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AfilCa [17]
2 years ago
12

WILL MARK BRAINLIEST!

Mathematics
1 answer:
Artist 52 [7]2 years ago
3 0

Answer:

Following are the responses to the given points:

Step-by-step explanation:

Dilation implies the triangle \Delta XYZ stretched through the factor "2".  

m\angle Y = m\angle C = 90^{\circ} \leftarrow given \\\\  

right triangles:

\Delta  XYZ and \Delta  ACB \\\\\angle X \cong \angle A \leftarrow given\\\\

complementary angles:  

\angle X \ and\  \angle Z

m\angle Z = 90^{\circ} - m\angle X \\\\

complementary angles:

\angle A \ and\  \angle B

m\angle B = 90^{\circ} - m\angle A \\\\\therefore \\\\ \angle Z \cong \angle B \\\\\Delta  XYZ \sim  \Delta ACB \\\\

Same triangles: proportional side are corresponding, congruence angles are respective.

\sin \angle X = \frac{5}{5.59} \leftarrow given \\\\\sin\angle X = \frac{YZ}{XY} \\\\YZ = 5 (units) \rightarrow leg in \Delta XYZ \\\\XZ = 5.59 (units) \rightarrow hypotenuse \ in\  \Delta XYZ\\\\

Calculating the length of leg XY:

XY = \sqrt{((5.59)^2 - 52)} \cong 2.4996 (units)\\\\\frac{CB}{YZ} = 2 \leftarrow given \\\\CD = 2YZ = 2 \times 5 = 10 \ (units)\\\\\frac{AC}{XY} = 2 \leftarrow  \ given\\\\AC = 2XY \cong 2 \times  2.4996 \cong 4.999\  (units)\\\\

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Answer:

E. 0.11

Step-by-step explanation:

We have these following probabilities:

A 10% probability that a person has the flu.

A 90% probability that a person does not have the flu, just a cold.

If a person has the flu, a 99% probability of having a runny nose.

If a person just has a cold, a 90% probability of having a runny nose.

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

P = \frac{P(B).P(A/B)}{P(A)}

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

In this problem, we have that:

What is the probability that a person has the flu, given that she has a runny nose?

P(B) is the probability that a person has the flu. So P(B) = 0.1.

P(A/B) is the probability that a person has a runny nose, given that she has the flu. So P(A/B) = 0.99.

P(A) is the probability that a person has a runny nose. It is 0.99 of 0.1 and 0.90 of 0.90. So

P(A) = 0.99*0.1 + 0.9*0.9 = 0.909

What is the probability that this person has the flu?

P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.1*0.99}{0.909} = 0.1089 = 0.11

The correct answer is:

E. 0.11

5 0
3 years ago
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