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2 years ago

B) Express 0.6363......as a rational number in its lowest term.

Mathematics

1 answer:

bulgar [2K]2 years ago

8 0

Answer:

$\frac{7}{11}$

Step-by-step explanation:

We require 2 equations with the repeating digits (63) placed after the decimal point.

let x = 0.636363..... (1) multiply both sides by 100

100x = 63.6363... (2)

Subtract (1) from (2) thus eliminating the repeating digits

99x = 63 ( divide both sides by 99 )

x = $\frac{63}{99}$ = $\frac{7}{11}$ ← in simplest form

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igomit [66]

Answer:

a. The margin of error for the survey is of 0.0308 = 3.08%.

b. The 95% confidence interval that is likely to contain the exact percent of all people who favor the home team winning is (65.96%, 78.04%).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

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The margin of error of the survey is:

$M = \sqrt{\frac{\pi(1-\pi)}{n}}$

The confidence interval can be written as:

$\pi \pm zM$

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$M = \sqrt{\frac{0.72*0.28}{212}} = 0.0308$

The margin of error for the survey is of 0.0308 = 3.08%.

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$\pi - zM = 0.72 - 1.96*0.0308 = 0.6596$

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$\pi + zM = 0.72 + 1.96*0.0308 = 0.7804$

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0.6596*100% = 65.96%

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The 95% confidence interval that is likely to contain the exact percent of all people who favor the home team winning is (65.96%, 78.04%).

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3 years ago

B) Express 0.6363......as a rational number in its lowest term. ​

B) Express 0.6363......as a rational number in its lowest term.