Consider the function f(x)=2e2sin(x). In this question, we will first use a linear approximation to estimate the value of f(0.1). Then, we will use a Taylor polynomial of degree three to estimate de value of f(0.1).

a) What is a good choice for the base point a of the linear approximation and the Taylor polynomial?

Answer: a=

b) Compute the derivative of f and evaluate it at x=a.

Answer: f′(x)=

               f′(a)=

c) The linear approximation L(x) of f(x) based at a is:

Answer: L(x)=

d) Use the linear approximation that you have found in (c) to estimate f(0.1).

Answer: f(0.1)≈    

e) Compute the second and third derivatives of f.

f′′(x)=

f′′′(x)=

f) Compute f′′(a) and f′′′(a).

f′′(a)=

f′′′(a)=

g) Find the Taylor polynomial of order three of f at the base point a.

T3(x)=

h) Use the Taylor polynomial that you found in (g) to estimate f(0.1).

Answer: f(0.1)≈   

i) Compute the error (in absolute value) of the two approximations of f(0.1) that you have found. Give your answer with an accuracy of five decimal places.

Answer: Error for the linear approximation:    

Error for the Taylor polynomial of order three:   

To appreciate the improvement in the approximation provided by the Taylor polynomial of degree three over the linear approximation, you should sketch the graph of f, L, and T3 near a.

An economist with a major bank wants to learn, quantitatively, how much spending on luxury goods and services can be explained based on consumers’ perception about the current state of the economy and what do they expect in the near future (6 months ahead).  Consumers, of all income and wealth classes, were surveyed.  Every year, 1500 consumers were interviewed.  The bank having all of the data from the 1500 consumers interviewed every year, computed the average level of consumer confidence (an index ranging from 0 to 100, 100 being absolutely optimistic) and computed the average dollar amount spent on luxuries annually.  Below is the data shown for the last 24 years.

Date                 X                     Y (in thousands of dollars)

1994                79.1                 55.6

1995                79                    54.8

1996                80.2                 55.4

1997                80.5                 55.9

1998                81.2                 56.4

1999                80.8                 57.3

2000                81.2                 57

2001                80.7                 57.5

2002                80.3                 56.9

2003                79.4                 55.8

2004                78.6                 56.1

2005                78.3                 55.7

2006                78.3                 55.7

2007                77.8                 55

2008                77.7                 54.4

2009                77.6                 54

2010                77.6                 56

2011                78.5                 56.7

2012                78.3                 56.3

2013                78.5                 57.2

2014                78.9                 57.8

2015                79.8                 58.7

2016                80.4                 59.3

2017                80.7                 59.9

Question:

1. Construct the linear regression model for the dollar amount spent on luxury goods and services.

Over the past two years, Kermit Stone, the controller of Hilton Company, has been concerned that the company has been paying a large amount of money for state unemployment taxes. On reviewing the “unemployment file” with the head accountant, Deborah Murtha, he learns that the company’s tax rate is near the top of the range of the state’s experience-rating system. After calling the local unemployment office, Stone realizes that the turnover of employees at Hilton Company has had an adverse effect on the company’s tax rates. In addition, after consulting with Murtha, he discovers that the eligibility reports that come from the state unemployment office are just signed and sent back to the state without any review. The eligibility reports are notices that an ex-employee has filed a claim for unemployment benefits. By signing these reports “blindly,” the company, in effect, tells the state that the employee is eligible for the benefits. Any benefits paid are charged by the state against Hilton Company’s account. Stone is convinced that the rates the company is paying are too high, and he feels that part of the reason is the “blind” signing of the eligibility reports. Besides this, he wonders what other steps the company can take to lower its contributions rate and taxes.

Question to be Answered: What are THREE recommendations that you could give to Stone that might help reduce the “unfair” burden that the state unemployment compensation taxes are leveling on the Hilton Company?

Compare gain scores (Test 1 & 2) between group 1 and the group 2 protocols with independent t-tests. Significance for the study will be considered as p≤0.05 (noting that p-values near the cutoff will be discussed relative to clinical relevance). I've highlighted the applicable gain scores below.

This will be two separate t-tests, correct? One for Test 1 and one for Test 2. However, do I then compare the two t-tests to each other??

I also have negative gain scores, this is possible, correct??

Currently lost on the next step or how to perform the t-tests.

A family practice that serves over 4,500 patients is owned by three brothers, all general practitioner medical doctors who have been closely watching how the new Patient Protection and Affordable Care Act (ACA or “Obamacare”) is developing, especially with the ongoing changes to the eligibilities of coverage for patients and reimbursements that now require their facility to change its systems and processes for compliance.

As a healthcare consultant, you have been retained by the family practice to perform a thorough audit and analysis of the facility, including its systems, processes, and procedures, with an emphasis on record keeping and coding/billing practices.

You have also spent some time with the owners of the family practice discussing what the future holds regarding the types of treatments, demographics of patients, and the effect of technology on the methodologies of patient treatment. Within this context, the client asks you to provide the following:

Questions:

When comparing the overall health care system in America, how does it compare to just 40

years ago?

Provide some examples of what specifically is critical for the healthcare organization to consider regarding how treatments are performed on patients.

What technological advancements do you predict in health care in the next 15 years, especially those that can be opportunities for a family medical clinic scenario?

What are the regulatory agency changes coming in the near future?

What are your predictions for the success of the ACA, especially in the next 5 years?

