A mosquito is walking at random on the nonnegative number line. She starts at $1$. When she is at $0$, she always takes a step $1$ unit to the right, but, from any positive position on the line, she randomly moves left or right $1$ unit with equal probability. What is the expected number of times the mosquito will visit $0$ before the first time she visits $4$?

Answers

Answer 1

The expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.

Given that repeatedly throwing a fair tetrahedral die, trying to get a 4 (success) before getting a number from 1 to 3 (failure), which follows a geometric distribution.

To find the expected number of visits to 0 before reaching 4, analyze two cases:

success (reaching 4 before 0) and failure (reaching 0 before 4).

By the given data, the probabilities of two cases are:

P(success) p = 1/4,

P(failure)=3/4.

The expected count of failures, X, can be found in terms of success probability p as

[tex]E[X]=\sum_{x=0}^{+\infty}[x(1-p)^xp][/tex]

On substituting p = 1/4 gives:

[tex]E(X) = 0(1/4)+1(3/4)(1/4)+2(3/4)^2(1/4)+3(3/4)^3(1/4)+.........[/tex]

On taking (1/4) gives

[tex]E(X) = 1/4[3/4+(3/4)^2+(3/4)^3+......+\infty]----(1)[/tex]

Consider [tex]3/4+(3/4)^2+(3/4)^3+......+\infty[/tex]

This forms a geometric series tends to infinity and the sum is given by :

[tex]S_\infty = a/(1-r)[/tex]

Here: a= 3/4

r = 3/4

Plugging these values into formula gives:

[tex]3/4+(3/4)^2+(3/4)^3+......+\infty = S_\infty[/tex]

[tex]S_\infty= 3/4/(1-3/4)[/tex]

On subtracting the denominator gives:

= 3/4/(1/4)

On taking reciprocal gives:

= 3/4 * 4

On simplifying gives:

= 3

Substituting these value into given equation 1 gives:

E(X) = 1/4*[3]

On multiplying gives:

E(X) = 3/4.

Therefore, the  expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.

Learn more probability about here:

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i need help on this please​

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3 answer to 7+(-4)

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Answers

Answer:

D. T= I/PR

Step-by-step explanation:

PRT are multiplyed so you divide PR to get T by itself.

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Answer:

There wouldn't be a fraction form because its a whole number which is 9

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Answer:

-1/2

Step-by-step explanation:

It’s y2 - y1 over x2-x1

- 2 - 3

— - -—-

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= -5/10

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Answer: 1/2

Step-by-step explanation:

If p = 2 and q = 8, the value of p3 + V64 q ls____​

Answers

Answer:

518

Step-by-step explanation:

P = 2

Q = 8

p3 + 64q

Multiply "p" (which is 2) with 3

Multiply "q" (which is 8) with 8

Add the two numbers you get

And you have you answer

I hope this helps. :)

The answer I got was: {{ 2,8}}

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The gross domestic product (GDP) of France is about $2.00 × 10 12 12 , and the GDP of Tuvalu is about $4.00 × 10 7 7 . How many times larger is the GDP of France than the GDP of Tuvalu?

Answers

Answer:

France's GDP is 50 000 times larger than Tuvalu's GDP.

Step-by-step explanation:

Given: Gross Domestic Product (GDP) of France = $2.0 x [tex]10^{12}[/tex]

            Gross Domestic Product (GDP) of Tuvalu = $4.0 x [tex]10^{7}[/tex]

To determine the number of times in which the GDP of France is greater than that of Tuvalu, divide the GDP of France by the GDP of Tuvalu.

[tex]\frac{2.0*10^{12} }{4.0*10^{7} }[/tex] = [tex]\frac{2000000000000}{40000000}[/tex]

           = [tex]\frac{200000}{4}[/tex]

           = 50000

Therefore, France's GDP is 50 000 times larger than Tuvalu's GDP.

Please Help?!
A lab technician needs to determine whether cells in a test tube are prokaryotic or eukaryotic. The technician has several dyes she could use to stain the cells. Four of the dyes are described below. Which dye should she use to determine if the cells are prokaryotic or eukaryotic?

Answers

Answer:

nile blue should be the correct answer

Step-by-step explanation:

ab (3a-5b) equals to?

Answers

Answer:

3a^2b-5ab^2

Step-by-step explanation:

Answer:

3a²b-5ab²

Step-by-step explanation:

Distribution method:

ab (3a-5b) = 3a²b-5ab²

A ticket for the spring musical is $4.50. Which table show the relationship between the number of tickets purchased and the total price paid?

Answers

Answer:

mwe.n pa konen men tenyen ooooo

Helpp me plzzz!!

A.) Side - Side - Side
B.) Side - Angle - Side
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D.) Angle - Angle - Side
E.) Hypotenuse - Leg

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Answer:

side angle side. Seems contrary

Answer:

side angle side. Seems contrary

Step-by-step explanation:

what does x = ? need help with the pythagorean theorem

Answers

Answer:

The answer is 9

Step-by-step explanation:

set up the equation as 12^2 + b^2 = 15^2

solve the exponents and you get 144 + b^2 = 225

Then subtract 144 from both sides and get 81

After that just do the square root of 81 and you get 9

pls mark brainliest

Every week, Hector’s 20 hours earns $210.00. He earns a constant amount of money per hour.

Part B
Write an equation that can be used to determine Hector's earnings, in dollars, m, for h hours of work.

Answers

Answer: 20 weeks in 1 week

in 2 weeks 40

Step-by-step explanation:

This proves that the equation is true

In triangle ABC, the measure of angle A is 48° and the measure of angle C is 24°. What type of triangle is triangle ABC?

