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Allisa [31]
2 years ago
12

The random variable X is exponentially distributed, where X represents the waiting time to be seated at a restaurant during the

evening. If X has an average value of 19 minutes, what is the probability that the wait time is greater than 14 minutes
Mathematics
1 answer:
erastova [34]2 years ago
7 0

Answer:

The probability that the wait time is greater than 14 minutes  is 0.4786.

Step-by-step explanation:

The random variable <em>X</em> is defined as the waiting time to be seated at a restaurant during the evening.

The average waiting time is, <em>β</em> = 19 minutes.

The random variable <em>X</em> follows an Exponential distribution with parameter \lambda=\frac{1}{\beta}=\frac{1}{19}.

The probability distribution function of <em>X</em> is:

f(x)=\lambda e^{-\lambda x};\ x=0,1,2,3...

Compute the value of the event (<em>X</em> > 14) as follows:

P(X>14)=\int\limits^{\infty}_{14} {\lambda e^{-\lambda x}} \, dx=\lambda \int\limits^{\infty}_{14} {e^{-\lambda x}} \, dx\\=\lambda |\frac{e^{-\lambda x}}{-\lambda}|^{\infty}_{14}=e^{-\frac{1}{19} \times14}-0\\=0.4786

Thus, the probability that the wait time is greater than 14 minutes  is 0.4786.

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Write 54 + 63 as the product of the GCF of 54 and 63 and another sum
levacccp [35]

Answer:

9*(6+7)

Step-by-step explanation:

First, we have to find the Greatest Common Factor (GCF), to do this we have to see all the factors of 54 and 63 and find the greatest factor that they have in common.

Factors of 54

1,2,3,6,9,18,27,54

Factors of 63

1,3,7,9,21,63

The GCF is 9 because is the greatest factor that is common to both numbers.

Now we have to divide 54/9 and 63/9

54/9 = 6

63/9 = 7

So now we can write the product of the GCF and another sum:

9*(6+7)

<em>We can prove this by solving both expressions:</em>

<em>54+63 = 9*(6+7)</em>

<em>117 = 9*13</em>

<em>117 = 117 </em>

<em>The results are equal so we prove it is right.</em>

8 0
2 years ago
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The midpoint M and one endpoint of JK are given. Find the coordinates of the other endpoint. J(7,2) and M(1,-2)
djverab [1.8K]

Step-by-step explanation:

Xj + Xk/2 = Xm

7 + Xk/2 = 1

to get rid of the bracket, multiply all two sides by the denominator.

2(7 + Xk/2) = 1(2)

7 + Xk = 2

Xk = 2 - 7

Xk = -5

Yj + Yk/2 = Ym

2 + Yk/2 = -2

to get rid of the bracket, multiply all two sides by the denominator.

2(2 + Yk/2) = -2(2)

2 + Yk = -4

Yk = -4 - 2

Yk = -6

Therefore the coordinates of point K is (-5,-6)

3 0
3 years ago
A circle has a circumference of 907.46.<br> What is the diameter of the circle?
Anna007 [38]

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3 years ago
I need help quick!
atroni [7]
This one is tricky....but I'll go for D cause your multiplying a number towards 5



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3 years ago
Which results only in a horizontal compression of Y = by a factor of 6?
elena55 [62]

Answer:

Y = 6*y

Step-by-step explanation:

We have Y = b * y by a factor of 6.

That is, b = 6.

now, to find what results only in a horizontal compression of y = b * y by a factor of 6.

By transformation rule, the function would be a horizontal compression f (a * x) if a> 1.

Therefore, knowing the above, the answer would be:

Y = 6 * y

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