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Math 26101 Exam 2 EC
Due: 12:30 pm on March 14th
Name : _____________________________________________________________________________
This optional assignment could up to 10 points extra credit to your Exam 2 grade. Please show appropriate work and use terminology and notation correctly. Unless specified otherwise, you should give exact answers. Partial credit will be given sparingly, if at all. Each problem is worth 1 point. Remember that these should help you practice some of the concepts you will be tested over, but this assignment should not be interpreted as a sample exam.
1. Find the curvature of the curve 𝑟𝑟⃗(𝑡𝑡)=<4sin(2𝑡𝑡),4cos(2𝑡𝑡),4𝑡𝑡>.
2. At what point on the curve 𝑥𝑥=𝑡𝑡3,𝑦𝑦=5𝑡𝑡,𝑧𝑧=𝑡𝑡4 is the normal plane parallel to the plane 3𝑥𝑥+5𝑦𝑦−4𝑧𝑧=2?
3. Find the position vector of a particle that has the given acceleration and the given initial velocity and position:
𝑎𝑎⃗(𝑡𝑡)=sin(2𝑡𝑡),𝑣𝑣⃗(0)=1,𝑟𝑟⃗(0)=1
.
.
Name : ______________________________________________________________________
.. Page 2
4. (a) Evaluate the limit:
(b) Evaluate the limit: .
Name : ______________________________________________________________________
.. Page 3
5. Find for .𝑧𝑧=𝑦𝑦𝑦 𝑦 𝑦𝑦(6𝑥𝑥).
6. Find the equation of the tangent plane to the given surface at the specified point.
Name : ______________________________________________________________________
.. Page 4
7. Let and suppose that (x, y) changes from (2, –1) to (2.01, –0.98)
(a) Compute Δz. (b) Compute dz.
8. Use the Chain Rule to find .
.
Name : ______________________________________________________________________
.. Page 5
9. Find the directional derivative of the function 𝑓𝑓(𝑥𝑥,𝑦𝑦)=(𝑥𝑥+6)𝑒𝑒𝑦𝑦at the point P(3, 0) in the direction of the unit vector that makes the angle 𝜃𝜃=𝜋𝜋3 with the positive xaxis.
10. Find and classify the relative extrema and saddle points of the function
𝑓𝑓(𝑥𝑥,𝑦𝑦)=𝑥𝑥2+2𝑦𝑦2+𝑥𝑥2𝑦𝑦+11
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Buy your research paper Online_Financial Mathematics and Business Statistics: Individual Coursework
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Financial Mathematics and Business Statistics: Individual Coursework
Instructions
This coursework tests your basic financial mathematics and statistical modelling skills, using spreadsheet software (Excel – formulae, financial maths, graphical features, Data Analysis and Solver tools) as well as your awareness of the reality of how financial products work. Your answers are to be presented in an essay/report format, for which you will use a word processor. In writing your report, please:
 state and explain all assumptions, on which your answers are based;
 clearly indicate your answer/recommendations;
 no evidence of use of excel will result in a fail mark for this element of the coursework component of your mark;
 support any answers with the appropriate calculations to arrive at the answer;
 include selected screens of formulae underlying computed values. Failure to demonstrate you have created appropriate formulations on excel will be severely penalised. Despite the fact that you will be submitting the Excel file as well, your report is a standalone document, meaning a reader should not be required to look at the Excel file to understand your analysis, findings and recommendations;
 please note that adequate usage of the excel calculations in the report is important. This means that the key data/findings needs to be included in the report and appropriate referencing needs to be done, i.e. the relevant cell/table/range in the relevant tab of the excel file mentioned at the point of the report when it should be consulted.
The report will have a maximum of 10 pages (including any Appendixes; penalties will be applied for longer submissions – you are required to develop your judgement on what is and isn’t important). Ten percent of the total mark is allowed for quality of the presentation and these marks are distributed among the questions.
You will need to submit a Word document with the report (see instructions above) and an Excel file with the calculations.
Also, please note that late submissions will be penalised, no matter how small and irrespective of computer or internet crashes or any other last minute unexpected problem, so make sure you plan your submission allowing enough time to overcome any last minute problems. This includes keeping uptodate backups of your work!
Notes:
This coursework is your own (individual) work. Any student found guilty of plagiarism will be penalised. Standard penalties for late submissions are applicable.
Question 1: (10%)
With the reduction in sales driven by the financial crisis which have not fully recovered yet, Office Trade, a wholesaler of office equipment has been conducting a review of its stock ordering system. The management of the company has asked each of the analysts in its finance department, to look at each of its products, and you were asked to look at book shelving units. Having made your research, you have determined that it is uncertain when the recovery will start, so you have established the following demand scenarios for the next 12 months:
Scenario  Crisis Continues  Slow Recovery  Medium Recovery  Fast Recovery 
Probability  20%  40%  35%  5% 
Demand  25,000  35,000  50,000  75,000 
Considering the cost per order is £30 and the average carrying cost per unit is £2:
 Determine the Economic Order Quantity given the data above.
 Produce sensitivity analysis assuming a change of up to 10% up or down on each of the factors individually and on all factors simultaneously.
 Make a final recommendation to the board of the company, as to the number of units it should include in each order.
Question 2: (15%)
A car manufacturer is looking to reorganise and increase the efficiency of its manufacturing operations, and is currently looking at an engine assembly line, which makes three different engines (1.8, 2.0 and 2.5litre). The prices charged for the engines are £2,500, £2,850 and £3,750 respectively, while the inputs required to make each of the engines are listed in the table below:
Product  Basic  Medium  High  Max. Available 
Aluminium  10 units  11 units  12 units  52,000 
Other Metals  5 units  7 units  6 units  30,000 
Other Materials  6 units  4 units  9 units  28,000 
Labour  2 hours  2 ¼ hours  2 ½ hours  10,000 
The costs for the inputs are £25 per hour for Labour and £100, £120 and £35 per unit for Aluminium, Other Metals and Other Materials, respectively. There is also a maximum daily demand for the engines, which is 4,000 1.8litre, 3,500 2.0litre and 2,000 2.5litre.
Formulate this problem as a linear program and use Excel’s Solver to arrive at a solution. Write a short report describing your procedure, justify your formulation and give a recommendation to the firm on the best daily production mix.
Question 3: (30%)
The majority of banks, when making decisions on mortgage applications, will look at two indicators: salary and borrowing as a percentage of purchase price. On the first indicator, banks are normally willing to lend 2.5 times one’s salary or 3.25 times joint salary in a joint mortgage application, while currently most banks will lend up to 75% of the property price on their best rate with penalties for higher percentages. John and Julia are getting married and decided to buy a flat to move into once they do and are looking to take on a 25year mortgage. You have been given the following data:
 John’s current salary is £39,000 p.a. and Julia’s is £37,500 p.a. plus a bonus likely to be around £5,000 (based on previous 3 years experience);
 Both have jobs where they partly telecommute, so on average each works from home 2 days a week;
 Their total savings at the moment are £25,000;
 John owns a flat which he plans to sell, and has been advised that he should be able to sell it for £150,000. The mortgage outstanding on this flat is £112,000;
 The average price of flats in the area they would like to move into is as follows: studios £150,000; 1bedroom £220,000; 2bedroom £325,000; 3bedroom £450,000; 4bedroom £600,000
 Having contacted a financial adviser at the end of January, he has identified the following as the best available mortgage rates:
 Repayment fixed rate for 2years of 1.89%. After that period, the rate reverts to the bank’s standard variable rate, which currently is 3.69%;
 repayment fixed rate for 5years of 2.34%. After that period, the rate reverts to the bank’s standard variable rate, which currently is 3.69%;
 interest only mortgage at 5% for the life of the loan. In this instance, you would be required to create an investment fund, which pays an interest rate of 3.9% to cover the repayment of the mortgage.
 All the rates above are for loans of up to 75% of the property value. There is an increase of 1.5%age points if borrowing is up to 90% of the property value.
Assess:
 What is the maximum John and Julia can borrow while taking advantage of the bank’s best mortgage rate;
 The amount you advise them to borrow, given their financial and professional situation;
 Which is the best mortgage that John and Julia to take out (assume they take out the amount you recommended in b);
 Whether that advice would change if interest rates went up or down by up to three percentage points.