Brandtly Industries invests a large sum of money in R&D; as a result, it retains and reinvests all of its earnings. In other words, Brandtly does not pay any dividends, and it has no plans to pay dividends in the near future. A major pension fund is interested in purchasing Brandtly's stock. The pension fund manager has estimated Brandtly's free cash flows for the next 4 years as follows: $4 million, $6 million, $12 million, and $14 million. After the fourth year, free cash flow is projected to grow at a constant 7%. Brandtly's WACC is 13%, the market value of its debt and preferred stock totals $42 million; and it has 21 million shares of common stock outstanding.

Write out your answers completely. For example, 13 million should be entered as 13,000,000.

1. What is the present value of the free cash flows projected during the next 4 years? Round your answer to the nearest cent. Do not round your intermediate calculations.
   
   $
2. 
   
3. What is the firm's horizon, or continuing, value? Round your answer to the nearest cent.
   
   $
4. 
   
5. What is the firm's total value today? Round your answer to the nearest cent. Do not round your intermediate calculations.
   
   $
6. 
   
7. What is an estimate of Brandtly's price per share? Round your answer to the nearest cent. Do not round your intermediate calculations.

Wk 2 - Compensation Evaluation Assignment Content Resource: Compensation Evaluation Grading Guide You were hired to work as a HR consultant for a small local hospital, with the task of expanding the workforce of certified medical assistants. Looking at the current three employees, you find a discrepancy in compensation between Susi, a 2-year employee at $28,000; Tom, 5-year employee at $27,000; and Raul, a 10-year employee at $33,000. All are employed as certified medical assistants, yet they all earn different salaries. According to survey data, all three employees are below the market rate for this job in the local job market. All three employees are also exemplary employees with near perfect scores in their most recent performance evaluation. Write a 700- to 1,050-word paper that includes the following: Explain the discrepancy in pay among the current employees. Describe the strategy you would take to correct the internal equity issue. Describe the strategy you would take to correct the external equity issue. Explain how you will ensure new hires will be paid equitably, both internally and externally. Explain how an organization's Total Compensation strategy affects its financial operations and its ability to attract, motivate, and retain top talent. Cite all sources according to APA formatting guidelines.

Scenario:

A family practice that serves over 4,500 patients is owned by three brothers, all general practitioner medical doctors who have been closely watching how the new Patient Protection and Affordable Care Act (ACA or “Obamacare”) is developing, especially with the ongoing changes to the eligibilities of coverage for patients and reimbursements that now require their facility to change its systems and processes for compliance.

As a healthcare consultant, you have been retained by the family practice to perform a thorough audit and analysis of the facility, including its systems, processes, and procedures, with an emphasis on record keeping and coding/billing practices.

You have also spent some time with the owners of the family practice discussing what the future holds regarding the types of treatments, demographics of patients, and the effect of technology on the methodologies of patient treatment. Within this context, the client asks you to provide the following:

Questions:

When comparing the overall health care system in America, how does it compare to just 40

years ago?

Provide some examples of what specifically is critical for the healthcare organization to consider regarding how treatments are performed on patients.

What technological advancements do you predict in health care in the next 15 years, especially those that can be opportunities for a family medical clinic scenario?

What are the regulatory agency changes coming in the near future?

What are your predictions for the success of the ACA, especially in the next 5 years?

1. According to Fredrick Taylor, creator of "Taylorism" or "Scientific Management," the best way to control shirking was to

a. pay wages higher than prevailing market wages so employees will take care not to quit their job with the company

b. create residual claimants

c. pay workers piece rate wages

d. have supervisors closely watch and monitor workers

e. instill a strong motivation in workers to do their best

2. Following its near bankruptcy in 1922, General Motors pioneered the decentralized management structure in which the firm was reorganized into semi-independent profit centers. Vice-presidents were appointed to manage these profit centers and were told that their bonuses would depend on the profitability of their division. This reorganization was designed to

a. reduce management costs
b. better capture economies of scale
c. create a more centralized management system
d. decentralize decision making and create residual claimants
e. put managerial compensation on a "piece rate" basis

3. What happens to a firm if its economic profits = 0?

a. It will immediately go out of business

b. It will eventually go out of business

c. It will be earning an accounting profit that is normal

d. Other firms will enter the industry and take profits even lower for all

e. Its profits will rise as other firms in this industry will quickly get out of this industry

Question B.2

Leyton and Dustin run a service station in a country town, the service station sells petrol and a number of other goods, which are displayed near the cash register and outside the office. Leyton and Dustin are partners in the business, though they have an old written agreement that states that neither will order goods or services over the value of $3,000 unless the contract contains signatures from both partners.

Leyton has been approached by a supplier of magazines who offers the business the delivery of 100 copies of a particular publication each month. Leyton convinced that the magazine is popular and will make some money, signs a contract with a promise to pay $5,000 in instalments for the delivery of the magazines.

The magazines arrive and Dustin is very upset, first because the magazine is quite unsuitable for display in the business and may result in a loss of customers if they see this publication, but he is also upset that Leyton has made an agreement without consulting him. There is an argument between the partners and Leyton takes sick leave and stays at home to recover from the stress of the argument. In the meantime, Dustin communicates with the supplier of the magazines and declares that the agreement to supply the publication is invalid due to a breach of the partnership agreement, and that the magazines will be returned and no payments will be forthcoming from the business.

Explain, with reference to partnership law:

a.     Whether Dustin can cancel the contract with supplier of the magazines?       

[Answer here]

b.     Whether Dustin can be liable for the actions of Leyton?