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3 years ago

Hi! please help. thank you!

Mathematics

1 answer:

vfiekz [6]3 years ago

8 0

Answer:

Step 6 is done by Additive Property of Equality, also known as Compatibility of Equality with Addition, which is defined by the following expression:

$a = b \to a + c = b + c$ , $\forall\,a,b, c\,\in \,\mathbb{R}$

Step-by-step explanation:

Step 6 is done by Additive Property of Equality, also known as Compatibility of Equality with Addition, which is defined by the following expression:

$a = b \to a + c = b + c$ , $\forall\,a,b, c\,\in \,\mathbb{R}$

1) $(7\cdot x - 3) + 3 = (2\cdot x + 7) + 3$ Associative property/Compatibility with addition

2) $7\cdot x + [3 + (-3)] = 2\cdot x + (7 + 3)$ Associative and commutative properties/Definition of subtraction

3) $7\cdot x + 0 = 2\cdot x + 10$ Existence of the additive inverse/Definition of addition

4) $7\cdot x = 2\cdot x + 10$ Modulative property/Result

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A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from s

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Answer:

a) $P=1-\frac{\lambda}{\mu}=1-\frac{20}{30}=0.33$ and that represent the 33%

b) $p_x =\frac{\lambda}{\mu}=\frac{20}{30}=0.66$

c) $L_s =\frac{20}{30-20}=\frac{20}{10}=2 people$

d) $L_q =\frac{20^2}{30(30-20)}=1.333 people$

e) $W_s =\frac{1}{\lambda -\mu}=\frac{1}{30-20}=0.1hours$

f) $W_q =\frac{\lambda}{\mu(\mu -\lambda)}=\frac{20}{30(30-20)}=0.0667 hours$

Step-by-step explanation:

Notation

P represent the probability that the employee is idle

$p_x$ represent the probability that the employee is busy

$L_s$ represent the average number of people receiving and waiting to receive some information

$L_q$ represent the average number of people waiting in line to get some information

$W_s$ represent the average time a person seeking information spends in the system

$W_q$ represent the expected time a person spends just waiting in line to have a question answered

This an special case of Single channel model

Single Channel Queuing Model. "That division of service channels happen in regards to number of servers that are present at each of the queues that are formed. Poisson distribution determines the number of arrivals on a per unit time basis, where mean arrival rate is denoted by λ".

Part a

Find the probability that the employee is idle

The probability on this case is given by:

In order to find the mean we can do this:

$\mu = \frac{1question}{2minutes}\frac{60minutes}{1hr}=\frac{30 question}{hr}$

And in order to find the probability we can do this:

$P=1-\frac{\lambda}{\mu}=1-\frac{20}{30}=0.33$ and that represent the 33%

Part b

Find the proportion of the time that the employee is busy

This proportion is given by:

$p_x =\frac{\lambda}{\mu}=\frac{20}{30}=0.66$

Part c

Find the average number of people receiving and waiting to receive some information

In order to find this average we can use this formula:

$L_s= \frac{\lambda}{\lambda -\mu}$

And replacing we got:

$L_s =\frac{20}{30-20}=\frac{20}{10}=2 people$

Part d

Find the average number of people waiting in line to get some information.

For the number of people wiating we can us ethe following formula"

$L_q =\frac{\lambda^2}{\mu(\mu-\lambda)}$

And replacing we got this:

$L_q =\frac{20^2}{30(30-20)}=1.333 people$

Part e

Find the average time a person seeking information spends in the system

For this average we can use the following formula:

$W_s =\frac{1}{\lambda -\mu}=\frac{1}{30-20}=0.1hours$

Part f

Find the expected time a person spends just waiting in line to have a question answered (time in the queue).

For this case the waiting time to answer a question we can use this formula:

$W_q =\frac{\lambda}{\mu(\mu -\lambda)}=\frac{20}{30(30-20)}=0.0667 hours$

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Answer: Enlargement

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Rita discovered that a lab thermometer in her Chemistry class is not accurate. She created the table to show the relationship be

NARA [144]

The correct answer is letter B

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3 years ago

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The numbers of pages in the books in a library follow a normal distribution. If the mean number of pages is 180 and the standard

schepotkina [342]

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3 years ago

Jessie loves to go hiking on rustic trails through trees and along rivers.One day in 20 minutes of hiking, she hiked 1 mile. If

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Answer:

Jessie hiked at a constant rate of 3 miles/hour

Step-by-step explanation:

Constant rate can also be called speed

The formula for constant rate /Speed = Distance (miles)/ time in hours

Distance = 1 mile

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Converting to hours

60 minutes = 1 hour

20 minutes =

20/60

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