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3 years ago

If ac−b=1, which expression represents c? i wil lmark you the brainliest

Mathematics

1 answer:

dolphi86 [110]3 years ago

6 0

Answer:

The expression for c is

$c = \frac{b + 1}{a}$

Step-by-step explanation:

The given equation is

$ac - b = 1$

To find an expression that represents,c we need to make c the subject.

Add b to both sides

$ac = 1 + b$

We now divide both sides by 'a'

$\frac{ac}{a} = \frac{b + 1}{a}$

Simplify the LHS to get:

$a= \frac{b + 1}{a}$

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zheka24 [161]

Answer:

The sample size needed if the margin of error of the confidence interval is to be about 0.04 is 18.

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.

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

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

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

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So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

Past studies suggest this proportion will be about 0.15

This means that $p = 0.15$

Find the sample size needed if the margin of error of the confidence interval is to be about 0.04

This is n when M = 0.04. So

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

$0.04 = 1.96\sqrt{\frac{0.15*0.85}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.15*0.85}$

$\sqrt{n} = \frac{1.96\sqrt{0.15*0.85}}{0.04}$

$(\sqrt{n})^{2} = (\frac{1.96\sqrt{0.15*0.85}}{0.04})^{2}$

$n = 17.5$

Rounding up

The sample size needed if the margin of error of the confidence interval is to be about 0.04 is 18.

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