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AlekseyPX
3 years ago
9

Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-6, -4),A(−6

,−4),A, left parenthesis, minus, 6, comma, minus, 4, right parenthesis, comma B(-4,-4)B(−4,−4)B, left parenthesis, minus, 4, comma, minus, 4, right parenthesis, C(-4, -2)C(−4,−2)C, left parenthesis, minus, 4, comma, minus, 2, right parenthesis, and D(-6, -2)D(−6,−2)D, left parenthesis, minus, 6, comma, minus, 2, right parenthesis.
What is the perimeter of rectangle ABCDABCDA, B, C, D?

units

Mathematics
1 answer:
Lelu [443]3 years ago
8 0

Answer:

8

Step-by-step explanation:

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0.314 = 31.4% probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

f(x) = \mu e^{-\mu x}

In which \mu = \frac{1}{m} is the decay parameter.

The probability that x is lower or equal to a is given by:

P(X \leq x) = \int\limits^a_0 {f(x)} \, dx

Which has the following solution:

P(X \leq x) = 1 - e^{-\mu x}

The probability of finding a value higher than x is:

P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}

In this question:

m = 0.5, \mu = \frac{1}{0.5} = 2

What is the probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours?

P(0.4 \leq X \leq 1) = P(X \leq 1) - P(X \leq 0.4)

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P(X \leq 1) = 1 - e^{-2} = 0.8647

P(X \leq 0.4) = 1 - e^{-2*0.4} = 0.5507

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P(0.4 \leq X \leq 1) = P(X \leq 1) - P(X \leq 0.4) = 0.8647 - 0.5507 = 0.314

0.314 = 31.4% probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours

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