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3 years ago

Which fraction is equivalent to 0.16 the 6 is repeating. Please show the work .

Mathematics

2 answers:

chubhunter [2.5K]3 years ago

4 0

The answer would be 1/6.

To show work, you can just divide 1 by 6. This would give you the answer of 0.166666666...

sergiy2304 [10]3 years ago

3 0

Answer:

Answer is 1/6

Step-by-step explanation:

To convert 1/6 to decimal, just divide 1 by 6

(That's what the fraction is showing; a fraction = numerator ÷ denominator)

1 ÷ 6 = 0.16666666 ...

So that is 1 6 in decimal form!

( 0.16 recurring)

Note that per in percent means each and perc e n t means 100.

Therefore, percentage is just the quantity out of 100

! Simple!

So, multiply the decimal form of

1 6 by 100

(That is why I did decimal first)

0.16666666 ... ·(x) 100 = 16.66666 ... ... . %

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Answer:

(a) Margin of error ( E) = $2,000 , n = 54

(b) Margin of error ( E) = $1,000 , n = 216

(c) Margin of error ( E) = $500 , n= 864

Step-by-step explanation:

Given -

Standard deviation $\sigma$ = $7,500

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(a) Margin of error ( E) = $2,000

Margin of error ( E) = $Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$

E = $Z_{\frac{.05}{2}}\frac{7500}{\sqrt{n}}$

Squaring both side

$E^{2} = 1.96^{2}\times\frac{7500^{2}}{n}$

$n =\frac{1.96^{2}}{2000^{2}} \times 7500^{2}$

n = 54.0225

n = 54 ( approximately)

(b) Margin of error ( E) = $1,000

E = $Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$

1000 = $Z_{\frac{.05}{2}}\frac{7500}{\sqrt{n}}$

Squaring both side

$1000^{2} = 1.96^{2}\times\frac{7500^{2}}{n}$

$n =\frac{1.96^{2}}{1000^{2}} \times 7500^{2}$

n = 216

E = $Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$

500 = $Z_{\frac{.05}{2}}\frac{7500}{\sqrt{n}}$

Squaring both side

$500^{2} = 1.96^{2}\times\frac{7500^{2}}{n}$

$n =\frac{1.96^{2}}{500^{2}} \times 7500^{2}$

n = 864

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