trapped in a cell that contains 3 doors. The first door leads to a tunnel that returns her to back tothe cell after 2 days of travel. The second door leads to a tunnel that returns her back to the cell after 4days of travel. The third door leads her freedom after 1 day of travel. If it is assumed that Ally will alwaysselect doors 1, 2, and 3 with probabilities 0.5, 0.3, and 0.2 (respectively), what is the expected number ofdays until she reaches freedom

Answers

Answer 1

Answer:

The expected number of days until prisoner reaches freedom is 12 days

Step-by-step explanation:

From the given information:

Let X be the random variable that denotes the number of days until the prisoner reaches freedom.

We can evaluate E(X) by calculating the doors selected, If Y be the event that the prisoner selects a door, Then;

E(X) = E( E[X|Y] )

E(X) = E [X|Y =1 ] P{Y =1} + E [X|Y =2 ] P{Y =2} + E [X|Y =3 ] P{Y =3}

[tex]E(X) = (2 + E[X])\dfrac{1}{2}+ (4 + E[X])\dfrac{3}{10}+ 1 (\dfrac{2}{10})[/tex]

[tex]E(X) = (2 + E[X])0.5+ (4 + E[X])0.3+ 0.2[/tex]

Solving for E[X]; we get

E[X] = 12


Related Questions

Aden started with 6 cups of water. Throughout the day he drank the following amounts: 1 1/3 cups, 1 1/2 cups, 1 2/3 cups, and 3/4 cup. How many cups of water are left?
A. 2/3
B. 3/4
C. 1 1/3
D. 1/4

Answers

Answer:

B. 3/4 cup of water

Step-by-step explanation:

1 1/3 + 1 1/2 + 1 2/3 + 3/4 = 5 1/4

6 - 5 1/4 = 3/4

Answer: B or 3/4

Step-by-step explanation:

ok first add all the amounts he drank together

1 1/3 + 1 1/2 + 1 2/3 + 3/4

because the denominators are all different, you have to change them to a common denominator, which is 12. i've also changed them to improper fractions.

1 1/3 = 4/3 = 16/12    1 1/2 = 3/2= 18/12    1 2/3 = 5/3= 20/12   3/4 = 9/12

now add them all together

16/12 + 18/12 + 20/12 + 9/12 = 63/12

now convert the original 6 cups to an improper fraction with the denominator of 12

6 = 72/12

now subtract 63/12 (the amount he drank) from 72/12 (the amount he started with)

72/12 - 63/12 = 9/12

9/12 is able to be simplified to 3/4

so the correct answer is B, or 3/4

Select the expressions that are equivalent to 34

Answers

Answer:

81 9^2

Step-by-step explanation:

3•3= 9

3•3=9

9•9=81

and 9•9=81

which of the following represents the equation with a slope of 3 and a y-intercept of 2?

Answers

Answer:

c is the correct answer

Step-by-step explanation:

"Five less than
the quotient of
a number and
3 is -7°
A. 5 - X/3-7
B. -7 +x/3
C. X3 - 5 =-7
D. 5 - 4/2 = -7

Answers

The answer is C. I hope it helps

Which shows the use of the associative and commutative properties to make simplifying 3.2 + 20 – 3+ 4.8 + 19 easier?​

Answers

Answer:

B

Step-by-step explanation:

(3.2+4.8)+[20+19+(-4)]

8. +. 47. -4

=43

how many milligrams (mg) are
in a levothyroxine 88mcg tablet?

Answers

Answer: 0.088 mg. Hope this helps!!

1 1/2 x 4 1/4 = ?
PLZ ANSWER QUICKLY

Answers

451/8=56.38 is what i got

If you rotate figure GTR 270° clockwise about the origin. What will be the coordinates of G’T’R’ (Please Help I need this done in five minutes.)

Answers

Answer:

C.  G' (4,-7), R' (2,-3), T'(6,-4)

Step-by-step explanation:

Get a piece of paper and draw 2 intersecting lines, like how a graph looks like. Then get another paper that's transparent enough, and place a dot roughly where R would be. Rotate it 270* clockwise (3 times around 90 degrees), and R would be in the bottom right area. That means the figure would be around that area and you can base the coordinates from that.

