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Ivahew [28]
2 years ago
14

a rectangle is 12 feet long and 5 feet wide. if the length of the rectangle is increased by 25% and the width is decreased by 20

% what is the change in the area of the rectangle
Mathematics
1 answer:
Verizon [17]2 years ago
4 0

Answer:

60% decrease in area

Step-by-step explanation:

12 x5 == 60 sq feet (original area)

9 x 4 == 36 sq feet (new area)

36/60 = 6/10 = 60%

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Answer:

(a) P (X = 6) = 0.12214, P (X ≥ 6) = 0.8088, P (X ≥ 10) = 0.2834.

(b) The expected value of the number of small aircraft that arrive during a 90-min period is 12 and standard deviation is 3.464.

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Step-by-step explanation:

Let the random variable <em>X</em> = number of aircraft arrive at a certain airport during 1-hour period.

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(a)

For <em>t</em> = 1 the average number of aircraft arrival is:

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The probability distribution of a Poisson distribution is:

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P(X\geq 6)=1-P(X

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(b)

For <em>t</em> = 90 minutes = 1.5 hour, the value of <em>λ</em>, the average number of aircraft arrival is:

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The expected value of the number of small aircraft that arrive during a 90-min period is 12.

The standard deviation is:

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The standard deviation of the number of small aircraft that arrive during a 90-min period is 3.464.

(c)

For <em>t</em> = 2.5 the value of <em>λ</em>, the average number of aircraft arrival is:

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P(X\leq 10)=\sum\limits^{10}_{x=0}(\frac{e^{-20}(20)^{x}}{x!})\\=0.01081\\\approx0.0108

Thus, the probability that at most 10 small aircraft arrive during a 2.5-hour period is 0.0108.

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