a dividend of $3 a share. The common stock sells for $20 per share and has a beta of 0.7. There are 2 million common shares outstanding. The market risk premium is 12%, the risk-free rate is 8%, and the firm’s tax rate is 21%. BOOK-VALUE BALANCE SHEET (Figures in $ millions) Assets Liabilities and Net Worth Cash and short-term securities $ 1.0 Bonds, coupon = 6%, paid annually (maturity = 10 years, current yield to maturity = 8%) $ 15.0 Accounts receivable 4.0 Preferred stock (par value $20 per share) 3.0 Inventories 8.0 Common stock (par value $0.10) 0.2 Plant and equipment 24.0 Additional paid-in stockholders’ equity 10.8 Retained earnings 8.0 Total $ 37.0 Total $ 37.0 a. What is the market debt-to-value ratio of the firm? b. What is University’s WACC?
In: Finance
1
The number of goals in a World Cup soccer match has a Poisson distribution with a mean of 3. For a soccer player in World Cup, the probability of having an age over 30 is 0.2.
a. What is the probability of having 0 goal in a World Cup soccer match? (3 pts) What is the probability of having more than 1 goal in a World Cup soccer match?
b. What is the probability that 0 out of the 11 players in a World Cup soccer team are older than 30 ?
c. The probability that a soccer team wins a World Cup match is 0.7 if none of its players are older than 30. The probability that a soccer team wins a World Cup match is 0.4 if some players are older than 30. The probability that “no players are older than 30 in a World Cup soccer team” is your result from question b. A soccer team just won the latest World Cup match. Given this information, what is the probability that NO players in the team have an age over 30?
In: Statistics and Probability
Teenager Mike wants to borrow the car. He can ask either parent for permission to take the car. If he asks his mom, there is a 20% chance she will say ”yes,” a 30% chance she will say ”no,” and a 50% chance she will say, ”ask your father.” Similarly, that chances of hearing ”yes”/”no”/”ask your mother” from his dad are 0.1, 0.2, and 0.7 respectively. Imagine Mike’s efforts can be modeled as a Markov chain with state (1) talk to Mom, (2) talk to Dad, (3) get the car (”yes”), (4) strike out (”no”). Assume that once either parent has said ”yes” or ”no,” Mike’s begging is done.
1. Construct the one-step transition matrix for this Markov chain.
2. Identify the absorbing state(s) of the chain.
3. Determine the mean times to absorption.
4. Determine the probability that Mike will eventually get the car if (1) he asks Mom fist and (2) he asks Dad first. Whom should he ask first?
In: Statistics and Probability
The following table gives the approximate values of the coefficient of static friction μ, for various materials
Option/ Materials/ μ
1 /Metal on metal/ 0.2
2 /Wood on wood /0.35
3/ Metal on wood /0.4
4/ Rubber on concrete/ 0.7
To start moving a weight W, on a horizontal surface, you must
push with a force F, where F=μW.
Write an m-file that achieves the following:
1. Uses fprintf to print out the option and material information to
the command window
2. Prompt the user to input a value of W and the type of
materials/option
Check if the input values are valid (e.g. negative weights or
non-integer/incorrect option numbers). Your
program should continue prompting the user to enter values until
they are valid.
3. Use a switch statement to compute the force required. Use
fprintf to print a statement including the materials
used and the force required.
Hint: You may want to use a while loop to ensure that the user
enters valid inputs.
In: Computer Science
In an article in the Journal of Marketing, Bayus
studied the differences between "early replacement buyers” and
"late replacement buyers” in making consumer durable good
replacement purchases. Early replacement buyers are consumers who
replace a product during the early part of its lifetime, while late
replacement buyers make replacement purchases late in the product’s
lifetime. In particular, Bayus studied automobile replacement
purchases. Consumers who traded in cars with ages of zero to three
years and mileages of no more than 35,000 miles were classified as
early replacement buyers. Consumers who traded in cars with ages of
seven or more years and mileages of more than 73,000 miles were
classified as late replacement buyers. Bayus compared the two
groups of buyers with respect to demographic variables such as
income, education, age, and so forth. He also compared the two
groups with respect to the amount of search activity in the
replacement purchase process. Variables compared included the
number of dealers visited, the time spent gathering information,
and the time spent visiting dealers.
