Find an ordered pair to represent a in the equation<br> a=2b+c if b=(6,3) and c=(-4,8)

In triangle ABC, medians AD, BF, and CE intersect at G. What is the length of GE is CH=12?

sashaice [31]

You do not have any point labeled "H" in your diagram.

What I can tell you is that point "G" (where all 3 medians meet) is called a centroid.
<span>
Along </span>each<span> median:</span>
the distance from EACH vertex to the centroid (point G) is TWICE the distance from the centroid to the side.
<span>CG = 2*GE AG = 2*GD BG = 2*GF

</span>

6 0

3 years ago

Suppose we are interested in analyzing the weights of NFL players. We know that on average, NFL players weigh 247 pounds with a

tigry1 [53]

Answer:

$SE= \frac{\sigma}{\sqrt{n}} = \frac{47}{\sqrt{30}}= 8.58$

$ME= 1.64 *\frac{\sigma}{\sqrt{n}} = 1.64*\frac{47}{\sqrt{30}}= 14.073$

$\bar X - ME = 237- 14.073 = 222.927$

$\bar X + ME = 237+ 14.073 = 251.073$

$n=(\frac{1.640(47)}{5})^2 =237.65 \approx 238$

So the answer for this case would be n=238 rounded up to the nearest integer

Null hypothesis: $\mu \geq 247$

Alternative hypothesis: $\mu$

$z=\frac{237-247}{\frac{47}{\sqrt{30}}}=-1.165$

$p_v =P(z$

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the true mean is lower than 247 at 10% of significance.

Step-by-step explanation:

For this case we have the following data given:

$\bar X =237$ represent the sample mean

$\sigma = 47$ represent the population deviation

$n =30$ represent the sample size selected

$\mu_0 = 247$ represent the value that we want to test.

The standard error for this case is given by:

$SE= \frac{\sigma}{\sqrt{n}} = \frac{47}{\sqrt{30}}= 8.58$

For the 90% confidence the value of the significance is given by $\alpha=1-0.9 = 0.1$ and $\alpha/2 = 0.05$ so we can find in the normal standard distribution a quantile that accumulates 0.05 of the area on each tail and we got:

$z_{\alpha/2}= 1.64$

And the margin of error would be:

$ME= 1.64 *\frac{\sigma}{\sqrt{n}} = 1.64*\frac{47}{\sqrt{30}}= 14.073$

The confidence interval for this case would be given by:

$\bar X - ME = 237- 14.073 = 222.927$

$\bar X + ME = 237+ 14.073 = 251.073$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

Replacing into formula (b) we got:

$n=(\frac{1.640(47)}{5})^2 =237.65 \approx 238$

So the answer for this case would be n=238 rounded up to the nearest integer

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is lower than 247 pounds, the system of hypothesis would be:

Null hypothesis: $\mu \geq 247$

Alternative hypothesis: $\mu$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{237-247}{\frac{47}{\sqrt{30}}}=-1.165$

P-value

Since is a left tailed test the p value would be:

$p_v =P(z$

Conclusion

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the true mean is lower than 247 at 10% of significance.

5 0

3 years ago

A rectangle has an area 12cm². If the length of the rectangle is ( x + 1 )cm and the width is x cm, find the possible value(s) o

Komok [63]

X can be 3 because:
(3+1)(3)=(4)(3)=12
I believe that is the only possible value for x.
Good luck to you!

5 0

3 years ago

Read 2 more answers

Find the area<br> cant solve

Alex73 [517]

Answer:

36in²

Step-by-step explanation:

<h3>Area of the White Region: </h3>

A = l * w

The rectangle is 3 by 2.

A = 3 * 2

A = 6

The white part of the rectangle is 6in².

<h3>Area of the blue region:</h3>

A = l * w

The rectangle is 6 by 7.

A = 6*7

A = 42

The blue part of the rectangle is 42in².

<h3>Area of the shaded region:</h3>

[area of the blue part] - [area of the white part]

42 - 6 = 36

The area of the shaded region should be 36in².

8 0

3 years ago

Nayo draws a quadrilateral. it has adjacent sides measuring 16 inches and 20 inches and a diagonal measuring 25 inches. is her q

Serggg [28]

No, the one that Nayo draw was not a quadrilateral since the measurements given does not give a right triangle. The values 16,20 and 25 does not agree with Pythagorean Theorem. Hope this answers the question. Have a nice day. Feel free to ask more questions.

6 0

3 years ago

Find an ordered pair to represent a in the equation a=2b+c if b=(6,3) and c=(-4,8)