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Mila [183]
3 years ago
15

Find the value (64)3/2

Mathematics
1 answer:
faltersainse [42]3 years ago
3 0
(64)^3/2 = (sqrt(64))^3 = 8^3 = 512.
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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
Colin Sarah and Gordon share some sweets in the ratio 2:5:3 calling gets 26 sweets how many sweets are there at altogether toget
nikitadnepr [17]

Answer:

Collin: 26, Sarah: 65, Gordon: 39, so 130 altogether

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Tameka bought 50 cans of soda ( cola, grape, and orange) to serve at a party. She has 8 more colas than grape sodas, and 3 less
Gwar [14]

Answer:

Orange = 12

Grape = 15

Cola = 23

Step-by-step explanation:

Turning this into equations you can give each soda a variable

Cola = C | Grape = G | Orange = R

Then you get:

8 + G = C

R + 3 = G

C + G + R = 50

We want to get a variable all by itself in an equation so first I'm going to put the second equation (R + 3 = G) in the first (8 + G = C) by replacing the G to get

8 + (R + 3) = C  Combine the variables 11 + R = C and put that new equation into the last equation

(11 + R) + G + R = 50    

Now plug our original second equation (R + 3 = G) into our third to get

(11 + R) + (R + 3) + R = 50    

Combine and get

14 + 3R = 50      Subtract over the 14

3R = 36              Divide by 3

Orange Sodas = 12

Our new 3rd Equation is now:   C + G + 12 = 50, subtract over 12 to get

C + G = 38

Plug either equation 1 or 2 into that one, I'll do 1

(8 + G) + G = 38

8 + 2G = 38

2G = 30

Grape Sodas = 15

Now our 3rd equation is C + 15 = 38, subtract over 15

Cola Sodas = 23

Orange = 12

Grape = 15

Cola = 23

12 + 15 + 23 = 50

7 0
3 years ago
What is 45 divided by 8
Alenkasestr [34]
45 divided by 8 is 5 r. 5. You can write this like 5 5/8 too. 
5 0
3 years ago
Read 2 more answers
Can someone seriously help me
ElenaW [278]

Answer:

<em>6 inches</em>

Step-by-step explanation:

The mode is the most frequently occurring number.

The mode of Martha's Fish is 21.

The mode of Jamie's Fish is 15.

21 - 15 = 6

The mode of Martha's fish is<em> 6 inches</em> longer than the mode of Jamie's fish.

8 0
3 years ago
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