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2 years ago

Pls help.

Mathematics

1 answer:

DIA [1.3K]2 years ago

5 0

Answer:

${ (15x)}^{2}$

$15 \times x \times 15 \times x$

$225 {x}^{2}$

${(x - 2)}^{2}$

$(x - 2) \times (x - 2)$

${x}^{2} - 2x - 2x + 4$

${x}^{2} - 4x + 4$

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A realtor would like to create a 95% confidence interval for the average price of a house in Franklin County, Ohio. To accomplis

VMariaS [17]

Answer:

$320128-1.96\frac{50324}{\sqrt{529}}=315839.52$

$320128+1.96\frac{50324}{\sqrt{529}}=324416.48$

So on this case the 95% confidence interval would be given by (315839.52;324416.48)

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".

$\bar X=320128$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=50324$ represent the population standard deviation

n=529 represent the sample size

Solution to the problem

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

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

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$320128-1.96\frac{50324}{\sqrt{529}}=315839.52$

$320128+1.96\frac{50324}{\sqrt{529}}=324416.48$

So on this case the 95% confidence interval would be given by (315839.52;324416.48)

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3 years ago

Can i get help? Don’t really understand.

Rufina [12.5K]

First option: correct. This is because angles WOX and XOZ are supplementary, so

$m\angle WOX=180^\circ-104^\circ=76^\circ$

Second option: correct. By the inscribed angles theorem, we have

$m\angle XWZ=m\angle XYZ=\dfrac{113^\circ}2=56.5^\circ$

Angles WOX and YOZ are congruent because they form a vertical pair; they both have measure 76 degrees. This means angles WXY and WZY are also congruent, since the interior angles of any triangle sum to 180 degrees in measure. Therefore triangles WXO and YZO form a side-side-side pair, and all SSS triangles are similar.

Third option: not correct. There is a theorem (not sure what the name is) regarding intersecting chords that asserts the average of the measures of arcs WY and XZ is the same as the measure of angle XOZ. This means

$\dfrac{m\widehat{WY}+113^\circ}2=104^\circ\implies m\widehat{WY}=95^\circ$

Fourth option: not correct. This is because arcs WX and XZ are not "supplementary" in the sense that they do not form a semicircle and their measures do not add to 180 degrees. We know this because it's clear that point O is not the center of the circle. If it was, then angle XOZ would be a central angle and its measure would be the same as the arc XZ it subtends.

Fifth option: correct. The theorem mentioned in the assessment of the third option makes itself useful here. We have

$\dfrac{m\widehat{WX}+m\widehat{YZ}}2=m\angle WOX\implies m\widehat{WX}+m\widehat{YZ}=2\cdot76^\circ=152^\circ$

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2 years ago