Kevin and his children went into a restaurant and he bought 31.50

Answers

um kevin bought 31.50 of what? food?

Lydia receives a $2,000 gift and wants to open a savings account. Which bank interest would be the best for her if the current inflation rate is 3.5%?

Answers

Answer:

the best interest rate would be a minimum of 3.5% annual interest

Step-by-step explanation:

An inflation rate of 3.5% would mean that the buying power of Lydia's money would decrease by 3.5% every single year. Therefore, the best interest rate would be a minimum of 3.5% annual interest. That way she would at least maintain the same buying power with her money as the day that she first placed it in the account. Any interest rate higher than 3.5% would be even better as Lydia will begin to make a profit from her savings.

1. Assume that men’s weights are normally distributed with a mean given by  = 172lb and a standard deviation given by  =29lb. Using the Central Limit Theorem to solve the following exercises(1) If 36 men are randomly selected, find the probability that they have a mean weight greater than 160lb.(2) If 81 men randomly selected, find the probability that they have a mean weight between 170lb and 175lb.

Answers

Answer:

1) 0.99348

2) 0.55668

Step-by-step explanation:

Assume that men’s weights are normally distributed with a mean given by  = 172lb and a standard deviation given by  =29lb. Using the Central Limit Theorem to solve the following exercises

When given a random number of samples, we use the z score formula:

z-score is z = (x-μ)/σ/√n where

x is the raw score

μ is the population mean

σ is the population standard deviation.

(1) If 36 men are randomly selected, find the probability that they have a mean weight greater than 160lb.

For x > 160 lb

z = 160 - 172/29/√36

z = 160 - 172/29/6

z = -2.48276

Probability value from Z-Table:

P(x<160) = 0.0065185

P(x>160) = 1 - P(x<160) = 0.99348

(2) If 81 men randomly selected, find the probability that they have a mean weight between 170lb and 175lb.

For x = 170 lb

z = 170 - 172/29/√81

z = 170 - 172/29/9

z = -0.62069

Probability value from Z-Table:

P(x = 170) = 0.2674

For x = 175 lb

z = 175 - 172/29/√36

z = 175- 172/29/6

z = 0.93103

Probability value from Z-Table:

P(x = 175) = 0.82408

The probability that they have a mean weight between 170lb and 175lb is calculated as:

P(x = 175) - P(x = 170)

0.82408 - 0.2674

= 0.55668

Help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

A, 2 5/8 cups

Step-by-step explanation:

Since six dozen brownies is three times as much as two dozen, we can multiply 7/8 cups by 3. 3 x 7/8 = 21/8 If we simplify this fraction, it is 2 5/8. Therefore the answer is A, 2 5/8 cups.

I think the answer is the last one the 3 and 1/2

which statement is true regarding the functions on the graph?

Answers

Answer:

f(3)=g(3)

Step-by-step explanation:

the only one i see is that

f(3)=g(3)

because the two functions intersect there

that means the two values are the same

Is this a function???

Answers

Answer:

pfft no lol

Step-by-step explanation:

yeah no

have a good day!  :)

plz give me brainliest

Answer:

yes

Step-by-step explanation:

i think,because it goes past the center it all

4,0000000000×10,00000000

Answers

Answer:

yes 40

Step-by-step explanation:

she got it correct

are any of these equations linear or nonlinear if yes what is the standard form
a. y=-7+6x
b. y=2x+5

Answers

Answer:

both are linear

a) 6x - y = 7

b) 2x - y = -5

Step-by-step explanation:

The population of Garden City in 1995 was 2,400. In 200, the population was 4,000. Write a linear equation in slope-intercept form that represents this data.

Answers

Answer:

[tex]y = 320x +2080[/tex]

Step-by-step explanation:

Given

Population in 1995 = 2400

Population in 2000 = 4000

Required

Determine the linear equation

Let the years be represented with x.

