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Ray Of Light [21]
3 years ago
13

What are the coordinates of the midpoint of the segment whose endpoints are (-4,6) and (-8,-2)

Mathematics
1 answer:
umka2103 [35]3 years ago
4 0
The formula to find the midpoint of a segment is ((x1 + x2)/2,),(y1 + y2)/2).

The x coordinate of the first point is -4, and the x coordinate of the second point is -8.  The y coordinate of the first point is 6, and the y coordinate of the second point is -2.  Now, we can plug these into our formula.

((-4 + (-8))/2), (6 + (-2))/2)) = (-12/2), (4/2) = (-6, 2)

So, (-6, 2) is the midpoint of the segment.
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Refer to attachment

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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".

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\bar X=1.1 represent the sample mean for the sample  

\mu population mean (variable of interest)

s=4.9 represent the sample standard deviation

n=51 represent the sample size  

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

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=51-1=50

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,50)".And we see that t_{\alpha/2}=2.02

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

1.1-2.02\frac{4.9}{\sqrt{50}}=-0.30    

1.1+2.02\frac{4.9}{\sqrt{50}}=2.50    

So on this case the 90% confidence interval would be given by (-0.30;2.50)    

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