What's the value of the following game: You roll a 100 sided die with sides 1-100. You can either take this number of dollars, or pay $1 to roll again. You can keep on paying $1 to roll for as long as you like.

Answers

Answer 1

You roll a 100 sided die with sides 1-100. The optimal strategy is to stop and cash out only if the dice shows 87 or higher , else keep spending $1 to roll again n again, leading to expected winning of $87.35.

Can a die have 100 sides?

The 100-sided die Lou Zocchi created is known by the trademark "Zocchihedron," and it made its debut in 1985. It assumes the appearance of a ball with 100 flattened planes, unlike other polyhedran dice. It is also known as "Zocchi's Golfball."

optimal strategy is to stop and take dollar if roll > x, and to pay $1 and continue when roll <= x (as applicable to all/any turn/roll). We need to find x in order to maximize E.

Assuming optimal expected value to be E, once you cast the first roll, there are two possible scenario:

1) we get roll value > x with probability (100-x)/100, and decide to take that amount, expected winning = (x+1+100)/2 (that amount varies uniformly from x+1 to 100 in this case, take the average)

2) we get roll value <= x with probability x/100 and decide to continue, with future expected winning again = E and 1$ loss in fee. Total expected winning in this scenario = E-1

[math]E=\frac{(100-x)}{100}\times\frac{ (x+1+100)}{2}[/math][math] + \frac{x}{100}\times(E-1)[/math]

[math]E = \frac{(100-x)(101+x) - 2x}{200 - 2x}[/math]

maximizing E w.r.t. x,

dE/dx = 0

2x^2 - 400x + 19600 = 0

x = ( 400+/- sqrt(160000-4*2*19600) ) / 4

Since, 1<= x <= 100, therefore x = ( 400+ sqrt(160000-4*2*19600) ) / 4

x = 85.85786

We just have to calculate E(x=85) and E(x=86) and compare.

E((x=86) = 87.35 and E(x=85) = 87.33

so optimal strategy is to stop and cash out only if the dice shows 87 or higher , else keep spending $1 to roll again n again, leading to expected winning of $87.35.

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Related Questions

Which equation could be used to find the length of the missing side of
the right triangle?
22 cm
7 cm
bcm

Answers

Step-by-step explanation:

use Pythagoras theorem

[tex]b = \sqrt{h ^{2} - p ^{2} } [/tex]

The state transportation commission counted cars traveling east and west across a toll bridge. The commission counted 486 cars traveling east and 189 cars traveling west. What percentage of the cars were traveling east?

Answers

The percentage of cars traveling east is 28% of the total number of cars.

What is the percentage?

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, The commission counted 486 cars traveling east and 189 cars traveling west.

We know percentage change we'll divide the net amount change by the original amount and multiply it by 100%.

From this concept, the percentage of the cars were traveling east would be

The cars traveling east divided by the total numbers of cars time s100%.

= (189/486 + 189)×100%.

= (189/675)×100%.

= 0.28×100%.

= 28%.

So, 28% of the total cars traveling east.

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Find the total volume of the solid (both shapes added together)

Answers

Answer:

93.33 ft³

Step-by-step explanation:

The solid comprises of a prism and a pyramid.

Volume of the solid:

V  = 5*2*8 + 1/3*5*2*4 = 93.33 ft³

find the area of the figure below:

Answers

You can solve by splitting up the figure into 2 rectangles by cutting it vertically.
To solve for 1 rectangle you do:
9 • 5 = 45

And for the other rectangle you do:
6 • 3 = 18

Add up the areas:
45 + 18 = 63

63m^2

Answer:

63 m^2 would be your answer

Step-by-step explanation:

finding the area is preety easy

look at pic

help me plssss hurry

Answers

Answer:

1. 1

2. m<1

3. h=8

4. h>8

Step-by-step explanation:

hope that helps!!:)

Answer:

1. m=1

2. m=0, 1

3. h=8

4. h=11, 17

Step-by-step explanation:

The variables stand for numbers. Replace the variables with any of the given numbers to make the equation or inequality true.

