What is the midpoint of the coordinate F( -2, 4) and G(6, 1)

Mathematics

1 answer:

Marrrta [24]3 years ago

6 0

Answer:

$\huge\boxed{\left(2; 2\dfrac{1}{2}\right)}$

Step-by-step explanation:

$\text{The formula of a midpoint:}\\\\M\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)\\\\\text{We have the points}\ F(-2,\ 4),\ G(6,\ 1).\\\\\text{Substitute:}\\\\M_{FG}\left(\dfrac{-2+6}{2};\ \dfrac{4+1}{2}\right)\to M_{FG}\left(\dfrac{4}{2};\ \dfrac{5}{2}\right)\to M_{FG}\left(2; 2\dfrac{1}{2}\right)$

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a) The 90% confidence interval of the percentage of all mangoes on the truck that fail to meet the standards is: (7.55%, 12.45%).

b) The margin of error is: 2.45%.

c) The 90% confidence is the level of confidence that the true population percentage is in the interval.

d) The needed sample size is: 271.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions has the bounds given by the rule presented as follows:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

The margin of error is given by:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

The variables are listed as follows:

$\pi$ is the sample proportion, which is also the estimate of the parameter.

z is the critical value.

n is the sample size.

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of $\frac{1+0.90}{2} = 0.95$ , so the critical value is z = 1.645.