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3 years ago

Which ordered pair is a solution to the graphed inequality?

Mathematics

1 answer:

aleksandr82 [10.1K]3 years ago

8 0

Given:

The graph of a system of inequalities.

To find:

The ordered pair which is a solution to the graphed inequality.

Solution:

The boundary lines are:

$x-2y=4$

$2x-y=4$

From the given graph it is clear that only point (3,1) lies in the shaded region.

Points (2,-1) and (4,0) lie on the boundary line $x-2y=4$ but the boundary line is dotted. It means the points on the line are not in the solution set.

point (0,-1) does not belong to the shaded region.

Therefore, the correct option is A.

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3 years ago

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Each year, more than 2 million people in the United States become infected with bacteria that are resistant to antibiotics. In p

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Answer:

Reject H₀. There is a significant difference in drug resistance between the two states.

Step-by-step explanation:

In this case we need to determine whether the data suggest a statistically significant difference between the proportions of drug-resistant cases in the two states.

The significance level of the test is, α = 0.02.

(1)

The hypothesis can be defined as follows:

H₀: There is no difference between the proportions of drug-resistant cases in the two states, i.e. $p_{1} - p_{2}= 0$ .

Hₐ: There is a statistically significant difference between the proportions of drug-resistant cases in the two states, i.e. $p_{1} - p_{2}\neq 0$ .

(2)

Compute the sample proportions and total proportion as follows:

$\hat p_{1}=\frac{12}{189}=0.063\\\\\hat p_{2}=\frac{8}{429}=0.019\\\\\hat p=\frac{12+8}{189+429}=0.032\\$

Compute the test statistic value as follows:

$Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat p(1-\hat p)\times [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}$

$=\frac{0.063-0.019}{\sqrt{0.032(1-0.032)\times [\frac{1}{189}+\frac{1}{429}]}}\\\\=2.86$

The test statistic value is 2.86.

(3)

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

Compute the p-value as follows:

$p-value=2\cdot P(Z>2.86)=2\times 0.00212=0.00424$

p-value = 0.00424 < α = 0.02.

The null hypothesis will be rejected at 0.02 significance level.

Reject H₀. There is a significant difference in drug resistance between the two states.

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3 years ago

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Considering the margin of error, it is found that the 95% confidence interval for the percentage of adults who say vaccines should be required is (64.9%, 71.1%).

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

It is given by the sample statistic plus/minus the margin of error.

In this problem, 68% of adults say such vaccines should be required, with a margin of error of 3.1%, hence:

68% - 3.1% = 64.9%.

68% + 3.1% = 71.1%.

The 95% confidence interval for the percentage of adults who say vaccines should be required is (64.9%, 71.1%).

More can be learned about confidence intervals at brainly.com/question/25890103

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