In 1995, x = 1 i.e. the first year

In 2000, x = 6

Let y represents the population

When x = 1; y = 2400

When x = 6; y = 4000

First, we calculate the slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{4000 - 2400}{6 - 1}[/tex]

[tex]m = \frac{1600}{5}[/tex]

[tex]m = 320[/tex]

Next, we calculate the line equation as follows:

[tex]y - y_1 = m(x - x_1)[/tex]

[tex]y - 2400 = 320(x - 1)[/tex]

[tex]y - 2400 = 320x - 320[/tex]

[tex]y = 320x - 320 + 2400[/tex]

[tex]y = 320x +2080[/tex]

At a sale, dresses were sold for $22 each. This price was 55% of a dress's original price. How much did a dress originally cost? Answer: Submit Answer attempt 1 out o Privacy Policy Terms of Service acer​

Answers

Answer:

$9.90

Step-by-step explanation:

what type of transformation maps abc onto def

Answers

Answer:

The answer is translation :)

what is this answer!!!!!!!!

Answers

Step-by-step explanation:

what is this answer

(3x + 40) + (5x - 52) = 180°

8x - 12 = 180°

8x = 180 + 12

8x = 192

8x = 24

x = 3

X=3 ......
Hope it helps

Perform the following operation
and express the answer in
scientific notation.
6.300x10^-5 – 7.200x10^-3

[?]*10

Answers

Answer:

Step-by-step explanation:

6.3 x10^-5 -7.200 x10^-3= - 0.007137=7.137x10-3

Answer:-7.137 x 10^-3

Step-by-step explanation:

Simplify each expression. (Will Give Brainlest)

Answers

Answer:

0.88

Step-by-step explanation:

-5.37 + 8.14 - 1.89

-5.37 + 6.25

= 0.88

Step-by-step explanation:

please i worked on paper worksheet

please see it

The portion of the parabola y²=4ax above the x-axis, where is form 0 to h is revolved about the x-axis. Show that the surface area generated is
A=8/3π√a[(h+a)³/²-a³/2]
Use the result to find the value of h if the parabola y²=36x when revolved about the x-axis is to have surface area 1000.​

Answers

Answer:

See below for Part A.

Part B)

[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]

Step-by-step explanation:

Part A)

The parabola given by the equation:

[tex]y^2=4ax[/tex]

From 0 to h is revolved about the x-axis.

We can take the principal square root of both sides to acquire our function:

[tex]y=f(x)=\sqrt{4ax}[/tex]

Please refer to the attachment below for the sketch.

The area of a surface of revolution is given by:

[tex]\displaystyle S=2\pi\int_{a}^{b}r(x)\sqrt{1+\big[f^\prime(x)]^2} \,dx[/tex]

Where r(x) is the distance between f and the axis of revolution.

From the sketch, we can see that the distance between f and the AoR is simply our equation y. Hence:

[tex]r(x)=y(x)=\sqrt{4ax}[/tex]

Now, we will need to find f’(x). We know that:

[tex]f(x)=\sqrt{4ax}[/tex]

Then by the chain rule, f’(x) is:

[tex]\displaystyle f^\prime(x)=\frac{1}{2\sqrt{4ax}}\cdot4a=\frac{2a}{\sqrt{4ax}}[/tex]

For our limits of integration, we are going from 0 to h.

Hence, our integral becomes:

[tex]\displaystyle S=2\pi\int_{0}^{h}(\sqrt{4ax})\sqrt{1+\Big(\frac{2a}{\sqrt{4ax}}\Big)^2}\, dx[/tex]

Simplify:

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax}\Big(\sqrt{1+\frac{4a^2}{4ax}}\Big)\,dx[/tex]

Combine roots;

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax\Big(1+\frac{4a^2}{4ax}\Big)}\,dx[/tex]

Simplify:

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax+4a^2}\, dx[/tex]

Integrate. We can consider using u-substitution. We will let:

[tex]u=4ax+4a^2\text{ then } du=4a\, dx[/tex]

We also need to change our limits of integration. So:

[tex]u=4a(0)+4a^2=4a^2\text{ and } \\ u=4a(h)+4a^2=4ah+4a^2[/tex]

Hence, our new integral is:

[tex]\displaystyle S=2\pi\int_{4a^2}^{4ah+4a^2}\sqrt{u}\, \Big(\frac{1}{4a}\Big)du[/tex]

Simplify and integrate:

[tex]\displaystyle S=\frac{\pi}{2a}\Big[\,\frac{2}{3}u^{\frac{3}{2}}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]

Simplify:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[\, u^\frac{3}{2}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]

