Cars arrive at an automatic car wash system every 10 minutes on average. The cars inter-arrival times are exponentially distributed. Washing time for each is 6 minutes per car and is purely deterministic (i.e., the waiting line system is M/D/c). Assuming that the car wash has a single bay to serve the cars, what is the average number of cars waiting in line (L.)?

Answers

Answer 1

Answer:

the average number of cars waiting in line L[tex]q[/tex] is 0.45

Step-by-step explanation:

Given the data in the question;

Cars arrive at an automatic car wash system every 10 minutes on average.

Car arrival rate λ = 1 per 10 min = [ 1/10 × 60 ]per hrs = 6 cars per hour

Washing time for each is 6 minutes per car

Car service rate μ = 6min per car = [ 1/6 × 60 ] per hrs = 10 cars per hour

so

P = λ/μ = 6 / 10 = 0.6

Using the length of queue in M/D/1 system since there is only one service bay;

L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ P² / ( 1 - P ) ]

so we substitute

L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ (0.6)² / ( 1 - 0.6 ) ]

L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ 0.36 / 0.4 ]

L[tex]q[/tex] = [tex]\frac{1}{2}[/tex][ 0.9 ]

L[tex]q[/tex] = 0.45

Therefore, the average number of cars waiting in line L[tex]q[/tex] is 0.45


Related Questions

A tumor is injected with 0.3 grams of Iodine-125, which has a decay rate of 1.15% per day. To the nearest day, how long will it take for half of the Iodine-125 to decay?

Answers

Answer:

The time required is 60.3 days.

Step-by-step explanation:

initial amount, No = 0.3 g

rate, r = 1.15 % per day = 0.0115 per day

final amount, N = 0.15 g

Let the time is t.

[tex]N = No e^{-rt}\\\\0.15 = 0.3 e^{-0.0115 t}\\\\0.5 =e^{-0.0115 t}\\\\- 0.6931 = - 0.0115 t \\\\t = 60.3 days[/tex]

What is the length of CD? In this diagram, AABC ~ AEDC. 20-% c * 7 21​

Answers

Answer:

[tex]\frac{BC}{DC}=\frac{AC}{EC}[/tex]

[tex]\frac{20-x}{x} =\frac{21}{7}[/tex]

[tex]\frac{20-x}{x} =3[/tex]

[tex]20-x=3x[/tex]

[tex]4x=20[/tex]

[tex]x=5[/tex]

[tex]So, CD=5[/tex]

OAmalOHopeO

A machining center is in charge of producing 225 parts per day. The parts width. Any parts produced between 250mm and 260mm are considered gless than 250mm must be reworked at an additional cost of $8 per part. 260mm must be reworked at an additional cost of $2.50 per part. The varquantified as a standard deviation of 5.0mm. Measurements on these parhave the ability to set up the machine to achieve whatever mean width value you wish.

Required:
Setup a data table to determine the mean width setting that will minimize expected rework cost ($8 per small part and $2.50 per large part).

Answers

Answer: 5.0•2.50
Reason: it’s first grade level math

9 3/5 % as a decimal, rounded to 3 decimal places, is:

Answers

9 3/5 as a decimal rounded to 3 decimal places is 9 3/5 = 9.6

Yogi is 6 years older than Michelle. The sum of their ages is 26. Write a system of linear equations to represent this information. What are their ages?

Answers

Answer:

10 and 16, x+(x+6)=26

Step-by-step explanation:

Michelle has an age we don't know, so we put her age as x.

Yogi is 6 years older than her, so her age is x+6

Michelle=x

Yogi=x+6

we know both their ages equal 26. so we set it up as

x+(x+6)=26

combining like terms we get

2x+6=26

subtract 6 from both sides

2x=20

divide both sides by 2

x=10

now that we have the value for x, we plug it into their original ages

Michelle is 10, because her age is just x.

