9. Empty taxis pass by a street corner at a Poisson rate of two per minute and pick up a passenger if one is waiting there. Passengers arrive at the street corner at a Poisson rate of one per minute and wait for a taxi only if there are less than four persons waiting; otherwise they leave and never return. Ella arrives at the street corner at a given time. Find her expected waiting time, given that she joins the queue. Assume that the process is in steady-state.

Answers

Answer 1

Answer:

0.37

Step-by-step explanation:

To resolve the given problem we will apply

persistent time Markov chain :   n = 0, 1, . . . , 4

 n = number of individuals pausing

where The equalization conditions are : πn = ( πn - 1/2 )

Given that  :

n = 0,1,2,3,4

π0 = 1/( 1 + 2−1 + 2−2 + 2−3 + 2−4) = 0.52 = 16/31

Also the normal number of travelers found by Ella will be represented as

E(N) = (π1 + 2π2 + 3π3) / ( π0 + π1 + π2 + π3) ------- ( 1 )

where : π1 = 8,  π2 = 4,  π3 = 2 , π0 = 16/31  input values into equation 1

E ( N ) =  22/30

given that the True to form hanging tight time = 0.5

hence Holding holding time = E(N ) * 0.5

therefore  the expected waiting time for Ella = ( 22/30 ) * 0.5 = 0.37


Related Questions

Please help me please I only have a couple hours left and this is taking soooo much time

Answers

Answer:

it would be the first answer

Step-by-step explanation:

you can draw the net of the shapes, and count each corner there

12 people can fit in a room that is 9 feet by 4 feet. How many people will fit in a room that is 6 yards by 6 yards

Answers

Answer:

Number of people fit in 6 feet by 6 feet room = 12 people

Step-by-step explanation:

Given:

Number of people fit in 9 feet by 4 feet room = 12 people

Find;

Number of people fit in 6 feet by 6 feet room

Computation:

Surface area of 9 feet by 4 feet room = 9 x 4

Surface area of 9 feet by 4 feet room = 36 feet²

So,

Surface area of 6 feet by 6 feet room = 6 x 6

Surface area of 6 feet by 6 feet room = 36 feet²

Surface area of both rooms are equal. so number of people are also equal

Number of people fit in 6 feet by 6 feet room = 12 people

Find C. Give your answer in the simplest form.

Answers

Using the pythagoras theorem in the given figure, the required length of c is [tex]49\sqrt{6}[/tex].

What is pythagoras theorem?

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean Theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides.

Who is pythagoras theorem named after?

The pythagoras theorem is named after the Greek mathematician-philosopher Pythagoras.

To solve for c, first taking the small triangle in the left of the figure,

since one of the angle is 45 degree and another is 90 degree, the unlabelled angle is 45 degree. Which makes this triangle a isosceles triangle, hence the sides a and b are equal in length. i.e a = b

Using pythagoras theorem in this triangle,

[tex](7\sqrt{2} )^{2} = \sqrt{a^{2}+\ a^{2} }[/tex]

Therefore, a = 49[tex]\sqrt{2}[/tex]

Now Taking the small triangle in the right of the given figure,

tan 30 = a/c

or, [tex]\frac{1}{\sqrt{3} }[/tex] *c = 49[tex]\sqrt{2}[/tex]

Therefore , c = 49[tex]\sqrt{6}[/tex]

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fatima flies her drone 5 feet above the ground diamond she rotates the drone to the right so far the drone has flown a total of 12 feet how far is the drone from the start point

Answers

Therefore , the solution of the given problem of triangle comes out to be the distance of  the drone from the start point is  13feet.

What is the triangle?

Given that it has three sides and three vertices, a triangle qualifies as a polygon. It is a fundamental geometric figure. Triangle ABC is the term used to refer to a triangle containing the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.

