Problem 5.A miner is trapped inside a mine and has access to 3 doors. The first door leads to a tunneland can take him to safety in 3 hours. The second door is a trap and brings him back to the mine againafter 5 hours through a tunnel. The third door also is a trap that brings him back to the mine after 7 hoursthrough a tunnel. The miner at all times is equally like to choose any of the doors. (In the darkness he canhardly distinguish the three). What is the expected length of time until he reaches safety

Answers

Answer 1

Answer:

Expected time is 15 hours for him to get to safety.

Step-by-step explanation:

We define X as the time that this miner would get to safety.

We define Y as the door he chooses initially.

P(Y= 1) = P(Y=2)=P(Y=3) = 1/3

We have E[X|Y=1] = 3

E[X|Y] = 5 hours + E[X}

E[X|Y] = 7 hours + E[X]

Then we have

E[X] = 1/3(3 + 5 + E[X] + 7 + E[X])

We cross multiply

3*E[X] = (15 + 2E[x])

3E[X] - 2E[X] = 15

E[X] = 15

So the time it would take to get him to safety is 15 hours


Related Questions

Find two consecutive whole numbers that √45 falls between.

Answers

It would fall between 6 and 7.

Information about three circles is listed below.

• Circle P has a diameter of 26 cm.
• Circle Q has a diameter of 52 cm.
• Circle R has a radius of 52 cm. Based on this information, which statement is true?



A.The diameter of circle P is the same length as the diameter of circle R.

B. The radius of circle P is the same length as the radius of circle Q.

C The diameter of circle P is the same length as the radius of circle Q.

D. The radius of circle P is the same length as the diameter of circle R.​

Answers

Answer:

C The diameter of circle P is the same length as the radius of circle Q.

Step-by-step explanation:

factor the trinomial completely. 10x^2+7x-12

Answers

Answer: i think the answer is (5x - 4)(2x +3) if it id wrong i am sorry ok

don't forget to drop a heart

Answer:

the answer is (2x + 3)(5x - 4)

Step-by-step explanation:

helpppppp ill give brainliest answer if you know

Answers

Answer:

16 in squared

Step-by-step explanation:

Need help on this question

Answers

Answer:

c Christopher

Step-by-step explanation:

hope this helps

C. Christopher would be the answer because no matter which way 6.15 is farthest from 0.

Ben starts walking along a path at 2 mi/h. One and a half hours after Ben leaves, his sister Amanda begins jogging along the same path at 7 mi/h. How long (in hours) will it be before Amanda catches up to Ben?

Answers

Answer:

Amanda will catch up Ben after 0.6 hours.

Step-by-step explanation:

Amanda begins jogging along the same path at 7 mi/h.

This means that Amanda's position, after t hours, is given by:

[tex]A(t) = 7t[/tex]

Ben starts walking along a path at 2 mi/h.

Amanda leaves after one and a half hour, which means that Ben will be at position 2*1.5 = 3. So Ben's position after t hours is given by:

[tex]B(t) = 3 + 2t[/tex]

How long (in hours) will it be before Amanda catches up to Ben?

This will happen when:

[tex]A(t) = B(t)[/tex]

So

[tex]7t = 3 + 2t[/tex]

[tex]5t = 3[/tex]

[tex]t = \frac{3}{5}[/tex]

[tex]t = 0.6[/tex]

Amanda will catch up Ben after 0.6 hours.

It would take Amanda 0.6 hours or 6/10 hours to catch up with Ben.

This question comes from a topic in mathematics called rates and it's used to compare two values with each other and how one value affects the other value.

Let s represent the distance Amanda travels until she meet Ben.

We can set a timer on our phone when she leaves in order to track the time taken.

Let t represent the time taken.

Set of Equation

We can come up with two equations from these scenario

d - 3 = 2t------ equation (i)d = 7t ----- equation (ii)

Substitute equation (ii) into equation (i)

[tex]7t -3 =2t[/tex]

collect like terms

[tex]7t-2t=3\\5t=3\\t=3/5\\t=0.6[/tex]

From the above, we can see it took her 0.6 hours to catch up with Ben.

