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3 years ago

Find the exact value of the indicated trigonometric functions for the acute angle a:

Mathematics

1 answer:

amid [387]3 years ago

7 0

Tan=24/10 ≈ 2.4

using Pythagoras theorem

x²=(24)²+(10)²

x²=576+100

x²=57600

x=√57600 => 240

Therefore

sina=24/240 => 0.1

cota=1/tana => 1/(24/10) => 10/24

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Karen needs to take her pet kitten, Scooter, to the vet for a checkup. It's hard to get Scooter into his carrying case for the trip to the vet. He never wants to go! Scooter's carrying case has a rectangular front that is 11 inches wide and 9 inches tall. The case is 16 inches long. What is the volume of Scooter's carrying case?

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3 years ago

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How large a sample should be selected to provide a 95% confidence interval with a margin of error of 6? Assume that the populati

marshall27 [118]

Using the z-distribution, it is found that a sample of 171 should be selected.

<h3>What is a z-distribution confidence interval?</h3>

The confidence interval is:

$\overline{x} \pm z\frac{\sigma}{\sqrt{n}}$

The margin of error is:

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

In which:

$\overline{x}$ is the sample mean.

z is the critical value.

n is the sample size.

$\sigma$ is the standard deviation for the population.

For this problem, the parameters are:

$z = 1.96, \sigma = 40, M = 6$

Hence we solve for n to find the needed sample size.

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

$6 = 1.96\frac{40}{\sqrt{n}}$

$6\sqrt{n} = 40 \times 1.96$

$\sqrt{n} = \frac{40 \times 1.96}{6}$

$(\sqrt{n})^2 = \left(\frac{40 \times 1.96}{6}\right)^2$

n = 170.7.

Rounding up, a sample of 171 should be selected.

More can be learned about the z-distribution at brainly.com/question/25890103

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2 years ago

The wavelength of red light in a spectrum is about 0.0000007 meters. Which

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Answer:

$0.0000007$

And if we count the number of zeros before the number 7, we can rewrite the number like this:

$7x10^{-7}$

We cansolve this problem also counting the number of positions that we need to move the decimal point to the right in order to obtain the first number (7)

And the best option would be:

B. 7 x 10-7

Step-by-step explanation:

For this case we have the following number given:

$0.0000007$

And if we count the number of zeros before the number 7, we can rewrite the number like this:

$7x10^{-7}$

We cansolve this problem also counting the number of positions that we need to move the decimal point to the right in order to obtain the first number (7)

And the best option would be:

B. 7 x 10-7

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3 years ago

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3 years ago

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