Here,

Given : Height of drone  = 5 feet

and  distance of drone covered is 12 feet

Thus ,

to calculate the distance of  the drone from the start point

distance can be represented as H

Since it forms right triangle.

By using pythagoras theorem,

=> 5² + 12² = H²

=> H² = 169

=> H = √169

=> H = 13

Therefore , the solution of the given problem comes out to be the distance of  the drone from the start point is  13feet.

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PLEASE HELP THIS IS DUE IN 15 MINS !!!!!
(I GIVE BRAINLIEST)

Answers

Step-by-step explanation:

1100-825= Markup

Markup= 275

Solve the following equation 3x - 2(x + 3) = 4x - 7

Answers

I don’t know man I’m sorry

Answer:

3x-2x-6=4x-7

x-6. =4x-7

3x=1

X=1/3

EXAMPLE 3.1.30. Let R be the relation on Z defined by ïRy ⇒ x − y is divisible by 3. Then R is an equivalence relation on Z. Find [0], [1], [2], [4], [-1]​

Answers

equation in slope-intercept form of the line that pae through the point (4, 7) and is parallel to the line represented by y = 2x - 5 is ( y - y1 ) = m( x - x1 ) => y - 7 = 2 (x-8) => 2x - y - 1 = 0

What is slope?

A number that specifies a line's direction and slope is known as the slope or slope of a line in mathematics. A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x).

equation is -

y = 2x - 5

since these are parallel to each other,

slope, m= 2

now the equation is -

( y - y1 ) = m( x - x1 )

y - 7 = 2 (x-8)

2x - y - 1 = 0

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which is a equivalent expression to 3^3x3^3x3?

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{3^3\times3^3\times3}[/tex]

[tex]\mathsf{3^3 = 3 \times3\times3 = 9\times 3 = \bf 27}[/tex]

[tex]\mathsf{27\times27\times3 =\ ? }[/tex]

[tex]\mathsf{27\times27 = \bf 729}[/tex]

[tex]\mathsf{729\times 3}[/tex]

[tex]\mathsf{= \bf 2,187}[/tex]

[tex]\large\text{So you are looking for: \bf 2,187}[/tex]

[tex]\large\text{Option A.}[/tex]

[tex]\mathsf{3^6}[/tex]

[tex]\mathsf{= 3\times3\times3\times3\times 3\times3}[/tex]

[tex]\mathsf{3\times 3 = \bf 9}[/tex]

[tex]\mathsf{= 9\times 9\times 9}[/tex]

[tex]\mathsf{9\times9 = \bf 81}[/tex]

[tex]\mathsf{= 81\times9}[/tex]

[tex]\mathsf{= \bf 729}[/tex]

[tex]\large\text{So Option A is NOT equivalent because it is too small }[/tex]

[tex]\large\text{Option B.}[/tex]

[tex]\mathsf{3^7}[/tex]

[tex]\mathsf{= 3\times3\times3\times3\times3\times3 \times3}[/tex]

[tex]\mathsf{3\times 3 = \bf 9}[/tex]

[tex]\mathsf{= 9\times9\times9\times3}[/tex]

[tex]\mathsf{9\times9 = \bf 81}[/tex]

[tex]\mathsf{81\times9\times3}[/tex]

[tex]\mathsf{81\times 9 = \bf 729}[/tex]

[tex]\mathsf{729\times3}[/tex]

[tex]\mathsf{= \bf 2,187}[/tex]

[tex]\large\text{Option B. could possibly be your answer}[/tex]

[tex]\mathsf{3^9}[/tex]

[tex]\mathsf{= \bf 19,683}[/tex]

[tex]\large\text{Option C. Can’t be your answer because it’s too big!}[/tex]

[tex]\mathsf{3^{12}}[/tex]

[tex]\mathsf{= \bf 531,441}[/tex]

[tex]\large\text{Option D. cannot be your answer because it is way too big}\\\ \large\text{similar to your original answer (2,187)}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: \huge Option B.}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer: ur answer is B mark me brainliest

Step-by-step explanation:

Question 5 of 35:
find the value of 10!/8!​

Answers

9514 1404 393

Answer:

  90

Step-by-step explanation:

10! = 10 × 9 × 8!

so 10!/8! = 10×9 = 90

__

The factorial of an integer is the product of that integer and all the positive integers less than it. So, 3! = 3×2×1, for example. 0! is defined as 1.

