2.5

7.In a survey of college​ students, each of the following was found. Of these​ students,

356356

owned a​ tablet,

294294

owned a​ laptop,

280280

owned a gaming​ system,

195195

owned a tablet and a​ laptop,

199199

owned a tablet and a gaming​ system,

137137

owned a laptop and a gaming​ system,

6868

owned a​ tablet, a​ laptop, and a gaming​ system, and

2626

owned none of these devices. Complete parts ​a) through ​e) below.

​a) How many college students were​ surveyed?

​(Simplify your​ answer.)

​b) Of the college students​ surveyed, how many owned a tablet and a gaming​ system, but not a​ laptop?

​(Simplify your​ answer.)

​c) Of the college students​ surveyed, how many owned a​ laptop, but neither a tablet nor a gaming​ system?

​(Simplify your​ answer.)

​d) Of the college students​ surveyed, how many owned exactly two of these​ devices?

​(Simplify your​ answer.)

​e) Of the college students​ surveyed, how many owned at least one of these​ devices?

​(Simplify your​ answer.)

4.

Thirty-five cities were researched to determine whether they had a professional sports​ team, a​ symphony, or a​ children's museum. Of these​ cities,

1919

had a professional sports​ team,

1717

had a​ symphony,

1414

had a​ children's museum,

1111

had a professional sports team and a​ symphony,

88

had a professional sports team and a​ children's museum,

66

had a symphony and a​ children's museum, and

44

had all three activities. Complete parts ​a) through ​e) below.

​a) How many of the cities surveyed had only a professional sports​ team?

​(Simplify your​ answer.)

​b) How many of the cities surveyed had a professional sports team and a​ symphony, but not a​ children's museum?

​(Simplify your​ answer.)

​c) How many of the cities surveyed had a professional sports team or a​ symphony

​(Simplify your​ answer.)

​d) How many of the cities surveyed had a professional sports team or a​ symphony, but not a​ children's museum?

​(Simplify your​ answer.)

​e) How many of the cities surveyed had exactly two of the​ activities?

​(Simplify your​ answer.)

3.2

7.

Construct the truth table for the compound statement q logical or left parenthesis p logical and tilde r right parenthesis .q ∨ (p ∧ ~r).

8.

Construct the truth table for the compound statement

left parenthesis p logical or tilde q right parenthesis logical or r(p ∨ ~q) ∨ r.

9.

Determine the symbolic form of the compound statement and construct a truth table for the symbolic expression. p ∨ (q ∨ r)

18.

Must the truth tables for

left parenthesis t logical and tilde s right parenthesis logical or tilde p(t ∧ ~s) ∨ ~p

and

left parenthesis s logical and tilde p right parenthesis logical or tilde t(s ∧ ~p) ∨ ~t

have the same number of trues in their answer​ columns?

Choose the correct answer below.

A.

​Yes, because the two expressions have exactly the same form and each term can be T or F regardless of which letter is being used or whether it is negated or not.

B.

​Yes, because the second expression contains the same three variables as the first expression.

C.

​No, the truth table for the first expression has 5 trues and the truth table for the second expression only has 3 trues.

D.

​No, because there is no relationship between the first expression and the second expression.

E.

​Yes, because half the answers for each expression will be true and half will be false.

Use Laplace Transform to solve the initial value problem.

Please show all work and steps clearly so I can follow your logic and learn to solve similar ones myself. I will also rate your answer. Thank you kindly!

y′′ + 4y = f(t), y(0) = 0, y′(0) = 0,
where; 
f(t)= 1 if 1 ≤ t < 2,

0 otherwise

The indicated function

y₁(x)

is a solution of the associated homogeneous equation. Use the method of reduction of order to find a second solution

y₂(x)

of the homogeneous equation and a particular solution

y_p(x)

of the given nonhomogeneous equation.

y'' − 3y' + 2y = x;    y₁ = e^x

Starting from the initial estimates (x0, y0) = (4, 4) calculate the first iteration in the N-R solution of the folllowing system of equations

f1(x, y) = x2 + xy − 10

f2(x, y) = y + 3xy2 − 57

Harnswell Sewing Machine Company

Phase 1: For more than 40 years, the Harnswell Sewing Machine Company has manufactured industrial sewing machines. The company specializes in automated machines called pattern tackers that sew repetitive patterns on such mass-produced products as shoes, garments, and seat belts. Aside from the sales of machines, the company sells machine parts. Because the company’s products have a reputation for being superior, Harnswell is able to command a price premium for its product line.

Recently, the operations manager, Natalie York, purchased several books related to quality. After reading them, she considered the feasibility of beginning a quality program at the company. At the current time, the company has no formal quality program. Parts are 100% inspected at the time of shipping to a customer or installation in a machine, yet Natalie has always wondered why inventory of certain parts (in particular, the half-inch cam rollers) invariably falls short before a full year lapses, even though 7,000 pieces have been produced for a demand of 5,000 pieces per year.