Yogi is 16, because her age is x+6

Solve the system using substitution. x+y=-2 and x-y=-8

Answers

Answer:

1) x+y=-2

x=-2-y

2) x-y=-8

substitude value of x

(-2-y)-y=-8

-2-2y=-8

-2y=-6

y=3

Substitute value of y in 1

x=-2-3

x=-5

Brainliest please~

Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your answer as a function of t.)
(s + 1)3

Answers

Expand the expression as

(s + 1)³/s ⁵ = (s ³ + 3s ² + 3s + 1)/s

… = 1/s ² + 3/s ³ + 3/s ⁴ + 1/s

Then taking the inverse transform, you get

LT⁻¹ [1/s ² + 3/s ³ + 3/s ⁴ + 1/s ⁵]

… = LT⁻¹ [1/s ²] + LT⁻¹ [3/s ³] + LT⁻¹ [3/s ⁴] + LT⁻¹ [1/s ⁵]

… = LT⁻¹ [1!/s ²] + 3/2 LT⁻¹ [2!/s ³] + 1/2 LT⁻¹ [3!/s ⁴] + 1/24 LT⁻¹ [4!/s ⁵]

… = t + 3/2 t ² + 1/2 t ³ + 1/24 t

Rewrite the fraction in the sentence below as a percentage. From 125 yards away, a marksman hit 11/20 of the targets last year.

Answers

Answer:

Step-by-step explanation:

11/20 = 55/100 = 55%

55%

11/20 is .55, which in percentage form is simply 55%.

Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.

I am authoring you to offer free insurance for a year the regular price is 6.99 this will save the customer almost_ a year

Answers

6.99*12 = $83.88 savings an year

A sample of 34 observations is selected from a normal population. The sample mean is 15, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.10 significance level. H0: μ ≤ 14 H1: μ > 14

Required:
a. Compute the value of the test statistic.
b. What is the p-value?

Answers

Answer:

1.944 ;

0.026

Step-by-step explanation:

Given :

Sample size, n = 34

Sample mean, xbar = 15

Population standard deviation, σ = 3

The hypothesis :

H0: μ ≤ 14

H1: μ > 14

The test statistic :

Test statistic = (xbar - μ) ÷ (σ/√(n))

Test statistic = (15 - 14) ÷ (3/√(34))

Test statistic = 1 / 0.5144957

Test statistic, Z = 1.944

The Pvalue :

Using the Pvalue from test statistic value :

Pvalue(1.944) = 0.026

Pvalue < α ; Reject H0

Need help ASAP

In the figure, if the measure of ∠8 = 72o, what's the measure of ∠14?

Four Bisecting Lines

Question 3 options:

108°


72°


98°


62°

Answers

Answer:

72°

Step-by-step explanation:

[tex] m\angle \: 6 = m \angle \: 8 \\ (corresponding \: \angle s) \\ m\angle \: 8 = 72 \degree \\ \therefore \: m\angle \: 6 = 72 \degree \\ \\ m\angle \: 14 = m \angle \: 6 \\ (corresponding \: \angle s) \\\therefore \: m\angle \: 14 = 72 \degree [/tex]

Simplify the trigonometric expression cos(2x)+1 using Double-Angle identities

Answers

9514 1404 393

Answer:

  C.  2cos²(x)

Step-by-step explanation:

The relevant identities are ...

  cos(2x) = cos²(x) -sin²(x)

  cos²(x) = 1 -sin²(x)

__

Then the expression can be simplified to ...

  cos(2x) +1 = (cos²(x) -sin²(x)) +1 = cos²(x) +(1 -sin²(x)) = cos²(x) +cos²(x)

  = 2cos²(x)

A function of the form f(x)=ab^x is modified so that the b value remains the same but the a value is increased by 2. How do the domain and range of a new function compare to the domain and range of the original function?

Answers

Answer:

The domain and range remain the same.

Step-by-step explanation:

Hi there!

First, we must determine what increasing a by 2 really does to the exponential function.

In f(x)=ab^x, a represents the initial value (y-intercept) of the function while b represents the common ratio for each consecutive value of f(x).

Increasing a by 2 means moving the y-intercept of the function up by 2. If the original function contained the point (0,x), the new function would contain the point (0,x+2).

The domain remains the same; it is still the set of all real x-values. This is true for any exponential function, regardless of any transformations.

The range remains the same as well; for the original function, it would have been [tex]y\neq 0[/tex]. Because increasing a by 2 does not move the entire function up or down, the range remains the same.

I hope this helps!

Let log base aU=X and log base aV=Y, then a to the x power =? and a to y power =?

Answers

Answer:

[tex]{ \bf{ log_{a}(U) = x}} \\ { \boxed{ \tt{ {a}^{x} = U}}} \\ \\ { \bf{ log_{a}(V) = y}} \\ { \boxed{ \tt{ {a}^{y} = V }}}[/tex]

if (a + b) = 73 and a b =65 find value of a²+ b²​

Answers

Step-by-step explanation:

Here,

by formula a^2+b^2=(a+b)^2-2ab

so,

or,(a+b)^2-2ab

or,(73)^2-2×65

or,5329-126

=5203 is the answer

Donald has x twenty dollar bills and 1 yen dollar bill. How much money does Donald have?
Write your answer as an expression

Answers

Y=20x+1

I think, hope this helps!