Solve each equation.

a.(8.5) ⋅ (- 3) = a

b.(- 7) + b = (-11)

c.c - (- 3) = 15

d.d⋅ (-4) = 32

Answers

A: 8293
B:8393738283737383838373738
C:82837282073
D:9193

Quad. PQRS ~ Quad. TUVW, Owe side of PORS has the length 12. The corresponding side of TUVW has length 15. The perimeter of TUVW is 35 and the perimeter of PQRS is?

Pls help me solve this!!

Answers

Therefore , the solution of the given problem of perimeter comes out to be  PQRS  = 29 units.

Establish a perimeter.

The perimeter, or total length, of a shape is referred to as its perimeter in geometry. A shape's perimeter is calculated by summing the lengths of all of its sides and edges. By adding together the lengths of all a shape's sides, one may determine its perimeter.  The circumference of a field, for instance, will be 78 yards for a rectangle with dimensions of 24 yards long by 15 yards wide.

Here,

Given : PQRS has the length 12

and TUVW has length 15.

thus ,

To find the perimeter of PQRS:

we find,

TUVW = 35 units

and

PQRS = 35 - 6

=> PQRS  = 29

Therefore , the solution of the given problem of perimeter comes out to be  PQRS  = 29 units.

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Find the limits given based on the graph.​

Answers

Limits of the functions shown in the graph are limx +f(x) = 0 and limx -f(x) = 0. The link between a group of inputs, each of which has a related output, is known as a function.

what are functions ?

The study of mathematics covers a variety of topics, including numbers, formulas and related structures, forms and the environments in which they exist, quantities and their variations, and the environments in which they exist.  An easy way to think of a function is as a relationship between inputs and outputs, where each input leads to a single, distinct result. Each function has a respective domain and a codomain, or scope. Functions are typically represented by the letter f. (x). input is x. The accessible functionalities fall into four categories. based on the following elements: on functions, one-to-one functions, many-to-one functions, and within functions.

given

We first take into account how f(x) behaves as x increases unboundedly for the function in the graph below. As x can always increase because the function has no limit, it can never be zero. However, the function's behavior when x rises.

Similar to how x decreases without bound or how we move leftward on the graph, f(x) also seems to be approaching zero.

So in this case we can write:

limx → +∞f(x) = 0

limx → - ∞f(x) = 0

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Select all the correct answers. A farmer wants to build two fenced-off sections within his field, one in the shape of a rectangle and the other in the shape of a square. The side of the square must be equal to the width of the rectangle, x feet. The length of the rectangle must be 50 feet longer than its width. The field the farmer wants to build the two fenced sections in has an area of y square feet. The difference of the area of this field and the area of the fenced, square section needs to be at least 1,000 square feet. In addition, the sum of the fenced areas must be less than the area of the field. This is the system of inequalities that represents this situation. Which points represent viable solutions?

Answers

(20, 2,200) and (5, 3,000) are the viable solutions of the given inequality.

What is Inequality?

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that the side of the square must be equal to the width of the rectangle, x feet.

The length of the rectangle must be 50 feet longer than its width

The field the farmer wants to build the two fenced sections in has an area of y square feet.

The difference of the area of this field and the area of the fenced, square section needs to be at least 1,000 square feet

the sum of the fenced areas must be less than the area of the field.

y≥x²+1000

y>2x²+50x

(20, 2,200) and (5, 3,000) are the viable solutions

Hence, (20, 2,200) and (5, 3,000) are the viable solutions of the given inequality.