1. 1+5=6, so m=1

2. 0+5=5. 5<6. 1+5=6. 6=6. The symbol ≤ is "less than or equal to", so m=0 or m=1.

3. 5*8=40. h=8.

4. 5*11=55. 55>40. 5*17=85. 85>40. h=55 or h=85.

How do you solve 9x 7 =- 7?

Answers

The value of x is 0

Now, According to the question:

Let's know:

How to find the value of 'x'

Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

The given equation is:

9x - 7 = -7

To solve the value of 'x'

9x - 7 = -7

Add 7 on both sides:

9x - 7 + 7 = -7 + 7

9x = 0

x = 0/9

x = 0

Hence, The value of x = 0

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The complete question is this:

How do you solve 9x - 7 = -7

6 less than 3 times a number 42 what is the number

Answers

Answer: -120

6 less than is 6 - and 3 times a number 42 is 3 x 42 so...

6 - (3 x 42) = -120

Let X_0, Y and Z be integers greater than 0. Let A_n be the product of the unique prime factors of X_n. What condition is needed to be met for the equation X_(n+1) = YA_n + Z to have X_p = X_q, where p =/= q?

Answers

On solving the provided question we can say that - the prime factors of 32 are 2 × 2 x 2 x 2 x 2 and of 64 are - 2 x 2 × 2 x 2 x 2 x 2

what is prime factor?

Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.

the prime factors of

32 are 2 × 2 x 2 x 2 x 2

64 are - 2 x 2 × 2 x 2 x 2 x 2

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What is the growth factor associated with the following growth rate: 30% decrease Your answer should be typed as a decimal.​

Answers

-0.30 i’m pretty sure???

What baseball stat does Lawrence Hinman suggest is the most important stat for determining the best player in the game in a given year

Answers

A range of fundamental, unchanging values may exist in the world, according to ethical pluralism.

What is meant by Ethical Pluralism?

According to ethical pluralism, the world may contain a variety of essential and unchangeable values. There may be more, but happiness and respect for people are two possible ones.

The notion of ethical plurality holds that there are various beliefs about what is "good" and "wrong" (moral norms), some of which may be incompatible and/or out of line with your own personal moral standards. Working in foreign societies, where you could encounter varying norms, is a component of international involvement.

The conviction that there are various viewpoints on a subject, each of which has some truth, but none of which contains the complete truth the conviction that while each moral theory somewhat captures the essence of what it means to live morally, none has the whole picture.

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Lawrence Hinman does not have a clear statement on the best baseball stat for determining the best player in a given year.

What do you mean by statistics?

Statistics are a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. In baseball, statistics are used to measure the performance of individual players, teams, and even entire leagues. Some common baseball statistics include batting average, home runs, runs batted in, earned run average, and wins. These statistics are used to evaluate the performance of players, compare them to other players, and even predict future performance.

What are some common baseball statistics?

Baseball statistics are a set of metrics used to measure the performance of individual players and teams in baseball. Some common baseball statistics include:

Batting average (BA)Home runs (HR)Runs Batted In (RBI)Wins (W)

It is likely that different analysts and experts would have different opinions on which stat is the most important for determining the best player in a given year. Some might argue that traditional stats like batting average, home runs, and RBIs are the most important, while others might argue that newer stats like on-base percentage, slugging percentage, and WAR are more informative.

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shown below PLEASE ANSWER FAST I ONLY HAVE 4 MORE MINUTES!

Answers

Answer:

15 lessons

Step-by-step explanation:

Your family travels from Bazooka, Iowa, to Dentyne, Missouri, a distance of 348 miles. Your car averages 14.5 miles per gallon on open road driving. If you filled your vehicle at a station where regular gasoline cost $1.83 per gallon, how much would the

Answers

Consequently, it would take polynomials roughly 690,64 years for the disintegrations to disappear.

what are polynomials?

