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3 years ago

7

An architect designs a diagonal path across a rectangular patio. The path is 29 meters long. The width of the patio is x meters,

and the length of the path is 5 meters more than the width.
Which equation can be used to find the dimensions of the patio?

0.5(x)(x + 5) = 29
0.5(x)(x + 5) = 841
x2 + (x + 5)2 = 29
x2 + (x + 5)2 = 841

1 answer:

Murljashka [212]3 years ago

7 0

The sides and diagonal of a rectangle form a right triangle. The Pythagorean theorem can be used to relate the dimensions of that triangle. The legs are x and x+5; the hypotenuse is 29. We know 29²=841, so the Pythagorean theorem tells you

... x² + (x+5)² = 841 . . . . . matches the last choice

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Option - A

<u>SOLUTION: </u>

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The distribution of $\hat p$ is given by:

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

We want to find this probability:

$P(\hat p>0.14)$

And using the z score given by:

$z = \frac{\hat p -\mu_p}{\sigma_p}$

Where:

$\mu_{\hat p} = 0.12$

$\sigma_{\hat p}= \sqrt{\frac{0.12*(1-0.12)}{474}}= 0.0149$

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$z = \frac{0.14-0.12}{0.0149}= 1.340$

So we want to find this probability:

$P(z>1.340)$

And using the complement rule and the normal standard distribution and excel we got:

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