After a great deal of reflection and with some apprehension, Natalie has decided that she will approach John Harnswell, the owner of the company, about the possibility of beginning a program to improve quality in the company, starting with a trial project in the machine parts area. As she is walking to Mr. Harnswell’s office for the meeting, she has second thoughts about whether this is such a good idea. After all, just last month, Mr. Harnswell told her, “Why do you need to go to graduate school for your master’s degree in business? That is a waste of your time and will not be of any value to the Harnswell Company. All those professors are just up in their ivory towers and don’t know a thing about running a business, like I do.”

As she enters his office, Mr. Harnswell invites Natalie to sit down across from him. “Well, what do you have on your mind this morning?” Mr. Harnswell asks her in an inquisitive tone. She begins by starting to talk about the books that she has just completed reading and about how she has some interesting ideas for making production even better than it is now and improving profits. Before she can finish, Mr. Harnswell has started to answer: “Look, everything has been fine since I started this company in 1968. I have built this company up from nothing to one that employs more than 100 people. Why do you want to make waves? Remember, if it ain’t broke, don’t fix it.” With that, he ushers her from his office with the admonishment of, “What am I going to do with you if you keep coming up with these ridiculous ideas?”

a. Based on what you have read, which of Deming’s 14 points of management are most lacking at the Harnswell Sewing Machine Company? Explain.

b. What changes, if any, do you think that Natalie York might be able to institute in the company? Explain.

Phase 2: Natalie slowly walks down the hall after leaving Mr. Harnswell’s office, feeling rather downcast. He just won’t listen to anyone, she thinks. As she walks, Jim Murante, the shop foreman, comes up beside her. “So,” he says, “did you really think that he would listen to you? I’ve been here more than 25 years. The only way he listens is if he is shown something that worked after it has already been done. Let’s see what we can plan together.”

Natalie and Jim decide to begin by investigating the production of the cam rollers, which are precision-ground parts. The last part of the production process involves the grinding of the outer diameter. After grinding, the part mates with the cam groove of the particular sewing pattern. The half-inch rollers technically have an engineering specification for the outer diameter of the roller of 0.5075 inch (the specifications are actually metric, but in factory floor jargon, they are referred to as half-inch), plus a tolerable error of 0.0003 inch on the lower side. Thus, the outer diameter is allowed to be between 0.5072 and 0.5075 inch. Anything larger is reclassified into a different and less costly category, and anything smaller is unusable for anything other than scrap.

The grinding of the cam roller is done on a single machine with a single tool setup and no change in the grinding wheel after initial setup. The operation is done by Dave Martin, the head machinist, who has 30 years of experience in the trade and specific experience producing the cam roller part. Because production occurs in batches, Natalie and Jim sample five parts produced from each batch. Table below presents data collected over 30 batches (stored in Harnswell).

a. Is the process in control? Why?

b. What recommendations do you have for improving the process?

Phase 3: Natalie examines the X and R charts developed from the data stored in Harnswell.xls from Phase 2. The R chart indicates that the process is in control, but the chart X t reveals that the mean for batch 17 is outside the LCL. This immediately gives her cause for concern because low values for the roller diameter could mean that parts have to be scrapped. Natalie goes to see Jim Murante, the shop foreman, to try to find out what had happened to batch 17. Jim looks up the production records to determine when this batch was produced. “Aha!” he exclaims. “I think I’ve got the answer! This batch was produced on that really-cold morning we had last month. I’ve been after Mr. Harnswell for a long time to let us install an automatic thermostat here in the shop so that the place doesn’t feel so cold when we get here in the morning. All he ever tells me is that people aren’t as tough as they used to be.”

Natalie is almost in shock. She realizes that what happened is that, rather than standing idle until the environment and the equipment warmed to acceptable temperatures, the machinist opted to manufacture parts that might have to be scrapped. In fact, Natalie recalls that a major problem occurred on that same day, when several other expensive parts had to be scrapped. Natalie says to Jim, “We just have to do something. We can’t let this go on now that we know what problems it is potentially causing.” Natalie and Jim decide to take enough money out of petty cash to get the thermostat without having to fill out a requisition requiring Mr. Harnswell’s signature. They install the thermostat and set the heating control so that the heat turns on a half hour before the shop opens each morning.

a. What should Natalie do now concerning the cam roller data? Explain.

b. Explain how the actions of Natalie and Jim to avoid this particular problem in the future have resulted in quality improvement.

PHASE 4: Because corrective action was taken to eliminate the special cause of variation, Natalie removes the data for batch 17 from the analysis. The control charts for the remaining days indicate a stable system, with only common causes of variation operating on the system. Then, Natalie and Jim sit down with Dave Martin and several other machinists to try to determine all the possible causes for the existence of oversized and scrapped rollers. Natalie is still troubled by the data. After all, she wants to find out whether the process is giving oversizes (which are downgraded) and undersizes (which are scrapped). She thinks about which tables and charts might be most helpful.

a. Construct a frequency distribution and a stem-and-leaf display of the cam roller diameters. Which do you prefer in this situation?

b. Based on your results in (a), construct all appropriate charts of the cam roller diameters.

c. Write a report, expressing your conclusions concerning the cam roller diameters. Be sure to discuss the diameters as they relate to the specifications.

