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Mathematics

1 answer:

Triss [41]2 years ago

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a. Based on the AA similarity theorem, Gilligan can conclude that, ΔABC ~ ΔSDC.

b. To the nearest tenth of a foot, the distance from the ship to the shore is: 847.8 ft.

<h3>What are Similar Triangles?</h3>

The ratios of the corresponding sides of two triangles that are similar are equal.

Two triangles with two pairs of congruent angles are similar to each other based on the AA similarity theorem.

a. In ΔABC and ΔSDC, there are two pairs of congruent angles - ∠DCS ≅ ∠BCA (vertical angles) and ∠ABC ≅ ∠SDC (right angles)

Therefore, based on the AA similarity theorem, Gilligan can conclude that, ΔABC ~ ΔSDC.

b. AB = 150 ft

Distance from the ship to the shore = SD = ?

DC = 130 ft

CB = 23 ft

Thus:

AB/SD = CB/DC

Substitute

150/SD = 23/130

SD = (150×130)/23

SD = 847.8

Thus, to the nearest tenth of a foot, the distance from the ship to the shore is: 847.8 ft.

Learn more about similar triangles on:

brainly.com/question/11899908

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Suppose 52% of the population has a college degree. If a random sample of size 563563 is selected, what is the probability that

amm1812

Answer:

The value is $P(| \^ p - p| < 0.05 ) = 0.9822$

Step-by-step explanation:

From the question we are told that

The population proportion is $p = 0.52$

The sample size is n = 563

Generally the population mean of the sampling distribution is mathematically represented as

$\mu_{x} = p = 0.52$

Generally the standard deviation of the sampling distribution is mathematically evaluated as

$\sigma = \sqrt{\frac{ p(1- p)}{n} }$

=> $\sigma = \sqrt{\frac{ 0.52 (1- 0.52 )}{563} }$

=> $\sigma = 0.02106$

Generally the probability that the proportion of persons with a college degree will differ from the population proportion by less than 5% is mathematically represented as

$P(| \^ p - p| < 0.05 ) = P( - (0.05 - 0.52 ) < \^ p < (0.05 + 0.52 ))$

Here $\^ p$ is the sample proportion of persons with a college degree.

$P( - (0.05 - 0.52 ) < \^ p < (0.05 + 0.52 )) = P(\frac{[[0.05 -0.52]]- 0.52}{0.02106} < \frac{[\^p - p] - p}{\sigma } < \frac{[[0.05 -0.52]] + 0.52}{0.02106} )$