Factor the polynomial y^5+32

The sum of two consecutive odd integers is 84. Find the two integers.

Rudik [331]

Answer: n + (n + 2) = 84

Step-by-step explanation:

If n is the smallest integer, the other integer must be two more than that, because it has to be odd. The two numbers add up to 84, so the other side of the equation is 84.

5 0

3 years ago

Read 2 more answers

A government report gives a 99% confidence interval for the proportion of welfare recipients who have been receiving welfare ben

juin [17]

Answer:

The estimation for the proportion for this case is $\hat p = 0.21$

And we know that the 99% confidence interval is given by:

$0.21 \pm 0.045$

So then the margin of error at 99% of confidence is 0.045, and the margin of error is given by this formula:

$ME= z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

If we decrease the confidence level this margin of error can't be higher than 0.045 so then the correct answer for this case would be:

d. 21% ± 4.8%

Because if the z value decrease from 2.58 to 1.96 not makes sense that the margin of error increase from 0.045(4.5%) to 0.048(4.8%)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

The estimation for the proportion for this case is $\hat p = 0.21$

And we know that the 99% confidence interval is given by:

$0.21 \pm 0.045$

So then the margin of error at 99% of confidence is 0.045, and the margin of error is given by this formula:

$ME= z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

If we decrease the confidence level this margin of error can't be higher than 0.045 so then the correct answer for this case would be:

d. 21% ± 4.8%

Because if the z value decrease from 2.58 to 1.96 not makes sense that the margin of error increase from 0.045(4.5%) to 0.048(4.8%)

5 0

3 years ago

-2(2x+3)=-4(x+1) - 2

mario62 [17]

Answer:

All real numbers are solutions

Step-by-step explanation:

Let's solve your equation step-by-step.

−2(2x+3)=−4(x+1)−2

Step 1: Simplify both sides of the equation.

−2(2x+3)=−4(x+1)−2

(−2)(2x)+(−2)(3)=(−4)(x)+(−4)(1)+−2(Distribute)

−4x+−6=−4x+−4+−2

−4x−6=(−4x)+(−4+−2)(Combine Like Terms)

−4x−6=−4x+−6

−4x−6=−4x−6

Step 2: Add 4x to both sides.

−4x−6+4x=−4x−6+4x

−6=−6

Step 3: Add 6 to both sides.

−6+6=−6+6

0=0

Answer:

All real numbers are solutions.

8 0

3 years ago

How much simple interest is earned on $6000 principal, with an annual interest rate of 3.7% over 5 years?

diamong [38]

I = PRT
P (principal) = 6000
R (rate) = 3.7%.....u need decimal form = 0.037
T (time) = 5

I = (6000)(0.037)(5)
I = 1110.00 <===

u dont need years as a decimal...u need rate as a decimal

8 0

3 years ago

Read 2 more answers

Rectangle abcd is the image of rectangle abcd after a dilation. What is the scale factor of the dilation? Enter your answer in t

Ivanshal [37]

The scale factor of dilation is 1/2 or
$\frac{1}{2}$
because the number of rectangle one is multiplied by 1/2 to make rectangle 2

good luck

6 0

3 years ago

Read 2 more answers

Factor the polynomial y^5+32​

Factor the polynomial y^5+32