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01 Sep 2022, 01:13
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E
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Difficulty:
25%
(medium)
Question Stats:
73% (00:53) correct
27%
(01:23)
wrong
based on 156
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Date
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What is the value of \((\sqrt[3]{800\%})^2\)
A. \(0.04\%\)
B. \(0.4\)
C. \(100\%\)
D. \(2\)
E. \(400\%\)
A. \(0.04\%\)
B. \(0.4\)
C. \(100\%\)
D. \(2\)
E. \(400\%\)
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30 Aug 2024, 08:48
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Official Solution:
What is the value of \((\sqrt[3]{800\%})^2\)?
A. \(0.04\%\)
B. \(0.4\)
C. \(100\%\)
D. \(2\)
E. \(400\%\)
Worth knowing that "per cent" from Latin literally means "per one hundred" or "out of one hundred", so for example, \(x\%\) is \(\frac{x}{100}\) (\(x\) per one hundred) and say \(5\%\) is \(\frac{5}{100} = 0.05\) (5 out of one hundred). On the other hand, we can write 0.05 as \(0.05*100\% = 5\%\) and say 20 as \(20*100\% = 2000\%\).
Basically, "%" symbol just means "per 100", or algebraically, "/100". Thus:
To drop "%" symbol, so to convert the percentage into a ratio, just divide by 100: \(m\% = \frac{m}{100}\). For example, \(10\%=\frac{10}{100}=\frac{1}{10}=0.1\) and \(400\%=\frac{400}{100}=4\).
To get "%" symbol, so to convert the ratio into a percentage, just multiply by 100%: \(n=n*100\%\) (100% is just 100/100 = 1, so we are essentially multiplying by 1). For example, \(0.4=0.4*100\%=40\%\) and \(15=15*100\%=1500\%\).
To sum up: \(x\%\) and \(\frac{x}{100}\) are just two different ways of writing the same thing: as a percentage and as a ratio.
Back to the question..
\((\sqrt[3]{800\%})^2 =\)
\(=(\sqrt[3]{\frac{800}{100}})^2 =\)
\(=(\sqrt[3]{8})^2 =\)
\(=(2)^2 =\)
\(=4 =\)
\(=400\%\)
Answer: E
What is the value of \((\sqrt[3]{800\%})^2\)?
A. \(0.04\%\)
B. \(0.4\)
C. \(100\%\)
D. \(2\)
E. \(400\%\)
Worth knowing that "per cent" from Latin literally means "per one hundred" or "out of one hundred", so for example, \(x\%\) is \(\frac{x}{100}\) (\(x\) per one hundred) and say \(5\%\) is \(\frac{5}{100} = 0.05\) (5 out of one hundred). On the other hand, we can write 0.05 as \(0.05*100\% = 5\%\) and say 20 as \(20*100\% = 2000\%\).
Basically, "%" symbol just means "per 100", or algebraically, "/100". Thus:
To drop "%" symbol, so to convert the percentage into a ratio, just divide by 100: \(m\% = \frac{m}{100}\). For example, \(10\%=\frac{10}{100}=\frac{1}{10}=0.1\) and \(400\%=\frac{400}{100}=4\).
To get "%" symbol, so to convert the ratio into a percentage, just multiply by 100%: \(n=n*100\%\) (100% is just 100/100 = 1, so we are essentially multiplying by 1). For example, \(0.4=0.4*100\%=40\%\) and \(15=15*100\%=1500\%\).
To sum up: \(x\%\) and \(\frac{x}{100}\) are just two different ways of writing the same thing: as a percentage and as a ratio.
\((\sqrt[3]{800\%})^2 =\)
\(=(\sqrt[3]{\frac{800}{100}})^2 =\)
\(=(\sqrt[3]{8})^2 =\)
\(=(2)^2 =\)
\(=4 =\)
\(=400\%\)
General Discussion
01 Sep 2022, 21:57
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800%=8; Cube root is 2; 2 squared is 4 which is 400%.
Answer E
Answer E
