What is the decimal number 34.576 written in expanded form?

What happens to the volume of a cylinder when the radius is doubled?

wlad13 [49]

When the radius is doubled, the volume of a cylinder quadruple

5 0

3 years ago

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A candidate for a US Representative seat from Indiana hires a polling firm to gauge her percentage of support among voters in he

UkoKoshka [18]

Answer:

a) The minimum sample size is 601.

b) The minimum sample size is 2401.

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:

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

For this problem, we have that:

We dont know the true proportion, so we use $\pi = 0.5$ , which is when we are are going to need the largest sample size.

95% confidence level

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

a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)

This is n for which M = 0.04. So

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

$0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.04\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.04}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2$

$n = 600.25$

Rounding up

The minimum sample size is 601.

b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

Now we want n for which M = 0.02. So

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

$0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.02\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.02}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.02})^2$

$n = 2401$

The minimum sample size is 2401.

4 0

3 years ago

Christian wants to make an A in his class. There are 5 exams this year, and he has taken 4 of them. His grades were 84, 88, 95,

ioda

Answer:

last test grade=x x ≥ 79 so 79%

Step-by-step explanation:

(84/5)+(88/5)+(95/5)+(104/5)+(x/5) ≥ 90

Simplify: (371/5)+(x/5) ≥ 90

Subtract (371/5) from both sides

Then you have (x/5) ≥ (79/5)

Then multiply both sides by 5 and you have x ≥ 79

P.S. If it was helpful please consider giving me brainliest. =)

3 0

3 years ago

21 divided by 15.015 step my step diving decimals

ser-zykov [4K]

Answer:

0.715

Step-by-step explanation:

4 0

3 years ago

Let ∠Q be an acute angle such that tanQ=0.04. Use a calculator to approximate the measure of ∠Q to the nearest tenth of a degree

Digiron [165]

We have been given that ∠Q is an acute angle such that $\text{tan}(Q)=0.04$ . We are asked to find the measure of angle Q to nearest tenth of a degree.

We will use arctan to solve for measure of angle Q as:

$Q=\text{tan}^{-1}(0.04)$

Now we will use calculator to solve for Q as:

$Q=2.290610042639^{\circ}$

Upon rounding to nearest tenth of degree, we will get:

$Q=2.3^{\circ}$

Therefore, measure of angle Q is approximately 2.3 degrees.

7 0

2 years ago