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3 years ago

Find the measure of S

Mathematics

1 answer:

KatRina [158]3 years ago

8 0

Answer:

151°

Step-by-step explanation:

Pentagons interior angles are always 540°. So to solve, you must put

540= (5x+2)+(10x-3)+(8x-19)+(7x-11)+(13x-31). After solving this you will get x=14 and you can now substitute x in for measure s.

13(14) -31

182 - 31

measure of s = 151°

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The Pew Research Center has conducted extensive research on the young adult population (Pew Research website, November 6, 2012).

Rudik [331]

Answer:

a) $0.93 - 1.96\sqrt{\frac{0.93(1-0.93)}{500}}=0.908$

$0.93 + 1.96\sqrt{\frac{0.93(1-0.93)}{500}}=0.952$

The 95% confidence interval would be given by (0.908;0.0.952)

b) $0.21 - 2.58\sqrt{\frac{0.21(1-0.21)}{500}}=0.163$

$0.21 + 2.58\sqrt{\frac{0.21(1-0.21)}{500}}=0.257$

The 99% confidence interval would be given by (0.163;0.0.257)

c) The margin of error for part a is:

$ME= 1.96\sqrt{\frac{0.93(1-0.93)}{500}}=0.0224$

And for part b is:

$ME=2.58\sqrt{\frac{0.21(1-0.21)}{500}}=0.0470$

So then the margin of error is larger for part b.

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".

The population proportion have the following distribution

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

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:

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

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:

$0.93 - 1.96\sqrt{\frac{0.93(1-0.93)}{500}}=0.908$

$0.93 + 1.96\sqrt{\frac{0.93(1-0.93)}{500}}=0.952$

The 95% confidence interval would be given by (0.908;0.0.952)

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:

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

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:

$0.21 - 2.58\sqrt{\frac{0.21(1-0.21)}{500}}=0.163$

$0.21 + 2.58\sqrt{\frac{0.21(1-0.21)}{500}}=0.257$

The 99% confidence interval would be given by (0.163;0.0.257)

Part c

The margin of error for part a is:

$ME= 1.96\sqrt{\frac{0.93(1-0.93)}{500}}=0.0224$

And for part b is:

$ME=2.58\sqrt{\frac{0.21(1-0.21)}{500}}=0.0470$

So then the margin of error is larger for part b.

7 0

3 years ago

Jim is hiking 4 1/2 mile trail.He has already hiked 2 5/8 miles.How much further does he have to hike?

musickatia [10]

Answer:

1 7/8

Step-by-step explanation:

2 5/8

+1 7/8= 4 1/2

7=3+4
5+3=8
2 5/8 + 3/8= 3
3 + 1= 4
4 + 4/8= 4 4/8
4 4/8 = 4 1/2

3 0

3 years ago

2. If all the letters in the word ENVELOPE are randomly rearranged, what is the probability the letters will

Aleonysh [2.5K]

The answer is D sorry if it’s wrong

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3 years ago

a skydiver jumps out of an airplane after 0.8 second she has fallen 100 feet after 3.1 seconds she has fallen 500 feet Emtiaz sa

Dennis_Churaev [7]

The answer may be no, because half of 500 is 250, and half of 3 is 1.5. If this is true, than the skydiver should fall 250 ft in 1.5 seconds.

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3 years ago

Read 2 more answers

A suitcase is a rectangular prism whose dimensions are 1 1/4 feet by 1 1/2 feet by 2 1/4 feet.Find the volume of the suitcase.

NNADVOKAT [17]

Answer:

The answer is " $\bold{\frac{135}{32}}$ ".

Step-by-step explanation:

$Volume= length \times width \times height\\\\\to 1\frac{1}{4}= \frac{5}{4}\\\\\to 1\frac{1}{2}=\frac{3}{2}\\\\\to 2\frac{1}{4}=\frac{9}{4}\\\\\to Volume= \frac{5}{4} \times \frac{3}{2}\times \frac{9}{4} = \frac{135}{32}$

7 0

3 years ago