FTC:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[(4ah+4a^2)^\frac{3}{2}-(4a^2)^\frac{3}{2}\Big][/tex]

Simplify each term. For the first term, we have:

[tex]\displaystyle (4ah+4a^2)^\frac{3}{2}[/tex]

We can factor out the 4a:

[tex]\displaystyle =(4a)^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]

Simplify:

[tex]\displaystyle =8a^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]

For the second term, we have:

[tex]\displaystyle (4a^2)^\frac{3}{2}[/tex]

Simplify:

[tex]\displaystyle =(2a)^3[/tex]

Hence:

[tex]\displaystyle =8a^3[/tex]

Thus, our equation becomes:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[8a^\frac{3}{2}(h+a)^\frac{3}{2}-8a^3\Big][/tex]

We can factor out an 8a^(3/2). Hence:

[tex]\displaystyle S=\frac{\pi}{3a}(8a^\frac{3}{2})\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

Simplify:

[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

Hence, we have verified the surface area generated by the function.

Part B)

We have:

[tex]y^2=36x[/tex]

We can rewrite this as:

[tex]y^2=4(9)x[/tex]

Hence, a=9.

The surface area is 1000. So, S=1000.

Therefore, with our equation:

[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

We can write:

[tex]\displaystyle 1000=\frac{8\pi}{3}\sqrt{9}\Big[(h+9)^\frac{3}{2}-9^\frac{3}{2}\Big][/tex]

Solve for h. Simplify:

[tex]\displaystyle 1000=8\pi\Big[(h+9)^\frac{3}{2}-27\Big][/tex]

Divide both sides by 8π:

[tex]\displaystyle \frac{125}{\pi}=(h+9)^\frac{3}{2}-27[/tex]

Isolate term:

[tex]\displaystyle \frac{125}{\pi}+27=(h+9)^\frac{3}{2}[/tex]

Raise both sides to 2/3:

[tex]\displaystyle \Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}=h+9[/tex]

Hence, the value of h is:

[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]

You seem to have left out that 0 ≤ x ≤ h.

From y² = 4ax, we get that the top half of the parabola (the part that lies in the first quadrant above the x-axis) is given by y = √(4ax) = 2√(ax). Then the area of the surface obtained by revolving this curve between x = 0 and x = h about the x-axis is

[tex]2\pi\displaystyle\int_0^h y(x) \sqrt{1+\left(\frac{\mathrm dy(x)}{\mathrm dx}\right)^2}\,\mathrm dx[/tex]

We have

y(x) = 2√(ax)   →   y'(x) = 2 • a/(2√(ax)) = √(a/x)

so the integral is

[tex]4\sqrt a\pi\displaystyle\int_0^h \sqrt x \sqrt{1+\frac ax}\,\mathrm dx[/tex]

[tex]=\displaystyle4\sqrt a\pi\int_0^h (x+a)^{\frac12}\,\mathrm dx[/tex]

[tex]=4\sqrt a\pi\left[\dfrac23(x+a)^{\frac32}\right]_0^h[/tex]

[tex]=\dfrac{8\pi\sqrt a}3\left((h+a)^{\frac32}-a^{\frac32}\right)[/tex]

Now, if y² = 36x, then a = 9. So if the area is 1000, solve for h :

[tex]1000=8\pi\left((h+9)^{\frac32}-27\right)[/tex]

[tex]\dfrac{125}\pi=(h+9)^{\frac32}-27[/tex]

[tex]\dfrac{125+27\pi}\pi=(h+9)^{\frac32}[/tex]

[tex]\left(\dfrac{125+27\pi}\pi\right)^{\frac23}=h+9[/tex]

[tex]\boxed{h=\left(\dfrac{125+27\pi}\pi\right)^{\frac23}-9}[/tex]

21. Transportation A youth group with 26 members is going skiing. Each of the five
chaperones will drive a van or sedan. The vans can seat seven people, and the
sedans can seat five people. Assuming there are no empty seats, how many of each
type of vehicle could transport all 31 people to the ski area in one trip?

Answers

Answers:

2 sedans and 3 vans

=====================================================

Work Shown:

s = number of sedans

v = number of vans

1 sedan = 5 seats

s sedans = 5s seats

1 van = 7 seats

v vans = 7v seats

5s+7v = all seats

5s+7v = 31

Let's go through all the values of s to see which values of v work.

