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3 years ago

Jika sin x = p, dengan x tumpul, maka cos(x + 60) =

Mathematics

1 answer:

Novay_Z [31]3 years ago

5 0

Menjawab:

[(√1-p²) -3√p] / 2

Penjelasan langkah demi langkah:

Dari identitas trigonometri, pemuaiannya benar:

Cos (A + B) = cosAcosB-sinAsinB

Menerapkan ini dalam memperluas cos (x + 60).

cos (x + 60) = cosxcos60 - sinxsin60

Jika sinx = p = berlawanan / sisi miring

opp = p, hyp = 1

adj² = 1²-p²

adj = √1-p²

Cos (x) = adj / hyp = √1-p² / 1

Cos (x) = √1-p²

Cos60 = 1/2 dan sin60 = √3 / 2

Mengganti nilai-nilai ini ke dalam rumus

cos (x + 60) = cosxcos60 - sinxsin60

cos (x + 60) = √1-p² (1/2) - p (√3 / 2)

cos (x + 60) = (√1-p²) / 2 - √3p / 2

Temukan KPK tersebut

cos (x + 60) = [(√1-p²) -3√p] / 2

Oleh karena itu cos (x + 60) = [(√1-p²) -3√p] / 2

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An insurance company is interested in conducting a study to to estimate the population proportion of teenagers who obtain a driv

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Answer:

n=1041 or higher

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

2) Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.04$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Since we don't have a prior estimation for th proportion of interest, we can use this value as an estimation $\hat p =0.5$ And replacing into equation (b) the values from part a we got: