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3 years ago

Find the perimeter of the polygon defined by the coordinates (5, 8), (12, 0), (-5, 0), and (-12, 8). (Round to nearest tenth)

1 answer:

4 0

$\displaystyle\\\text{We have the points:}\\E(5,~8)\\F(12,~0)\\G(-5,~0)\\H(-12,~8)\\\\EF=\sqrt{(5-12)^2+(8-0)^2}=\sqrt{(-7)^2+8^2}=\\=\sqrt{49+64}=\sqrt{113}\approx\boxed{\bf10.63}\\\\FG=12-(-5)=12+5=\boxed{\bf17}\\\\GH=\sqrt{(-5-(-12))^2+(0-8)^2}=\sqrt{7^2+(-8)^2}=\\=\sqrt{49+64}=\sqrt{113}\approx\boxed{\bf10.63}\\\\HE=|-12-5|=|-17|=\boxed{\bf17}\\\\P=EF+FG+GH+HE=10.63+17+10.63+17=55.26\approx\boxed{\bf55.3}\\\\\text{Correct answer: }~B)$

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A recent survey of 50 executives who were laid off during a recent recession revealed it took a mean of 26 weeks for them to fin

drek231 [11]

Answer:

The pvalue of 0.0113 < 0.05 means that there is sufficient evidence to conclude that the mean time to find another position is less than 28 weeks at the 5% level of significance

Step-by-step explanation:

The null hypothesis is:

$H_{0} = 28$

The alternate hypotesis is:

$H_{1} < 28$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

A recent survey of 50 executives who were laid off during a recent recession revealed it took a mean of 26 weeks for them to find another position.

This means that $n = 50, X = 26$

Assume the population standard deviation is 6.2 weeks.

This means that $\sigma = 6.2$

Does the data provide sufficient evidence to conclude that the mean time to find another position is less than 28 weeks at the 5% level of significance

We have to find the pvalue of Z, looking at the z-table, when $\mu = 28$ . It if is lower than 0.05, it provides evidence.

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{26 - 28}{\frac{6.2}{\sqrt{50}}}$

$z = -2.28$

$z = -2.28$ has a pvalue of 0.0113 < 0.05.

The pvalue of 0.0113 < 0.05 means that there is sufficient evidence to conclude that the mean time to find another position is less than 28 weeks at the 5% level of significance

5 0

2 years ago

Triangle MNP is dilated according to the rule DO,1.5 (x,y)Right arrow(1.5x, 1.5y) to create the image triangle M'N'P, which is n

Vikki [24]

Given:

The vertex of a triangle MNP are M(-4, 6), N(2, 6), and P(-1, 1).

The rule of dilation is:

$(x,y)\to (1.5x,1.5y)$

The image of triangle MNP after dilation is M'N'P'.

To find:

The coordinates of the endpoints of segment M'N'.

Solution:

The end points of MN are M(-4, 6) and N(2, 6).

The rule of dilation is:

$(x,y)\to (1.5x,1.5y)$

Using this rule, we get

$M(-4,6)\to M'(1.5(-4),1.5(6))$

$M(-4,6)\to M'(-6,9)$

And,

$N(2,6)\to N'(1.5(2),1.5(6))$

$N(2,6)\to N'(3,9)$

The endpoints of M'N' are M'(-6, 9) and N'(3, 9).

Therefore, the correct option is B.

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3 years ago

Richard works from 11:00am to 3:00am dinner break is 75% of the way though work shift what time is his dinner break

Marrrta [24]

Answer:

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Step-by-step explanation:

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3 years ago

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Elena-2011 [213]

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3 years ago

QF Q7.) Use properties of logarithms to expand the logarithmic expression as much as possible. Evaluate logarithmic expressions

Softa [21]

Attached is the solution.
The following log properties are used:
$log(x^n) = nlog(x)$
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3 years ago

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