Question 4: (20%)
Garnett plc has seen sales in one of its product lines decline over the last two years. The production is currently subcontracted and any changes require a six month notice, so Garnett has to decide now what to do for their most important advertising period, which is in September every year. The options it has identified are:
 Option A – Invest £1million to make small changes to the product design and manufacturing process, which will generate increased cash flows in the short term;
 Option B – completely redesign the product and production process, which will have a longer lasting effect on cash flows, but will require an investment of £7million.
Garnett’s required rate of return on investments is 12.5% and the estimated cash flows for the two options are as follows (in ‘000s):
Year  Option A  Option B 
1  1,000  300 
2  1,500  1,500 
3  1,750  3,000 
4  500  3,000 
5  3,000  
6  3,000  
7  2,700  
8  2,000  
9  1,500  
10  1,000 
Required:
 Discuss and compare the different types of investment appraisal methods Garnett can use, including a discussion of the advantages and disadvantages of each.
 If Garnett had a rule that all investment projects need to payback within 3 years, what project would be chosen? Comment.
 Make a recommendation as to which project should be undertaken.
 If Garnett believes there is an opportunity to start exporting its product line to another country once sales are finished in its home country (i.e. from year 5), and it thinks it will be able to generate cash flows of £250,000 in the first year, £750,000 in the second and £1,250,000 in the subsequent four years, would your answer to part c) change? How? (Note: production can’t be further increased in the future if option B is chosen now)
Question 5: (15%)
The table below represents data for the profits, sales, average shop size and number of product lines sold by the 20 branches of a retailing company. You have been asked to analyse the data, using the Data Analysis tool in Excel, and make recommendations, including the following:
 Summarise the distribution of profits of the twenty branches and comment on the results, including identification of any particularly good or poorly performing branches.
 Identify whether there is evidence that the average number of lines stocked per branch is significantly different from 150.
 Identify whether there is a significant difference between the profits of two groups of branches, split by the level of sales, with the threshold being £600,000.
 Based on this sample, provide a 98% confidence interval for the profits of the twenty branches and comment on the outcome.
Profit (£000s)  Sales (£000s)  Size (000s sq. ft.)  Lines 
77.5  613.9  3.2  80 
91  217.4  4.3  200 
20.7  900.9  3.1  164 
40.8  673.4  1.5  150 
45.8  424.7  3.2  69 
41.1  542.2  1.8  128 
47.5  564.6  2.5  75 
80.4  662.1  3.1  182 
16.5  583.6  4.2  126 
22.3  720.2  0.6  164 
40.8  881.5  1.8  145 
68.1  227.7  0.8  130 
17.7  807.4  3.8  154 
66.2  656.4  0.3  124 
31.3  632.8  2.3  142 
15  548.5  5  178 
67.8  533.6  1.5  173 
55  147.5  1.7  199 
8.6  311.4  3.8  98 
16.5  450.1  4.6  148 
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 There is one required question you must answer
 You must also answer 3 out of 7 additional questions
 Each response is limited to a maximum of 350 words
 Which three questions you choose to answer are up to you: But you should select questions that are most relevant to your experience and that best reflect your individual circumstances.
Keep in mind
 All questions are equal: All questions are given equal consideration in the application review process, which means there is no advantage or disadvantage to choosing certain questions over others.
 There is no right or wrong way to answer these questions: It’s about getting to know your personality, background, interests and achievements in your own unique voice.
Questions & guidance
Remember, the personal questions are just that — personal. Which means you should use our guidance for each question just as a suggestion in case you need help. The important thing is expressing who are you, what matters to you and what you want to share with UC.
Required question
Please describe how you have prepared for your intended major, including your readiness to succeed in your upperdivision courses once you enroll at the university.
Things to consider: How did your interest in your major develop? Do you have any experience related to your major outside the classroom — such as volunteer work, internships and employment, or participation in student organizations and activities? If you haven’t had experience in the field, consider including experience in the classroom. This may include working with faculty or doing research projects.
If you’re applying to multiple campuses with a different major at each campus, think about approaching the topic from a broader perspective, or find a common thread among the majors you’ve chosen.
Choose to answer any three of the following seven questions:
 Describe an example of your leadership experience in which you have positively influenced others, helped resolve disputes, or contributed to group efforts over time.
Things to consider:A leadership role can mean more than just a title. It can mean being a mentor to others, acting as the person in charge of a specific task, or taking lead role in organizing an event or project. Think about your accomplishments and what you learned from the experience. What were your responsibilities?
Did you lead a team? How did your experience change your perspective on leading others? Did you help to resolve an important dispute at your school, church in your community or an organization? And your leadership role doesn’t necessarily have to be limited to school activities. For example, do you help out or take care of your family?
2. Every person has a creative side, and it can be expressed in many ways: problem solving, original and innovative thinking, and artistically, to name a few. Describe how you express your creative side.
Things to consider: What does creativity mean to you? Do you have a creative skill that is important to you? What have you been able to do with that skill? If you used creativity to solve a problem, what was your solution? What are the steps you took to solve the problem?
How does your creativity influence your decisions inside or outside the classroom? Does your creativity relate to your major or a future career?
3. What would you say is your greatest talent or skill? How have you developed and demonstrated that talent over time?
Things to consider: If there’s a talent or skill that you’re proud of, this is the time to share it. You don’t necessarily have to be recognized or have received awards for your talent (although if you did and you want to talk about, feel free to do so). Why is this talent or skill meaningful to you?
Does the talent come naturally or have you worked hard to develop this skill or talent? Does your talent or skill allow you opportunities in or outside the classroom? If so, what are they and how do they fit into your schedule?
4. Describe how you have taken advantage of a significant educational opportunity or worked to overcome an educational barrier you have faced.
Things to consider: An educational opportunity can be anything that has added value to your educational experience and better prepared you for college. For example, participation in an honors or academic enrichment program, or enrollment in an academy that’s geared toward an occupation or a major, or taking advanced courses that interest you — just to name a few.
If you choose to write about educational barriers you’ve faced, how did you overcome or strived to overcome them? What personal characteristics or skills did you call on to overcome this challenge? How did overcoming this barrier help shape who are you today?
5. Describe the most significant challenge you have faced and the steps you have taken to overcome this challenge. How has this challenge affected your academic achievement?
Things to consider: A challenge could be personal, or something you have faced in your community or school. Why was the challenge significant to you? This is a good opportunity to talk about any obstacles you’ve faced and what you’ve learned from the experience. Did you have support from someone else or did you handle it alone?
If you’re currently working your way through a challenge, what are you doing now, and does that affect different aspects of your life? For example, ask yourself, “How has my life changed at home, at my school, with my friends, or with my family?”
6. What have you done to make your school or your community a better place?
Things to consider: Think of community as a term that can encompass a group, team or a place – like your high school, hometown, or home. You can define community as you see fit, just make sure you talk about your role in that community. Was there a problem that you wanted to fix in your community?
Why were you inspired to act? What did you learn from your effort? How did your actions benefit others, the wider community or both? Did you work alone or with others to initiate change in your community?
7. What is the one thing that you think sets you apart from other candidates applying to the University of California?
Things to consider: Don’t be afraid to brag a little. Even if you don’t think you’re unique, you are — remember, there’s only one of you in the world. From your point of view, what do you feel makes you belong on one of UC’s campuses? When looking at your life, what does a stranger need to understand in order to know you?
What have you not shared with us that will highlight a skill, talent, challenge, or opportunity that you think will help us know you better? We’re not necessarily looking for what makes you unique compared to others, but what makes you, YOU.
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MT560 Algebraic Topology Autumn 2016 – Homework 2
MT560 Algebraic Topology Autumn 2016 – Homework 2
1. Suppose that X,Y are spaces with Y Hausdorﬀ and f : X → Y is continuous. Show that the graph of f, Gr(f) = {(x,f(x)) ; x ∈ X}, is a closed subset of X ×Y .
