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kolezko [41]
3 years ago
15

Can someone help plz

Mathematics
1 answer:
Ksenya-84 [330]3 years ago
7 0

Answer: x=-7

Step-by-step explanation:

1) The angles of a triangle are equal to 180

2) Add your angles together and set them equal to 180 like this:

x+59+x+51+84=180

3) Combine like terms:

2x+ 194 =180

4) Subtract 195 from both sides:

2x+ 194 =180

    - 194   -194

2x = -14

5) Divide by 2 on both sides

2x= -14

/2     /2

x= -7

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Answer:

\huge\boxed{\sf 87.5 \ \%}

Step-by-step explanation:

35 marks out of 40<u> as a fraction:</u>

35 / 40

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The Washington, DC, region has one of the fastest-growing foreclosure rates in the nation, as 15,613 homes went into foreclosure
Ilia_Sergeevich [38]

Answer:

a) 0.6226 = 62.26% probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure.

b) 0.7837 = 78.37% probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure.

c) The proportion of foreclosures in the Nation is lower than in Washington, which means that with a sample size of 100, it is likely to have a small number(fewer than 2) of foreclosures than Washington DC.

Step-by-step explanation:

For each home, there are only two possible outcomes. Either it goes into foreclosure, or it does not. The probability of a home going into foreclosure is independent of other homes. This means that we use the binomial probability distribution 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.

a. What is the probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure?

The foreclosure rate is 1.31% for the Washington, DC area, which means that p = 0.0131

We wanto to find, with n = 100:

P(X < 2) = P(X = 0) + P(X = 1)

In which

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

P(X = 0) = C_{100,0}.(0.0131)^{0}.(0.9869)^{100} = 0.2675

P(X = 1) = C_{100,1}.(0.0131)^{1}.(0.9869)^{99} = 0.3551

P(X < 2) = P(X = 0) + P(X = 1) = 0.2675 + 0.3551 = 0.6226

0.6226 = 62.26% probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure.

b. What is the probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure?

Foreclosure rate of 0.87% for the nation, which means that p = 0.0087. So

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

P(X = 0) = C_{100,0}.(0.0087)^{0}.(0.9913)^{100} = 0.4174

P(X = 1) = C_{100,1}.(0.0087)^{1}.(0.9913)^{99} = 0.3663

P(X < 2) = P(X = 0) + P(X = 1) = 0.4174 + 0.3663 = 0.7837

0.7837 = 78.37% probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure.

c. Comment on the above findings.

The proportion of foreclosures in the Nation is lower than in Washington, which means that with a sample size of 100, it is likely to have a small number(fewer than 2) of foreclosures than Washington DC.

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