A polynomial is a mathematical statement made up of coefficients and uncertainty that exclusively uses additions, subtractions, multiplications, and positive integer powers of variables. A single indeterminate x polynomial is represented by the expression x2 4x + 7. A polynomial is an expression in mathematics that consists of variables (sometimes referred to as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic expression made up of coefficients and variables. The only operations that an expression can contain are addition, subtraction, multiplication, and non-negative integer exponents. These expressions are known as polynomials.

The formula for this is Activity = decay constant x atoms.

1238 = 2.64 x 1010 times the decay constant

decay constant is equal to 4.76 x 10-8 min-1.

Currently, the disintegrations are being slowed to 809 disintegrations per minute.

Ln(809) = Ln(2.64 x 1010) - Ln(4.76 x 10-8 x t)

t=3.63x108min = 690.64y

Consequently, it would take roughly 690,64 years for the disintegrations to disappear.

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How do you find the 3rd side of a triangle?

Answers

Answer:

a2 = b2 + c2 2bc cos(0)

Step-by-step explanation:

Can somebody help please .

Answers

Answer:

easy just think thoroughly

Step-by-step explanation:

1 is A

2 is C

3 is B

4 is D

I'm not sure about this question. Could anyone help? Geometry.

Answers

Answer: length of EF is 18 units.

Step-by-step explanation:

similar triangles (as displayed in the photo) have the same angle measures, but can have different side lengths. however, these side lengths are proportional to each other, meaning that with similar triangles, there will ALWAYS be a number you can multiply the first triangle by to get its similar triangle.

you can find this number by dividing one side length of whichever triangle is bigger with its corresponding side on the other triangle (for example, sides DF and AC correspond, so you'd divide whichever value's bigger by the smaller one. in this case you'd divide 21 by 14.) this gives you 1.5, which tells you that triangle DEF is 1.5 times larger than triangle ABC. so to get EF, just multiply BC (which is 12) by 1.5. this gives you 18. so, EF equals 18. hope this helped :3

I really need an answer for this FAST so if anybody can answer id really appreciate it :)

Answers

both Square and Rectangle


because all squares are rectangles, but not all rectangles are squares. Hope this helps. :)

The spray from a spinning lawn sprinkler creates a circle with a radius of 50 feet.

What is the area of the circle covered by the lawn sprinkler, in square feet?

A= 2500
B= 100
C= 625
D= 50

Answers

A because it can’t be 100 and it can’t be 625 and it can’t be 50 so it has to be A

The wind force f on a sail varies jointly as the area a of the sail and the square of the wind speed w. The force on a sail with an area of 500 ft^2 is 64. 8 pounds when the wind speed is 18 mph. What would be the force for a sail with an area of 250 ft^2 with a wind speed of 35 mph

Answers

Answer:

122.5 pounds.

Step-by-step explanation:

f = kaw^2

So, k = f/aw^2

From the given data:

k = 64.8/(500*18)

  = 0.0004

When a = 250 and w = 35:

f = 0.0004*250*35^2

 = 122.5

QUESTION 1 OF 10
If √62-9 =z, what is the value of ?

Answers

The required value of z is "i√6" to the given expression√(6/2 - 9) = z.

What is a complex number?

A complex number is a combination of real values and imaginary values. It is denoted by z = a + ib, where a, and b are real numbers and i is an imaginary number.

The expression is given in the question, as follows:

√(6/2 - 9) = z

We have to determine the value of z to the given expression.

As per the question, we have

⇒ √(6/2 - 9) = z

⇒ √(3 - 9) = z

⇒ √(- 6) = z

⇒ √(6 × -1 ) = z

⇒ (√6 × √-1 ) = z    [∵ imaginary number i = √-1 ]

⇒ (√6 × i ) = z

⇒ z = i√6

Therefore, the required value of z is "i√6" to the given expression.

