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3 years ago

Suppose △JMN≅△KQR .

Mathematics

1 answer:

OverLord2011 [107]3 years ago

6 0

The true statements are ∠M≅∠Q, QK¯¯¯¯¯¯≅MJ¯¯¯¯¯¯ and MN¯¯¯¯¯¯¯≅QR¯¯¯¯¯.

In order to determine these, we need to note that where the letter is listed in the original statement determines its congruency. Because they are both first J and K are always the same. This is the same for the ones in the middle (M and Q) and the ones at the end (K and J).

So as an example MN¯¯¯¯¯¯¯≅QR¯¯¯¯¯ is true because MN involves the middle and then first term. QR does the same and is therefore congruent.

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Answer:

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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

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Which is Bigger?

igomit [66]

A)
$43\%=\frac{43}{100} \\ \\
\frac{24}{60}=\frac{4}{10}=\frac{40}{100} \\ \\
43>40 \Rightarrow \frac{43}{100} > \frac{40}{100} \Rightarrow 43\% > \frac{24}{60}$

43% is bigger.

b)
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0.51=\frac{51}{100} \\ \\
60>51 \Rightarrow \frac{60}{100} > \frac{51}{100} \Rightarrow \frac{18}{30} >0.51$

18/30 is bigger.

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Answer:

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Step-by-step explanation:

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