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(100 points) Need help asap!


The function f(x) is defined below. What is the end behavior of f(x)?

[tex]f(x)=\frac{1}{9} x^{12}[/tex]


A. as x→−∞,f(x)→−∞ and as x→∞,f(x)→∞

B. as x→−∞,f(x)→−∞ and as x→∞,f(x)→−∞

C. as x→−∞,f(x)→∞ and as x→∞,f(x)→−∞

D. as x→−∞,f(x)→∞ and as x→∞,f(x)→∞


The function f(x) is defined below. What is the end behavior of f(x)?

[tex]f(x)=-\frac{1}{10} x^{18}[/tex]


A. as x→−∞,f(x)→−∞ and as x→∞,f(x)→∞

B. as x→−∞,f(x)→−∞ and as x→∞,f(x)→−∞

C. as x→−∞,f(x)→∞ and as x→∞,f(x)→−∞

D. as x→−∞,f(x)→∞ and as x→∞,f(x)→∞

Answers

The end behavior of the function f(x) = 1/9 x¹² is

D. as x→−∞,f(x)→∞ and as x→∞,f(x)→∞

The end behavior of the function f(x) = -1/10 x¹⁸ is

B. as x→−∞,f(x)→−∞ and as x→∞,f(x)→−∞

What is end behavior?

The end behavior of function typically says the characteristics of the function at the ends

How to find the end behavior of function

The given function is:

f(x) = 1/9 x¹²

The positive exponents will mean that x will always yield positive values hence f(x) is always positive

f(x) = -1/10 x¹⁸

The positive exponents will mean that x will always yield positive values however the negative constant -1/10 will make f(x) always negative hence f(x) is always negative

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if its a linear equation in two variables

Answers

Answer:

SOLVE A SYSTEM OF LINEAR EQUATIONS BY GRAPHING.

Graph the first equation.

Graph the second equation on the same rectangular coordinate system.

Determine whether the lines intersect, are parallel, or are the same line.

Identify the solution to the system. ...

Check the solution in both equations.

Step-by-step explanation:

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.

4) Edgar builds a sand castle with a rectangular base. The side lengths of the base are 25 in, and 16 in. He wants
to surround the castle's base with a moat that is w inches wide. Write a quadratic function, A, in standard form to
represent the combined area taken up by the castle and the moat.
16in.
25 in.

Answers

Answer:

4w² + 82w + 400

Step-by-step explanation:

A polynomial is an expression consisting of variables and coefficients involving addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A quadratic function is a polynomial of degree 2. The standard form of a quadratic equation is:

ax² + bx + c

The moat has width of w inch. Therefore:

combined width of castle and moat = 16 in + w in + w in = 16 + 2w in

combined length of castle and moat = 25 in + w in + w in = 25 + 2w in

The combined area = length * width = (16 + 2w)(25 + 2w) = 400 + 32w + 50w + 4w² = 4w² + 82w + 400

Answer:

A(w) = 4 w^2 + 82 w + 400

Step-by-step explanation:

Person above me is correct. :)

Only answer if you’re sure :) thank you

Answers

Your answer is 1/2
Hope this helps!

Answer:

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

sasha needs 3/4 cup of flour to make a batch of muffins and 1 2/3 cups of flour to make loaf of bread. How many cups of flour does sasha need to make both a batch of muffins and a loaf of bread

Answers

Using the addition operation, the number of cups of flour Sasha needs to make both a batch of muffins and a loaf of bread is 2⁵/₁₂ cups.

How is the number or quantity determined?

We can use the addition operation to determine the quantity of flour that Sasha needs.

We add the cups of flour needed for both items to determine the total quantity.

