4a) The vertices of a triangle are P(-7, -4) Q(-7, -8) and R(3, -3). What are the

bonufazy [111]

Step-by-step explanation:

$sin(360 \degree - \theta) \\ = sin \: 360 \degree \: cos \: \theta - cos \: 360 \degree \: sin \: \theta \\ = 0 \times \: cos \: \theta - 1 \times sin \: \theta \\ = 0 - sin \: \theta \\ = - sin \: \theta \\ \red{ \boxed{\bold{ \therefore \: sin(360 \degree - \theta) = - sin \: \theta}}}\\$

7 0

2 years ago

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In a random sample of 80 teenagers, the average number of texts handled in a day is 50. The 96% confidence interval for the mean

Nastasia [14]

Answer:

a) $\bar X =\frac{46+54}{2}=50$

And the margin of error is given by:

$ME= \frac{54-46}{2}= 4$

The confidence level is 0.96 and the significance level is $\alpha=1-0.96=0.04$ and the value of $\alpha/2 =0.02$ and the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

We can calculate the critical value and we got:

$z_{\alpha/2} = 2.05$

And if we solve for the deviation like this:

$\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}$

And replacing we got:

$\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45$

b) $ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828$

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor $\sqrt{2}$

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".

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma$ represent the population standard deviation

n=80 represent the sample size

Solution to the problem

Part a

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

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

For this case we can calculate the mean like this:

$\bar X =\frac{46+54}{2}=50$

And the margin of error is given by:

$ME= \frac{54-46}{2}= 4$

The confidence level is 0.96 and the significance level is $\alpha=1-0.96=0.04$ and the value of $\alpha/2 =0.02$ and the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

We can calculate the critical value and we got:

$z_{\alpha/2} = 2.05$

And if we solve for the deviation like this:

$\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}$

And replacing we got:

$\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45$

Part b

For this case is the sample size is doubled the margin of error would be:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828$

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor $\sqrt{2}$

5 0

2 years ago

the formula F=9/5C+32 changes a temperature reading from the Celsius scale C to the Fehrenheit scale F. What temperature measure

cestrela7 [59]

Answer:

23

Step-by-step explanation:

F=(9/5)c + 32

F=(9/5)(-5) + 32

F=(-9) + 32

F=23

6 0

3 years ago

1.

belka [17]

B)subtraction hopes this help:)

5 0

2 years ago

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Help me please giving more than 5 points!

Scilla [17]

To find the median you need to lay out all the answers by lowest to highest. Then, you’ll need to find the number that’s in the middle and that’s the median. However, if there’s 2 middle numbers you’ll need to add them then divide it by 2 and that’s the median.

5 0

2 years ago

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