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2 years ago

Pleaseeeeeeee I need help nowwwww

Mathematics

1 answer:

Tanya [424]2 years ago

6 0

Answer:

(2)

Step-by-step explanation:

One property of a parallelogram is

• opposite angles are congruent, hence

∠L = ∠N and ∠M = ∠P

Using ∠L = ∠N, then

8x - 41 = 6x + 3 ( subtract 6x from both sides )

2x - 41 = 3 ( add 41 to both sides )

2x = 44 ( divide both sides by 2 )

x = 22

-------------

∠M = 2x + 1 = (2 × 22) + 1 = 44 + 1 = 45°

∠P = ∠M = 45° → (2)

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Answer:

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

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And rounded up we have that n=1068

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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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 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

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 $ME =\pm 0.03$ 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)

We don't have a prior estimation for the proportion $\hat p$ so we can use 0.5 as an approximation for this case

And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

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