The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 10 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution with a service rate of 12 requests per hour. What is the probability that no requests for assistance are in the system

Answers

Answer 1

Answer:

0.1667

Step-by-step explanation:

We are given;

Arrival rate, λ = 10 requests per hour

Service rate, μ = 12 requests per hour

From queuing theory, we know that;

ρ = λ/μ

Where ρ is the average proportion of time which the server is occupied.

Thus;

ρ = 10/12

ρ = 0.8333

Now, the probability that no requests for assistance are in the system is same as the probability that the system is idle.

This is given by the Formula;

1 - ρ

probability that no requests for assistance are in the system = 1 - 0.8333 = 0.1667


Related Questions

find the slope of the line that passes through these two points

Answers

Answer:

Step-by-step explanation:

Find an equation of the circle whose diameter has endpoints (-6, -1) and (-2,3).

Answers

Step-by-step explanation:

Let find the distance of the diameter. using distance formula.

[tex](3 + 1) {}^{2} + ( - 2 + 6) {}^{2} = \sqrt{8} [/tex]

The diameter is sqr root of 8 units.

A circle equation is

[tex] {x}^{2} + {y}^{2} = {r}^{2} [/tex]

where r is the radius. The radius is half the diameter so

[tex]r = \frac{ \sqrt{8} }{2} = \frac{ \sqrt{8} }{ \sqrt{4} } = \sqrt{2} [/tex]

[tex] {r}^{2} = { \sqrt{2} }^{2} = 2[/tex]

So our radius is 2.

Now we need to find the midpoint or Center of the diameter.

[tex] \frac{ - 6 - 2}{2} = - 4[/tex]

[tex] \frac{3 - 1}{2} = 1[/tex]

So the center of the circle is (-4,1). So our equation of the Circle us

[tex](x + 4) {}^{2} + (y - 1) {}^{2} = ( \sqrt{2} ) {}^{2} [/tex]

inveres laplace transform (3s-14)/s^2-4s+8​

Answers

Complete the square in the denominator.

[tex]s^2 - 4s + 8 = (s^2 - 4s + 4) + 4 = (s-2)^2 + 4[/tex]

Rewrite the given transform as

[tex]\dfrac{3s-14}{s^2-4s+8} = \dfrac{3(s-2) - 8}{(s-2)^2+4} = 3\times\dfrac{s-2}{(s-2)^2+2^2} - 4\times\dfrac{2}{(s-2)^2+2^2}[/tex]

Now take the inverse transform:

[tex]L^{-1}_t\left\{3\times\dfrac{s-2}{(s-2)^2+2^2} - 4\times\dfrac{2}{(s-2)^2+2^2}\right\} \\\\ 3L^{-1}_t\left\{\dfrac{s-2}{(s-2)^2+2^2}\right\} - 4L^{-1}_t\left\{\dfrac{2}{(s-2)^2+2^2}\right\} \\\\ 3e^{2t} L^{-1}_t\left\{\dfrac s{s^2+2^2}\right\} - 4e^{2t} L^{-1}_t\left\{\dfrac{2}{s^2+2^2}\right\} \\\\ \boxed{3e^{2t} \cos(2t) - 4e^{2t} \sin(2t)}[/tex]

Any number that CAN be divided by 2 without having remainder is considered an _______ number

Answers

Step-by-step explanation:

Any number that can be divided by 2 without having remainder is considered an even number.

I hope it helped U

stay safe stay happy

What does si mean in temperature

Answers

Answer:

The kelvin (abbreviation K), also called the degree Kelvin (abbreviation, o K), is the SI unit of temperature. One Kelvin is 1/273.16 (3.6609 x 10 -3 ) of the thermodynamic temperature of the triple point of pure water (H 2 O). The ampere (abbreviation, A) is the SI unit of electric current.