2. Let (X,T) be a topological space and ‘∗’ a ‘point’ not in the set X. Let X0 = X ∪{∗}. (a) Let T0 = T ∪{X0}. Show that T0 is a topology on X0. (b) Show that X is a subspace of X0. (c) Show that (X0,T0) is compact. (d) Suppose X is Hausdorﬀ. Does it follow that X0 is Hausdorﬀ?
3. Alexandroﬀ 1point compactiﬁcation. Let (X,T) be a topological space and ∗ a ‘point’ not in the set X. Let ˆ X = X ∪{∗}. (a) Let TA := T ∪{U ∪{∗} ; X − U is closed and compact in X}. Show that ( ˆ X,TA) is a compact topological space containing X asa subspace. (Note that X is open in ˆ X.) (b) Suppose that X is Hausdorﬀ and locally compact (i.e. for each x ∈ X, there exists an open set U such that x ∈ U, and its closure, ¯ U, is compact). Deduce that ˆ X is Hausdorﬀ. (c) Suppose X is not compact. Deduce that X is dense in ˆ X. Is this the case if X is compact? (d) Show that the Alexandroﬀ 1point compactiﬁcation of the open n cell en is homeomorphic to the nsphere Sn. Show that attaching the ndisc Dn to a 0cell ∗, via the constant map f : ∂Dn →{∗}, also gives the nsphere.
Homework HelpMath
Homework HelpMath
 How long will it take $10,000 to reach $50,000 if it earns 10% interest compounded semiannually?
 17 years
 33 years
 5 years
 5 years
 You require an 8% annual return on all investments. You will receive $1,000,
$2,000, and $3,000 respectively for the next three years (end of year) on a particular investment. What is the most you be willing to pay for this investment?
 $5,022
 $2,577
 $6,000
 $4,763
 Your partners have promised to give you $25,000 on your wedding day if you
Wait 10 years to get married. Your sister is getting married today. What amount should she receive in today’s dollars to match you gift? The appropriate discount rate is rate 12%.
 $8,049
 $10,000
 $22,321
 $25,000
 You want to start saving for retirement. If you deposit$2,000 each year at the end
Of the next 60 years and earn 11% on the investment, how much will you have when you retire?
 $792,000
 $1,048,114
 $9,510,132
 $10,556,246
 What is the present value of a semiannual ordinary annuity payment of $7,000
made for 12 years with a required annual return of 5%?
 $65,145
 $128,325
 $125,195
 $62,043
 You get a 25year loan of $150,000 with a 8% annual interest rate. What are the
annual payments?
 $14,052
 $2,052
 $13,965
 $13,427
 Your grandmother is offered a series of $6,000 starting one year from today. The
Payments will be made at the end of each of the next 10 years. Similar risk investments are yielding 7%. What should she pay for the investment?
 $60,000
 $45,091
 $42,141
 $30,501
 Company XYZ purchased some machinery and gave a fiveyear note with a
Maturity value of $20,000. The discount rate is 8% annually and the interest is discounted monthly. How much did the company borrow?
 $13,612
 $13,424
 $19,346
 $12,000
 Your father loans you $12,000 to make it through your senior year. His
Repayment schedule requires payments of $1401.95 at the end of year the next 15 years. What interest rate is he charging you?
 0%
 5%
 0%
 5%
 What is the future value of an annuity due if your required return is 10%, and
Payments are $1,000 for 10 years?
 $15,937
 $16,145
 $17,531
 $11,000
 You deposit $10,000 in a bank and plan to keep it there for five years. The bank
Pay 8% annual interest compounded continuously. Calculate the future value at the end of five years.
 $14,693
 $15,000
 $14,918
 $14,500
 Calculate the present value of $100,000 received in six months. Use an annual
discount rate of 10%. Do not adjust the discount rate to a semiannual rate. Keep it annual and adjust to the appropriate value.
 $95,346
 $56,447
 $90,909
 $100,000
 You get a twentyyear amortized loan of $100,000 with a 5% annual interest rate.
what are the annual payments?
 $8,718
 $37,689
 $4,762
 $8,024
 What is the present value of $100,000 received in fifteen years with an annual
Discount rate of 5% discounted monthly?
 $25,000
 $48,102
 $47,310
 $207,893
 A gallon of milk cost $3.59 today. How much will it cost you to buy a gallon of
milk for your grandchildren in 35 years if inflation averages 5% per year?
 $3.77
 $6.28
 $12.34
 $19.80
 You borrow $95,000 for 12 years at an annual rate of 12%. What are the monthly
Payments required to amortize this loan?
 $1,248
 $15,336
 $11,400
 $3,936
 As a gift from your parents, you just received $50,000 for your education for the
Next four years. You can earn an annual rate of 8% on your investments. How much can you withdraw each year (end of year) just using up the $50,000?
 $12,000
 $11,096
 $11,750
 $15,096
 You would like to retire on $1,000,000. You plan on a 7% annual investment rate
(3.5% semiannually) and will put away $7,500twice a year at the end of each semiannual period. How long before you can retire? Round to the nearest figure.
a.) 51years
b.) 25 years
c.) 35 years
d.) 66 years
 What is the present value of an annual annuity payment of $7,000 made for 12
Years with a required return of 5% with the first payment starting today?
 $3,898
 $65,145
 $62,043
 $11,200
 What a deal! Your new car only cost $28,300 after rebates and trade. If you
Finance it for 60 months at 6% annual interest, what will be you rmonthly payments?
 $471.67
 $544.40
 $547.12
 $1,751.08
Essay. Write your answer in the space provided or on a separate sheet of paper.
 Sum the present values of the following cashflows to be received at the end of
each of the next six years $1,500, $3,500, $$3,750, $4,250, $5,000 when the discount rate is 4%.
 How long it will take for $2,500 to become $8,865 if it is deposited and earns 5% per year compounded annually? (Calculate to the closet year.)
 Company XYZ purchased equipment and gave a threeyear note with maturity value of $12,006. The annual discount rate for the note was 14% discounted semiannually. Calculate how much they borrowed.
 Calculate the resent value of each of the alternatives below, if the discount rate is 12%.
 $45,000 today in one lump sum.
 $70,000 paid to you in seven equal payments of $10,000 at the end of each of the next seven years.
 $80,000 paid in one lump sum 7 years from now.
 A bank agrees to give you a loan of $12,000,000 and you have t pay $1,309,908
Per year for 26 years. What is your rate of interest? What would the payments be if this were a monthly payment loan?
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 (5 pts) Which of these graphs represent a onetoone function? Answer(s): ____________
(no explanation required.) (There may be more than one graph that qualifies.)
(A)  (B)  (C)  (D) 
 (5 pts) Convert to a logarithmic equation: 7^{x} = 2401. (no explanation required) 2. ______
 (10 pts) Based on data about the growth of a variety of ornamental cherry trees, the following logarithmic model about these trees was determined:
h(t) = 6.47 ln(t) + 2.83, where t = age of tree in years and h (t) = height of tree, in feet.
(Note that “ln” refers to the natural log function) (explanation optional)
Using the model,
(a) At age 3 years, how tall is this type of ornamental cherry tree, to the nearest tenth of a foot?
(b) At age 12 years, how tall is this type of ornamental cherry tree, to the nearest tenth of a foot?
 (5 pts) Solve the equation. Check all proposed solutions. Show work in solving and in checking, and state your final conclusion.
 (10 pts)
(a) _______ (fill in the blank)
(b) Let State the exponential form of the equation.
(c) Determine the numerical value of , in simplest form. Work optional.
 (10 pts) Let f (x) = 2x^{2} – x – 10 and g(x) = 3x + 1
(a) Find the composite function and simplify the results. Show work.
(b) Find . Show work.
 (15 pts) Let
(a) Find f ^{–}^{ 1 }, the inverse function of f. Show work.
(b) What is the domain of f ? What is the domain of the inverse function?
(c) What is f (2) ? f (2) = ______ work/explanation optional
(d) What is f ^{–}^{ 1} ( ____ ), where the number in the blank is your answer from part (c)? work/explanation optional
 (15 pts) Let f (x) = e ^{x – 1 }+ 4.
Answers can be stated without additional work/explanation.
(a) Which describes how the graph of f can be obtained from the graph of y = e^{x} ? Choice: ________
 Shift the graph of y = e^{x } to the left by 1 unit and up by 4 units.