If s = 0, then the equation turns into 7v = 31, but the solution for v isn't an integer.If s = 1, then the equation turns into 5+7v = 31 and that solves to v = 26/7 = 3.71 which also isn't an integerIf s = 2, then the equation becomes 10+7v = 31 and that solves to v = 3. So we found the answer. This means we need 2 sedans and 3 vans.

As a check:

2 sedans = 5*2 = 10 seats

3 vans = 7*3 = 21 seats

10+21 = 31 seats total

This confirms the answer.

The number of vans used is three and the number of sedans is two

Let :

v represent the number of vans

s represent the number of sedans

The following equations can be gotten

7v + 5s = 31 equation 1

v + s = 5 equation 2

The elimination method would be used to solve for v and s

Multiply equation 2 by 7

7v + 7s = 35 equation 3

Subtract equation 1 from 3

2s = 4

s = 4/2

s = 2

Substitute for s in equation 2

v + 2 = 5

v = 5 - 2

v = 3

To learn more about simultaneous equations, please check: brainly.com/question/23589883?referrer=searchResults

When a gas is kept at a constant temperature and pressure on it changes, its volume changes according to the following formula, known as Boyle’s law

where P1 and V1 are the pressure (in atm) and the volume (in litres) at the beginning, and P2 and V2 are the pressure and the volume at the end. Find the final pressure P2 if V1 = 1.5 litres, P1 = 4.5 atm and V2 = 3.5 litres. Round to the nearest tenth of a atm.

Answers

Answer:  Approximately 1.9 atm

============================================

Work Shown:

[tex]P_1*V_1 = P_2*V_2 \ \text{ ... Boyle's Law}\\\\4.5*1.5 = P_2*3.5\\\\6.75 = P_2*3.5\\\\P_2*3.5 = 6.75\\\\P_2 = \frac{6.75}{3.5}\\\\P_2 \approx 1.92857142857142\\\\P_2 \approx 1.9\\\\[/tex]

If the volume is 3.5 liters, then the pressure is approximately 1.9 atm.

Note the increase in volume leads to the reduction of pressure, and vice versa. The two variables have an inverse relationship.

-----------

As a check,

[tex]P_1*V_1 = P_2*V_2\\\\4.5*1.5 \approx 1.9*3.5\\\\6.75 \approx 6.65\\\\[/tex]

We don't get the exact thing on both sides, but the two sides are close enough. We have rounding error due to P2 being not exact.

A more accurate check could be

[tex]P_1*V_1 = P_2*V_2\\\\4.5*1.5 \approx 1.92857*3.5\\\\6.75 \approx 6.749995\\\\[/tex]

which has the two sides much closer to one another. This helps us verify the answer.

Use special right triangle ratios to find the length of the hypotenuse. Right Triangle Trig.

Answers

Answer:

11 sqrt(2)

Step-by-step explanation:

We know that in a 45 45 90 triangle, the lengths of the sides are x, x ,x sqrt(2)

the length of x is 11

so the lengths of the sides are 11, 11, 11 sqrt(2)

The hypotenuse is 11 sqrt(2)

A student is training for the track team during the first three months of the year by
running for 30 minutes every day, while averaging 5 miles each day. Select the graph
that correctly shows the total miles the student ran during the time of his training
program.
1)
Hous
500
2)
200
Hours
10
23
8
50
3)

Answers

Answer:

uhhh

Step-by-step explanation:

Answer:

This question is to perfect to answer.

Identify proportional relationships
Does the following table show a proportional relationship between the variables g and h?
g
3
6
9
9
36
81

Answers

Answer:

sure easy man the carrot is blue and green and orange there naswer soled

HELP IM IN CLASS DOING IT RIGHT NOW The absolute value of any number is always positive. True False

Answers

Answer:

True

Step-by-step explanation:

Answer:

[tex] \huge\purple{TRUE}[/tex]

Step-by-step explanation:

The absolute value of any number is always positive.

Max bought a new pair of basketball shoes that were on sale for 25% off. If the regular price of the shoes was $75.95, what is the amount of discount?

Answers

$56.96

1) 75.95 x .25= 18.9875= 18.99
2) 18.99 -75.95= 56.96
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