Marty's barber shop has one barber. Customers arrive at a rate of 2.2 per hour and haircuts are given at a rate of 5 customers per hour. Assume a Poisson arrival rate and an Exponential service time distribution.

Required:
a. What is the probability that one customer is receiving a haircut and one customer is waiting?
b. What is the probability that one customer is receiving a haircut and two customers are waiting?
c. What is the probability that more than two customers are waiting?

Answers

Answer 1

Answer:

Step-by-step explanation:

Arrival rate = ∧ = 2.2 customers per hour  

Service rate = u = 5 customers per hour  

1. Probability that one customer is receiving a haircut and one customer is waiting  

P(2 customers)=(∧/u)^2 * (1-∧/u)=(2.2/5)^2 * (1-2.2/5)=0.1936*0.56= 0.108416

 

2. Probability that one customer is receiving a haircut and two customers are waiting  

P(3 customers)= (∧/u)^3 * (1-∧/u)=(2.2/5)^3 * (1-2.2/5)= 0.085184  

* 0.56= 0.04770304

 

3. Probability that more than two customers are waiting  

P(more than 3 customers)=1- P(less than 3 customers) =  

1- [P(0)+P(1)+P(2)+P(3)]=  

= 1- [(1-2.2/5) +2.2/5*(1- 2.2/5) + 0.108416+0.04770304]=1-0.9625=0.0375


Related Questions

Help please!!!!! I’m using Plato

Answers

Answer:

[tex]\frac{y^{6} }{ x^{2} }[/tex]

Step-by-step explanation:

[tex]y^{6} x^{-2}[/tex]

Answer and Step-by-step explanation:

When there is a set of values within parenthesis, and an exponents on the values and on the parenthesis, you multiply the outer exponent with the inner exponent.

When a value has a negative exponent, the value that has the negative exponent will become a fraction and go to the denominator of the fraction (or go immediately to the denominator), or if it is already a fraction, goes to the denominator. If the value that has the negative exponent is in the denominator, the value will go to the numerator. In both instances, the negative exponent will then change to positive.

First, we need to simplify the expression inside the parenthesis.

[tex]y^{\frac{3}{2} } x^{-\frac{1}{2} } --> \frac{y^{\frac{3}{2} } }{x^{\frac{1}{2}} }[/tex]

Now we multiply the 4 to the exponents.

[tex]\frac{y^{\frac{3}{2} *\frac{x4}{1} } }{x^{\frac{1}{2}}*\frac{4}{1} } = \frac{y^{\frac{12}{2}} }{x^{\frac{4}{2}}} = \frac{y^6}{x^2}[/tex]

[tex]\frac{y^6}{x^2}[/tex] is the answer.

#teamtrees #PAW (Plant And Water)

Jill has 32 crayons. She loses 4 of the crayons. How many are left?

Answers

Answer:

the answer here is d

the answer is d

Answer:

28

Step-by-step explanation:

Total number of crayons = 32

Number of crayons lost = 4

Therefore, number of crayons she is left with is : 32 - 4 = 28

Working :  

    [tex]32\\04 - \\\overline{28}[/tex]

Jimmy thought he had purchased 7 folders, but purchased 6. What was his percent error?

Answers

Answer:

Step-by-step explanation:

Percent Error = | Actual Yield-Theoretical/ Theoretical Yield | *100%

Error= |-1/7|*100%= 14.29%

Which statement about y=x^2-14x+45 is true

Answers

It should be A. Just factor 45

For the same set of observations on a specified dependent variable, two different independent variables were used to develop two separate simple linear regression models. A portion of the results is presented below.
Based on the results given above, we can conclude that:_______.
A. A prediction based on Model 1 is better than a prediction based on Model 2.
B. A prediction based on Model 2 is better than a prediction based on Model 1.
C. There is no difference in the predictive ability between Model 1 and Model 2.
D. There is not sufficient information to determine which of two models is superior for prediction purposes.

Answers

Answer:

A. A prediction based on Model 1 is better than a prediction based on Model 2.

Step-by-step explanation:

Given :

Model 1 :

R² = 0.92

s = 1.65

Model 2 :

R² = 0.85

s = 1.91

The Coefficient of determination of the first model is 0.92 which is greater than the coefficient of determination of the Second model, the coefficient of determination gives the proportion of variation in the dependent variable which is caused by the regression line. Hence, we can say a prediction based on Model 1 is better than a prediction based on Model 2 because a larger proportion of the variation in the dependent variable is predictable from the independent variable.

Imagine that you need to compute e^0.4 but you have no calculator or other aid to enable you to compute it exactly, only paper and pencil. You decide to use a third-degree Taylor polynomial expanded around x =0. Use the fact that e^0.4 < e < 3 and the Error Bound for Taylor Polynomials to find an upper bound for the error in your approximation.

|error| <= _________

Answers

Answer:

0.0032

Step-by-step explanation:

We need to compute [tex]e^{0.4}[/tex] by the help of third-degree Taylor polynomial that is expanded around at x = 0.

