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3 years ago

if the perimeter of the rectangle was known to be 90 in what would the value of x be in order for this to be true

Mathematics

1 answer:

Fofino [41]3 years ago

8 0

Answer:

x = 30 in

Step-by-step explanation:

length of rectangle is (2/3)x + 10; width is (1/3)x + 5;

perimeter is 90 in; find x:

P = 90 in = 2(2/3)x + 2(10) + 2(1/3)x + 2(5), or

90 in = (6/3)x + 30 in

Solving for x, we get (2)x = 60 in, or x = 30 in

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In a random sample of 150 customers of a high-speed Internetprovider, 63 said that their service had been interrupted one ormore

erastovalidia [21]

Answer:

a) The 95% confidence interval would be given by (0.341;0.499)

b) The 99% confidence interval would be given by (0.316;0.524)

c) n=335

d)n=649

Step-by-step explanation:

1) Notation and definitions

$X_{IS}=63$ number of high speed internet users that had been interrupted one or more times in the past month.

$n=150$ random sample taken

$\hat p_{IS}=\frac{63}{150}=0.42$ estimated proportion of high speed internet users that had been interrupted one or more times in the past month.

$p_{IS}$ true population proportion of high speed internet users that had been interrupted one or more times in the past month.

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".

The population proportion have the following distribution

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

1) Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$t_{\alpha/2}=-1.96, t_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

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

If we replace the values obtained we got:

$0.42 - 1.96\sqrt{\frac{0.42(1-0.42)}{150}}=0.341$

$0.42 + 1.96\sqrt{\frac{0.42(1-0.42)}{150}}=0.499$

The 95% confidence interval would be given by (0.341;0.499)

2) Part b

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$t_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58$

The confidence interval for the mean is given by the following formula:

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

If we replace the values obtained we got:

$0.42 - 2.58\sqrt{\frac{0.42(1-0.42)}{150}}=0.316$

$0.42 + 2.58\sqrt{\frac{0.42(1-0.42)}{150}}=0.524$

The 99% confidence interval would be given by (0.316;0.524)

3) Part c

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.42(1-0.42)}{(\frac{0.05}{1.96})^2}=374.32$

And rounded up we have that n=335

4) Part d

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.42(1-0.42)}{(\frac{0.05}{2.58})^2}=648.599$

And rounded up we have that n=649

5 0

3 years ago

What is 144÷8 in distributive property

aivan3 [116]

18 it is this please look144÷8=18

6 0

2 years ago

I go bowling every week and keep track of how many strikes i get: 2,0,4,7,7,0,1,0 Find the mode median and mean of this set of d

natima [27]

Answer:

Mode is 0
Median is 1
Mean is 2.625

Step-by-step explanation:

To find the mode, or modal value, it is best to put the numbers in order. A number that appears most often is the mode.
0, 0, 0, 1, 2, 4, 7, 7 = mode is 0

To find the Median, place the numbers in value order and find the middle number.
0 , 0 , 0 , 1 , 2 , 4 , 7 , 7 = median is 1

The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are.
0 + 0 + 0 + 1 + 2 + 4 + 7 + 7 / 8 = mean is 2.625

5 0

2 years ago

A/b + c/b=? Simmmmmpppppllllliiiifffyyy

liubo4ka [24]

Answer:

\frac{A+c}{b}

Step-by-step explanation:

\frac{A}{b}+\frac{c}{b}

3 0

2 years ago

Read 2 more answers

Can someone explain how you find the answer!

ahrayia [7]

Answer:

21m

Step-by-step explanation:

So for the rectangle, do 5*6, and you will get the area of the whole backyard. Then to get the area of the grass, you do 3*3 to get 9.

Finally, to get the cement, you subtract the area of the grass from the area of the whole backyard so 30-9 to get 21.

5*6=30

3*3=9

30-9+21

Please mark brainliest if you can!

Funny, I think you put the question in 2 times, this is the second time I'm answering this same question by you. :D

7 0

3 years ago

if the perimeter of the rectangle was known to be 90 in what would the value of x be in order for this to be true​

if the perimeter of the rectangle was known to be 90 in what would the value of x be in order for this to be true