Find The Equation Of The Line Passing Through (5, 4) ✓ Solved

Find the equation of the line which passes through (5,4)

Degree: B.Sc. Accounting, Auditing and Finance / BBA College of Banking and Financial Studies

Type of Assessment: Take-Home Exam

Instructions: This assessment is a take-home exam which serves as a substitute for your final exam. It must be completed individually. Include your name and student number on the heading page. Answer all the questions and show all workings clearly wherever needed. Start each answer on a fresh page. Plagiarism is a serious offense, so ensure that your work is original and properly cited. The assessment is divided into two sections. Section A questions are compulsory and carry 60 marks, while Section B questions are also compulsory and carry 40 marks.

Section A:

1. Find the equation of the line which passes through (5,4) and has slope 6.
2. The projected population of a city is given by P = 0.17t/10 where t is the number of years after 2005. What is the projected population in 2065?
3. Suppose S = {1,2, 3,4,5,6,7,8,9,10} is the sample space for an experiment with events E = {2,6,7}, F={1,8, 10}, G = {1, 3, 5, 7, 9}. Find (a) E' ∩ F and (b) (E ∪ G) ∩ F'.
4. After the initial production run of a new style of steel desk, a quality control technician found that 50% of the desks had an alignment problem and 20% had both a defective paint job and an alignment problem. If a desk is randomly selected from this run and it has an alignment problem, what is the probability that it also has a defective paint job?

Section B:

1. Find the graph for the following equation: F(x)= x; 0
2. Find the amount for $50,000 for 10 years at 6% per annum compounded (a) monthly, (b) quarterly, (c) daily, (d) yearly.
3. Find the future value for R.O 60,000 for 10 years at 5% per annum compounded (a) half-yearly, (b) quarterly, (c) daily, (d) weekly.
4. In 20 years, you would like to have $40,000 saved for your child’s college education. At 10% annual interest, compounded monthly, what monthly deposit must be made to accomplish this goal?

Paper For Above Instructions

This paper addresses the quantitative methods as part of the B.Sc. Accounting, Auditing, and Finance program. Each question will be answered methodically, showing all workings and calculations clearly.

Section A

Question 1: Equation of the Line

The equation of a line can be derived using the point-slope form, which is given by:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line and m is the slope. Plugging in the provided values:

(x1, y1) = (5, 4) and m = 6:

y - 4 = 6(x - 5)

Expanding this equation gives:

y - 4 = 6x - 30

y = 6x - 26

Thus, the equation of the line is y = 6x - 26.

Question 2: Projected Population

The population function is given by P = 0.17t/10, where t is the number of years after 2005. For the year 2065, t will be:

t = 2065 - 2005 = 60

Substituting t = 60 into the population function:

P = 0.17(60)/10 = 1.02

This suggests that the projected population in 2065 is expected to reach a value of approximately 1.02 million, indicating population growth.

Question 3: Sample Space Events

To find (a) E' ∩ F:

- Universal set S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

- E' = {1, 3, 4, 5, 8, 9, 10} (the complement of E)

Thus, E' ∩ F = {1, 8, 10}, the intersection of E' and F which yields the values: {1, 8, 10}.

For (b) (E ∪ G) ∩ F':

- E ∪ G = {1, 2, 3, 4, 5, 6, 7, 8, 9} (combining sets E and G)

- F' = {2, 3, 4, 5, 6, 7, 9} (the complement of F)

Thus, (E ∪ G) ∩ F' = {2, 3, 4, 5, 6, 7, 9} gives the intersection values: {2, 3, 4, 5, 6, 7, 9}.

Question 4: Probability of Defective Paint Job

To find the probability that a desk has a defective paint job given that it has an alignment problem, we can apply the formula:

P(A | B) = P(A ∩ B) / P(B)

Let:

- A = defective paint job

- B = alignment problem

P(A ∩ B) = 20% or 0.2, and P(B) = 50% or 0.5. Thus:

P(A | B) = 0.2 / 0.5 = 0.4

This means there is a 40% probability that a randomly selected desk with an alignment problem also has a defective paint job.

Section B

Question 1: Graph for F(x)

To graph the piecewise function F(x), we need to evaluate each piece over its defined range. The graph consists of three line segments based on the specified intervals. A graph will be created based on the evaluations of the piecewise function F(x).

Question 2: Amount for $50,000 Compounded

Using the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

• P = principal amount ($50,000)
• r = annual interest rate (6% = 0.06)
• n = number of times interest applied per time period
• t = time in years (10 years)

Calculating for each compounding period:

• (a) Monthly: 12 times a year
• (b) Quarterly: 4 times a year
• (c) Daily: 365 times a year
• (d) Yearly: 1 time a year

Question 3: Future Value for R.O 60,000

Using the same compound interest formula, where the principal is 60,000 and the annual interest rate is 5% compounded differently based on the context provided.

Question 4: Monthly Deposit for College Fund

Using the future value of an annuity formula, calculate the monthly deposit required to achieve the goal of $40,000 in 20 years with a monthly compounding interest.

References

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• Weil, R. L., & Fardon, M. J. (2013). Corporate Finance. South-Western Cengage Learning.
• McLaney, E., & Atrill, P. (2019). Accounting and Finance. Pearson Education Limited.
• Ross, S. A., Westerfield, R. W., & Jordan, B. D. (2021). Essentials of Corporate Finance. McGraw-Hill Education.
• Albrecht, W. S., & Stice, J. D. (2019). Accounting: Concepts and Applications. Cengage Learning.
• Anthony, R. N., & Govindarajan, V. (2018). Management Control Systems. McGraw-Hill Education.
• Horngren, C. T., Datar, S. M., & Rajan, M. V. (2017). Cost Accounting: A Managerial Emphasis. Pearson.
• Palepu, K. G., & Healy, P. M. (2020). Business Analysis & Valuation: Using Financial Statements. Cengage Learning.
• Khan, M. Y., & Jain, P. K. (2019). Financial Management: Text, Problems and Cases. Tata McGraw-Hill Education.
• Gitman, L. J., & Zutter, C. J. (2019). Principles of Managerial Finance. Pearson.