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3 years ago

Which of the following points is a solution to y ≤ −2x + 3?

Mathematics

1 answer:

Alika [10]3 years ago

5 0

Answer:

d; below; y = −2x + 2

Step-by-step explanation:

the equality ≤ means left to right that y is equal or less than. We see that 2 is equal or less than 3.

We check the resulting equation also and see that if we +3 it = 1 and if we +2 it equals 0 so we know +2 in answer format can be less than also. But with questions we are measuring the units and +2 is less than +3.

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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

quester [9]

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:

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

6 0

3 years ago

Read 2 more answers

The coordinates of LMN are L (4,5), M (5,-2), and N (0,0). If the triangle is rotated 270° about point N, what are the coordinat

tester [92]

Answer: (-2,-5)

Step-by-step explanation:

The rotation rule for rotating a figure about $270^{\circ}$ is given by :-

$(x,y)\to (y,-x)$ , where (x,y) is the coordinates for pre-image and (y,-x) is the coordinates for image. (1)

Given : The coordinates of LMN are L (4,5), M (5,-2), and N (0,0).

If the triangle is rotated 270° about point N

Then, the coordinates of M , will be :

$(5,-2)\to (-2,-5)$ (Using the rule described in (1))

Hence, the coordinates of M after rotated 270° about point N=(-2,-5).

8 0

4 years ago

The sets L and B are given below.

trapecia [35]

$L= (-2, 2, 8) \\ B= (-2, 1, 2, 4, 8) \\ L \: n \: B \: = \: ( - 2, 2, 8) \\ L \: u \: B = ( - 2, 2, 1, 4, 8)$

7 0

4 years ago

Whole Numbers include both positive and negative numbers. t or f

Alex

Answer:

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

The cities of los Angeles and new York are located 35 inches apart on a map. If the actual distance between the two cities is 24

Vsevolod [243]

2450 miles / 35 inches = 70 miles / inch

(big freaking map!)

6 0

3 years ago