 Shift the graph of y = e^{x } to the right by 1 unit and up by 4 units.
 Reflect the graph of y = e^{x } across the xaxis and shift up by 4 units.
 Reflect the graph of y = e^{x } across the yaxis and shift up by 4 units.
(b) What is the domain of f ?
(c) What is the range of f ?
(d) What is the horizontal asymptote?
(e) What is the yintercept? State the approximation to 2 decimal places (i.e., the nearest hundredth).
(f) Which is the graph of f ?
GRAPH A GRAPH B GRAPH C GRAPH D
NONLINEAR MODELS – For the latter part of the quiz, we will explore some nonlinear models.
 (15 pts) QUADRATIC REGRESSION
Data: On a particular summer day, the outdoor temperature was recorded at 8 times of the day, and the following table was compiled. A scatterplot was produced and the parabola of best fit was determined.

Quadratic Polynomial of Best Fit:
y = 0.3476t^{2} + 10.948t – 6.0778 where t = Time of day (hour) and y = Temperature (in degrees)
REMARKS: The times are the hours since midnight. For instance, 7 means 7 am, and 13 means 1 pm.
(a) Using algebraic techniques we have learned, find the maximum temperature predicted by the quadratic model and find the time when it occurred. Report the time to the nearest quarter hour (i.e., __:00 or __:15 or __:30 or __:45). (For instance, a time of 18.25 hours is reported as 6:15 pm.) Report the maximum temperature to the nearest tenth of a degree. Show algebraic work.
(b) Use the quadratic polynomial to estimate the outdoor temperature at 7:30 am, to the nearest tenth of a degree. (work optional)
(c) Use the quadratic polynomial y = 0.3476t^{2} + 10.948t – 6.0778 together with algebra to estimate the time(s) of day when the outdoor temperature y was 75 degrees.
That is, solve the quadratic equation 75 = 0.3476t^{2} + 10.948t – 6.0778 .
Show algebraic work in solving. State your results clearly; report the time(s) to the nearest quarter hour.
 (10 pts) EXPONENTIAL REGRESSION
Data: A cup of hot coffee was placed in a room maintained at a constant temperature of 69 degrees, and the coffee temperature was recorded periodically, in Table 1.
TABLE 1 
REMARKS:
Common sense tells us that the coffee will be cooling off and its temperature will decrease and approach the ambient temperature of the room, 69 degrees.
So, the temperature difference between the coffee temperature and the room temperature will decrease to 0.
We will fit the temperature difference data (Table 2) to an exponential curve of the form y=Ae^{–}^{bt}.
Notice that as t gets large, y will get closer and closer to 0, which is what the temperature difference will do. So, we want to analyze the data where t = time elapsed and y = C – 69, the temperature difference between the coffee temperature and the room temperature.

TABLE 2

Exponential Function of Best Fit (using the data in Table 2):
y = 89.976 e ^{–}^{ 0.023} ^{t} where t = Time Elapsed (minutes) and y = Temperature Difference (in degrees)
(a) Use the exponential function to estimate the temperature difference y when 25 minutes have elapsed. Report your estimated temperature difference to the nearest tenth of a degree. (explanation/work optional)
(b) Since y = C – 69, we have coffee temperature C = y + 69. Take your difference estimate from part (a) and add 69 degrees. Interpret the result by filling in the blank:
When 25 minutes have elapsed, the estimated coffee temperature is ________ degrees.
(c) Suppose the coffee temperature C is 100 degrees. Then y = C – 69 = ____ degrees is the temperature difference between the coffee and room temperatures.
(d) Consider the equation _____ = 89.976 e ^{– 0.023t} where the ____ is filled in with your answer from part (c).
Need HelpMathematics
Need HelpCollege Entry Essay (Mathematics)
Need HelpCollege Entry Essay (Mathematics)
Some students have a background, identity, interest, talent that is meaningful they believe their application would be incomplete without it. If it sounds like you than please share your story
Amid my school years and as ahead of schedule as in the fourth grade, I was staggered by the assortment of conceivable uses of arithmetic in regular daily existence. The way that even a straightforward thing, for example, leaves developing on a tree, can be put into a succession, a Fibonacci’s arrangement to be more precise, is simply noteworthy. Also, the rundown goes, on with PC frameworks and projects and additionally the web and applications that are all composed and modified utilizing distinctive numerical calculations like for instance Euclid’s calculation. I respect the excellence of head breaking oddities, which sound so natural and selfevident, where as in reality their confirmation is exceptionally troublesome and scientific and utilizes the Horse mystery or Zeno’s conundrum or Grandi’s arrangement. Wherever we turn, whatever we do, there is a math application and that is the manner by which it was since the getgo.
For me by and by arithmetic can clarify a great deal of exceptionally confounded thoughts in an extremely basic manner, and can be utilized to sum them up. Additionally in Mathematics there are a great deal of totally distinctive strategies for accomplishing the same arrangement what makes me much more spurred and inspired by it.
The fulfillment I get from fathoming a scientific errand is comparable to climbing a top of a mountain bluff. The main contrast is that the quantity of these precipices is ceaseless and sky is the breaking point! The themes I have explored the most are, synchronous conditions and Gaussian Elimination. I additionally looked into changed sorts of conditions with whole number arrangements, called Diophantine conditions and in actuality it turned into my investigation point for my IB Higher Level Mathematics Internal Assessment. In my first year of the IB program one of my most loved themes were capacities and separation, and what’s more I have been perusing about Leibniz’s documentations, which clarify a practical relationship between an autonomous and obscene variables and supernatural capacities. A few people like perusing fiction and some like finding out about the history and for me investigating the World of arithmetic is the thing that fulfills me the most.
However difficult the IB program abnormal state arithmetic are , I’ve been taking exams in the Russian secondary school amid each school break throughout the previous four years. I reached a conclusion that the methodology arithmetic is educated in Russia is some way or another not the same as in the school in the UK. This helped me to widen my perspectives and learning significantly all the more, particularly in the zones of unadulterated variable based math and hard trigonometry. I have altogether delighted in the utilization of science in these territories, despite the fact that it was very trying for me to study, in two distinct nations and in two unique dialects throughout the previous four years at the same time.
My enthusiasm for arithmetic is great to the point that last year I joined the Moscow Institute of Physics and Technology separation learning Olympiad school, keeping in mind the end goal to grow my insight into science much more and have the capacity to work and speak with individuals who share a comparable energy for arithmetic as me. This was a chance for me to increase more extensive supposition about various numerical issues furthermore have entry to some school level scientific issues and arrangements. I have totally delighted in this experience and it was an incredible fulfillment for me to acquire information in programming, material science and arithmetic.
I feel satisfied when I am included and adapting more about the extraordinary World of maths. Later on I might want to have the capacity to apply the information I have, all things considered, for instance in displaying PC projects or making new seeking calculations! I am likewise exceptionally inspired by utilizing arithmetic to foresee monetary patterns, and research into computerized reasoning, which could be executed into stock trade and connected financial matters.
SPSS Analysis
SPSS Analysis
1) For the variable HOME, what are the modes? Is the data normally distributed?
2) For the variable ARREST, what are the modes? Is the data normally distributed?
3) Why are we concerned about the distribution of data?
4) What difference does it make in the case of each of the variables (HOME and ARREST) if the data is not normally distributed?
All of the questions refer to the results of the SPSS analysis presented on pages 161165 of the textbook.
Which is the download plus show your word use references
Answer by the number must be answer by number
HelpProbability Assignment
HelpProbability Assignment
QUESTION 4
 Exercise 4.0a
You are visiting the rainforest, but unfortunately your insect repellent has run out. As a result, at each second, a mosquito lands on your neck with probability 0.5. If a mosquito lands, it will bite you with probability 0.2, and it will never bother you with probability 0.8, independently of other mosquitoes. What is the probability of being bit for the 1st time in the 5th second?
2 points
QUESTION 5
 Exercise 4.0b
You toss n = 10 fair coins, each showing heads with probability p_{1} = 0.5, independently of the other tosses. Each coin that shows tails is then tossed again, once. After following this process, what is the probability that exactly k = 6 coins show heads?
