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3 years ago

The points(1,r) and (5,-4) lie on a line with slope 5. find the missing coordinate r.

Mathematics

1 answer:

Arte-miy333 [17]3 years ago

5 0

The value of r is -24

Step-by-step explanation:

Given points are:

(1,r) and (5,-4)

Let the points be:

(x1,y1) = (1,r)

(x2,y2) = (5,-4)

m = 5

The slope is given by:

$m = \frac{y_2-y_1}{x_2-x_1}\\5 = \frac{-4-r}{5-1}\\5 = \frac{-4-r}{4}\\5 * 4 = -4-r\\20 = -4-r\\20+4 = -4-r+4\\24 = -r\\r = -24$

Hence,

The value of r is -24

Keywords: Slope, coordinates

Learn more about slope at:

#LearnwithBrainly

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Answer:

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We are 99% confident that this interval contains the true population proportion.

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Step-by-step explanation:

Data given and notation

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$\alpha=0.01$ represent the significance level

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The population proportion present the following distribution:

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Part a) Confidence interval

The confidence interval would be given by this formula

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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.

$z_{\alpha/2}=2.58$

And replacing into the confidence interval formula we got:

$0.55 - 2.58 \sqrt{\frac{0.55(1-0.55)}{2341}}=0.523$

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And the 99% confidence interval would be given (0.523;0.577).

We are 99% confident that this interval contains the true population proportion.

Part b) What sample size would be required for the width of a 99% CI to be at most 0.03 irrespective of the value of p??

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 $ME =\pm 0.03$ 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:

$n=\frac{0.55(1-0.55)}{(\frac{0.03}{2.58})^2}=1830.51$

And rounded up we have that n=1831

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Answer:

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The points(1,r) and (5,-4) lie on a line with slope 5. find the missing coordinate r. ​

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