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PLEASE HELP ASAP
Solve the right triangle. Round lengths to the nearest tenth and angles to the nearest degree

Answers

is there a picture to go along with this?

Order these numbers from least to greatest: 1.05, 0.95, 0.75, 1.01

Answers

Answer:

0.75 0.95 1.01 1.05

Step-by-step explanation:

Answer:

0.75,0.95,1.01,1.05

Step-by-step explanation:

Thats in order from smallest to biggest.

Hope this helped! If it did, please give me brainliest! That would help a lot! Thanks! :D

GggggghggggggggggggggggggggTry

Answers

Answer:

try this 20+10 =       20x10 =       20-10=

Step-by-step explanation:

add the first one, than times the other one, after subtract the last one.

8th grade math, please help.
I’ll give you brainliest if you want.

-Find the volume-

Answers

Answer:

113.10

Step-by-step explanation:

Answer:

how to make sugar cookies :)

Step-by-step explanation:

2 ¾ cups all-purpose flour

1 teaspoon baking soda

½ teaspoon baking powder

1 cup butter, softened

1 ½ cups white sugar

1 egg

1 teaspoon vanilla extract

Which method is the best method for solving the equation?
[tex]8x^{2} - 13x + 3 = 0[/tex]

Answers

Answer:

Step-by-step explanation:

Which Method Should Be Used to Solve a Quadratic Equation? Quadratic equations are of the form ax2 + bx + c = 0 where a, b and c are real numbers, a ≠ 0. Quadratic equations have two solutions, but it is possible that one solution may repeat. happy to help

What is the slope of the line?

Answers

Answer: 2

Step-by-step explanation:

Bags of flour at a local grocery store have a mean weight of 83 ounces with a standard deviation of 2 ounces. The manufacturer of the flour states that 5% or less of the bags are underweight. What is this weight?

Find the z-table here.

79.7 ounces
80.4 ounces
80.9 ounces
81.3 ounces

Answers

Answer is 80.4 ounces :)!!!!

Answer:

80.4

Step-by-step explanation:

Show work and explain how too find the answer please I’m not fully understand the question

Answers

Answer:

She would have 24 single shoes. This is because she has 12 pairs and there are 2 of something in each pair. Therefore, Danielle would have 24 single shoes. (12*2=24) Hope this helped!!

Hudson went shopping for a new pair of sneakers. The listed price of the pair of sneakers was $29, but the price with tax came to $31.61. Find the percent sales tax.

Answers

Answer:

18

Step-by-step explanation:

multiply then add a all together

wich expression is equivalent to 2,3/5 divided by 7/9​

Answers

it’s 27/35 so 27/1 * 1/35 sorry if im wrong

Answer:

117/35 is equalivent expression

Step-by-step explanation:

2 3/5 divided by 7/9

so you need to make 2 3/5 into a fraction

you do the denominator time the whole number plus the numerator to get 13/5

13/5 / 7/9

when you divided fractions you flip the seccond fraction and multiply to get....

   13/5 times 9/7

so you do. 13 times 9 and 5 times 7

you get 117/35

A right triangle has a base of 6 inches and a height of 10 inches.What is the area of the triangle

Answers

Answer:

dont know

Step-by-step explanation:

Answer:

I thinks it is 30 squared inches

The term-to-term rule for a sequence is " Add 1 and then double"
The first two terms are 2 and 6
Find the next term

Answers

i’m sorry, i don’t know.. :(

The next term of the sequence is 14.

What is Sequence?

A sequence in mathematics is a ordered set of objects or numbers which are related with something.

For example, 1, 3, 5, ..... is a sequence of odd numbers.

Given that,

The term-to-term rule for a sequence is " Add 1 and then double"

First term = 2

Second term = 6

6 is got by adding 1 to 2 and then doubling it.

2 + 1 = 3

3 × 2 = 6

In the same way,

Third term = (6 + 1)2 = 7 × 2 = 14

Hence the next term of the sequence is 14.

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What is the product of 3/7x2/5

Answers

Answer:

0.1714285714285714

Step-by-step explanation:

A drum used for percussion has sides modeled by a hyperbola. The total height of the drum is 35 inches. The diameter at the top of the drum is 16 inches, and the minimum diameter is 8 inches, occurring at a height of 22 inches. Determine the equation of a hyperbola that models the sides of the drum assuming that the center of the hyperbola occurs at the height where the diameter is the least.

