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Nostrana [21]
2 years ago
6

Please help me it is very urgent!!!

Mathematics
1 answer:
Helen [10]2 years ago
6 0

Answer:

A. ∆ABD ~ ∆CDE

B. x ≈ 5.3

Step-by-step explanation:

A. The Acute Angle Similarity Theorem states that when an acute angle in one right triangle is congruent to a corresponding acute angle in another, both right triangles are said to be similar to each other.

<B ≅ <D (both are right angles)

<A ≅ C,

Therefore, ∆ABD ~ ∆CDE

B. Since ∆ABD ~ ∆CDE, corresponding sides would be proportional to each other. This means that:

DE/BD = CD/AB

Substitute:

6/8 = 4/x

Cross multiply

6*x = 4*8

6x = 32

6x/6 = 32/6

x ≈ 5.3 (nearest tenth)

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Answer:

0.3874 = 38.74% probability that exactly 9 of the 10 consumers recognize her brand name.

0.6126 = 61.26% probability that the number who recognize her brand name is not nine.

Step-by-step explanation:

For each consumer, there are only two possible outcomes. Either they recognize the name, or they do not. The probability of a customer recognizing the name is independent of anu other customer. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

The brand name of Mrs. Fields (cookies) has a 90% recognition rate.

This means that p = 0.9.

Sample of 10

This means that n = 10

Find the probability that exactly 9 of the 10 consumers recognize her brand name.

This is P(X = 9). So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 9) = C_{10,9}.(0.9)^{9}.(0.1)^{1} = 0.3874

0.3874 = 38.74% probability that exactly 9 of the 10 consumers recognize her brand name.

Also, find the probability that the number who recognize her brand name is not nine.

1(100%) subtracted by those who recognize. So

1 - 0.3874 = 0.6126

0.6126 = 61.26% probability that the number who recognize her brand name is not nine.

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3 years ago
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the third term of an arithmetic sequence is 24 and the fifth is 32 if the first term is a1. which is an equation nth term of the
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An = a1 + (n - 1)(d)
Where a1 is the first term and d is the common difference.
First find d, the common difference.
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