Given :

[tex]e^{0.4}[/tex] < e < 3

Therefore, the Taylor's Error Bound formula is given by :

[tex]$|\text{Error}| \leq \frac{M}{(N+1)!} |x-a|^{N+1}$[/tex]   , where [tex]$M=|F^{N+1}(x)|$[/tex]

         [tex]$\leq \frac{3}{(3+1)!} |-0.4|^4$[/tex]

         [tex]$\leq \frac{3}{24} \times (0.4)^4$[/tex]

         [tex]$\leq 0.0032$[/tex]

Therefore, |Error| ≤ 0.0032

The function in the table is exponential:

True

False

Answers

Answer:

true ...

believe it or not there is an exponential sequence that can make that

result

f(x) = [tex]2^{(2(x+2) -1)}[/tex]

x   /// 2(x+2) -1

-1  /// 1

0 /// 3

1 /// 5

2 /// 7

[tex]2^{1} = 2\\2^{3} = 8\\\\2^{5} = 32\\\\2^{7 = 128\\\\[/tex]

Step-by-step explanation:

write an equation in slope intercept form for the line with slope 1/4 and y-intercept -6.​

Answers

Answer:

y=¼x-6

Step-by-step explanation:

y=mx+c

y=¼x+-6

y=¼x-6

Y=1/4x-6 is the answer to your question.

Robert paid $4.5 for 3 apples. Find the cost per apple.

Answers

Answer:

$1.50

Step-by-step explanation:

so its

4.5 ÷ 3

which

1.5

Please help, been stuck on this for a while.

Answers

Answer:its blurry

Step-by-step explanation:

cant see it

Answer:

x = 34.6

Step-by-step explanation:

[tex]x\:=\:\frac{\left(20\cdot \:sin\left(60\right)\right)}{sin\left(30\right)}[/tex]

Which function has a simplified base of 4RootIndex 3 StartRoot 4 EndRoot?



f(x) = 2(RootIndex 3 StartRoot 16 EndRoot) Superscript x

f(x) = 2(RootIndex 3 StartRoot 64 EndRoot) Superscript x

f(x) = 4(RootIndex 3 StartRoot 16 EndRoot) Superscript 2 x

f(x) = 4(RootIndex 3 StartRoot 64 EndRoot) Superscript 2 x



Answer is C f(x) = 4(RootIndex 3 StartRoot 16 EndRoot) Superscript 2 x

Answers

Answer:

c is answer

Step-by-step explanation:

yes

Answer:

C

Step-by-step explanation:

took test

write expanded notion of 752 863?​

Answers

Answer:

7 hundred thousands, 5 ten thousands, 2 thousands, 8 hundreds, 6 tens, 3 ones

Step-by-step explanation:

to write a number in expanded notation all you need to do is write out the number in words.

What is 233,193 rounded to the nearest thousand

Answers

233,190 is the answer
233,190 is the answer

Which function has least rate of change?
O y = 4x + 5
O 3x - y = 9
O x + y = 8
0 4x + 2y = 8

Answers

Answer:

O 4x+2y=8.

Hope this helps you

Match the graph with the correct equation.

A. Y-1 = -1/4(x+5)
B. Y+1= -1/4(x+5)
C. Y-1= -4(x+5)
D. Y-1 =-1/4 (x-5)

Answers

Answer:

y - 1 =  -1/4(x+5)

Step-by-step explanation:

Kobe is a basketball player. He is able to make a free throw 70% of the time. What is the probability that Kobe makes his 10th free throw on his 14th shot

Answers

Answer:

0.1636 = 16.36% probability that Kobe makes his 10th free throw on his 14th shot

Step-by-step explanation:

For each free throw, there are only two possible outcomes. Either he makes it, or he misses. The probability of making a free throw is independent of any other free throw, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

He is able to make a free throw 70% of the time.

This means that [tex]p = 0.7[/tex]

What is the probability that Kobe makes his 10th free throw on his 14th shot?

9 of his first 13(P(X = 9) when n = 13), and then the 10th with 0.7 probability.

Thus

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 9) = C_{13,9}.(0.7)^{9}.(0.3)^{3} = 0.2337[/tex]

0.7*0.2337 = 0.1636

0.1636 = 16.36% probability that Kobe makes his 10th free throw on his 14th shot

What was the original price of the car? Show all work

Answers

Answer:

I got u, it is litearly 16540/83.8 = $19737.5

Step-by-step explanation:

its very simple sincen 100-16.2=83.8

Select the correct answer.
Tom gets $12 off a box of chocolates that had an original price of $48. What percentage is the discount

Answers

Answer:

25

Step-by-step explanation:

divide 48 by 4 which is 25%

find the measures of m and n.