Hint: first calculate p_{2},the probability that a single coin shows heads (after following the 2step process), and then make use of the binomial PMF.
2 points
QUESTION 6
 Exercise 5.3a
Let a continuous random variable X be given that takes values in [0, 1], and whose distribution function F satisfies
F(x) = 2x^{2} − x^{4} for 0 ≤ x ≤ 1
 Compute P (1/4 ≤ X ≤ 3/4 )
QUESTION 10
 Exercise 5.14
Determine the 10th percentile of a standard normal distribution
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Lab 2 – Financials (Excel)
Lab 2 – Financials (Excel)
Project Objective
To offer an introduction to building spreadsheets, creating charts, and entering functions.
Part 1 – Financial Projections
One of the most important aspects of analyzing the feasibility and profitability of a new business is creating financial statements, projecting cash flows, and keeping track of information. For the purpose of this part, you will be creating a 3year income statement for two different business opportunities: 1) operating a plant in Location A or 2) operating a plant in Location B. This will allow you to assess the profitability of your new endeavor after a few years of commerce and therefore make an informed decision as to which opportunity you should pursue.
You will begin by creating the 3year income statement for Location A.
Income Projection for Location A
Figure 1: Location A Financials worksheet (dates and numbers may differ from instructions below).
Initial Layout:
Figure 2: Initial Data for Location A (use these numbers for location A)
Refer to figures 1 and 2 for the following tasks.
 Start Microsoft Excel. If you use Microsoft Excel 2010: You will notice you have three worksheets in your new Excel workbook. (Excel 2013 gives you only one sheet.)
 In Sheet1, enter the following text in cell B3: Location A’s Projected Income Statement.
 Select the cells B3:E3 and click on the Merge & Center button in the Home
 In cell A5, enter the text: Revenues.
 Enter the text in column A (cells A5:A37) as shown in Figure 2, including the text in the second table at the bottom (The Financial Summary Table). Cell A37 contains the text: * pre tax.
 In cell C31, enter the text: FINANCIAL SUMMARY.
 In cell B4, enter the text: YEAR. Enter 2017, 2018 and 2019 across the row (assuming the first year your imaginary business can make money is 2017).
 Enter numbers for your Revenues, Cost of Sales, and Operating Expenses for the next years. Use the numbers provided in Figure 2 above. Do not enter the Total amounts.
 Use the SUM function to calculate all of the totals for the Revenues, Cost of Sales, and Operating Expenses for cells C10, D10, E10, C16, D16, E16, C26, D26, and E26. There are numerous ways you can perform a SUM function. One way is to use ∑ AutoSum.
 Enter a formula to calculate the Gross Profit for the three years (cells C18:E18). For the first year, you would enter the following formula in cell C18: =C10C16.
 Use a formula to calculate the Net Revenue/Loss for all three years (cells C28:E28). For the first year, you would enter the following formula in cell C28: =C18C26.
 Format all of the values with $ and no cents. Under the Home tab, click the currency icon (dollar sign on Windows and dollar bill with coins on Mac), and click the Decrease Decimal button (.00à.0) twice.
 Use the shading, border, and font color features to make your income statement look like the one in Figure 1 above. The colors and widths do not need to be exact, but every feature must be utilized as per the specifications implied in Figure 1. Numbers in Fig. 1 and Fig. 2 may differ; use the numbers from Fig. 2.
 In Cell C1, enter your company’s name. Then merge & center it in cells C1:E1.
 Adjust the column widths as necessary to display all cell contents.
The Financial Summary Table:
 Use cell references in the Financial Summary Table to display the numbers for Revenues, Cost of Sales, Gross Profit, and Operating Expenses from the Income Statement above in the worksheet. Do not simply type the numbers in or your sheet will not work. For cell C32, enter = and then click on cell C10.
 Merge & center the text Financial Summary in cells C31:E31.
 Format the table similar to the table shown in Figure 1. If you would like, you can use the Cell Styles option in the Home
The 3Year Financial Statistics Table:
 Enter the text for Average, Largest, and Smallest Net Revenue/Loss in cells G32:G34.
 For cell K32, use the Average function to calculate the average net revenue/loss by using cells C28:E28.
 For cell K33, use the Max function to calculate the largest net revenue/loss by using cells C28:E28.
 For cell K34, use the Min function to calculate the smallest net revenue/loss by using cells C28:E28.
 Merge & center the text 3Year Financial Statistics in cells G31:K31.
 Format the table using shading, borders, and font colors. Again, make them similar, but they do not have to be exact.
The Chart
 Select all of the Revenues Totals (C10:E10), Cost of Sales Totals (C16:E16), and Operating Expenses Totals (C26:E26) simultaneously by holding down the [Ctrl] (or control) button and selecting the three sets of cells.
 Select the Insert
 Add a chart. There are many ways to do this in Excel. In Excel 2010 you can do this by selecting the Line pulldown, and then the Line with Markers In Excel 2013, after you have clicked the Insert tab, you’ll see that the tool ribbon is divided into numerous sections (it is possible that you won’t see a tool ribbon at all — if you see no tool ribbon, go online and Google “how to turn on ribbon in Excel 2013” and turn your ribbon on, and if need be, “pin it” with the pin icon at the right side. These instructions depend on you having your tool ribbon visible). Tool ribbon sections collapse if the Excel window is narrow, so if you don’t see a Charts section, you can widen the Excel window until you see it. At the lower right corner of the Charts section is a small pulldown arrow; clicking it causes an annoying popup (so don’t click it; if you get a popup that says you must select cells, you can simply click OK and close the popup). Instead, in the Charts section, look at the different “Recommended Charts” (don’t click “Recommended Charts” — that only causes the same annoying popup. If you want to help Microsoft improve its products, click “Was this information helpful?” and select “NO“). To the right of “Recommended Charts,” you see three rows of chart types. Mousing over them pops up their names. You want to click the “Insert Line Chart” icon. Then select the Line with Markers option.
 Define the parameters of the chart:
 Under the Chart Tools, select the Design In Excel 2013, you are automatically already in the Chart Tools / Design tab.
 Click the Select Data
 Look for the Horizontal (Category) Axis Labels section, and click Edit. Select the years cells (C4:E4) of your spreadsheet and hit the Enter
 Change the name of Series1, Series2, and Series3 to Revenues, Cost of Sales, and Operating Expenses, respectively, by selecting the Edit button under the Legend Entries (Series) Change them by clicking in the area for Series name and selecting the cell containing the label for Revenues. Do this for all three labels.
 In the Select Data Source window, press the OK
 Excel 2010: Under the design tab, expand the Chart Layouts area by clicking on the arrow below the down arrow. Select Chart Layout 5. Excel 2013: at the left end of the tool ribbon, click Quick Layout, and then select Layout 5.
 (If you are working in Excel 2013, skip down to step 30.b.) Excel 2010: Adjust the layout of your chart by selecting the Layout tab under Chart Tools:
 Remove the Yaxis label by going to Axis Titles à Primary Vertical Axis Title à None.
 Click on the Chart Title on the chart. Change the label to your company’s name.
 Excel 2013: Click on Add Chart Element, at left end of the tool ribbon, mouse over Axis Titles, and click Primary Vertical to remove the vertical axis title on your chart.
 The graph should now be complete. Move it to the right side of the spreadsheet and resize it, as per Figure 1.
Additional Items
 To rename the worksheet, rightclick on the Sheet1 tab at the bottom of the Excel sheet and select the Rename option (or just doubleclick the sheet name and type the new name). Enter Location A Financials.
 Add a textbox somewhere on your spreadsheet by selecting the Insert à Text Box Then “draw” the box, using your mouse. Comment on the trend by typing something like Net profit is decreasing or Net profit is increasing. Drag the text box to the proper location (near the Net Revenue/Loss numbers). Adjust the font and color of the text.
 Include a comment on cell E36 by rightclicking on the cell and selecting the Insert Comment option (or selecting the Review tab and the New Comment) Comment on the third year’s Net Revenue/Loss.
 Add a descriptive header and footer to your spreadsheet by selecting the Insert tab and the Header & Footer For the header, enter ITP 101 Spring 2017. For the footer, enter your name.