The quantity of flour for making a batch of muffins = 3/4 cups

The quantity of flour for making a loaf of bread = 1²/₃ cups

The total quantity of flour needed for making a batch of muffins and a loaf of bread = 2⁵/₁₂ cups (³/₄ + 1²/₃)

(³/₄ + 1²/₃)

= ³/₄ + ⁵/₃

= (9 + 20)/12

= 29/12

= 2⁵/₁₂

Thus, to make a batch of muffins and a loaf of bread, Sasha needs 2⁵/₁₂ cups of flour.

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If 4, x, y, 108 are the consecutive terms of a G.P., find x and y.

Answers

Given:

4, x, y, 108 are the consecutive terms of a G.P.

To find:

The x and y.

Solution:

The nth term of a G.P. is:

[tex]a_n=ar^{n-1}[/tex]

Where, a is the first term and r is the common ratio.

Let us consider 4, x, y, 108 are the first 4 terms of the G.P. Here 4 is the first term of the given G.P.

Suppose r  the common ratio, then 4th term of the given G.P. is:

[tex]a_4=4(r)^{4-1}[/tex]

[tex]a_4=4(r)^{3}[/tex]

The 4th term of the G.P. is 108.

[tex]4(r)^{3}=108[/tex]

[tex]r^{3}=\dfrac{108}{4}[/tex]

[tex]r^{3}=27[/tex]

[tex]r^{3}=3^3[/tex]

On comparing both sides, we get

[tex]r=3[/tex]

The common ratio is 3.

The second term of the given G.P. is:

[tex]x=4r[/tex]

[tex]x=4(3)[/tex]

[tex]x=12[/tex]

The third term of the given G.P. is:

[tex]y=xr[/tex]

[tex]y=12(3)[/tex]

[tex]y=36[/tex]

Therefore, the value x is 12 and the value of y is 36.

his mapping shows a functional relationship. A mapping diagram shows a relation, using arrows, between domain and range for the following ordered pairs: (2, 4), (negative 3, 0), (negative 1, negative 1), (4, 3). When f(x)=4, what is the value of x? 0 2 3 4

Answers

when f(x)=4, then the value of x is 2

What is a function?

A relation is a function if it has only One y-value for each x-value.

Given that A mapping diagram shows a relation, using arrows, between domain and range for the following ordered pairs:

The ordered pairs are (2, 4), (-3, 0), (- 1, -1), (4, 3)

We need to find value of x when f(x)=4

In the (x, y) ordered pair the x place represents the domain value and y place represents the range.

In the order pairs we have to look for the y value which has 4.

The corresponding element of 4 is the x value

So the value of x is 2 if f(x)=4

Hence, when f(x)=4, then the value of x is 2

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Is the value of the first 7 ten times as great as the value of the second 7 in 7237

Answers

Answer:

no

Step-by-step explanation:

helo i need help with my math please thanky uo i need help with question 3

Answers

On one tank of gas Charlie will drive 612 km

At a cost of 149.9, Charlie will fill the tank with the sum of 8994

Annual cost of filling the tank 467688

How to find how far Charlie can drive on one tank of gas

Information from the problem have it that the efficiency if the Volkswagen golf is 10.2 km/L

Hence, on one liter rides 10.2 km and on a tank which is 60 L Charlie will ride

= 60 * 10.2

= 612 km

Cost of filling the tank

The cost per liter is 149.9 for 60 L we have

= 149.9 * 60

= 8994

Filling the tank once week, the cost for filling in one year is

1 year is 52 weeks

= 8994 * 52

= 467688

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what is an expression for "m decreased by 2."

Answers

Answer:

M - 2

Step-by-step explanation:

Decreased is a math term indicating that we’re deal with subtraction

Answer:

M-2

Step-by-step explanation:

The m should be a variable.

Variable is a symbol like x or y that is used in mathematical or logical expressions to represent a variable quantity.

Decreased is subtract should have a minus sign.

Decreased is to reduced made less in size or amount or degree.

Decreased: ⇒ - (minus sign)

m-2, which is our answer.

