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Answer :
Sure, I'd be happy to provide a detailed step-by-step solution for each question!
### Solve each proportion.
15. [tex]\(\frac{\pi}{6} = \frac{7}{2}\)[/tex]
This is incorrect because:
[tex]\[\frac{\pi}{6} \approx 0.524 \quad \text{and} \quad \frac{7}{2} = 3.5\][/tex]
Since [tex]\(0.524 \neq 3.5\)[/tex], the given proportion is not valid.
16. [tex]\(\frac{3}{5} = \frac{x}{15}\)[/tex]
Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\[3 \cdot 15 = 5 \cdot x\][/tex]
[tex]\[45 = 5x\][/tex]
[tex]\[x = \frac{45}{5} = 9\][/tex]
So, [tex]\(x = 9\)[/tex].
17. [tex]\(\frac{4}{x} = \frac{10}{11}\)[/tex]
Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\[4 \cdot 11 = 10 \cdot x\][/tex]
[tex]\[44 = 10x\][/tex]
[tex]\[x = \frac{44}{10} = 4.4\][/tex]
So, [tex]\(x = 4.4\)[/tex].
18. [tex]\(\frac{6}{9} = \frac{4}{x}\)[/tex]
Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\[6 \cdot x = 9 \cdot 4\][/tex]
[tex]\[6x = 36\][/tex]
[tex]\[x = \frac{36}{6} = 6\][/tex]
So, [tex]\(x = 6\)[/tex].
### Write each as a percent.
19. [tex]\(6 \text{ out of } 100\)[/tex]
[tex]\(\frac{6}{100}\)[/tex] as a percent is:
[tex]\[6\%\][/tex]
20. [tex]\(\frac{1}{2}\)[/tex]
[tex]\[ \frac{1}{2} \times 100 = 50\%\][/tex]
21. [tex]\(0.6\)[/tex]
[tex]\[0.6 \times 100 = 60\%\][/tex]
22. [tex]\(1.8\)[/tex]
[tex]\[1.8 \times 100 = 180\%\][/tex]
23. [tex]\(\frac{4}{5}\)[/tex]
[tex]\[ \frac{4}{5} \times 100 = 80\%\][/tex]
24. [tex]\(0.02\)[/tex]
[tex]\[0.02 \times 100 = 2\%\][/tex]
### Write and solve a proportion for each problem.
25. What percent of 60 is 3?
Set up the proportion:
[tex]\[ \frac{3}{60} = \frac{x}{100} \][/tex]
Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\[3 \cdot 100 = 60x\][/tex]
[tex]\[300 = 60x\][/tex]
[tex]\[x = \frac{300}{60} = 5\][/tex]
So, [tex]\(3\)[/tex] is [tex]\(5\%\)[/tex] of [tex]\(60\)[/tex].
26. Find [tex]\(15\%\)[/tex] of [tex]\(200\)[/tex].
Set up the proportion:
[tex]\[\frac{15}{100} \cdot 200 = x\][/tex]
Calculate [tex]\(x\)[/tex]:
[tex]\[ x = \frac{15}{100} \times 200 = 30\][/tex]
So, [tex]\(15\%\)[/tex] of [tex]\(200\)[/tex] is [tex]\(30\)[/tex].
27. Five is [tex]\(2\%\)[/tex] of what number?
Set up the proportion:
[tex]\[ \frac{5}{x} = \frac{2}{100} \][/tex]
Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\[5 \cdot 100 = 2x\][/tex]
[tex]\[500 = 2x\][/tex]
[tex]\[x = \frac{500}{2} = 250\][/tex]
So, [tex]\(5\)[/tex] is [tex]\(2\%\)[/tex] of [tex]\(250\)[/tex].
28. What is [tex]\(6\%\)[/tex] of \[tex]$140?
Set up the proportion:
\[\frac{6}{100} \cdot 140 = x\]
Calculate \(x\):
\[x = \frac{6}{100} \times 140 = 8.4\]
So, \(6\%\) of \(\$[/tex]140\) is [tex]\(\$8.40\)[/tex].
I hope this helps! If you have any more questions, feel free to ask!
