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3 years ago

What is the equation of a line parallel to the line y = 4x + 7 and passes through the point (3, 0)?

1 answer:

5 0

Two lines to be parallel their slopes have to be equal.

so m1 = m = 4

y = mx + b ( Slope intercept form)

y = 4x + b

(3,0) is on the line:

0 = 12 + b

b = -12

y = 4x - 12

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A survey of 40 employees at a company found that 22 of them preferred to eat lunch at their desk rather than at the cafeteria or

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55 percent of the surveyed employees preferred to eat lunch at their desk.

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Here, the total number of surveyed employees = 40

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andre [41]

Answer:

0.7788 = 77.88% probability that more than three customers arrive in 10 minutes

Step-by-step explanation:

Exponential distribution:

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

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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, we have that:

The time between arrivals of customers at an automatic teller machine is an exponential random variable with a mean of 4 minutes, and we have three customers, which means that $m = 3*4 = 12, \mu = \frac{1}{12} = 0.0833$

(a) What is the probability that more than three customers arrive in 10 minutes

This is P(X > 3). So

$P(X > 3) = e^{-0.0833*3} = 0.7788$

0.7788 = 77.88% probability that more than three customers arrive in 10 minutes

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