Answer:

kelvin is si unit of tempreature

The following 3 points are on a parabola defining the edge of a ski.
(-4, 1), (-2, 0.94), (0,1)

The general form for the equation of a parabola is:
Ax^2 + Bx + C= y

Required:
a. Use the x- and y-values of 1 of the points to build a linear equation with 3 variables: A, B, and C.
b. Record your equation here. Repeat this process with 1 of the other 2 points to build a 2nd linear equation.
c. Record your equation here. Repeat this process with the other point to build a 3rd equation.
d. Record your equation here. Build a matrix equation that represents this system of equations.
e. Record your matrix equation here. Use a graphing calculator or other graphing utility to find the inverse of the coefficient matrix.
f. Record your result here. Use the inverse matrix to solve the system of equations. Record the equation of the parabola here.

Answers

a. The linear equation for the first point (-4,1) is 16A-4B+C=1

b. The linear equation for the second point (-2, 0.94) is 4A-2B+C=0.94

c. The linear equation for the third point (0,1) is 0A+0B+C=1

d. The matrix equation looks like this:

[tex]\left[\begin{array}{ccc}16&-4&1\\4&-2&1\\0&0&1\end{array}\right]*\left[\begin{array}{c}A\\B\\C\end{array}\right]=\left[\begin{array}{c}1\\0.94\\1\end{array}\right][/tex]

e. The inverse of the coefficient matrix looks like this:

[tex]A^{-1}=\left[\begin{array}{ccc}\frac{1}{8}&-\frac{1}{4}&\frac{1}{8}\\\frac{1}{4}&-1&\frac{3}{4}\\0&0&1\end{array}\right][/tex]

f. The equation of the parabola is: [tex]\frac{3}{200}x^{2}+\frac{3}{50}x+1=y[/tex]

a. In order to build a linear equation from the given points, we need to substitute them into the general form of the equation.

Let's take the first point (-4,1). When substituting it into the general form of the quadratic equation we end up with:

[tex](-4)^{2}A+(-4)B+C=1[/tex]

which yields:

[tex]16A-4B+C=1[/tex]

b. Let's take the second point (-2,0.94). When substituting it into the general form of the quadratic equation we end up with:

[tex](-2)^{2}A+(-2)B+C=0.94[/tex]

which yields:

[tex]4A-2B+C=0.94[/tex]

c. Let's take the third point (0,1). When substituting it into the general form of the quadratic equation we end up with:

[tex](0)^{2}A+(0)B+C=1[/tex]

which yields:

[tex]0A+0B+C=1[/tex]

d. A matrix equation consists on three matrices. The first matrix contains the coefficients (this is the numbers on the left side of the linear equations). Make sure to write them in the right order, this is, the numbers next to the A's should go on the first column, the numbers next to the B's should go on the second column and the numbers next to the C's should go on the third column.

The equations are the following:

16A-4B+C=1

4A-2B+C=0.94

0A+0B+C=1

So the coefficient matrix looks like this:

[tex]\left[\begin{array}{ccc}16&-4&1\\4&-2&1\\0&0&1\end{array}\right][/tex]

Next we have the matrix that has the variables, in this case our variables are the letters A, B and C. So the matrix looks like this:

[tex]\left[\begin{array}{c}A\\B\\C\end{array}\right][/tex]

and finally the matrix with the answers to the equations, in this case 1, 0.94 and 1:

[tex]\left[\begin{array}{c}1\\0.94\\1\end{array}\right][/tex]

so if we put it all together we end up with the following matrix equation:

[tex]\left[\begin{array}{ccc}16&-4&1\\4&-2&1\\0&0&1\end{array}\right]*\left[\begin{array}{c}A\\B\\C\end{array}\right]=\left[\begin{array}{c}1\\0.94\\1\end{array}\right][/tex]

e. When inputing the coefficient matrix in our graphing calculator we end up with the following inverse matrix:

[tex]A^{-1}=\left[\begin{array}{ccc}\frac{1}{8}&-\frac{1}{4}&\frac{1}{8}\\\frac{1}{4}&-1&\frac{3}{4}\\0&0&1\end{array}\right][/tex]

Inputing matrices and calculating their inverses depends on the model of a calculator you are using. You can refer to the user's manual on how to do that.

f. Our matrix equation has the following general form:

AX=B

where:

A=Coefficient matrix

X=Variables matrix

B= Answers matrix

In order to solve this type of equations, we can make use of the inverse of the coefficient matrix to end up with an equation that looks like this:

[tex]X=A^{-1}B[/tex]

Be careful with the order in which you are doing the multiplication, if A and B change places, then the multiplication will not work and you will not get the answer you need. So when solving this equation we get:

[tex]\left[\begin{array}{c}A\\B\\C\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{8}&-\frac{1}{4}&\frac{1}{8}\\\frac{1}{4}&-1&\frac{3}{4}\\0&0&1\end{array}\right]*\left[\begin{array}{c}1\\\frac{47}{50}\\1\end{array}\right][/tex]

(Notice that I changed 0.94 for the fraction 47/50 you can get this number by dividing 94/100 and simplifying the fraction)

So, in order to do the multiplication, we need to multiply each row of the coefficient matrix by the answer matrix and add the results. Like this:

[tex]\frac{1}{8}*1+(-\frac{1}{4})(\frac{47}{50})+\frac{1}{8}*1[/tex]

[tex]\frac{1}{8}-\frac{47}{200}+\frac{1}{8}=\frac{3}{200}[/tex]

So the first number for the answer matrix is [tex]\frac{3}{200}[/tex]

[tex]\frac{1}{4}*1+(-1)(\frac{47}{50})+\frac{3}{4}*1[/tex]

[tex]\frac{1}{4}-\frac{47}{50}+\frac{3}{4}=\frac{3}{50}[/tex]

So the second number for the answer matrix is [tex]\frac{3}{50}[/tex]

[tex]0*1+0(\frac{47}{50})+1*1[/tex]

[tex]0+0+1=1[/tex]

So the third number for the answer matrix is 1

In the end, the matrix equation has the following answer.

[tex]\left[\begin{array}{c}A\\B\\C\end{array}\right]=\left[\begin{array}{c}\frac{3}{200}\\\frac{3}{50}\\1\end{array}\right][/tex]

which means that:

[tex]A=\frac{3}{200}[/tex]

[tex]B=\frac{3}{50}[/tex]

and C=1

so, when substituting these answers in the general form of the equation of the parabola we get:

[tex]Ax^{2}+Bx+C=y[/tex]

[tex]\frac{3}{200}x^{2}+\frac{3}{50}x+1=y[/tex]

For further information, you can go to the following link:

https://brainly.com/question/12628757?referrer=searchResults

Answer as soon as you can. a. 162 comes just after b. What comes just before 182. lies in between 99 and 101. c.​

Answers

Answer:

a. 161

b. 181

c. 100

Step-by-step explanation:

a. 162 comes just after 161 (160, 161, 162, 163...)

b. 181 comes just before 182 (180, 181, 182, 183...)

c. 100 is between 99 and 101 (98, 99, 100, 101, 102...)

Diego made the shape on the left and Elena made the shape on the right. Each shape uses 5 circles.

Answers

Answer:

a

Step-by-step explanation:

Which of the following statements are true?

Answers

Answer:

last one

Step-by-step explanation:

they both whole

Please help me to find out the answer

Answers

9514 1404 393

Answer:

  44.66 in

Step-by-step explanation:

The side opposite the marked angle is given, and the side adjacent to it is the one wanted. The relevant trig relation is ...

  Tan = Opposite/Adjacent

Solving for the Adjacent side, we find ...