### Solve each proportion.
15. [tex]\(\frac{\pi}{6} = \frac{7}{2}\)[/tex]
This is incorrect because:
[tex]\[\frac{\pi}{6} \approx 0.524 \quad \text{and} \quad \frac{7}{2} = 3.5\][/tex]
Since [tex]\(0.524 \neq 3.5\)[/tex], the given proportion is not valid.
16. [tex]\(\frac{3}{5} = \frac{x}{15}\)[/tex]
Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\[3 \cdot 15 = 5 \cdot x\][/tex]
[tex]\[45 = 5x\][/tex]
[tex]\[x = \frac{45}{5} = 9\][/tex]
So, [tex]\(x = 9\)[/tex].
17. [tex]\(\frac{4}{x} = \frac{10}{11}\)[/tex]
Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\[4 \cdot 11 = 10 \cdot x\][/tex]
[tex]\[44 = 10x\][/tex]
[tex]\[x = \frac{44}{10} = 4.4\][/tex]
So, [tex]\(x = 4.4\)[/tex].
18. [tex]\(\frac{6}{9} = \frac{4}{x}\)[/tex]
Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\[6 \cdot x = 9 \cdot 4\][/tex]
[tex]\[6x = 36\][/tex]
[tex]\[x = \frac{36}{6} = 6\][/tex]
So, [tex]\(x = 6\)[/tex].
### Write each as a percent.
19. [tex]\(6 \text{ out of } 100\)[/tex]
[tex]\(\frac{6}{100}\)[/tex] as a percent is:
[tex]\[6\%\][/tex]
20. [tex]\(\frac{1}{2}\)[/tex]
[tex]\[ \frac{1}{2} \times 100 = 50\%\][/tex]
21. [tex]\(0.6\)[/tex]
[tex]\[0.6 \times 100 = 60\%\][/tex]
22. [tex]\(1.8\)[/tex]
[tex]\[1.8 \times 100 = 180\%\][/tex]
23. [tex]\(\frac{4}{5}\)[/tex]
[tex]\[ \frac{4}{5} \times 100 = 80\%\][/tex]
24. [tex]\(0.02\)[/tex]
[tex]\[0.02 \times 100 = 2\%\][/tex]
### Write and solve a proportion for each problem.
25. What percent of 60 is 3?
Set up the proportion:
[tex]\[ \frac{3}{60} = \frac{x}{100} \][/tex]
Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\[3 \cdot 100 = 60x\][/tex]
[tex]\[300 = 60x\][/tex]
[tex]\[x = \frac{300}{60} = 5\][/tex]
So, [tex]\(3\)[/tex] is [tex]\(5\%\)[/tex] of [tex]\(60\)[/tex].
26. Find [tex]\(15\%\)[/tex] of [tex]\(200\)[/tex].
Set up the proportion:
[tex]\[\frac{15}{100} \cdot 200 = x\][/tex]
Calculate [tex]\(x\)[/tex]:
[tex]\[ x = \frac{15}{100} \times 200 = 30\][/tex]
So, [tex]\(15\%\)[/tex] of [tex]\(200\)[/tex] is [tex]\(30\)[/tex].
27. Five is [tex]\(2\%\)[/tex] of what number?
Set up the proportion:
[tex]\[ \frac{5}{x} = \frac{2}{100} \][/tex]
Cross-multiply to solve for [tex]\(x\)[/tex]:
[tex]\[5 \cdot 100 = 2x\][/tex]
[tex]\[500 = 2x\][/tex]
[tex]\[x = \frac{500}{2} = 250\][/tex]
So, [tex]\(5\)[/tex] is [tex]\(2\%\)[/tex] of [tex]\(250\)[/tex].
28. What is [tex]\(6\%\)[/tex] of \[tex]$140?
Set up the proportion:
\[\frac{6}{100} \cdot 140 = x\]
Calculate \(x\):
\[x = \frac{6}{100} \times 140 = 8.4\]
So, \(6\%\) of \(\$[/tex]140\) is [tex]\(\$8.40\)[/tex].
I hope this helps! If you have any more questions, feel free to ask!
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