(a) Suppose that a random sample of 807 early replacement buyers yields a mean number of dealers visited of x⎯⎯x¯ = 3.3, and assume that σ equals .79. Calculate a 99 percent confidence interval for the population mean number of dealers visited by early replacement buyers. (Round your answers to 3 decimal places.)
The 99 percent confidence interval is
[
, ].
(b) Suppose that a random sample of 493 late
replacement buyers yields a mean number of dealers visited of x⎯⎯x¯
= 4.2, and assume that σ equals .66. Calculate a 99
percent confidence interval for the population mean number of
dealers visited by late replacement buyers. (Round your
answers to 3 decimal places.)
The 99 percent confidence interval is
[
, ].
(c) Use the confidence intervals you computed
in parts a and b to compare the mean number of
dealers visited by early replacement buyers with the mean number of
dealers visited by late replacement buyers. How do the means
compare?
Mean number of dealers visited by late replacement buyers appears to be ( lower or higher?)
In: Advanced Math
1: State how many significant figures there are in each of the following calculations, and indicate which is the limiting value:
Part (a) (18.7)2:
1- 1 (limited by 2)
2-4 (limited by 18.7
3- 2 (limited by 18.7
4- 3 (limited by 18.7)
5- None of these.
Part (b) (1.60 × 10-19)(3712) :
1- 2 (limited by 3712)
2- 2 (limited by 1.60)
3- 4 (limited by 3712)
4- 3 (limited by 1.60)
5- None of these.
2: A student witnesses a flash of lightning and then t = 2.5 s later the student hears the associated clap of thunder.
Part (a) Sound travels at 343 m/s in the air. What distance from the student is the lightning strike, in meters?
Part (b) Light travels at 3.0 × 108 m/s in the air. How long, t1, in seconds did it take the light to reach the student's eyes after the lightning strike?
3: On a two-leg trip, a car travels the first leg, a distance D1 = 49 miles, in a time t1 = 1.1 hours, and travels the second leg, a distance D2 = 140 miles, in time t2 = 2.25 hours. Refer to the figure.
Part (d) What is the average speed for the whole trip in meters per second?
4: A student begins at rest and then walks north at a speed of v1 = 0.55 m/s. The student then turns south and walks at a speed of v2 = 0.92 m/s. Take north to be the positive direction. Refer to the figure.
Part (a) What is the student's overall average velocity vavg, in meters per second, for the trip assuming the student spent equal times at speeds v1 and v2?
Part (b) If the student travels in the stated directions for 30.0 seconds at speed v1 and for 20.0 seconds at speed v2, what is the net displacement, in meters, during the trip?
Part (c) If it takes the student 5.0 s to reach the speed v1 from rest, what is the magnitude of the student’s average acceleration, in meters per second squared, during that time?
In: Physics
1. Convert the following code shown below to C++ code:
| public class HighwayBillboard { |
| public int maxRevenue(int[] billboard, int[] revenue, int distance, int milesRes) { |
| int[] MR = new int[distance + 1]; |
| //Next billboard which can be used will start from index 0 in billboard[] |
| int nextBillBoard = 0; |
| //example if milesRes = 5 miles then any 2 bill boards has to be more than |
| //5 miles away so actually we can put at 6th mile so we can add one mile milesRes |
| milesRes = milesRes + 1; // actual minimum distance can be between 2 billboards |
| MR[0] = 0; |
| for (int i = 1; i <= distance; i++) { |
| //check if all the billboards are not already placed |
| if(nextBillBoard < billboard.length){ |
| //check if we have billboard for that particular mile |
| //if not then copy the optimal solution from i-1th mile |
| if (billboard[nextBillBoard] != i) { |
| //we do not have billboard for this particular mile |
| MR[i] = MR[i - 1]; |
| } else { |
| //we do have billboard for this particular mile |
| //now we have 2 options, either place the billboard or ignore it |
| //we will choose the optimal solution |
| if(i>=milesRes){ |
| MR[i] = Math.max(MR[i - milesRes] + revenue[nextBillBoard], MR[i - 1]); |
| }else{ |
| //there are no billboard placed prior to ith mile |
| //we will just place the billboard |
| MR[i] = revenue[nextBillBoard]; |
| } |
| nextBillBoard++; |
| } |
| }else{ |
| //All the billboards are already placed |
| //for rest of the distance copy the previous optimal solution |
| MR[i] = MR[i - 1]; |
| } |
| } |
| //System.out.println(Arrays.toString(MR)); |
| return MR[distance]; |
| } |
| public static void main(String[] args) { |
| int[] x = {6, 7, 12, 13, 14}; |
| int[] revenue = {5, 6, 5, 3, 1}; |
| int distance = 20; |
| int milesRestriction = 5; |
| HighwayBillboard h = new HighwayBillboard(); |
| int result = h.maxRevenue(x, revenue, distance, milesRestriction); |
| System.out.println("Maximum revenue can be generated :" + result); |
| } |
| } |
In: Computer Science
1 (a) Assume that the lights in your kitchen use 300 watts. How much energy and how much does it cost to leave the lights on 24 hours a day for a week if electricity is 8 cents/kilowatt hour?