PHASE 5: Natalie notices immediately that the overall mean diameter with batch 17 eliminated is 0.507527, which is higher than the specification value. Thus, the mean diameter of the rollers produced is so high that many will be downgraded in value. In fact, 55 of the 150 rollers sampled (36.67%) are above the specification value. If this percentage is extrapolated to the full year’s production, 36.67% of the 7,000 pieces manufactured, or 2,567, could not be sold as half-inch rollers, leaving only 4,433 available for sale. “No wonder we often have shortages that require costly emergency runs,” she thinks. She also notes that not one diameter is below the lower specification of 0.5072, so not one of the rollers had to be scrapped.

Natalie realizes that there has to be a reason for all this. Along with Jim Murante, she decides to show the results to Dave Martin, the head machinist. Dave says that the results don’t surprise him that much. “You know,” he says, “there is only 0.0003 inch variation in diameter that I’m allowed. If I aim for exactly halfway between 0.5072 and 0.5075, I’m afraid that I’ll make a lot of short pieces that will have to be scrapped. I know from way back when I first started here that Mr. Harnswell and everybody else will come down on my head if they start seeing too many of those scraps. I figure that if I aim at 0.5075, the worst thing that will happen will be a bunch of downgrades, but I won’t make any pieces that have to be scrapped.”

a. What approach do you think the machinist should take in terms of the diameter he should aim for? Explain.

b. What do you think that Natalie should do next? Explain.

You are valuing Soda City Inc. It has $110 million of debt, $90 million of cash, and 140 million shares outstanding. You estimate its cost of capital is 12.4%. You forecast that it will generate revenues of $700 million and $800 million over the next two years, after which it will grow at a stable rate in perpetuity. Projected operating profit margin is 20%, tax rate is 30%, reinvestment rate is 20%, and terminal EV/FCFF exit multiple at the end of year 2 is 15. What is your estimate of its share price?

Suppose there is a class with four people in it, and their overall grades in the course are 85, 92,78, and 75.

A. Write down every possible simple random sample of grades with sample sizen= 2.

B. Write down the sample space for the means x of the samples of size n= 2.

C. Find the mean of the sampling distribution from (b).

please explain the answers

Problem: Each student must create and solve an apportionment problem using what you have learned in this chapter. The problem must have at least four "states" and 30 "seats". You must choose one of the four methods presented in this chapter (Hamilton's, Jefferson's, Adams' or Webster's) to apportion the "seats". If you use Hamilton's Method, you must go on to demonstrate the occurrence of one of the paradoxes (Alabama, Population, or New States). If you use one of the divisor methods, it must violate the quota rule.

You are the building manager for a cylindrical skyscraper with a slanted roof. You must contract a window cleaner fwho works for $35 an hour and can clean 1 square meter of glass per minute. If you know the building is 120m tall at its highest point and 100m tall at its lowest point, and 20m wide, how much should you budget for the contract? Use a line integral of a scalar function to solve. Assume there are no windows to be cleaned on the roof.

Show which of the following models can be estimated by the OLS, where X, y and Z are variables and α,β,γ are parameters to be estimated. The models can be rearranged if necessary.

(1) y_t=α+βx_t+u_t [5 marks]

(2) y_t=e^α x_t^β e^(u_t ) [5 marks]

(3) y_t=α+βγx_t+u_t [5 marks]

(4) y_t=α+βx_t Z_t+u_t [5 marks]

Use normal vectors to determine the intersection, if any, for each of the following groups of three planes. Give a geometric interpretation in each case and the number of solutions for the corresponding linear system of equations. If the planes intersect in a line, determine a vector equation of the line. If the planes intersect in a point, determine the coordinates of the point.

a x + 2y + 3z = −4

b x + 2y + 3z = −4

2x + 4y + 6z = 7

2x + 4y + 6z = 7

x + 3y + 2z = −3

3x + 6y + 9z = 5

c x + 2y + z = −2

d x − 2y − 2z = 6 2x + 4y + 2z = 4 2x − 5y + 3z = −10 3x + 6y + 3z = −6 3x − 4y + z = −1

e. x − y + 3z = 4 x + y + 2z = 2 3x + y + 7z = 9

Let X be a set containing infinitely many elements, and let d be a metrio on X. Prove that X contains an open set U such that U and its complement Uc = X\U are both infinite

Suppose an electrical circuit contains a 1 H inductor, a 10 Ω resistor and a capacitor rated at 1/7 F. If the circuit is hooked up to an alternating voltage source described by E(t) = 68 cost V and initially q(0) = 1 C and i(0) = 0 A, find a function that describes the charge as a function of time.  Lq'' + Rq' + q/C = E(t).  

Please show work using a complementary and particular solution if possible.