  Adjacent = Opposite/Tan

  PQ = (29 in)/tan(33°) ≈ 44.66 in

A 26 foot ladder is lowered down a vertical wall at a rate of 3 feet per minute. The base of the ladder is sliding away from the wall. A. At what rate is the ladder sliding away from the wall when the base of the ladder is 10 feet from the wall

Answers

[tex]7.2\:\text{ft/s}[/tex]

Step-by-step explanation:

We can apply the Pythagorean theorem here:

[tex]26^2 = x^2 + y^2\:\:\:\:\:\:\:\:\:(1)[/tex]

where x is the distance of the ladder base from the wall and y is the distance of the ladder top from the ground. Taking the time derivative of the expression above, we get

[tex]0 = 2x\dfrac{dx}{dt} + 2y\dfrac{dy}{dt}[/tex]

Solving for [tex]\frac{dx}{dt},[/tex] we get

[tex]\dfrac{dx}{dt} = -\dfrac{y}{x}\dfrac{dy}{dt}[/tex]

We can replace y by rearranging Eqn(1) such that

[tex]y = \sqrt{26^2 - x^2}[/tex]

Therefore,

[tex]\dfrac{dx}{dt} = - \dfrac{\sqrt{26^2 - x^2}}{x}\dfrac{dy}{dt}[/tex]

Since y is decreasing as the ladder is being lowered, we will assign a negative sign to [tex]\frac{dy}{dt}[/tex]. Hence,

[tex]\dfrac{dx}{dt} = - \dfrac{\sqrt{26^2 - (10)^2}}{10}(-3\:\text{ft/min})[/tex]

[tex]\:\:\:\:\:\:\:= 7.2\:\text{ft/min}[/tex]

The breadth of a rectangular garden is 2/3 of its legth. If its perimeter is 40cm, find its dimensions.

Answers

Answer:

12; 8

Step-by-step explanation:

length-x

breadth-2/3x

2(x+2/3 x)=40

2×5/3x=40

10/3x=40

x=40÷10/3

x=40×3/10

x=12 (cm) length

2/3×12=8 (cm) breadth

Evaluate each expression if r = 3,q = 1, and W =-2

Answers

Answer:

2) - 12

3) - 1

4)y = 8

5)r = 4

6)x= -7/29

Hope it helps you

Land surveyors outlined a park as shown. What is the area of the park?

Answers

la cuadra se llama 6minutos

Write a quadratic equation having the given numbers as solutions. -7 and -5
The quadratic equation is ___ =0.

Answers

Answer:

x²+12x+35

Step-by-step explanation:

in factored form it would just be

(x+7)(x+5)=0

expand this

x²+12x+35=0

Terrell loves to listen to music, so he buys a subscription to a music-streaming service. He pays $4.99 each month. How much does the streaming service cost per year?

Answers

Answer:
$59.88

Solving Steps:
So $4.99 each month. There are 12 months in a year so you have to times $4.99x12. This is $59.88 which is the answer.

Nine Increased by the product of a number and 4 is greater than or equal to -15

Use the variable y for the unknown number

Answers

Answer:

9+4y ≥ -15

y ≥ -6

Step-by-step explanation:

Nine Increased by the product of a number

9+4y

is greater than or equal to -15

9+4y ≥ -15

Subtract 9 from each side

9-9+4y ≥ -15-9

4y ≥ -24

Divide by 4

4y/4 ≥ -24/4

y ≥ -6

13
R
S
12
What's the length of QR?
A) 1
B) 17.7
C) 6.7
OD) 5

Answers

Answer:

5

Step-by-step explanation:

This is a right triangle, so we can use the Pythagorean theorem

a^2+b^2 = c^2

where a and b are the legs and c is the hypotenuse

QR^2 + 12^2 = 13^2

QR^2 +144 =169

QR^2 = 169-144

QR^2 =25

Take the square root of each side

QR = sqrt(25)

QR =5

How to find joint and combined variation?