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10. Express the following as a single fraction.
x-1 +x+2 + x
2
5
4

Answers

Answer:

x+x+x=3x

2-1=1

3x+1

this is ansver

find the missing angle

Answers

Answer:

Step-by-step explanation:

180-120=60

60+50=110

180-110=70

the missing angle is 70 degrees

The 19th and 15th term of an AP are -5 and -7 1/2 repectively. What i the um of the firt 20 term

Answers

The sum of first 20 terms of the AP will be -206.25

As in AP, let us assume that the "a" be the first term and 'd' be the common difference.

So, the value of nth term can be determined by using formula: a_n=a+(n-1)d, where, n = number of terms, and d = common difference.

So, the value of 19th terms = a+(19-1)d = a+18d = -5 -----(i)

And the value of 15th term = a+(15-1)d = a+14d = -7(1/2) ----(ii)

Now subtracting (ii) from (i),

We will get,

4d = 2(1/2)

=>4d = 2.5

=>d = (2.5/4) = 0.625

Now putting value of "d" in (i)

We will get,

a+(18*0.625) = -5

a=-5-11.25 = -16.25

We have, the formula for finding the sum of terms:

Sum of terms can be determined by using formula:

Sum = (n/2) × [2a + (n-1)d]

Here, n = 20, a = -16.25, d = 0.625

We will get sum of first 20 terms as:

[tex](n/2)\times [2a + (n-1)d]\\(20/2) \times [2 \times -16.25+(20-1)0.625]\\[/tex]

10[-32.5+11.875]

=10(-20.625) =-206.25

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Which is the best estimate for the average rate of change for the quadratic function graph on the interval 1 ≤ x ≤ 3?

Answers

Answer:

I think it's either 1/2 or 1/3.

Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.
I don't want links.
I don't want links.
I don't want links.

Answers

The answer is 3(x-6)(x+5) no problem

Answer:

3(x+5)x(x-6)

Just fyi download photo math and it literally answers the question for you so you dont waste any more points

Step-by-step explanation:

Select the correct answer. Which graph represents the solutions to this equation? x2 + 8x = -20 A. Linear-quadratic system graph shows upward parabola with vertex at (minus 2, 4) and passing through x and y-axis (minus 8, 0), and (0, 0) B. Linear-quadratic system graph shows upward parabola with vertex at (minus 4, 4) and passing through (minus 2, 8), and (minus 6, 8) C. Linear-quadratic system graph shows upward parabola with vertex at (4, 0) and passing through (1, 4), and (6, 4) D. Linear-quadratic system graph shows a downward parabola with vertex at (0, 8) which intercepts the x-axis at 3 and minus 3 units.

Answers

A graph which represents the solutions to this equation x² + 8x = -20 include the following: B. Linear-quadratic system graph shows upward parabola with vertex at (minus 4, 4) and passing through (minus 2, 8), and (minus 6, 8).

What are quadratic functions?

In Mathematics, the graph of every quadratic functions (equations) is either an upward or downward parabola, which is typically a u-shaped curve. This ultimately implies that, the graph of a quadratic function (equation) would always form a parabolic curve.

Next, we would re-write the given quadratic function in standard form by equating it to zero (0) as follows;

x² + 8x = -20

Adding 20 to both sides of the linear-quadratic equation, we have the following:

x² + 8x + 20 = -20 + 20

x² + 8x + 20 = 0

In this scenario, we would use an online graphing calculator to plot the graph of the given quadratic function and then determine the point of intersection and vertex.

y = x² + 8x + 20

By critically observing the graph of the given quadratic function, we can logically deduce that the solutions and vertex are as follows;

x = -6, y = 8.

x = -2, y = 8.

Vertex = (-4, 4).

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Han has to build the figure below, which will serve as a counterweight, for his robotics project. Find the VOLUME of the finished object assuming it is empty inside.

Answers

Given:

A figure of a robotics project.

To find:

The volume of the finished object assuming it is empty inside.

Solution:

The given figure contains a triangular prism and a cuboid.

