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tankabanditka [31]
3 years ago
6

In BCD, H is the centroid. If DE=51 find HE.

Mathematics
1 answer:
jeyben [28]3 years ago
5 0

Answer:

HE=17 units.

Step-by-step explanation:

In a triangle, centroid is the intersecting point of the medians.

Centroid divides each of the medians in ratio 2:1

So,

\frac{DH}{HE}=\frac{2}{1}  \\\\\frac{DH}{HE}+1=\frac{2}{1}+1\\\\ \frac{DH+HE}{HE} =3\\\\\frac{DE}{HE}=3

Put DE=51 units

\frac{51}{HE}=3\\\\HE=\frac{51}{3}

HE=17 units.

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8.2-2.58\frac{2.2}{\sqrt{18}}=6.86    

8.2+2.58\frac{2.2}{\sqrt{18}}=9.54    

So on this case the 90% confidence interval would be given by (6.86;9.54)    And the error is given by:

ME= 2.58\frac{2.2}{\sqrt{18}} =1.338

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=8.2 represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma=2.2 represent the population standard deviation

n 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 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that z_{\alpha/2}=2.58

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

8.2-2.58\frac{2.2}{\sqrt{18}}=6.86    

8.2+2.58\frac{2.2}{\sqrt{18}}=9.54    

So on this case the 90% confidence interval would be given by (6.86;9.54)    And the error is given by:

ME= 2.58\frac{2.2}{\sqrt{18}} =1.338

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