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3 years ago

1-sin60÷cos60=1-Tan30÷1+Tan30

Mathematics

1 answer:

ipn [44]3 years ago

8 0

Step-by-step explanation:

LHS=(1-sin60)/cos60

=(1-√3÷2)/1÷2

=2(1-√3÷2)

=2-√3

RHS=(1-tan30)/(1+tan30)

={1-(1÷√3)}/{1+(1÷√3)}

={(√3-1)/√3}/{(√3+1)/√3}

=(√3-1)/(√3+1)

={(√3-1)(√3-1)}/{(√3+1)(√3-1)}

=(3-√3-√3+1)/(3-1)

=(4-2√3)/2

=2-√3

Therefore LHS=RHS

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2 years ago

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3 years ago

The U.S. and many other countries have recently tightened airport security. A sociologist is interested in estimating the propor

melisa1 [442]

Answer:

0.0073 < 0.05, which means that we reject the null hypothesis and conclude that the true proportion of interest is higher than 0.7.

Step-by-step explanation:

Conduct a test to determine whether the true proportion of interest is higher than 0.7.

This means that the null hypothesis is: $H_{0}: p = 0.7$

And the alternate hypothesis is: $H_{a}: p > 0.7$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.7 is tested at the null hypothesis:

This means that $\mu = 0.7, \sigma = \sqrt{0.7*0.3}$

The sociologist found that 375 of the 500 travelers randomly selected and interviewed indicated that the airports were safe.

This means that $n = 500, X = \frac{375}{500} = 0.75$

Value of the z-statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

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$z = 2.44$

P-value of the test:

Probability of z being larger than 2.44, that is, a proportion larger than 0.75.

This is, looking at the z-table, 1 subtracted by the pvalue of Z = 2.44. S

Z = 2.44 has a pvalue of 0.9927

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3 years ago