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3 years ago

plz explain to me step by step how I can solve for x and y using the system of equations (basically elimination)

Mathematics

1 answer:

IrinaVladis [17]3 years ago

3 0

You've already completed the first step by lining up terms with the same variables. Like addition, simply add them together column by column. x+(-x) equals 0 so it is cancelled out. 4y plus 6y is 10y. 9+11=20. We are left with 10y equals 20, so y equals 2. Then plug in the y value into either equation. I will use the first so x +4(2)=9. x must equal 1. Double check by plugging in both x and y into the second equation.

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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

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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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