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2 years ago

Find the coordinates of the midpoint of a segment with the given endpoints.

Mathematics

1 answer:

Step2247 [10]2 years ago

3 0

Answer:

a. (1,2), b. (1, 0)

Step-by-step explanation:

$\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\\\text{Substitute the values.}\\\frac{-3+5}{2},\frac{5+(-1)}{2}\\\text{Evaluate the numerators.}\\\frac{2}{2},\frac{4}{2}\\\text{Simplify.}\\1,2\\\text{The midpoint of (-3, 5) and (5, -1) is (1, 2).}$

$\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\\\text{Substitute the values.}\\\frac{-4+6}{2},\frac{-3+3}{2}\\\text{Evaluate the numerators.}\\\frac{2}{2},\frac{0}{2}\\\text{Simplify.}\\1,0\\\text{The midpoint of (-4, -3) and (6, 3) is (1, 0).}$

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Answer:

Use the distributive property on each side of the equation.

Explanation:

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3 years ago

Which fraction is halway between 1/2 and and 1 1/4

Igoryamba

Answer:

3/8

Step-by-step explanation:

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2 years ago

Read 2 more answers

In a survey, the planning value for the population proportion is p* = 0.35. How large a sample should be taken to provide a 95%

lions [1.4K]

Answer:

$n=\frac{0.35(1-0.35)}{(\frac{0.05}{1.96})^2}=349.59$

And rounded up we have that n=350

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".

$p$ represent the real population proportion of interest

$\aht p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

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

Solution to the problem

The population proportion have the following distribution

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

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 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by: