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ExtremeBDS [4]
3 years ago
6

With an average service rate of 15 customers per hour and an average customer arrival rate of 12 customers per hour, calculate t

he probability that actual service time will be less than or equal to five minutes.
Mathematics
1 answer:
RUDIKE [14]3 years ago
3 0

Answer:

probability that actual service time will be less than or equal to five minutes = P(X <= 5) = 1 - e-15(5/60) = 0.714 or 71.4%

Step-by-step explanation:

The identification of  the average arrival rate of customers(v) and the average service rate(u) must be done in order to solve this kind of problem .

In this case, on average, 12 customers arrive each hour. On average, the service rate is 15 customers per hour.

The arrival rate follows the exponential distribution.

probability that actual service time will be less than or equal to 't' minutes P(X <= t) = 1 - e-u(t/60)

probability that actual service time will be less than or equal to five minutes = P(X <= 5) = 1 - e-15(5/60) = 0.714 or 71.4%

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The product of two rational numbers is 2/5 , if one of them is -8/25, find the other.
Sergio [31]

Answer:

x=-5/4

Step-by-step explanation:

Let the number be  x and y

     x.y=2/5    (The product of two rational numbers is 2/5)

if  one of the number is  -8/25

x.(-8/25)=2/5

(Here Substituted the value of one of the number yoy may substitute the value -8/25 in place of x

x=(2/5) *(-25/8)    

x=-5/4  

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3 years ago
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Step-by-step explanation:

3 0
3 years ago
Find the measure of each angle using the triangle sum theorem and exterior angle theorem
Paladinen [302]

(please open my photo for reference as you read, I am a visual learner/explainer so it will make the most sense that way)

So the first thing you want to do is look at the exterior angle 130°. A straight line is 180°, and every Triangle's angular sum is 180°. How I think of it is that every straight line has a mini protractor on either side. It makes it a bit easier to understand.

180 - 130 = 50

You now know that two of the angles are 50°.

You now have two of the measurements for the triangle farthest to the left.

75° and 50°

75 + 50 = 125

180 - 125 = 55

a = 55°

Now that you have all the measurements for the first triangle, let's move onto the next one.

With two measurements for the second triangle, all you need to do is find their sum and subtract that from 180 and you will have the third measurement!

50 + 60 = 110

180 - 110 = 70

b = 70°


Finally, for the last triangle, you already have two of the measurements 60° and 85°.


85 + 60 = 145

180 - 145 = 35

c = 35°


Sorry if this explanation is a bit messy, it's hard to describe certain things without a letter or some kind of name to differentiate between them verbally.


I hope this helps! <3

3 0
3 years ago
An airplane climbs at an angle of 13 with the ground . What is the distance it has traveled when it has attained an altitude of
nevsk [136]
The distance traveled is the hypotenuse of the right triangle formed with the ground.

sinα=400/d

d=400/sinα, we are told α=13° so

d=400/sin13 ft

d≈1778ft (to nearest whole foot)
6 0
4 years ago
A TV studio has brought in 8 boy kittens and 10 girl kittens for a cat food commercial.
kondor19780726 [428]

Answer:

0.323 = 32.3% probability that the director chooses 3 boy kittens and 5 girl kittens.

Step-by-step explanation:

The kittens are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

A TV studio has brought in 8 boy kittens and 10 girl kittens for a cat food commercial.

This means that N = 8 + 10 = 18

We want 3 boys, so k = 8

The director is going to choose 8 of these kittens at random to be in the commercial.

This means that n = 8

What is the probability that the director chooses 3 boy kittens and 5 girl kittens?

This is P(X = 3).

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

P(X = 3) = h(3,18,8,8) = \frac{C_{8,3}*C_{10,5}}{C_{18,8}} = 0.323

0.323 = 32.3% probability that the director chooses 3 boy kittens and 5 girl kittens.

3 0
3 years ago
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