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3 years ago

6

the angle theta is located in quadrant 1 and cos of theta is 3/8. what is the value of sin of theta ?

1 answer:

ra1l [238]3 years ago

8 0

Answer: sin of theta = (√55)/8

Step-by-step explanation:

Cosine is the x-value divided by the hypotenuse. We now know that since cosine is 3/8, that the hypotenuse is 8. In order to find the third side of the triangle (which would be the v-value), we must use Pythagorean theorem. The third side is square root 55. Sine equals the y-value divides by the hypotenuse. We know both of those values, so Sine of theta = square root of 55 divided by 8.

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The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day.

valina [46]

Answer:

A sample of 179 is needed.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.85}{2} = 0.075$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.075 = 0.925$ , so Z = 1.44.

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.

A previous study found that for an average family the variance is 1.69 gallon?

This means that $\sigma = \sqrt{1.69} = 1.3$

If they are using a 85% level of confidence, how large of a sample is required to estimate the mean usage of water?

A sample of n is needed, and n is found for M = 0.14. So

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

$0.14 = 1.44\frac{1.3}{\sqrt{n}}$

$0.14\sqrt{n} = 1.44*1.3$

$\sqrt{n} = \frac{1.44*1.3}{0.14}$

$(\sqrt{n})^2 = (\frac{1.44*1.3}{0.14})^2$

$n = 178.8$

Rounding up

A sample of 179 is needed.

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3 years ago

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IgorC [24]

Answer:

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Step-by-step explanation:

The x in f(x) is replaced by x - 5 to give g(x).

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Step-by-step explanation:

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Troyanec [42]

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wariber [46]

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