Answers

Step-by-step explanation:

Z will stay the same since the 2 will divide into 1

What's 14,124 ÷ 44 ?
[tex]14124 \div 44[/tex]

Answers

Answer:

321

Step-by-step explanation:

14,124/44=321

Answer: 321

write an equivalent expression without negative exponent for 5 to the negative 4th power


Answers

Hi! I'm happy to help!

To solve this problem, we need to first solve [tex]5^{-4}[/tex].

Negative exponents divide the number by x instead of multiplying. So, [tex]5^{-4}[/tex] is 1/625. Since we can't use another negative exponent, we can use a number that would decrease with a positive exponent. In this situation, we can use the inverse of 5, which is [tex]\frac{1}{5}[/tex], and put this to the fourth power. [tex]\frac{1}{5} ^{4}[/tex]

This expression also equals 1/625.

I hope this was helpful, and keep learning! :D

Form a union for the following sets.
M = {1, 2, 4, 8)
N = (2,5,8)

Answers

Answer:

Step-by-step explanation:

When you are asked to find the union of sets you find numbers that are present in both sets.

So a number that appears in both the sets of M and N are 2 and 8.

So M U N = { 2,8} where U is the symbol for union.

a, b ∈q , then (a+ b)∈ …………… । *​

Answers

Answer:

this is an equation of closure property of rational numbers under addition

Step-by-step explanation:

this is the meaning of it

for every a and b belongs to q then a+b belongs to q

If 8x+5(3+x)-a=15+5x, then a = ?

Answers

Answer:

a = 8x

if you want to find x also, then x = a/8

Step-by-step explanation:

divide 15 and 27 by 3, 6, 9

Answers

Answer:

15: 5, 2.5, 1.6666......

27: 9, 4.5, 3

Step-by-step explanation:

For 15:

So first you divide 15 by 5, which equals 3

Long division:

then by 6. 15/6 can be simplified to 5/2, which can be easier to figure out.

And by nine. 15/9 can be simplified to 5/3 which is harder than 5/2, but you can figure it out by long division. 3 fits once in 5, and there is two left over. Add a decimal after 1 and a zero after the two. 3 fits 6 times into 20 (18), but the cycle continues forever resulting in 1.666666.......

For 27:

27/3 is nine

for 27/6 you can simplify to 9/2, which is like 90/2=45, just move the decimal over one spot to make 4.5

for 27/9, the answer is 3

PLEAZE HELPPPPPPPSPPSPAP

Answers

Answer:

Step-by-step explanation:

345ftyfthftyft.plk,k,

Answer:

Hello,

Anwser is C

Step-by-step explanation:

[tex]y=log_9(12x)\\\\9^y=12x\\\\9^x=12y\ inverting \ x \ and \ y \\\\y=\dfrac{9^x}{12} \\[/tex]

Difference between 5429 and 5907 to the greatest place.

Answers

answer- u have to subtract the great no. from the smaller one

Given numbers are 5429 and 5907..

To find the difference we should subtract..

5907

- 5429

-------------

478

_______

#Answered by: Cutest Ghost

solve 3 1/5 = y - 12/25

Answers

3 1/5 = y - 12/25

31/5+y = -12/25

31+y = -12/25×5

31+y = -12/5

y = -12/5-31

y = -143/5

y = -28.6

HOPE IT HELPS

a polynomial p has zeros when x=1/5,x=-4, andx=2 what could be the equation of p?​

Answers

Answer:

x^3 + (9/5)x^2 -(42/5)x + (8/5)

Step-by-step explanation:

since 1/5, -4, and 2 are all zeroes, (x-1/5)(x+4)(x-2) must be a factor of p. if you distribute the statement, you get

Help me please thanks guys

Answers

Answer:

B, D, F

Step-by-step explanation:

In a rational exponent, the numerator is an exponent, and the denominator becomes the index of the root.

[tex]a^{\frac{m}{n}} = \sqrt[n] {a^m}[/tex]

Answer: B, D, F

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