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Talja [164]
3 years ago
11

Assume a warehouse operates 24 hours a day. Truck arrivals follow Poisson distribution with a mean rate of 36 per day and servic

e (unloading using a single bay) operations follow exponential distribution with a rate of 48 trucks per day. What is the expected waiting time in the system (in hours) for a typical truck
Mathematics
1 answer:
kirill [66]3 years ago
5 0

The expected waiting time in system for typical truck is 2 hours.

Step-by-step explanation:

Data Given are as follows.

Truck arrival rate is given by,   α  = 36 / day

Truck operation departure rate is given,   β= 48 / day

A constructed queuing model is such that so that queue lengths and waiting time can be predicted.

In queuing theory, we have to achieve economic balance between number of customers arriving into system and that of leaving the system whether referring to people or things, in correlating such variables as how customers arrive, how service meets their requirements, average service time and extent of variations, and idle time.

This problem is solved by using concept of Single Channel Arrival with exponential service infinite populate model.

Waiting time in system is given by,

w_{s} = \frac{1}{\alpha - \beta  }

        where w_s is waiting time in system

                   \alpha is arrival rate described Poission distribution

                   \beta is service rate described by Exponential distribution

w_{s} = \frac{1}{\alpha - \beta  }

w_{s} = \frac{1}{48 - 36 }

w_{s} = \frac{1}{12 } day

w_{s} = \frac{1}{12 }  \times 24  hour        ...it is due to 1 day = 24 hours

w_{s} = 2 hours

Therefore, time required for waiting in system is 2 hours.

           

                   

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In how many ways can a committee of 5 people be chosen from a total of 30 possible people?
Stolb23 [73]

Answer:  142506

Step-by-step explanation:

Given : The total number of choices for people in committee = 30

The number of people need to be chosen =5

Since , here order doesn't matter, so we use combination.

The combination of r things taking from n at a time is given by :-

C(n,r)=\dfrac{n!}{(n-r)!r!}

Now, the number of possible combinations of 5 people be chosen from a total of 30 possible people :-

C(30,5)=\dfrac{30!}{(30-5)!5!}\\\\=\dfrac{30\times29\times28\times27\times26}{120}\\\\=142506

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3 0
2 years ago
Ling lives 2 miles from school. It took him 15 minutes to bike from school to home. The first half of the distance he biked at a
alexdok [17]
A) time = distance/speed
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.. (1 mi)/(12 mi/h) = (1/12) h = 5 minutes
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The speed for the last half of the trip was 6 mph.


b) The average speed was
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8 0
3 years ago
Jonas is planning out his route for an upcoming race. He uses negative numbers to represent points before
olya-2409 [2.1K]

Answer:

The finish line​

Step-by-step explanation:

Jonas is planning his trip using the finish line as reference point. He is using an interval scale (using meters as measurement) and the finish line = 0 meters or the starting point. Anything before the finish is negative and anything after is positive. In this case, his wife is located at 91 + 14 = 105 meters away from him. When you use an interval scale to measure distance, you must use absolute values to determine the distance because positive and negative points.  

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3 years ago
Convert 4 yards to inches.<br>A. 144 inches <br>B. 12 inches<br>C. 16 inches <br>D. 192 inches ​
Murrr4er [49]

Answer:

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Step-by-step explanation:

In one yard, there are 36 inches. You multiply the length value by 36.

4x36=144

Hope this helps, please mark brainliest if possible (:

8 0
2 years ago
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