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2 years ago

Rewrite \sqrt((1+cos45)/(2)) using a half-angle identity

1 answer:

7 0

$\stackrel{\textit{Half-Angle Identities}}{cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}}} \\\\[-0.35em] ~\dotfill\\\\ \sqrt{\cfrac{1+cos(45^o)}{2}}~~ = ~~cos\left( \cfrac{45^o}{2} \right)\implies \sqrt{\cfrac{1+cos(45^o)}{2}}~~ = ~~cos(22.5^o)$

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A random sample of 40 binomial trials resulted in 14 successes. test the claim that the population proportion of successes does

mylen [45]

Using the z-distribution, since the p-value of the test is of 0.057 > 0.05, there is not enough evidence that the population proportion of successes does not equal 0.50.

<h3>What are the hypotheses tested?</h3>

At the null hypotheses, we test if the proportion of successes equals 0.5, hence:

$H_0: p = 0.5$

At the alternative hypotheses, we test if it does not equal, hence:

$H_1: p \neq 0.5$

<h3>What is the test statistic?</h3>

The test statistic is given by:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

In which:

$\overline{p}$ is the sample proportion.

p is the proportion tested at the null hypothesis.

n is the sample size.

For this problem, the parameters are given by:

$n = 40, \overline{p} = \frac{14}{40} = 0.35, p = 0.5$

Hence the test statistic is given by:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

z = (0.35 - 0.5)/(0.5/sqrt(40))

z = -1.9.

<h3>What is the decision?</h3>

Using a z-distribution calculator, considering a two-tailed test, as we are testing if the proportion is different of a value, with z = -1.9, we get that the p-value of the test is of 0.057.

Since the p-value of the test is of 0.057 > 0.05, there is not enough evidence that the population proportion of successes does not equal 0.50.

More can be learned about the z-distribution at brainly.com/question/16313918

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5 0

1 year ago

Word choice refers to the

shtirl [24]

I think it’s d the readers choice of word when responding to a text .

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3 years ago

List the first 5 muliples

IceJOKER [234]

11: 22,33,44,55 8: 16,24,32,40,48 2: 4,6,8,10,12

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3 years ago

In how many ways can you write 32 as the product of three numbers. Write them.

jekas [21]

32 x 1 x 1

16 x 1 x 2

8 x 2 x 2

4 x 2 x 4

8 x 4 x 1

These are the ones that come to my mind

5 0

3 years ago

an angle bisector of a triangle divides the opposite side of the triangles into segments 6cm and 4cm long. A second side of tria

Dovator [93]

From the angle bisector theorem
we can first assume the third side is x, therefore
7.4/6 = x/4
x = 7.4 × 4/6
x = 4.93 cm
We can also use,
7.4/4 = x/6
x = 7.4 ×6/4
x = 11.1 cm
Therefore, the shortest length of the third side is 4.93 cm while the longest length is 11. 1 cm

6 0

3 years ago