Find the area.
A. 156 ft²
B. 126 ft²
C. 80 ft²
D. 39 ft²

Answers

Answer:

The answer is A

Step-by-step explanation:

12 x 5 = 60

16 x 6 = 96

60 + 96 =156 ft

Answer:

[tex]6 \times 5 + 6 \times 16 = 6 \times 21 = 126[/tex]

What is 4 5/7 + 4 1/4

Answers

Answer:

8 27/28 or 251/28

Step-by-step explanation:

Find common denominators then simply add.

Please help me I don’t understand this at all

Answers

Answer:

A and D

option A is correct because if you do 4/5 times 2/2 you get 8/10

so that means they both are Equal.

option D is also correct

because

after 6/10 It’s 7/10, 8/10..

3/4 of the children in a school have blue eyes the rest have brown eyes. if 84 children have blue eyes how many have brown eyes?

Answers

Answer:

Let the total number of people in the group=x

So total number of men =3x/8

Hence total number of women=5x/8

No. of men having brown eyes=2/3*3x/8=x/4

Total no. of people having brown eyes=3x/4

No.of women having brown eyes

=3x/4 -x/4=2x/4=x/2

No. of women who don't have brown eyes= 5x/8-x/2 = x/8

So the fraction is x/8x= 1/8

Step-by-step explanation:

Answer: 28 children

What is a ratio?

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare the numbers, and you can compare them using division.

First, we would need to figure out the total number of students. To do this, we can divide 84 by 3, then add that to the total.

84 ÷ 3 = 28

28 + 84 = 112

This means that there are 112 students in the classroom.

If 3/4 of the children in the school have blue eyes, we know that 1/4 of the children will have brown eyes. We can convert 1/4 into a decimal, or into a percentage, to get the number of children with brown eyes.

1/4 = 0.25 = 25%

To figure out how much 25% of 112 is, we can simply multiply 112 by 0.25.

112 × 0.25 = 28

So, this means that there are 28 children with blue eyes in the school.

PLEASE HELP ME EASYYYYYY MATH QUESTION BRAINLIEST

what percent is equivalent to the fraction 8/100? Enter your answer in the box. __ %

Answers

Answer:

8% is equivalent to the fraction 8/100

Step-by-step explanation:

What is the formula to find the perimeter of a pentagon


Answers

Answer:

For a regular polygon, the perimeter is equal to the product of one side length and the number of sides of the polygon. For example, the perimeter of a regular pentagon whose side length 8 cm, is given by; Perimeter of a regular pentagon = 8 x 5 = 40 cm.

Step-by-step explanation:

I hope I've helped :).

Answer:

perimeter = number of sides x the length of any side.

Step-by-step explanation:

brainliest pls

Figures A and b are similar. Figure A has an area of 18 square feet. Figure b has an area of 98 square feet and one of the sides lengths is 14 feet find the corresponding side length

Answers

Answer:

6 ft

Step-by-step explanation:

The ratio of the square of the sides of two similar figures = the ratio of their area

Let x represent the missing side corresponding side length

Therefore,

Area of figure B/area of figure A = square of side length of figure B/square of the side length of figure A

Thus:

98/18 = 14²/x²

98/18 = 196/x²

Cross multiply

98*x² = 196*18

98x² = 3,528

Divide both sides by 98

x² = 3,528/98

x² = 36

x = √36

x = 6

Therefore, missing corresponding side length = 6 ft

The corresponding side length is 2.57 feet

Similar shapes

Given that figures A and b are, hence the ratio of the area to the length is equal to a constant as shown:

[tex]\frac{A}{L} = \frac{a}{l}[/tex]

Substitute the given parameters into the formula to have:

A = 98 square feet

L = 14 square feet

a  18 square feet

[tex]\frac{98}{14} = \frac{18}{l}\\98l=252\\l = 2.57 feet[/tex]

Hence the corresponding side length is 2.57 feet

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