 Save your Excel workbook as Lastname_Firstname_Excel1, replacing Lastname and Firstname with your own last name (family name) and first name (given name).
Income Projection for Location B
Figure 3: Location B Financials worksheet (dates and numbers may differ from instructions below)
Copy Worksheet for Location A to Begin Analysis for Location B
Refer to figure 3, 4, and 5 for the following tasks.
 Copy the Location A Financials worksheet by rightclicking on it and selecting the Move or Copy… Refer to Figure 4 below.
Fig. 4. Move or Copy dialog
 Verify your worksheet is listed under To book.
 Below Before sheet, select “(move to end).”
 Click the Create a copy
 Click the OK
 Rename your copied worksheet to Location B Financials.
Figure 5: Financials for Location B (use these numbers for Location B)
 In the Location B Financials worksheet, use the exact values of the Revenues, Cost of Sales, and Operating Expenses for all three years as shown in Figure 5.
 Look at the source data at the bottom of Location B’s chart, and make sure the Operating Expenses, Cost of Sales, and Revenues in the chart are referring to the figures in Location B’s income statement.
 Rename the title in cell B3 to Location B’s Projected Income Statement.
 Change the message in the text box and the comment in E36.
 Save your Excel workbook, and upload it to Blackboard. Submit your Excel file on Blackboard (http://blackboard.usc.edu) under Assignments.
 Click on the Lab2 Part1
 Next to Attach File, click on the Browse My Computer
 Find your Lastname_Firstnamexlsx file and click the Choose button.
 Click on the Submit button in the bottom right corner.
Part 2 – Projections
When doing projections for future revenues and expenses with different scenarios possible, it is useful to have comparison charts for breaking down percentage of revenues and expenses.
For this part of the project, you will breakdown the revenues, cost of sales, and operating expenses for the first year of your business (note: illustrations show past years; you should work in present and future, not past years).
We will also create a chart showing growth in revenues and expenses. We will show later the adjustment growth based on inflation.
Figure 6: 2017 Projection Breakdowns worksheet (note: years and figures may vary from your worksheet)
Excel provides many ways to perform an action. If your version of Excel does not precisely match any of these directions, hunt around the toolbar and menus and sidebar. Don’t be afraid to try things. You can always backtrack by using ControlZ (Windows) or CommandZ (Mac).
 Use your existing Excel file (turned in for Lab2 Part 1), and work in a new sheet. Excel 2010: Rename Sheet2 to 2017 Projection Breakdowns. Excel 2013: create a new sheet and name it 2017 Projection Breakdowns.
 Excel 2010: Insert a new Pie Chart by selecting the Insert tab, clicking on the Pie pulldown and selecting the Pie in 3D Excel 2013: remember the discussion re the graph in the Location A sheet, about how the Excel tool ribbon works. In your new blank sheet, click the Insert tab. Look for the Charts section of the tool ribbon. Just above the C in Charts, you should see a tiny pie chart (it looks a little bit like PacMan). Click PacMan, and select 3D Pie. A blank chart area appears (there is no pie chart yet because you haven’t selected the data for it yet).
 Select the Design tab (Excel 2013: you are already in the Chart Tools/Design tab), and select the Select Data That opens the Select Data Source dialog.
Figure 7: Select Data Source window
 Put the cursor in the Chart data range text field at the top of the dialog, then go to the Location A Financials worksheet and select cells C6:C9. Now your “Chart data range” shows =’Location A Financials’!$C$6:$C$9 (Note: if you wish, you can type that into your “Chart data range” field.) These numbers (C6 to C9) give you the amounts that will determine the pie wedges in your first chart.
 Now look at the left side of the dialog, under the Legend Entries (Series) label, and click on the Edit button (“Series 1” is highlighted, and you’re editing Series 1).
 In the Edit Series window, for the Series name type Location A Projected Revenues, 2017 and then click the OK Now you’ve written the title of your pie chart. NOTE: there is a problem that can occur during the process of typing the Series name, if you hold down the Shift key while hitting the Space bar on your keyboard. Some unwanted text will appear in your series name, like the illustration below. Do not press Shift and Space at the same time while typing the series name!
 Now look at the right side of the dialog and find Horizontal (Category) Axis Labels, and click on the Edit
 In the Axis Labels window, for the Axis Label range go to Location A Financials worksheet and select cells A6:A9. Click the OK You have now selected the labels for your pie segments (see image below).
 Now you are back in the Select Data Source window. You’re done here, so click the OK
 Now you’re going to change the layout of your pie chart. In Excel 2010: Under the Design tab in the Chart Layouts section, click the pulldown and select the Chart Layout 2 Excel 2013: at the left end of the tool ribbon, click Quick Layout and select Layout 2.
 Position the chart so it approximately takes up the space from A1 through E15. Note: in Excel 2013, if you pull the edge of the chart area too close to the edge of A1, the whole chart will just bounce back – so leave a smidgeon of space at the edge.
 Click on the Pie Chart. Rightclick inside the pie to bring up some dialog options, and select the Format Data Labels… Depending on whether you have Excel 2010 or 2013, you’ll see one of the following menus (Figure 8):
Left: Excel 2010 (dialog) Right: Excel 2013 (sidebar)
Figure 8: Format Data Label(s)
 In the Format Data Label dialog or sidebar, for the Label Contains checkboxes, select the Value (Percentage and Show Leader Lines should already be checked.) For the Label Position radio buttons, select the Inside End (or Best Fit) option. For the Separator pulldown, select the (New Line) option. Excel 2010: Click the Close button. Excel 2013: if you want to close the sidebar, click the X icon at upper right corner of the sidebar.
Important point for Excel 2013. The Format Data Label window has been rolled into the properties sidebar at the right side of the interface. Rightclicking on a specific part of the chart will pull up a popup menu that allows you to engage this side properties menu relating to the content you rightclicked. As examples:
 Clicking on the pie chart itself will reveal “Format Data Series…”.
 Clicking on the chart title will reveal “Format Chart Title…”
 Clicking on the data labels will reveal “Format Data Labels…”
The content of the sidebar is populated based upon what you selected or clicked most recently. This allows one section of the interface to service a range of different operations and functions. Since many of Excel 2013’s features rely on this menu, if you aren’t seeing an option or menu you are looking for, it may be worth rightclicking on the specific chart element to see if it can be modified in the sidebar.
Lastly… If you are looking to add chart elements you may find those elements in the Chart Tools Design Tab via “Add Chart Element”
 Now change the pie’s rotation settings. In Excel 2010: Under the Layout tab, click on the 3D Rotation In Excel 2013: rightclick the pie chart itself, and select 3D Rotation…
 In the Format Chart Area window, set the X value to 310, the Y value to 30, and the Perspective value to 20. While you are changing values, click the up and down arrows to change the angles, and watch the pie chart to see what happens. Excel 2010: when done, click the Close Excel 2013: you don’t need to close the sidebar. Why not just leave it open.
 Excel 2010: Under the Design tab, change the Chart Style to whatever you wish. Excel 2013: to change the chart style, click the paintbrush icon at the upper right side of your chart’s box (see image above – if you don’t see a paintbrush icon in your program, click in the chart area); you can alter the Style and/or the Color by clicking the tabs at top. Note that the colors come in color groups, and cannot be individually changed. To close the Style/Color dialog (see image below), click in an empty cell.
 Select the entire pie chart by clicking its center. Excel 2010: Under the Format tab, click on the Shape Effects pulldown and select the Bevel à Circle This will soften the edge of the chart. Excel 2013: in the sidebar, click the Pentagon icon and click 3D FORMAT to select your desired top and bottom bevels. You can also change the Material if desired.
 Change the size of the font of the Title so it fits nicely in the chart. Select the title, go to the Home tab, and reduce the size of the font, if necessary.
 Now you’ve made a pie chart for the Location A Revenues. Repeat these same steps and make pie charts for the Location A Cost of Sales and Operating Expenses, and the Location B Revenues, Cost of Sales, and Operating Expenses. That’s six pie charts in all, all in the same worksheet. Arrange the charts so that all three of Location A charts are on top and all three of Location B charts are on the bottom as shown in Figure 6. Try to get the values inside of the chart’s “pie slices” by changing the perspectives. Note: if desired, you can copy your first pie chart and make five copies of it, then change the data and labels of each. Know, however, that this may not be a timesaver in the end.