Answers

look at the screen shot ya know

The equation of a hyperbola that models the sides of the drum assuming that the center of the hyperbola is (35 + a)²/a² - 8²/b² = 1 and (22+ a)²/a² - 4²/b² = 1

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that the total height of the drum is 35 inches.

The diameter at the top of the drum = is 16 inches, and

The minimum diameter is 8 inches, occurring at a height of 22 inches.

The equation of the hyperbola be denoted as;

x²/a² - y²/b² = 1

From the question, with x and y coordinates representing height and radius respectively,

Then,

When  x = 35 + a, y is = 16/2 = 8 and

At x = 22+ a, y  is = 8/2 = 4

Thus,

(35 + a)²/a² - 8²/b² = 1

(22+ a)²/a² - 4²/b² = 1

By solving, we have, a = 128.95 and b = 14.75

Therefore a= 128.95 and b = 14.75

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Plzzzzzzz help this is tonight plzzzzzzz

Answers

Answer:

Step-by-step explanation:

tto blurrry

PLZ HELP PLZZZZZZZZZZZZZZZZ

Answers

Answer:

d

Step-by-step explanation:

The answer is d ddddddddddddddd

The solution to a system of equations is (6,3) choose 2 equations that might make up the system

Answers

Answers: 2y=6 and y=x/2

brainly plus if u help

Answers

Answer:

huh

Step-by-step explanation:

A farmer sells 8.5 kilograms of pears and apples at the farmer's market. 2 5 of this weight is pears, and the rest is apples. How many kilograms of apples did she sell at the farmer's market?

Answers

Answer:

6 kilograms of apples

Step-by-step explanation:

8.5-2.5=6

Hope I helped

Please help and thanks in advance


Add 0.65 and 0.24. How many tenths are in the sum?

Answers

there are 8 tenths in the sum. .65+.24 is .89. tenths are the first digit to the right of the decimal. 80 and 8x10=80

Number of tenths are in the sum is 8

What is Decimal number?

The decimal numeral system is the standard system for denoting integer and non-integer numbers.

What is Addition?

Addition is the action or process of adding something to something else.

Given,

The numbers 0.65 and 0.24

Add them together

0.65 + 0.24 = 0.89

Here the number is a decimal number that is 0.89

If a number has a decimal point , then the first digit to the right of the decimal point indicates the number of tenths.

Therefore number 8 is in the tenth place

Hence, the number of tenths in the sum is 8

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help plz ill give extra points ?

Answers

Answer:

Step-by-step explanation:

Not sure

Answer:

45 degrees

Step-by-step explanation:

they are both the same half so 90 divided by 2 is 45

PLEASE HELP!!!! A diver is in a diving board located 11 feet above the surface of a pool. A swimmer is directly below the diver 4 feet below the surface of the pool. What is the difference between the height of the diver and the height of the swimmer?

Answers

Answer:

I think it is a 7 foot difference between both sorry if wrong

I thinks it’s 6 sorry if wrong.

Match each indicated measure in the first column for

O
⊙O.

Answers

Answer:

Step-by-step explanation:

By the property,

"Measure of the intercepted arc is double of the inscribed angle"

m(arc BC) = 2×48°

                = 96°

By using the same property,

m(arc AC) = 2 × m(∠B)

m(∠B) = [tex]\frac{110}{2}[/tex]

          = 55°

m(∠A) + m(∠B) + m(∠C) = 180° [Triangle sum theorem]

48° + 55° + m(∠C) = 180°

m(∠C) = 180° - 103°

          = 77°

m(arc AB) = 2 × (m∠C)

                = 2×77

                = 154°

the regular price of a camera 180.00.the camera is on sale for 25% off the regular price.what is the sale price of the camera in dollars and cents​

Answers

Answer: $135

Step-by-step explanation:
180 decrease 25% =
180 × (1 - 25%) = 180 × (1 - 0.25) = 135

Hope this helps (:
The answer is 135.00
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