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The midpoint of RS¯¯¯¯¯¯¯ is M. Use the given endpoint R(23, 14) and midpoint M(13, 8) to find the coordinates of the other endp

Oksanka [162]

The coordinates of other endpoint S is (3, 2)

<h3><u>Solution:</u></h3>

Given that midpoint of RS is M

Given endpoint R(23, 14) and midpoint M(13, 8)

To find: coordinates of the other endpoint S

<em><u>The formula for midpoint is given as:</u></em>

For a line containing containing two points $(x_1, y_1)$ and $(x_2, y_2)$ midpoint is given as:

$m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

Here in this problem,

m(x, y) = (13, 8)

$(x_1, y_1) = (23, 14)\\\\(x_2, y_2) = ?$

Substituting the given values in above formula, we get

$(13,8)=\left(\frac{23+x_{2}}{2}, \frac{14+y_{2}}{2}\right)$

Comparing both the sides we get,

$\begin{aligned}&13=\frac{23+x_{2}}{2} \text { and } 8=\frac{14+y_{2}}{2}\\\\&26=23+x_{2} \text { and } 16=14+y_{2}\\\\&x_{2}=3 \text { and } y_{2}=2\end{aligned}$

Thus the coordinates of other endpoint S is (3, 2)

8 0

3 years ago

"flower, heart, circle." what is The 35th shape is

kramer

Answer:

heart

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

PLEASE HEEEEEEEEEEEEEEEEEELP

inna [77]

I’m pretty sure it’s 3 and a 2

8 0

3 years ago

What is the equation of the line with a slope of -3 and passes through the point (-6,-3)

Taya2010 [7]

Answer:

f(x) = -3x - 21

Step-by-step explanation:

Graphed this equation and it passes through (-6, -3), also known as Point A.

7 0

2 years ago

Many high school students take the AP tests in different subject areas. In 2007, of the 144,796 students who took the biology ex

Nataly [62]

Answer:

$(0.582-0.485) - 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.0942$

$(0.582-0.485) + 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.09978$

And the 90% confidence interval would be given (0.0942;0.09978).

We are confident at 90% that the difference between the two proportions is between $0.0942 \leq p_A -p_B \leq 0.09978$

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".

$p_A$ represent the real population proportion female for Biology

$\hat p_A =\frac{84199}{144796}=0.582$ represent the estimated proportion female for biology

$n_A=144796$ is the sample size for A

$p_B$ represent the real population proportion female for calculus AB

$\hat p_B =\frac{102598}{211693}=0.485$ represent the estimated proportion female for Calculus AB

$n_B=211693$ is the sample size required for B

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 90% confidence interval the value of $\alpha=1-0.90=0.1$ and $\alpha/2=0.05$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.64$

And replacing into the confidence interval formula we got:

$(0.582-0.485) - 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.0942$

$(0.582-0.485) + 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.09978$

And the 90% confidence interval would be given (0.0942;0.09978).

We are confident at 90% that the difference between the two proportions is between $0.0942 \leq p_A -p_B \leq 0.09978$

5 0

3 years ago