Figure 9: Financial Trends worksheet
 Rename Sheet3 to Financial Trends. If you need to add a new slide (Excel 2013 users will need to), click on the Insert Worksheet button (it looks like a plus sign in a circle) at the bottom and then rename the sheet.
 Excel 2010: Insert a new column chart by selecting the Insert tab, clicking on the Column pulldown and selecting the Clustered Column Excel 2013: the Column charts are the topleft icon in the Charts section of the tool ribbon.
 Under the Design tab, click on the Select Data
 In the Select Data Source window, under the Legend Entries (Series) label, click on the Add
 In the Edit Series window, for the Series name enter Location A Revenues. (Note: when typing a series name, be careful not to accidentally hold the Shift key down while hitting the Space bar.) For the Series values, delete the text that is there (by using the delete or backspace key). Go to the Location A Financials worksheet and highlight cells C10:E10. Click the OK
 In the Select Data Source window, under the Horizontal (Category) Axis Labels label, click on the Edit
 In the Axis Labels window for the Axis label range, click on the Location A Financials worksheet and select cells C4:E4 (the years). Click the OK
 Back in the Select Data Source window, repeat the previous steps (2326) for Location B Revenues, Location A Cost of Sales, Location B Cost of Sales, Location A Operating Expenses, and Location B Operating Expenses. You will need to use your brain and select the appropriate worksheet and cells. Once you are done, click the OK
 Under the Chart Tools/Design tab, click on the Chart Layouts pulldown (Excel 2010) and select Layout 7. Excel 2013: you’ll need to click Quick Layout (in the Chart Layouts section of the tool ribbon, left side of the window) to find Layout 7.
 Excel 2010: Under the Design tab, click on the Chart Styles pulldown and choose a style.
Excel 2013. You can select from a few different styles and color combinations by clicking the paintbrush icon to the right of your chart. You can fiddle with the formatting by selecting sections of your chart and using the sidebar (pentagon icon), but Excel 2013 is not very friendly (you can adjust one series at a time — not all the columns at once, unless you discover a secret method). Just make a nicelooking clustered column chart.
 Remove all axis titles by clicking on the Layout tab (Excel 2013: click Add Chart Element, mouse over Axis Titles) and using the Axis Titles option, remove both horizontal and vertical titles.
 Add a chart title by going to the Layout tab (Excel 2013: click Add Chart Element, mouse over Chart Title) and using the Chart Title Enter the title Revenue and Expense Projections.
 Save your file under a new name: Lastname_Firstnamexlsx
 Submit your Excel file on Blackboard (http://blackboard.usc.edu) under Assignments.
 Click on the Lab2 Part2
 Next to Attach File, click on the Browse My Computer
 Find your Lastname_Firstnamexlsx file and click the Choose button.
 Click on the Submit button in the bottom right corner.
Part 3 – Further Financial Analysis
Quite often, economic conditions govern which investment a company should make. The financial calculation of an investment’s net present value enables a company to consider these economic conditions and make an educated decision as to which investment to make. In this exercise, you will learn how to use Excel as a tool to make these kinds of informed decisions.
For this part of the project, you will be assessing the expansion of your business. Your company, whether it is a retailer or manufacturer, will be opening up a new location for business operations. You will choose between the two locations that you earlier created income statements. Each location will generate different revenues, which you previously estimated. This assignment will allow you to determine which location will be the most lucrative, based upon the prevailing economic conditions.
You will first use Excel’s builtin functions to “look up” values based upon certain criteria. Then, you will calculate the Net Present Value so as to compare investment in the two different locations with varying returns over the next three years under different economic inflationary conditions. Using an IfThen function, you will have Excel determine which location you should invest in. Then using a Payment function you will determine the required monthly payments when the cost of investing in each location is borrowed. Finally, you will chart the results of the Net Present Value calculations to “see” the complete potential of the two locations under the varying economic conditions and to determine at which inflationary rate both locations become equally attractive.
Figure 10: NPV worksheet (note: dates may vary)
The NPV Sheet Layout
Refer to Figure 10 for the following tasks.
 Using your most recent Excel file (turned in for Lab2 Part2), create a new worksheet by clicking on the New Worksheet icon at the bottom (Excel 2013: looks like a circle with a plus sign in it).
 In the new worksheet, create the spreadsheet shown in Figure 10, including the cell formats shown. Merge & center the text Net Present Value at Various Inflationary Rates in cells F12:K12. The only numbers you will enter manually are the Square Footage and %NPV
 For the %NPV rates (cells F13:K13), enter in 0, 01, 0.02, 0.03, 0.04, and 0.05, and then format them as a Percentage.
 The text in cell A8 that display the tax rate needs to be wrapped. In the Home tab, click the Wrap Text button (which is above the Merge & Center button).
 In cell A1, enter your name.
 In cell H1, type in your USC email address. Then select this cell by rightclicking on it and choose Hyperlink. Click on the email address button on the left, and type in your USC email address.
 Under Comparison of Two Locations, reference the Net Revenue/Loss amount from the Location A and Location B Financials worksheets for 2017, 2018, and 2019. For cell B15, you would reference cell C28 on the Location A Financials You will not have a value for B14 and C14, which is the amount you would have paid for the locations today.
 Rename the worksheet to NPV.
The Purchase Costs Sheet Layout
Figure 11: Purchase Costs worksheet
Refer to Figure 11 for the following tasks.
 Create a new worksheet.
 Rename the worksheet to Purchase Costs.
 In the new worksheet, enter the text and values as shown in Figure 11.
 Format the numbers as currency with no cents. Format the interest rates as percentages.
 Format the Purchase and Remodeling Costs Based Upon Square Footage data similar as it appears above. Under the Home tab, use the Format as Table Excel 2013: when you do this, you’ll get a Format As Table dialog, which wants to know which parts of your table are data, and whether or not the table has headers. If you selected A1:C9, you’ll see =$A$1:$C$9, and “My table has headers” is checked. The dollar signs are for absolute referencing (as opposed to relative referencing). Change $1 to $2, and hit OK. That’ll give you the format seen in figure 11, except that your row 1 is shown unformatted. Merge and center A1:C1, and format the table title to look similar to the headers in row 2. You’ll probably need to resize columns A through G; just highlight columns A through G and drag any column divider to the right, to resize all the selected columns.
 Give the loan table a range name by highlighting cells B13:G14. Click on the Formulas tab, select the Define Name option and enter LoanRates for the Name. Click the OK Alternatively, you may enter LoanRates in the Name Box (to the left of the formula box).
 In cells F3 and G3 reference the two locations’ square footage from the NPV Do not simply type in their values. In the formula bar, enter an =, click the NPV sheet, click the appropriate cell, and hit the enter key.
 In cells F4 and G4 use the VLOOKUP function to determine the purchase costs for the two different locations based upon the Purchase and Remodeling Cost table. For the VLOOKUP function for Location A, the first argument is F3, the second argument is $A$3:$C$9, and the third argument is 2 since we want the value from the second column.
 In cells F5 and G5, use the VLOOKUP function to determine the remodeling costs for the two locations. For the third argument you want the value from the third column.
 Use the ∑ AutoSum function in cells F6 and G6 to calculate the costs before taxes. Do not include the value for the Square Footage.
 Save your workbook.
Calculate Total Cost:
 Return to the NPV
 In cells B6 and C6, reference the purchase costs that were determined on the Purchase Costs worksheet for Location A and Location B.
 In cells B7 and C7, reference the remodeling costs that were determined on the Purchase Costs worksheet for Location A and Location B.
 In cells B8 and C8, calculate the 8.75% tax on the purchase cost of each location in cells B7 and C7 by using the appropriate formulas and cell references. For cell B8, enter =B6*8.75%. Display the results to the nearest dollar by utilizing the currency formatting.
 In cells B9 and C9, use the AutoSum function to add up the total cost of the two locations after taxes. Be careful not to include the value for the square footage in your AutoSum calculation.
