Henry borrows $1025 at 10.5% simple interest. He makes a partial payment of $195 at the end of 9 month(s), and a partial payment of $390 at the end of 13 months. Determine the amount required to settle the debt at the end of 19 months using (a) Merchant's Rule and (b) U.S. Rule.

(a) Merchant's Rule: $

(b) U.S. Rule: $

Factor Values Find the numerical value of the following factors using (a) linear interpolation (b) the appropriate formula

1. (F/P,18%,33)

2. (A/G,12%,54)

Please round to the nearest cent for all answers.

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Compare the monthly payment and total payment for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs.

You need a ​$160,000 loan.

Option​ 1: a​ 30-year loan at an APR of 7.25%.

Option​ 2: a​ 15-year loan at an APR of 6.8%.

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Find the monthly payment for each option.

The monthly payment for option 1 is​what.

The monthly payment for option 2 is what.

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

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Find the total payment for each option.

The total payment for option 1 is what?

The total payment for option 2 is what?

​(Round to the nearest cent as​ needed.)

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Compare the two options. Which appears to be the better​option?

A. Option 1 will always be the better option.

B. Option 1 is the better​ option, but only if the borrower plans to stay in the same home for the entire term of the loan.

C. Option 2 is the better​ option, but only if the borrower can afford the higher monthly payments over the entire term of the loan.

D. Option 2 will always be the better option.

Discuss and compare the group summations and consolidation tools used with Excel. You may need to look up (research) the group summations.

Under what circumstances would you use each of these features? Do they both serve the same purpose, or is each one used under different scenarios? Give examples of how each can be used.

Objective: Apply elementary mathematical concepts and quantitative methods in business decision making under certainty.

Create a context: Introduce a real-world business situation or an imagined business scenario that may benefit from the "math" presented in the prior two weeks (Weeks 1 and 2 - see the objective stated in bold above). While creating the context, ask yourself: What business use cases may benefit from the quantitative methods offered last week and this week? Basi algebraic numbers, binary operations, integral exponents, equations, functions, or derivates. Pick one. You can use Google or other search tools, or your own workplace experience, to create the context.

Show with examples how the "math" or quantitative methodology introduced in the prior two weeks relate to the business use case you introduced. (e.g., does the math/methodology help to resolve a business problem?) Be specific in your description of how you can use the quantitative information in connection with the business case (your context) you described. Give examples. Use technical terminology when necessary.

Reflect on your learning by answering these questions: What changes have you observed in your own learning or knowledge of math/quantitative methods as a result of the topics introduced in Weeks 1 and 2 of this course? What did you find most valuable or useful for your MBA education and/or your current/future career? (As you articulate your thoughts for Part 3, be original: Do not repeat the business context or situation you described in Parts 1 and 2.

Suppose that it is impractical to use all the assets that are incorporated into a specified portfolio (such as a given efficient portfolio). One alternative is to find the portfolio, made up of a given set of n stocks, that tracks the specified portfolio most closely—in the sense of minimizing the variance of the different returns. Specifically, suppose that the target portfolio has (random) rate of return rM. Suppose that there are n assets with (random) rates of return r1, r2, … rn. We wish to find the portfolio rate of return: r = α1r1+ α2r2 + … + αnrn (with ∑_(i=1)^n▒αI = 1) minimizing var(r - rM) Find a set of equations for the αn’s Although this portfolio tracks the desired portfolio most closely in terms of variance, it may sacrifice the mean. Hence a logical approach is to minimize the variance of the tracking error subject to achieving a given mean return. As the mean is varied, this results in a family of portfolios that are efficient in a new sense, say tracking efficient. Find the equations of the αi’sthat are tracking efficient.

2. According to Newton’s Law of Cooling, the rate of change of the temperature of an object can be modeled using the following differential equation:

dT/dt = k(T-T_R)

where T is the temperature of the object (in ◦F), TR is the room temperature (in ◦F), and κ is the constant of proportionality.
On a crime show, the detective discovers a dead body in a hotel room.
(a) Write the differential equation to describe the change in temperature of the body if κ = −0.405 and thermostat in the hotel room is set at 70◦F.
(b) Solve the differential equation using an appropriate method. State the method you used and show your work.
(c) Assuming the victim was a healthy 98.6◦F at the time of the murder, we have the initial condition that T(0) = 98.6. Find the particular solution to the IVP.
(d) If the body temperature is 85◦F when the crime scene is discovered, how long has the victim been dead? (Assume t is measured in hours.)

