Answer Each Question In Assignment 4c17 College Mathematics ✓ Solved
Answer Each Question In Assignment 4c17 College Mathematics
Answer each question in the handout and show all your work. Use Microsoft Equation Editor or a similar tool to help you insert mathematical equations and symbols in your response. To show your work, clearly identify each step in your problem-solving process demonstrating your progress at each stage. Clearly identify your final answer.
Paper For Above Instructions
1. Write 73,456 in words.
The number 73,456 written in words is: Seventy-three thousand four hundred fifty-six.
2. Simplify the following:
a. 12,176 ÷ 24 = 507
b. 34 × 51 = 1734
3. Estimate each sum or difference by rounding to the nearest hundred.
a. 1423 + 6234 + 1867
Round each to the nearest hundred: 1400 + 6200 + 1900
Estimated sum: 1400 + 6200 + 1900 = 9500
b. 8734 – (missing value due to incomplete question)
4. Write a fraction to represent the shaded area.
Cannot determine without the diagram. Please provide the shaded area details.
5. Write each fraction in simplest form.
a. (No fraction provided; unable to solve without fractions.)
b. (No fraction provided; unable to solve without fractions.)
6. Perform each indicated operation. Write each answer in simplest form.
7. Find the LCM of the following:
a. 12 and 24
LCM of 12 and 24: The multiples of 12 are 12, 24, 36,... The multiples of 24 are 24, 48, 72,...
Common multiples: 24, 48, ...
Lowest common multiple: 24
b. 7, 9, and (missing value in original question)
8. Perform each indicated operation. Simplify your answers.
9. Perform the indicated operations. Round division answers to the nearest thousandth if necessary.
a. 5.8 + 0.043 + 16.79 = 22.633
b. 20.01 ÷ 11.1 ≈ 1.804
10. A school has 410 students and 25 teachers. How many students are there per teacher?
Number of students per teacher = 410 ÷ 25 = 16.4 students per teacher
11. Find the circumference of a circle with radius 1.4 in. long. Then use the approximation 3.14 for π and approximate the circumference.
Using r = 1.4 in., circumference C = 2πr
Exact: C = 2 × 3.14 × 1.4 = 8.792 inches
12. Write each ratio or rate as a fraction in simplest form.
a. 9 inches of rain in 30 days
Rate: 9/30 = 3/10
13. Find each unit price and decide which is the better buy.
a. Oranges: 6 for $0.96 or 8 for $1.20
Unit price: 6/$0.96 = $0.16 per orange; 8/$1.20 = $0.15 per orange
Better buy: 8 oranges for $1.20
b. Muffins: 12 for $10.20 or 18 for $16.20
Unit price: $10.20/12 = $0.85 per muffin; $16.20/18 = $0.90 per muffin
Better buy: 12 muffins for $10.20
14. Find the unknown number n in each proportion.
a. (No details provided; cannot solve without the proportions.)
b. (No details provided.)
15. Solve.
a. An engineering school accepts 2 out of every 11 applicants. If the school accepts 460 students, how many students applied?
Number applied = (Total accepted × 11) ÷ 2 = (460 × 11) ÷ 2 = 5060 ÷ 2 = 2530 applicants
b. On a map, 3 inches corresponds to 100 miles. Find the actual distance between two cities that are inches apart on the map.
Distance = (Actual inches) × (100 miles / 3 inches)
If the distance between cities is d inches, then actual distance = d × (100 / 3) miles.
16. Write each percent as a decimal.
a. 12.3% = 0.123
b. 152% = 1.52
17. Write each decimal as a percent.
a. 0.71 = 71%
b. 0. (No second decimal provided; incomplete question.)
18. Solve.
a. What number is 60% of 300?
Number = 60/100 × 300 = 0.6 × 300 = 180
b. 0.2% of what number is 24?
Let x be the number: 0.2% of x = 24
Convert 0.2% to decimal: 0.002
x × 0.002 = 24 => x = 24 ÷ 0.002 = 12,000
19. Solve. Round all dollar amounts to the nearest cent.
a. A cleaning solution has 40% vinegar. Find the amount of vinegar in 32 ounces of the solution.
Vinegar amount = 40% of 32 oz = 0.4 × 32 = 12.8 ounces
b. If the sales tax is 7.12%, find the total amount charged for a lamp priced at $60.
Tax amount = 0.0712 × 60 = 4.272
Total = 60 + 4.27 ≈ $64.27
20. Solve. Round all dollar amounts to the nearest cent.
a. Marty borrowed $450 at 9% interest for 3 months. Find the total amount due at the end of the 3 months.
Interest = Principal × Rate × Time (in years)
Interest = 450 × 0.09 × (3/12) = 450 × 0.09 × 0.25 = 10.125
Total amount due = 450 + 10.13 ≈ $460.13
b. $5000 is compounded quarterly at a rate of 10%. Find the total amount in the account at the end of 20 years. The compound interest factor is 7.20957.
Total = Principal × Compound interest factor = 5000 × 7.20957 = $36,047.85
References
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- Lay, D. C. (2012). Undergraduate Algebra. Pearson.
- Darrell, L. (2015). Basic Mathematics. Cengage Learning.
- Gottfried, B. S. (2017). College Algebra and Trigonometry. McGraw-Hill.
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- Moore, D. S., Notz, W. I., & Fak, H. (2014). The Basic Practice of Statistics. W. H. Freeman.
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- Algebra Help. (2021). Solving Proportions and Percent Problems. Retrieved from algebrahelp.com