 In cells B14 and C14, use cell references to include the cost of the two locations in the comparison table for Today. Since the values for the years are the net revenues/loss (if positive, then these are profits), the Today values for each location are the costs negated. For cell B14, the value is =B9. These values should be negative which will be represented with a negative sign or parenthesis or red text.
Calculate the loan amounts:
 Return to the Purchase Costs
 In cells F7 and G7, use cell references to get the total cost from cells B9 and C9 from the NPV This is your loan amount.
 To determine the annual interest rate for the two locations, an HLOOKUP will be necessary. In cell F9, use the HLOOKUP function to get the interest rate. The first argument will be the total cost, since the interest rate is dependent on the principle. The second argument is the table LoanRates. The third argument is the row index number, which is 2 since we are trying to retrieve the values from the second row of the LoanRates table.
 Change the format of cells F9 and G9 to Percentage.
 In cells F10 and G10, calculate the monthly payments for the loan amount using the PMT
 The first argument for the PMT function is the interest rate for the period of the payment. Since our interest rate is annual, and our payments are monthly, we have to divide by 12. So the value should reference cells F9 and G9, divided by 12.
 The second argument for the PMT function is the number of payments. Since there are 12 months in a year and we have a 3 year loan, the value is 36.
 The third argument for the PMT function is the present value. Since this is a loan, use the loan amount.
Calculate the NPV values:
 Return to the NPV
 Use the NPV function in cells F14:K15 to calculate the Net Present Values for the two locations under different inflationary rates.
 The first argument for the NPV function is the rate of discount over the length of one period. This is the inflationary rate. For cell F14, this argument is F13.
 The second argument is a range for the income. For cell F14 which is for Location A, this argument is $B$15:$B$17. For cells that need to reference Location B, use $C$15:$C$17.
 For the cells F14:K15, the value of Today needs to be added to the NPV result. For cell F14, the value is NPV(…)+$B$14.
 In cells D19 and D20, use an appropriate IF function to have Excel determine the correct answers to the two questions in rows 19 and 20 based upon the results of your NPV calculations.
 The first argument for the IF function is the logical test. Compare the values in the Net Present Values For cell D19 which asks at 1% inflation, this argument is G14>G15.
 The second argument for the IF function is the value if the logical test is true. For cell D19, we want to print the text Location A since location A would be more appealing. Thus this argument is E14.
 The third argument for the IF function is the value if the logical test is false. For cell D19, we want to print the text Location B since location B would be more appealing. Thus this argument is E15.
 In cells D21 and D22, reference the monthly payment values calculated on the Purchase Costs Do not simply type in the calculated values from the sheet.
Creating the NPV chart:
Figure 12: Sample NPV Chart (Note: your chart may differ)
On the NPV worksheet, create a line chart displaying the NPV values. Your chart data may differ from the above chart. Adjust your commentary accordingly.
 Select the range of cells you want to use for the chart (E13:K15).
 Select the Insert tab, click on the Line option (in the Charts area) and select the 2D Line Excel 2013: Insert/Charts/Line (chart type 1).
 Under Chart Tools, select the Layout Use the Chart Title option to add the following title above the chart: Net Present Value Calculation. Excel 2013: just click the chart title and type its new name.
 Use the Axis Titles option (Excel 2013: this is in Add Chart Element) to add the following title to the Horizontal Axis below the values: Inflationary Rates.
 Remove the chart’s background pattern and border by selecting Plot Area à None. Excel 2013: rightclick within the chart box but not within the chart area itself, and select Format Chart Area. The sidebar appears, with the title Format Chart Area. Click the Chart Options dropdown and select Plot Area. Select No line under BORDER.
 Remove the gridlines by selecting Gridlines à Primary Horizontal Gridlines à None and Gridlines à Primary Vertical Gridlines à None. Excel 2013: click Add Chart Element (left side of the tool ribbon), mouse over Gridlines, and click on Primary Horizontal Gridlines. Repeat for Primary Vertical Gridlines if there are vertical gridlines in your chart.
 Change the Yaxis to remove some of the unneeded white space at top and bottom of the chart. To do this:
 Select the Vertical (Value) Axis section in the chart and click on the Format Selection option. (Excel 2013: first leftclick then rightclick a number at the left of the chart, then select Format Axis, and look at the sidebar.)
 In the Axis Options section of the Format Axis window, for the Minimum option select the Fixed radio button (Excel 2013: there is no Fixed button) and change the value in the Minimum text field to be the nearest major dollar amount below the lines (to reduce the amount of white space in the chart).
 Note: the Minimum value is shown above the Maximum value, which can be confusing for the visuallyoriented.
 If you see a value such as “2.7E6” that means “2.7 million.” E6 is “ten to the sixth power.”
 Change the Maximum option to be the nearest major value above the lines (again: to reduce the amount of white space).
 The Major unit amount may be either 50000 (50,000) or 100000 (100,000).
 (Excel 2013: you may not need to perform the following step.) Select the Number option, and change the Category to Currency and the Decimal places text field to 0.
 (Excel 2013: skip the following step.) Click the Close button.
 Change the two Location NPV data lines to thicker lines. Select each line and click on the Format Selection (Excel 2013: click a line and look at the sidebar.) Click on the Line Style option, and change the Width to 4 pt.
 Make sure the tick marks cross the X and Yaxes, and the Xaxis labels should align with the tick marks. To do this:
 Click on the Horizontal (Category) Axis section (the percentages) in the chart, and select the Format Selection (Excel 2013: first leftclick then rightclick one of the percentages in the horizontal axis in your chart, and select Format Axis, and open the Tick Marks section. If you do not see the Tick Marks option, rightclick the horizontal axis number again and select Format Axis again.) In the Format Axis window, make sure the Axis Options is selected. For the Major tick mark type, change the pulldown to Cross. For the Position Axis, select the On tick marks radio button.
 Click on the Vertical (Value) Axis section in the chart, and select the Format Selection (Excel 2013: if your sidebar is still open, you want Format Axis / Axis Options/ [three columns icon]/TICK MARKS.) For the Major tick mark type, change the pulldown to Cross. Click the Close button (Excel 2013: close the sidebar with the X at upper right corner).
 Add a Text Box to the worksheet. Under the Layout tab in the Insert section (Excel 2013: under the Text section of the Insert tab), click the Text Box
 If the two lines cross, then the two locations are equally attractive at the corresponding inflation rate. In the text box, enter a message stating the inflation rate such as (for example) “The locations are equally attractive at 10%.”
 If the two lines do not intersect, then one location is always preferable. In the text box, enter a message stating the preferable location such as “Location A is preferable.”
Final checks:
 Verify all dollar amounts are to the nearest dollar (no decimals) on all sheets. Every dollar amount should be formatted using the standard accounting format.
 To test the project once you have finished, change the Square Footage on the NPV For example, change Location A to 6000 and Location B to 8000. All the cell values that you calculated, including the Chart, should change.
 Change the square footage back to 5575 for Location A and 3750 for Location B. (Hitting ControlZ twice should return those values to what they were before.)
 Check all sheets for formatting. Match font boldness and cell borders and cell color fills to the illustrations in these instructions. (You may choose different colors, but where a cell is colorfilled in the illustrations, they should be colorfilled in your file.)
Data1  Data2  relative  relative  absolute  absolute  abs col, rel row  abs col, rel row  rel col, abs row  rel col, abs row 
1  10  1  1  1  1  
2  20  
3  30  
4  40  
5  50  
6  60  
7  70  
8  80  
9  90  
10  100  
Start at one of the thick boxes (C2, E2, G2, I2)  
Auto complete down the column (C, E, G, I)  
Auto complete to the right of the column (D, F, H, J) 
Submitting the project
 There should be a total of 6 worksheets in your Excel workbook. Arrange them in the following order: Location A Financials, Location B Financials, 2017 Projection Breakdowns, Financial Trends, NPV, Purchase Costs.
 Save the Excel file as Lastname_Firstnamexlsx, where Lastname and Firstname are replaced with your Lastname (family name) and Firstname (given name).
 Submit your Excel file on Blackboard (http://blackboard.usc.edu) under Assignments.
 Click on the Lab2 Part3
 Next to Attach File, click on the Browse My Computer
 Find your Lastname_Firstnamexlsx file and click the Choose button.
 Click on the Submit button in the bottom right corner.