Write a function called alternate that takes two positive integers, n and m, as input arguments (the function does not have to check the format of the input) and returns one matrix as an output argument. Each element of the n-by-m output matrix for which the sum of its indices is even is 1. All other elements are zero. For example, here is an example run:

>> alternate(4,5)

ans =

1 0 1 0 1

0 1 0 1 0

1 0 1 0 1

0 1 0 1 0

Once again, using the zeros function can help, but it is not necessary

Create A FMEA MATRIX With The Following Information:Failure modes and effects analysis is an approach or methodology that is used for the identification of possible failures in a process be it a design, a product or manufacturing and assembly operation. While analyzing the FMEA the following steps are follwed; Step 1: Detect a failure mode Step 2: Severity number (SEV) Step 3: Probability number (Occur) Step 4: Detection number (Detec) Arrive at the risk priority number (RPN) = SEV* Occur* Detec Analyze the actions again and check and reevaluate if necessary So now you can pick any topic you wish to. Let us consider for example the process of filling out a prescription; 1. The failure mode would include; wrong prescription might be filled out wrong dosage prescription may be switched while giving to customer generic medicine gievn instead of branded medicine 2. Severity of each of these failures have to be determined now(on a scale of 1-10),(the following is based on my opinion and you can change it) wrong prescription might be filled out- severity is 8 wrong dosage - severity is 9 prescription may be given to wrong customer- severity is 8 generic medicine given instead of branded- severity is 1 3. next step is to arrive at the proabability of occurrence (again 1-10); wrong prescription-2 wrong dosage- 4 wrong customer- 2 generic medicine -7 4. detection is again given in between 1-10 wrong prescription-2 wrong dosage- 3 wrong customer- 8 generic medicine-10 Now you can arrive at the RPN with the above information on your own. Analyzing the RPN will give you an insight on which of the identified failure mode has the greatest Risk. ow to place controls. Wrong prescription: Label each bottle clearly and donot place similar sounding or coloured bottle next to each other. Before filling out each prescription ensure book entry either manually or in electronic format so that there is a second review before the prescription goes to the next process of billing, etc Wrong dosage: Register entry after taking the weight of the prescription will put a check on this. Wrong customer ;either fill out as FIFO-First in First ot mode or place bar codes on each prescription pac, etc Generic medicine :this actually does not need to have a strict control as the risk to customer is minimal or highly unlikely.

1) A morbid inquiry: Which is greater – the number of people alive in the world at this moment or the number of people that have died in all of history? Think about how integration is part of the analysis to this question. Also consider that the total human population of the earth is accurately estimated for all of recorded history – let this function be P (t)

a) Use an integral to define a function Q (t) that expresses the cumulative sum of people who have lived and died up to a date t .

b) Do some quick research and speculate on whether or not Q(t) ≥ P(t) at this point in time. Justify your answer.

Induction

Say which of the following statement is correct. The implicit domain of all quantifiers is
N = {0, 1, 2, ...}. If you mark a statement as incorrect then state briefly what the problem is.
1. If p(0) and ∀n>0 (p(n) → p(n+1)) then ∀n p(n)
2. If p(1) and ∀n>0 (p(n−1) → p(n)) then ∀n p(n)
3. If p(0) and ∀n>0 (p(n−1) → p(n)) then ∀n>3 p(n)
4. If p(0) and ∀n>0 (p(n−1) → p(n+1)) then ∀n p(2n)
5. If p(0) and ∀n≥0 (¬p(n) ∨ p(n+1)) then ∀n p(n)

don't understand these questions.

Using Euclidean algorithm, Find integers x and y with 65537x + 3511y = 17.

1) Explain what it means to solve something by analytical, numerical, and graphical methods. What is the value and limitation of each method?

A First Course in Abstract Algebra Chapter S.22, Problem 27E

Let F be a field of characteristic zero and let D be the formal polynomial differentiation map, so that. D(a0 + a1x + a2x^2 + ••• + anx^n) = a1 + 2 • a2x + •••+n• anxn-1, i.e.

F be a field of characteristic zero , D:F[x]→F[x].

C) Find the image of F[x] under D. Is it important which characteristic the field has? Can you explain this enough?

http://www.chegg.com/homework-help/wooden-cubes-size-painted-different-color-face-make-children-chapter-S.22-problem-27E-solution-9780201763904-exc