College Math Milestone 4
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School
Arapahoe Community College *
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Course
120`092
Subject
Industrial Engineering
Date
Feb 20, 2024
Type
Pages
11
Uploaded by BarristerQuail3079
oD SR UNIT 4 — MILESTONE 4 5/8 5/ 8 < that's 63% RETAKE @ 5 questions were answered correctly. 3 guestions were answered incorrectly. T @ You start a new job as a manufacturing sales representative. You are paid $22 per hour plus a 16% commission on all of your sales. How much will you earn if you work 2,400 hours and sell $300,000 worth of product this year? O $57,600 O $88,900 O $92,400 © O $100,800 RATIONALE To find the answer, determine your annual earnings from your regular wage by multiplying it by the number of hours you work in the year. Determine your earnings from commissions by converting the percentage into a decimal.
oD SR UNIT 4 — MILESTONE 4 5/8 CONCEPT — Gross Pay Report an issue with this question 2 @ You want to buy a new car. The bank offers you a loan for $30,000 at a 3% interest rate. You are willing to pay $4,500 in interest over the life of the loan. Using a simple interest calculation, how many years must you pay off the loan to meet your goal? O 6 years P o 5 years O 7/ years O 3 years RATIONALE To find the answer, use the formula for simple interest: | = PRT First, convert the interest rate to a decimal. Place the numbers into the simple interest formula.
oD SR UNIT 4 — MILESTONE 4 5/8 ‘ ‘ Solution. CONCEPT — Simple Interest Report an issue with this question 3 @ Suppose $28,000 is deposited into an account paying 5.25% interest, which is compounded continuously. How much money will be in the account after 4 years if no withdrawals or additional deposits are made? © O $34,542.99 O $30,904.77 O $36,72116 O $32,748.23 RATIONALE If an account is being continuously compounded, the following formula can be used:
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oD SR UNIT 4 — MILESTONE 4 5/8 L= Tiariper Ol yedis — 4 Substitute the known values and solve for A, the account balance after 4 years: CONCEPT — Continuously Compounding Interest Report an issue with this question 4 @ Suppose an account pays 2.5% interest that is compounded annually. At the beginning of each year, $10,000 is deposited into the account (starting with $10,000 for the first year). Assuming no withdrawals or other deposits are made and that the interest rate is fixed, the balance of the account (rounded to the nearest dollar) after the seventh deposit is $77,201 Q© © 74,581 O $74,58 $76,816 O $75,474
oD SR UNIT 4 — MILESTONE 4 5/8 To find the account balance that was compounded annually AND also had $10,000 deposited each year, use the following formula: where: = initial balance = 10,000 r = growth factor (1+ APR) =1+ 0.025 =1.025 n = number of years/deposits = 7 Substitute the known values and solve for , the total balance after 7 years: CONCEPT — Savings With Regular Investments using Geometric Sequence Report an issue with this question 5 @ If $30,000 is invested at 5% annual interest compounded monthly, how long would it take for the account balance to reach $90,000? Round your answer to the nearest tenth.
oD SR UNIT 4 — MILESTONE 4 To find the answer, use the formula for compound interest and solve for t: where: A =90,000 P =30,000 r=5% or 0.05 n=12 To begin, substitute the known values and simplify the formula first by adding the values in the parentheses and dividing both sides by the coefficient. To undo the variable exponent, apply a logarithm to both sides and use the Power Property of Logs to move the variable outside the log. 5/8 ° o L 1.7 _yCGI o] O 19.4 years O 20.5 years RATIONALE
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oD SR UNIT 4 — MILESTONE 4 5/8 CONCEPT — Solving for Growth Time using Compound Interest Formula Report an issue with this question c @ To collect data on the signal strengths in a neighborhood, Tracy must drive from house to house and take readings. She has a graduate student, Dave, to assist her. Tracy figures it would take her 8 hours to complete the task working alone, and that it would take Dave 12 hours if he completed the task by himself. How long will it take Tracy and Dave to complete the task together? O 7.2 hours O 3.6 hours O 6.0 hours © O 4.8 hours RATIONALE
oD SR UNIT 4 — MILESTONE 4 5/8 denote the time as t. When we multiply the rate and time together, we get Tracy's work at (notice how the units for hours cancel). We can repeat this process for Dave. Dave's rate is 1task in 12 hours. We do not know the time it will take them to work on the project together, so we will just denote the time as t. When we multiply the rate and time together, we get Dave's work at . Now we can create a rational equation by adding Tracy and Dave's work together. The work is 1 task, so their combined work is equal to 1 task. In the rational equation, t is the amount of time it takes Tracy and Dave to complete the task together. With rational equations, we can add them together once they have common denominators. A simple way to find common denominators is to multiply the denominators of the fractions together. Make sure that you are doing this to all terms to ensure they all end up with the same denominator. Next, evaluate the multiplication. Now we have three fractions with common denominators. Once we have this, we can solve for t using the expressions in the numerator. To solve for t, first combine like terms. 12t plus 8t is equal to 20t. Finally divide both sides by 20 to solve for t. It will take Tracy and Dave 4.8 hours to complete the task together. CONCEPT — Determining Work Productivity Report an issue with this question 7 @ Rahul plans to invest $25,000 in a retirement account that compounds 6% monthly. He has 25 years left until he retires.
N SR UNIT 4 — MILESTONE 4 5/8 $705,638.91 O $92,483.55 O $101,230.57 O $111,624.25 © O RATIONALE To find the answer, use the formula for compound interest. First, convert the interest rate to a decimal. Place the numbers into the compound interest formula. Follow the order of operations (PEMDAS) to calculate the total, beginning with the parentheses. Next, calculate the exponent. Solution. CONCEPT — Compound Interest Report an issue with this question 8 @ Michelle earns $65,000/year at her job as an executive secretary and is paid monthly. Her most recent paycheck includes the
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oD SR UNIT 4 — MILESTONE 4 5/8 State income tax $95.00 Health insurance $244.25 Retirement savings $400.00 Considering her deductions, what percentage of her gross pay did Michelle take home? O 74.04% © O 69.87% O 73.18% © O 71.68% RATIONALE To determine the answer, begin by calculating Michelle’s monthly gross pay. Divide her annual salary by the number of months in the year. Next, add all of Michelle’s deductions together. Subtract the deductions from Michelle's gross pay to find her net pay. Divide her net pay by her gross pay. Multiply the amount by 100 to convert the answer into a percentage.
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