The dimensions of the cuboid are 6 cm, 8 cm and 5 cm. So, the volume of the cuboid is:

[tex]V_1=length\times width\times height[/tex]

[tex]V_1=6\times 8\times 5[/tex]

[tex]V_1=240[/tex]

So, the volume of the cuboid is 240 cubic cm.

The area of a triangle is:

[tex]Area=\dfrac{1}{2}\times base\times height[/tex]

So, the area of the base of the triangular prism whose base is 8 cm and height 4 cm, is:

[tex]B=\dfrac{1}{2}\times 8\times 4[/tex]

[tex]B=16[/tex]

The volume of a triangular prism is:

[tex]V_2=Bh[/tex]

Where, B is the base area and h is the height of the prism.

The base area of the triangular prism is 16 square cm and the height is 5 cm. So, the volume of a triangular prism is:

[tex]V_2=16(5)[/tex]

[tex]V_2=80[/tex]

Now, the volume of the given figure is:

[tex]V=V_1+V_2[/tex]

[tex]V=240+80[/tex]

[tex]V=320[/tex]

Therefore, the volume of the finished object is 320 cubic cm.

what is the answer??????????????

Answers

Answer:

2x = 10y, 0x=8y, 4x=12y

Step-by-step explanation:

So, lets go over what we know.

Y=x+8

We need to figure out what y is for x equals:

2

0

4

So, lets plug in these number:

Lets start with 2:

y=2+8

=

y=10

So the first y value is 10.

Next we have:

y=0

y=0+8

=

y=8

So the second y value is 8.

Next we have:

y=4

y=4+8

=

y=12

So the last y value is 12.

Hope this helps! :D

50% of 188 is equal to what number?

Answers

Answer:

Step-by-step explanation:

a.50%=[tex]\frac{1}{2}[/tex]

b.so 50% of 188 means 188·[tex]\frac{1}{2}[/tex]=94

answer is 94

The correct answer would be 94 because 1% of 188 is 1.88 so you would just multiply that by 50.

Triangles a and b are right angled. show that the two shorter sides in triangle a have the same length as the two shorter sides in triangle B
i got 2/4 of the marks pls help

Answers

Answer:

Step-by-step explanation:

Two right-angled triangles are said to be congruent to each other if the hypotenuse and one side of the right triangle are equal to the hypotenuse and the corresponding side of the other right-angled

plane flew from Red Deer to Winnipeg, a flying distance of 1260 km. On the return journey, due to a strong head wind, the plane travelled 1200 km in the same time it took to complete the outward journey. On the outward journey, the plane was able to maintain an average speed 20 km/hr greater than on the return journey. Calculate the average speed of the plane from Winnipeg to Red Deer.

Answers

The average speed of the plane from Winnipeg to Red Deer is 400 km/h

What is average speed?

Average speed is total distance travelled over total time taken.

What is the average speed of the plane from Winnipeg to Red Deer?

Since a plane flew from Red Deer to Winnipeg, a flying distance of 1260 km. On the return journey, due to a strong head wind, the plane travelled 1200 km in the same time it took to complete the outward journey. On the outward journey, the plane was able to maintain an average speed 20 km/hr greater than on the return journey.

Let

v = speed of plane on outward journey , v' = speed of plane return journey and t = time of travel

Since the plane travels 1260 km on the outward journey, we have that

1260 = vt  (1)

Also,  the plane travels 1200 km on the inward journey, we have that

1200 = v't  (2)

Since the plane was able to maintain an average speed 20 km/hr greater than on the return journey, we have that

v = v' + 20 (3)

Substituting equation (3) into (1), we have that

1260 = (v' + 20)t  (4)

The required equations are

1260 = v't + 20t  (4)

1200 = v't  (2)

Subtracting equations, (2) from (4), we have that

1260 = v't + 20t  (4)

-

1200 = v't  (2)

60 = 20t

t = 60/20

t = 3 h

From equation (2), we have that the average speed

v' = 1200/t

Substituting t = 3 into the equation, we have that

v' = 1200/3

v' = 400 km/h

So, the average speed is 400 km/h

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