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3 years ago

Determine if JK and LM parallel, perpendicular, or neither .

Mathematics

1 answer:

Digiron [165]3 years ago

6 0

Answer:

3 - Perpendicular.

4 - Parallel.

Step-by-step explanation:

$\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

$JK = \frac{1-(-7)}{-4-(-10)} = \frac{8}{6} = \frac{4}{3}$

$LM = \frac{-2-2}{-6-(-3)} = \frac{-4}{3}$

Perpendicular, because two lines are considered perpendicular if their slopes are opposite reciprocals.

$JK = \frac{-2-(-2)}{3-11} = \frac{0}{-8} = 0$

$LM = \frac{-2-(-7)}{1-1} = \frac{5}{0} = 0$

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4 years ago

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7nadin3 [17]

Answer:

The sample must be of at least 48 pizzas.

Step-by-step explanation:

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$\alpha = \frac{1-0.9}{2} = 0.05$

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So it is z with a pvalue of $1-0.05 = 0.95$ , so $z = 1.645$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

How large a sample must she take if she wants the margin of error to be under 0.5 inch?

She needs a sample of at least n, in which is found when $M = 0.5, \sigma = 2.1$

$M = z*\frac{\sigma}{\sqrt{n}}$

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$0.5\sqrt{n} = 2.1*1.645$

$\sqrt{n} = \frac{2.1*1.645}{0.5}$

$(\sqrt{n})^{2} = (\frac{2.1*1.645}{0.5})^{2}$

$n = 47.73$

Rounding up

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3 years ago