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satela [25.4K]
3 years ago
10

Which statement is true about the graphs of the two lines and ? y= -8x -5/4 and y = 1/8x + 4/5

Mathematics
1 answer:
Ronch [10]3 years ago
7 0
Y = -8x - 5/4......slope here is -8 or -8/1
y = 1/8x + 4/5...slope here is 1/8

what u have here are negative reciprocal slopes....negative reciprocal of a number can be found by flipping the number and changing the sign. So the negative reciprocal of -8/1 is 1/8 (see how I flipped the number and changed the sign)...and when u have negative reciprocal slopes, this means that ur lines are perpendicular.
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The Information Technology Department at a large university wishes to estimate the proportion of students living in the dormitor
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Answer:

n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16  

And rounded up we have that n=385

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".  

Solution to the problem

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 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)  

We can use as an estimator for p \hat p =0.5. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16  

And rounded up we have that n=385

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3 years ago
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