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d1i1m1o1n [39]
2 years ago
11

Find the value of x. Area of circle = 25(pi) radius = x + 3

Mathematics
1 answer:
horsena [70]2 years ago
6 0

\\\text{Given that, radius, r =x+3}\\\\\text{Area of circle} = 25 \pi\\\\\implies \pi r^2 = 25 \pi\\\\\implies r^2 = 25\\\\\implies r = \sqrt{25} =5\\\\\implies x+3 = 5\\\\\implies x = 5-3 =2

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The computer that controls a bank's automatic teller machine crashes a mean of 0.6 times per day. What is the probability that,
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Answer:

0.2103 = 21.03% probability that, in any seven-day week, the computer will crash less than 3 times.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

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7 day week, so \mu = 7*0.6 = 4.2

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P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

In which

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 0) = \frac{e^{-4.2}*(4.2)^{0}}{(0)!} = 0.0150

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P(X = 2) = \frac{e^{-4.2}*(4.2)^{2}}{(2)!} = 0.1323

So

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0150 + 0.0630 + 0.1323 = 0.2103

0.2103 = 21.03% probability that, in any seven-day week, the computer will crash less than 3 times.

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