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lisabon 2012 [21]
3 years ago
14

What are the values of sin α and tan α, if: cosα=0.6

Mathematics
1 answer:
olganol [36]3 years ago
6 0

Positive cosine is first or fourth quadrant.  So we don't know the sign of the sine or the tangent.

Everybody's favorite right triangle is 3/4/5 and here we have

\left(\dfrac 3 5 \right)^2 + \left(\dfrac 4 5 \right)^2 = 1

So if

\cos \alpha = 0.6 = \dfrac 3 5

then

\sin \alpha = \pm \dfrac{4}{5} = \pm 0.8

and

\tan \alpha = \dfrac{\sin \alpha}{\cos \alpha} = \dfrac{\pm 0.8}{0.6}=\pm \dfrac 4 3

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Anton [14]

Answer:

4x - 2

Step-by-step explanation:

3(2x - 2) - 2(x - 2) [Distributive Property]

6x - 6 - 2x + 4

4x - 2

7 0
2 years ago
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A simple random sample of items resulted in a sample mean of . The population standard deviation is . a. Compute the confidence
Varvara68 [4.7K]

Answer:

(a): The 95% confidence interval is (46.4, 53.6)

(b): The 95% confidence interval is (47.9, 52.1)

(c): Larger sample gives a smaller margin of error.

Step-by-step explanation:

Given

n = 30 -- sample size

\bar x = 50 -- sample mean

\sigma = 10 --- sample standard deviation

Solving (a): The confidence interval of the population mean

Calculate the standard error

\sigma_x = \frac{\sigma}{\sqrt n}

\sigma_x = \frac{10}{\sqrt {30}}

\sigma_x = \frac{10}{5.478}

\sigma_x = 1.825

The 95% confidence interval for the z value is:

z = 1.960

Calculate margin of error (E)

E = z * \sigma_x

E = 1.960 * 1.825

E = 3.577

The confidence bound is:

Lower = \bar x - E

Lower = 50 - 3.577

Lower = 46.423

Lower = 46.4 --- approximated

Upper = \bar x + E

Upper = 50 + 3.577

Upper = 53.577

Upper = 53.6 --- approximated

<em>So, the 95% confidence interval is (46.4, 53.6)</em>

Solving (b): The confidence interval of the population mean if mean = 90

First, calculate the standard error of the mean

\sigma_x = \frac{\sigma}{\sqrt n}

\sigma_x = \frac{10}{\sqrt {90}}

\sigma_x = \frac{10}{9.49}

\sigma_x = 1.054

The 95% confidence interval for the z value is:

z = 1.960

Calculate margin of error (E)

E = z * \sigma_x

E = 1.960 * 1.054

E = 2.06584

The confidence bound is:

Lower = \bar x - E

Lower = 50 - 2.06584

Lower = 47.93416

Lower = 47.9 --- approximated

Upper = \bar x + E

Upper = 50 + 2.06584

Upper = 52.06584

Upper = 52.1 --- approximated

<em>So, the 95% confidence interval is (47.9, 52.1)</em>

Solving (c): Effect of larger sample size on margin of error

In (a), we have:

n = 30     E = 3.577

In (b), we have:

n = 90    E = 2.06584

<em>Notice that the margin of error decreases when the sample size increases.</em>

4 0
3 years ago
Answer if you do know
Alex777 [14]

Answer:

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Radda [10]

Answer:

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