Answers

Answer:

m = 4

n = 5

Step-by-step explanation:

[tex]m + 8 = 3m\\\\m - 3m = - 8\\\\-2m = - 8\\\\m = 4[/tex]

[tex]2n - 1 = 9 \\\\2n = 9 + 1\\\\2n = 10\\\\n = 5[/tex]

The endpoints of a line are (10, 4) and (-2, 8). Find the slope of
the line.

Answers

your answer would be m= -1/3

Write the geometric sequence in function notation.
4,2,1,1/2,1/4,...
A) AX) = (2) - (1/4)x - 1
OB) Ax) = (2) - (1/2)x - 1
C) Ax) = (4) · (/4)x - 1
D AX) = (4) · (1/2)x - 1

Answers

Answer:

D

Step-by-step explanation:

What is the expression (x+1)(x2+3x+2) as a polynomial in standard form?

Answers

Step-by-step explanation:

hope u like it.......

find the slope of the tangent line [tex]m_{tan}[/tex] = f'(a) and then find the equation of the tangent line to f at x = a

f(x) = [tex]\frac{10}{x}[/tex] ; a = 3

Answers

9514 1404 393

Answer:

 10x +9y = 60

Step-by-step explanation:

The equation for the tangent line at a point is ...

  y -f(a) = f'(a)(x -a)

For the given function,

  f(x) = 10/x

The derivative is ...

  f'(x) = -10/x^2

Then the equation of the tangent line is ...

  y -10/3 = -10/9(x -3) . . . . equation of the tangent line (point-slope form)

Clearing fractions, we have ...

  9y -30 = -10(x -3) = -10x +30

  10x +9y = 60 . . . . . equation in standard form

what is the solution to the system of equations below 2x - y = 10 and y=1/2 x+5​

Answers

Answer:

(10, 10 )

Step-by-step explanation:

Given the 2 equations

2x - y = 10 → (1)

y = [tex]\frac{1}{2}[/tex] x + 5 → (2)

Substitute y = [tex]\frac{1}{2}[/tex] x + 5 into (1)

2x - ([tex]\frac{1}{2}[/tex] x + 5) = 10 ← distribute parenthesis on left side by - 1

2x - [tex]\frac{1}{2}[/tex] x - 5 = 10

[tex]\frac{3}{2}[/tex] x - 5 = 10 ( add 5 to both sides )

[tex]\frac{3}{2}[/tex] x = 15 ( multiply both sides by 2 to clear the fraction )

3x = 30 ( divide both sides by 3 )

x = 10

Substitute x = 10 into (2) and evaluate for y

y = [tex]\frac{1}{2}[/tex] (10) + 5 = 5 + 5 = 10

solution is (10, 10 )

The degree of polynomial 8x^2y^2-5x^2y^2-x^3y is​

Answers

Answer:

The degree is the highest number exponent....

that is hard to see in your question...

it does appear to be a 2?

Step-by-step explanation:

Help please I don’t get may I please have help with this

Answers

Answer:

[tex]1)\:2\frac{2}{3} ft[/tex]

[tex]2)\:4[/tex]

[tex]3)\:\frac{20}{3} ft^{2}[/tex]

[tex]4)\:10\frac{2}{3} ft^{2}[/tex]

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

hope it helps...

have a great day!!

Explain relationship between ≠2 and the factor x – 2.

Answers

Answer:

It has a difference of x=2 of -4

Step-by-step explanation:

It has a difference of x=2 of -4

What is factor ?A number or algebraic expression that evenly divides another number or expressioni.e., leaves no remainder—is referred to as a factor in mathematics. As an illustration, 3 and 6 are factors of 12 because 12 3 = 4 and 12 6 = 2, respectively. 1, 2, 4, and 12 are the other components that make up 12.

Given ,

           x ≠ 2 ,

           x - 2 =0

So, we put x = -2 because in question x ≠ 2 .

Then,      x - 2 = 0

              -2 -2 = 0

               - 4 =0

Therefore, it has a difference of x= -2 of -4.

Learn more about factor brainly.com/question/19426180

#SPJ2

Please help asap I needs someone to find the addition property added

Answers

A

Step-by-step explanation:

you can notice that at step 2 9 is added on both sides that is the addition property of equality

Find the interquartile range of the data set represented by this box plot.



25
20
45
35

Answers

Answer:

25

Step-by-step explanation:

im pretty sure i think only ok i think no saying bad things in the comment

16.3 m 16.7 m What is the perimeter of the whole garden? LI m busti 2027​

Answers

The perimeter of the whole garden would be 66m.

Hope this helps! :)

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