Find the scale factor where the pre-image is the large triangle and the image is the small triangle.
A. 4/5
B. 3/2.4
C. 2.4/3
D. 5/4

Answers

Answer:

Option B

Step-by-step explanation:

If the larger triangle (Preimage) is dilated by a scale factor 'k' to form the image triangle (small triangle),

Scale factor = [tex]\frac{\text{Length of one side of the image triangle}}{\text{Length of one side of the preimage}}[/tex]

                 k = [tex]\frac{3}{2.4}[/tex]

Therefore, Option B will be the correct option.

Solve equation by using the quadratic formula

Answers

Answer:

x = -2

Step-by-step explanation:

x^2 + 4x + 4 = 0

quadratic formula:

-b +or- sqrt(b^2-4ac)/2a

-4 +/- sqrt ((-4)^2-4*1*4)/2*1

-4+/- sqrt(16-16) / 2

-4 +/- 0 / 2

-4/2

-2

The numbers of home runs that Barry Bonds hit in the first 18 years of his major league baseball career are listed below. Find the mean and median number of home runs. Round the mean to the nearest whole number. Which measure of central tendency- the mean or the median- best represents the data? Explain your reasoning.

16 25 24 19 33 25 34 46 37
33 42 40 37 34 49 73 46 45

Answers

Answer:

Mean = 35.56

Median = 35.5

Step-by-step explanation:

Given the data:

16 25 24 19 33 25 34 46 37

33 42 40 37 34 49 73 46 45

Reordered data :

16, 19, 24, 25, 25, 33, 33, 34, 34, 37, 37, 40, 42, 45, 46, 46, 49, 73

The mean = ΣX / n

n = sample size ; ΣX = sum of values

The mean = 658 / 18

The mean = 36.56

The Median = 1/2(n+1)th term

1/2(18+1)th term = 1/2(19)th term = 9.5 term

Median = (9th + 10th) / 2 = (34 + 37) / 2 = 35.5

Zelina scored 10% higher on her second quiz than on her first quiz. On her third quiz, Zelina scored 20% higher than on her second quiz. Her third quiz score is what percent higher than her first quiz score?

Answers

Answer:

30%

Step-by-step explanation:

you just add 10% and 20%

Hope it helps c:

Zelina scored 32% higher on the third quiz than on her first quiz.

What is the percentage?

The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %.

Given that:-

Zelina scored 10% higher on her second quiz than on her first quiz. On her third quiz, Zelina scored 20% higher than on her second quiz.

From the given data we will see that:-

1 ) Zelina scored 10% higher on her second quiz than on her first quiz.

SQ = 1.10 FQ

2 ) On her third quiz, Zelina scored 20% higher than on her second quiz

TQ = 1.20SQ

From the above to expression solve for the first quiz:-

TQ = 1.20 x  1.10 FQ

TQ = 1.32FQ

Therefore Zelina scored 32% higher on the third quiz than on her first quiz.

To know more about percentages follow

https://brainly.com/question/24304697

#SPJ2

I don’t know the answer!!
I’m new to this app and I need help if you know the answer please tell me I don’t know English very good please help me.

Answers

Answer:

A. 2.04 seconds

B. 5.92

C: 1.48 -  0.4 = 1.08 seconds    

Step-by-step explanation:

~~~~~~~~~~~~~~~~~~~~~

USE THIS TO GET "B"

the f(-b/2a) is the highest point,

the vertex of the parabola [-b/2a, f(-b/2a)] will give you the time

and height of the highest point

