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3 years ago

Hey! I have some geometry questions today!

Mathematics

1 answer:

Volgvan3 years ago

8 0

Answer:

Step-by-step explanation:

<h3>Question 1</h3>

It is assumed the chords have equal length: PQ = SR

If the vertexes connected with the center, the both chords will form a right triangle, with the hypotenuse being the radius.

Then the radius is found using Pythagorean theorem:

r = $\sqrt{20^2 + 21^2}$ = $\sqrt{841}$ = 29

<h3>Question 2</h3>

Use the intersecting secants theorem: and solve for x:

FS*FT = FP*FQ
4(4 + x) = 5(5 + 3)
16 + 4x = 40
4x = 24
x = 6

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3 years ago

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We conclude that the proportion of dropouts has changed from the historical value of 0.081.

Step-by-step explanation:

We are given that in 2009, the high school dropout rate was 8.1%. A polling company recently took a survey of 1000 people between the ages of 16 and 24 and found 6.5% of them are high school dropouts.

The polling company would like to determine whether the proportion of dropouts has changed from the historical value of 0.081.

Let p = proportion of school dropouts rate

SO, Null Hypothesis, $H_0$ : p = 0.081 {means that the proportion of dropouts has not changed from the historical value of 0.081}

Alternate Hypothesis, $H_A$ : p $\neq$ 0.081 {means that the proportion of dropouts has changed from the historical value of 0.081}

The test statistics that will be used here is One-sample z proportion statistics;

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where, $\hat p$ = sample proportion of high school dropout rate = 6.5%

n = sample of people = 1000

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= -2.05

Also, P-value is given by the following formula;

P-value = P(Z < -2.05) = 1 - P(Z $\leq$ 2.05)

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Now at 5% significance level, the z table gives critical values between -1.96 and 1.96 for two-tailed test. Since our test statistics does not lies within the range of critical values of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the proportion of dropouts has changed from the historical value of 0.081.

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4 years ago

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