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1 year ago

What is the Value Of X,

Mathematics

1 answer:

Zina [86]1 year ago

7 0

The value of x in the figure is 9.72

<h3>How to determine the value of x?</h3>

The given shape is a triangle, and the value of x can be calculated using the following laws of cosine

a^2 = b^2 + c^2 - 2bc * cos(a)

So, the equation becomes

x^2 = 14^2 + 10^2 - 2 * 14 * 10 * cos(44)

Evaluate the value of cos(44)

x^2 = 14^2 + 10^2 - 2 * 14 * 10 * 0.7193

Evaluate the product

x^2 = 296 - 201.404

Evaluate the difference

x^2 = 94.596

Evaluate the exponent

x = 9.72

Hence, the value of x in the figure is 9.72

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A random sample of 864 births in a state included 426 boys. Construct a 95% confidence interval estimate of the proportion of bo

oksian1 [2.3K]

Using the z-distribution, it is found that the 95% confidence interval is (0.46, 0.526), and it does not provide strong evidence against that belief.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which:

$\pi$ is the sample proportion.

z is the critical value.

n is the sample size.

In this problem, we have a 95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so the critical value is z = 1.96.

We have that a random sample of 864 births in a state included 426 boys, hence the parameters are given by:

$n = 864, \pi = \frac{426}{864} = 0.493$

Then, the bounds of the interval are given by:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.493 - 1.96\sqrt{\frac{0.493(0.507)}{864}} = 0.46$

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.493 + 1.96\sqrt{\frac{0.493(0.507)}{864}} = 0.526$

The 95% confidence interval estimate of the proportion of boys in all births is (0.46, 0.526). Since the interval contains 0.506, it does not provide strong evidence against that belief.

More can be learned about the z-distribution at brainly.com/question/25890103

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