(b) For a month (assume 30 days/month)?
(c) For a year?
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2 (a) How much energy and how much money do you use to run your window air conditioner rated at 1500 watts continuously for the month of July (assume 8¢/kWh)?
(b) If you assume that coal was used to produce the electricity for your air conditioner, how much coal was burned to produce the electricity used?
(c) How much CO2 was produced by the electricity used to run your air conditioner?
-----------------------------------------------------------------------------------------------------------------------
3 (a) An average incandescent light bulb has a life expectancy of 1,000 hours. How much energy would a typical 60 watt bulb use in a lifetime, assuming it lasts for 1,000 hours?
(b) At 8¢/kWh, how much would it cost over its lifetime?
-----------------------------------------------------------------------------------------------------------------------
4 (a) A compact fluorescent bulb uses 15 watts and has a life expectancy of 10,000 hours. How much energy and how much would it cost to use a compact fluorescent for 10,000 hours?
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5 (a) If your car gets 20 miles per gallon (MPG), and you drive an average of 10,000 miles each year, how many gallons of gas do you use a year?
(b) At $3.00 per gallon, how much will you spend on gasoline for the year?
(c) If the combustion of each gallon of gasoline produces 22 lbs of CO2, how much CO2 does your car produce each year?
(d) If you traded your car in & bought one that got 25 MPG, how much gasoline would you save in one year?
(e) How much money would you save?
(f) How much less CO2 would be emitted into the atmosphere from your improved car?
In: Physics
As part of a study designed to compare hybrid and similarly equipped conventional vehicles, Consumer Reports tested a variety of classes of hybrid and all-gas model cars and sport utility vehicles (SUVs). The following data show the miles-per-gallon rating Consumer Reports obtained for two hybrid small cars, two hybrid midsize cars, two hybrid small SUVs, and two hybrid midsize SUVs; also shown are the miles per gallon obtained for eight similarly equipped conventional models.
| Make/Model | Class | Type | MPG |
|---|---|---|---|
| Honda Civic | Small Car | Hybrid | 37 |
| Honda Civic | Small Car | Conventional | 28 |
| Toyota Prius | Small Car | Hybrid | 44 |
| Toyota Corolla | Small Car | Conventional | 32 |
| Chevrolet Malibu | Midsize Car | Hybrid | 27 |
| Chevrolet Malibu | Midsize Car | Conventional | 23 |
| Nissan Altima | Midsize Car | Hybrid | 32 |
| Nissan Altima | Midsize Car | Conventional | 25 |
| Ford Escape | Small SUV | Hybrid | 27 |
| Ford Escape | Small SUV | Conventional | 21 |
| Saturn Vue | Small SUV | Hybrid | 28 |
| Saturn Vue | Small SUV | Conventional | 22 |
| Lexus RX | Midsize SUV | Hybrid | 23 |
| Lexus RX | Midsize SUV | Conventional | 19 |
| Toyota Highlander | Midsize SUV | Hybrid | 24 |
| Toyota Highlander | Midsize SUV | Conventional | 18 |
At the α = 0.05 level of significance, test for significant effects due to class, type, and interaction.
Find the value of the test statistic for class. (Round your answer to two decimal places.)
Find the p-value for class. (Round your answer to three decimal places.)
p-value =
Find the value of the test statistic for type. (Round your answer to two decimal places.)
Find the p-value for type. (Round your answer to three decimal places.)
p-value =
Find the value of the test statistic for interaction between class and type. (Round your answer to two decimal places.)
Find the p-value for interaction between class and type. (Round your answer to three decimal places.)
p-value =
In: Statistics and Probability