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4 years ago

NEED AN EXPERT ANSWER

Mathematics

1 answer:

aksik [14]4 years ago

8 0

So my title in Brainly isn't Expert and people probably don't call me that in real life, but we have been studying this in my math class.
Domain is the extent of X values while range is Y. The shown quadratic equation continues to the left an infinite amount as well as to the right. The answer is all real numbers since it continues to infinity both directions.

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An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers t

olchik [2.2K]

Answer:

a) 0.0282 = 2.82% probability that all of the sprinklers will operate correctly in a fire

b) 0.6496 = 64.96% probability that at least 7 of the sprinklers will operate correctly in a fire.

Step-by-step explanation:

For each sprinkler, there are only two possible outcomes. Either they will operate correctly, or they will not. The sprinklers activate correctly or not independently, which 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 researchers estimate the probability of a sprinkler to activate correctly to be 0.7.

This means that $p = 0.7$

10 sprinklers.

This means that $n = 10$

a. What is the probability that all of the sprinklers will operate correctly in a fire?

This is $P(X = 10)$ . So

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

$P(X = 10) = C_{10,10}.(0.7)^{10}.(0.3)^{0} = 0.0282$

0.0282 = 2.82% probability that all of the sprinklers will operate correctly in a fire.

b. What is the probability that at least 7 of the sprinklers will operate correctly in a fire?

This is:

$P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

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

$P(X = 7) = C_{10,7}.(0.7)^{7}.(0.3)^{3} = 0.2668$

$P(X = 8) = C_{10,8}.(0.7)^{8}.(0.3)^{2} = 0.2335$

$P(X = 9) = C_{10,9}.(0.7)^{9}.(0.3)^{1}= 0.1211$

$P(X = 10) = C_{10,10}.(0.7)^{10}.(0.3)^{0} = 0.0282$

Then

$P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.2668 + 0.2335 + 0.1211 + 0.0282 = 0.6496$

0.6496 = 64.96% probability that at least 7 of the sprinklers will operate correctly in a fire.

7 0

3 years ago

Answer the following questions CORRECTLY I will know if this is wrong. I WILL REPORT ANY INCORRECT ANSWERS!

nexus9112 [7]

Answer by JKismyhusbandbae: D) yards

Why: Quarts are used to find capacity. Pounds are used to find weight. Inches are used to find length of small objects. Yards are used to find length of larger objects. So, the answer is yards.

6 0

4 years ago

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Selena and Drake are evaluating the expression (StartFraction r s Superscript negative 2 Baseline Over r squared s Superscript n

Anastasy [175]

Answer: A- Selena is incorrect because she should have substituted the values for the variables first, and then simplifed

i just took the test. i know that drake is correct because his finale answer was -1/2 and Selenas finale answer was 1/2 if she would have substituted her vaules before simplifying she would have gotten the answer 1/-2 instead of -1/-2 which resulted in her finale answer to be 1/2

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4 years ago

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Kitty plus doggy equals????

salantis [7]

Answer - A new species

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3 years ago

What is the median 12,10,14,6,7

Nimfa-mama [501]

For this case we have that by definition, the median is the number of half in a set of numbers. To find it, the numbers are placed in order and the middle number is found.

If we order the given data we have:

6,7,10,12,14

The middle number is 10. So the median is 10.

Answer:

4 0

3 years ago