Answers

Answer:108 degrees

Step-by-step explanation:

Answer:

Scalene triangle

Step-by-step explanation:

24+48= 72

180-72=108

All three angles are different meaning that the triangle must be a scalene triangle.

Evaluate -9x-2 when x =-4

Answers

Answer:

34

Step-by-step explanation:

So -9x is 36,36-2=34

Answer:

34

Step-by-step explanation:

-9(-4)-2

36-2

34

Help will give a crown!!

Answers

Answer:

okay

Step-by-step explanation:

1) Each side length is 12

2) Each side length is 2

In triangleABC, a = 1.4 cm, b = 1.5 cm and c=1.5 cm. Find the measure of angleA to the nearest 10th of a degree.​

Answers

Answer:55.6

Step-by-step explanation:

Answer:

55.6

Step-by-step explanation:

Solve the system of equations by the elimination method: \large 9x+y=-8 and \large 4x+y=2. Then fill in the solution as an ordered pair:

Answers

Answer:

rrrrrrrrrrrrrrrrrrrrrwwwwwwwwwwwwwwwwww44444444444444wwwwwwwwwwwwww

Step-by-step explanation:

you are easydsssssdfewatg3

what is halfway between 5.3 and 5.4

Answers

Answer:

5.35

Step-by-step explanation:

5.31 5.32 5.33 5.34 5.35

The answer will be 5.35

I WILL GIVE BRAINLIEST
Given ΔDEF : ΔRST, find x.



12
15
16
64

Answers

Answer:

The answer would be 12, I am very sure. :)

A carpenter use 65 shelves to make 13 bookcases. She uses the same number of shelves for each bookcase. Are 32 shelves enough to build 6 more bookcases?

Answers

Answer:

Yes.

Step-by-step explanation:

First, find the unit rate for 1 bookcase.

65 ÷ by 13 = 5 (unit rate)

Then, multiply the unit rate by the bookcases the carpenter wants to make.

6 · 5 = 30

Finally, subtract the shelves the carpenter wants to use by 30.

32 - 30 = 2 shelves.

Therefore, 32 shelves is enough to build 6 more bookcases. <3

A rectangular lawn 4m by 10m has a garden of uniform width added to one end. Then, along the combined side length of the lawn and garden , another garden is added, whose width is twice that of garden . The total area of the lawn and both gardens is 72 m2

Answers

Answer and explanation:

A rectangle's width is longer than the length

And so given a rectangular lawn 4m by 10m,

the width of the lawn= 10m

the length of the lawn= 4m

If a garden of uniform width is added, then garden's width = 10m

The garden of uniform width is added to the width side of the rectangular lawn( since along the combined side length of the lawn and garden, another garden is added)

The garden added to the combined side length of the lawn and garden has width twice that of the garden = 2*10= 20m

Given that total area of the lawn and two gardens = 72m²

Total area of lawn and 2 gardens(Area of rectangle(lawn+2 garden's)) is length * width

= 4*10+ 10*x+ 20*y=72

Therefore equation for total area of lawn and both gardens is 40+10x+20y=72

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x can be solved

40+10x+20y=72

10x+20y=72-40

10x+20y=32

10x=32-20y

x=32-20y/10

Y can be solved

40+10x+20y=72

10x+20y=72-40

10x+20y=32

20y=32-10x

y=32-10x/20

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Answers

Answer:

-3

Step-by-step explanation:

since it is a gap of 6 the first one gave ...so 3-6=-3

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Answers

The correct answer is f^-1(x)=1/2x+2.

1. Substitute y for f(x). ( y=2x+4 )

2. Interchange the variables x and y. ( x=2y-4 )

3. Swap the sides. ( 2y-4=x )

4. Move the constant to the right. ( 2y=x+4 )

5. Divide both sides by 2. ( y=1/2x+2 )

6. Use substitution to substitute f^-1(x) for y.

Thus the inverse is f^-1(x)=1/2x+2

There are 60 seconds in a minute and 60 minutes in an hour. How many seconds are in one hour?

Answers

Answer:

3,600 seconds

Step-by-step explanation:

multipy how many hours by 3,600

(so 1 times 3,600)

Answer:

3,600 seconds

Step-by-step explanation:

[tex]\frac{60 seconds}{1 minute} (\frac{60 minutes}{1 hour} )=\frac{3,600 seconds}{1 hour}[/tex]

do yall know this one? ​

Answers

Answer:

8x

Step-by-step explanation:

it's the slope

y = 8x or y = 8/1x

Do not place /1.

The system understands that there is a invisible 1 that's how all whole number can turn into equations.

A turtle is 20 5/6 inches below the surface of the pond. It dives to a depth of 32 1/4. What is the change of the turtles posistion. HELP ASAP PLEAS AND THEANK YOU!

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Answer:

I believe it's 11

Step-by-step explanation:

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Step-by-step explanation:

subtraction if that wut u askim

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Answers

Answer:

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Step-by-step explanation:

7a(3b - 2c + 4)


Help?

Answers

Answer:

21ab-14ac+28a

Step-by-step explanation:

[tex]7a(3b - 2c + 4)\\\\\mathrm{Distribute\:parentheses}\\\\=7a\times \:3b+7a\left(-2c\right)+7a\times\:4\\\\\mathrm{Apply\:minus-plus\:rules}\\\\+\left(-a\right)=-a\\\\=7\times\:3ab-7\times\:2ac+7\times\:4a\\\\Simplify\\\\21ab-14ac+28a[/tex]

1. To graph any linear equation in the calculator it needs to be in the slope
y intercept form. What is the slope y-intercept form for the equation
4y – 20x = -8

Answers

Answer:

y=mx+b no judgement i think this is right but i coukldbe completely off

Step-by-step explanation:

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