~~~~~~~~~~~~~~~~~~~

USE THIS TO GET "A"... you will get two answers one will be negative

ignore that one , the positive one is the time to hit the ground

if you factor the equation (use the quadratic formula) you will get

the "zeros" that is where the ball is on the ground...

~~~~~~~~~~~~~~~~~~~~~~~

THIS IS FOR PART "C"

if you set the equation equal to 4.5 meters and factor that for the "zeros" you will get the two times that the ball is at that height.. subtract the two times for the duration

What is 5x4 please help

Answers

Answer:

5 x 4 = 20.

Step-by-step explanation:

5 + 5 = 10

5 + 10 = 15

5 + 15 = 20!

Please mark brainliest!

- KanaKittyKat

Answer:

5 x 4 = 20

5 + 5 + 5 + 5 = 20

If a number is divisible by 6 and 8 then is it also divisible by 48?

Answers

Answer:

No

Step-by-step explanation:

Let's look at an example

24

24 is divisible by 6   24/6 = 4  

24 is divisible by 8   24/8 = 3

24 is not divisible by 48  24/48 = 1/2  which is not an integer

12,963 rounded to the nearest hundredth

Answers

9514 1404 393

Answer:

12,963.00 (in the US)12,96 (some other places)

Step-by-step explanation:

In the US, a decimal point is represented by a period. This value is interpreted as an integer with no fractional part, so the fractional part is zero:

 12,963.00

__

Some other places, a comma is used to identify the beginning of the decimal fraction. In that form, this number has a fractional part that has 3 as its thousandths digit. The value of 3 is less than 5, so the number is simply truncated at the hundredths place.

  12,96

If the thousandths digit were 5 or greater, then 1 hundredth would be added to the truncated number.

The graph of a quadratic function has x-intercepts of -7 and -1, and passes through the point (-4,36). Determine the equation of the quadratic function in the form
f(x) = a(x - m)(x − n).

Answers

9514 1404 393

Answer:

  f(x) = -4(x +7)(x +1)

Step-by-step explanation:

The x-intercepts tell us that m=-7 and n=-1. We can use the given point to find 'a'.

  f(-4) = 36

  a(-4+7)(-4+1) = 36

  a = 36/-9 = -4 . . . . divide by the coefficient of 'a'

Filling in the known values, ...

  f(x) = -4(x +7)(x +1)

obtain the value of X for which (X+1),(X-5),(X-2) is a geometric progression.hence find the sum of the first 12 terms of the progression.​

Answers

If x + 1, x - 5, and x - 2 are in a geometric progression, then there is some constant r for which

x - 5 = r (x + 1)

==>   r = (x - 5) / (x + 1)

and

x - 2 = r (x - 5)

==>   r = (x - 2) / (x - 5)

Then

(x - 5) / (x + 1) = (x - 2) / (x - 5)

Solve for x :

(x - 5)² = (x - 2) (x + 1)

x ² - 10x + 25 = x ² - x - 2

-9x = -27

x = 3

It follows that the ratio between terms is

r = (3 - 5) / (3 + 1) = -2/4 = -1/2

Now, assuming x + 1 = 4 is the first term of the G.P., the n-th term a(n) is given by

a(n) = 4 (-1/2)ⁿ⁻¹

The sum of the first 12 terms - denoted here by S - is then

S = 4 (-1/2)⁰ + 4 (-1/2)¹ + 4 (-1/2)² + … + 4 (-1/2)¹¹

Solve for S :

S = 4 [(-1/2)⁰ + (-1/2)¹ + (-1/2)² + … + (-1/2)¹¹]

(-1/2) S = 4 [(-1/2)¹ + (-1/2)² + (-1/2)³ + … + (-1/2)¹²]

==>   S - (-1/2) S = 4 [(-1/2)⁰ - (-1/2)¹²]

==>   3/2 S = 4 (1 - 1/4096)

==>   S = 8/3 (1 - 1/4096)

==>   S = 1365/512

Question 1 of 10
If f(x)= 2 -3 and g(x) = 4x2 + x - 4, find (f+ g)(x).
O A. 4x+x-7
O B. 4x2 +5x-1
O c. 6x2 - 7
OD 6+x-1
A
SUBMIT

Answers

Answer:

I believe it's A

Step-by-step explanation:

I'm not sure sorry if its wrong

Which number can be distributed across two terms
inside parentheses? 3/5 V
X-6
18-4x-1
5
tep 2 Combine like terms that are on the same side of
the equation. Which terms can be combined?
18 and -1
3/5x and 4x
6 and 1
Check
Intro

Answers

9514 1404 393

Answer:

3/5 can be distributed (correct answer is shown)18 and -1 can be combined

Step-by-step explanation:

The only factor outside parentheses that contain 2 terms is the factor 3/5. It can be distributed. (The correct response is shown.)

  3/5 can be distributed

__

The only like terms that reside on the same side of the equal sign are ...

  18 and -1

When a closed curve is parameterized by {x[t], y[t]}, then as you advance along the curve in the direction of the parameterization, which way do the tangent vectors {x'[t], y'[t]} at {x[t], y[t]} point; in the direction you are going, or in the direction opposite to the direction you are going?

Answers

Answer:

In the direction you are going,

Explanation:

We know that the tangent to  {x[t], y[t]} are  {x'[t], y'[t]}. Since  {x'[t], y'[t]} are tangents at  {x[t], y[t]}, we know that the tangent at a point is always parallel to the direction of the function at that point and in the direction of the function. So, the tangent vectors {x'[t], y'[t]} at {x[t], y[t]} point in my direction of motion as I move along the curve.

So, the tangent vectors {x'[t], y'[t]} at {x[t], y[t]} point in the direction you are going.

An angle measures 19.4° more than the measure of its complementary angle. What is the measure of each angle?

Answers

Answer:

37.8+52.2=90

Step-by-step explanation: x + (x + 14.4) = 90

2x + 14.4 = 90

2x = 75.6

x = 37.8  (one angle)

And (x + 14.4) = 52.2 (other angle).

Other Questions
Find the area of the quadrilateral. The five number summary of a dataset is given as0, 4, 12, 14, 20An observation is considered an outlier if it is below _______An observation is considered an outlier if it is above _______The five number summary of a dataset is given as2, 8, 14, 18, 20An observation is considered an outlier if it is below _______An observation is considered an outlier if it is above _______.. Highlight themes explored in feminist dramas? Kermit plans to open a boutique. The initial investment is $10,000. He has to spend $1,500 in annual operations and maintenance. The boutique generates $3,000 in revenues every year. Kermit uses a 10 year planning horizon and a MARR of 12%. The correctly calculated Rate of Return for this project is ________________%. Based on periodic properties, choose the more metallic element from each of the following pairs. Match the words in the left column to the appropriate blanks in the sentences on the right. Between Sr and Sb, the more metallic element is ______Between \rm Sr and \rm Sb, the more metallic element is _______Between As and Bi, the more metallic element is ______Between \rm As and \rm Bi, the more metallic element is _______ Between Cl and O, the more metallic element is ______Between \rm Cl and \rm O, the more metallic element is ______ Between S and As, the more metallic element is ______Between \rm S and \rm As, the more metallic element is _______ If the cube root parent function is horizontally stretched by a factor of 4, then translated 5 units right and 3 units up, write an equation to represent the new function? radio waves are electromagnetic waves that travel at the speed of light 300 000 kilometers per second what is the wave length of FM radio waves received 100 megahertz on your radio dial Choose the inequality that represents the following graph. Each marble bag sold by Debra's Marble Company contains 8 yellow marbles for every 4 blue marbles. If a bag has 56 yellow marbles, how many blue marbles does it contain? 2.Lucy shares 42 marbles between her and her 6 friends. How many does each child? The lender charges you $9 per week for each $100 you borrow.Assuming you borrow $300 for 2 weeks, what APR will you be paying? what is Human Development Index why should it be high Maya express charges 15 dollar for each person and great holiday charges fixed 84dollar and extra 12 dollar for a person. If the total amount charged by each company is same find the number of people going on holiday 59,8x60,2 bng bao nhiu As a part of the life cycle of plants, the plant must begin with an embryo. What statement best describes where the embryo can be found in flowering and non-flowering plants? In a flowering plant, the embryo is in seeds found in the flower, and in non-flowering plants, the embryo is in seeds found in the cone. In a non-flowering plant, the embryo is in spores found in the stem, and in a flowering plant, the embryo is in seeds found in the flower. In a non-flowering plant, the embryo is in seeds in the leaves, and in a flowering plant, the embryo is in seeds found in the spores. In a flowering plant, the embryo is in spores found in the flower, and in a non-flowering plant, the embryo is in seeds found in the spores. A DVD is on sale for $1.05 off. This is a 15% discount from the original price. Use an equation to find the original price. A. $16.05, B. $15.75, C. $10.50, D. $7.00 Help on this pls if you dont mind Which point should Julio use to determine the amount of pizza sauce he needs to bring?ABCDOn a coordinate plane, a graph titled Pizza Recipe has Pizzas on the x-axis and Cups of Pizza Sauce on the y-axis. Point A is (3, 2), point B is (4, 2.6), point C is (4.5, 3), point D is (6, 4). plz give a correct answer for the question how do canine and molar differ. help fast I'm dum and I'm sorry if I keep spamming this.Curtis types 48 words in 1 minute how many words does Curtis type in 8 minutes? use the following equivalent rates to help solve the problem. how many words does Curtis type in 8 minutes?