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3 years ago

Find the coordinates of the vertices of the figure formed by each system of inequalities.

Mathematics

1 answer:

siniylev [52]3 years ago

6 0

Answer:

D(1, –5), (7, 1), (–11, 7)

Step-by-step explanation:

The given inequalities are:

y + x ≥ –4

y ≥ x – 6

3y + x ≤ 10

We graph the inequalities as shown in the attachment.

The coordinates of the vertices of the figure formed by the given system of inequalities are:

(1, –5), (7, 1), (–11, 7)

The correct choice is D.

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A sample of 5 strings of thread is randomly selected and the following thicknesses are measured in millimeters. Give a point est

liq [111]

Answer:

$s^2 = \frac{(1.48-1.502)^2 +(1.45-1.502)^2 +(1.54-1.502)^2 +(1.52-1.502)^2 +(1.52-1.502)^2}{5-1} =0.00132$

And for the deviation we have:

$s= \sqrt{0.00132}=0.0363$

And that value represent the best estimator for the population deviation since:

$E(s) =\sigma$

Step-by-step explanation:

For this case we have the following data:

1.48,1.45,1.54,1.52,1.52

The first step for this cae is find the sample mean with the following formula:

$\bar X =\frac{\sum_{i=1}^n X_}{n}$

And replacing we got:

$\bar X= \frac{1.48+1.45+1.54+1.52+1.52}{5} = 1.502$

And now we can calculate the sample variance with the following formula:

$s^2 =\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}$

And replacing we got:

$s^2 = \frac{(1.48-1.502)^2 +(1.45-1.502)^2 +(1.54-1.502)^2 +(1.52-1.502)^2 +(1.52-1.502)^2}{5-1} =0.00132$

And for the deviation we have:

$s= \sqrt{0.00132}=0.0363$

And that value represent the best estimator for the population deviation since:

$E(s) =\sigma$

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Step-by-step explanation:

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