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ArbitrLikvidat [17]
3 years ago
15

Angie mows lawns in her neighborhood to make money. She charges $25 per lawn and buys a new mower for $200. If x is the number o

f lawns, and p is her profit, which of the following would you use to find Angie's profit?
a. 200=25x+p
b. 25x−200=p
c. 25x=p−200
d. 25x+200=p
Mathematics
1 answer:
natali 33 [55]3 years ago
7 0

Answer: Angie's profit equation is 25x−200=p

Step-by-step explanation:

Let x represent the number of lawns that Angie mows in her neighborhood.

Let p represent the profit made by mowing x lawns.

Profit = Revenue - cost

She charges $25 per lawn. This means that the amount charged for x lawns = 25×x = 25x

So her revenue is 25x

She buys a new mower for $200. Thus, the cost is $200. Therefore, Angie's profit,p is expressed as

p = 25x - 200

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Assume a warehouse operates 24 hours a day. Truck arrivals follow Poisson distribution with a mean rate of 36 per day and servic
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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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Step-by-step explanation:

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|x| = √(25/36) = 5/6

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The area of the bounded region is given by the integral

\int\limits^{5/6}_{-5/6} {(25-36 \, x^2)} \, dx = (25x - 12 \, x^3)\, |_{x=-5/6}^{x=5/6} = 25*5/6 - 12*(5/6)^3 - (25*(-5/6) - 12*(-5/6)^3) = 250/9

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Answer:

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Step-by-step explanation:

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