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2 years ago

The sum of two numbers is "-1" One number is 12 more than the other one. Find the numbers.

Mathematics

1 answer:

ruslelena [56]2 years ago

7 0

Answer:

x = 5.5

y = - 6.5

Step-by-step explanation:

Let one of the numbers = x

Let the other number = y

x + y = - 1

x = y + 12 Put the second equation into the first one

y + 12 + y = - 1 Subtract 12 from both sides

y + y = - 1 - 12 Combine both left and right sides

2y = - 13 Divide by 2

2y/2 = - 13/1

y = - 6.5

x + y = - 1

x - 6.5 = - 1 Add 6.5 to both sides

x = 5.5

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Answer:

There is a significant difference between the two proportions.

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The (1 - <em>α</em>)% confidence interval for difference between population proportions is:

$CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}$

Compute the sample proportions as follows:

$\hat p_{1}=\frac{80}{250}=0.32\\\\\hat p_{2}=\frac{40}{175}=0.23$

The critical value of <em>z</em> for 90% confidence interval is:

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Compute a 90% confidence interval for the difference between the proportions of women in these two fields of engineering as follows:

$CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}$

$=(0.32-0.23)\pm 1.645\times\sqrt{\frac{0.32(1-0.32)}{250}+\frac{0.23(1-0.23)}{175}}\\\\=0.09\pm 0.0714\\\\=(0.0186, 0.1614)\\\\\approx (0.02, 0.16)$

There will be no difference between the two proportions if the 90% confidence interval consists of 0.

But the 90% confidence interval does not consists of 0.

Thus, there is a significant difference between the two proportions.

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