Here’s my dilemma, I can accept a $1000 bill or play a game ten times. For each roll of the single die, I win $500 for rolling 1 or 2, I win $400 for rolling 3; and I lose $300 for rolling 4,5,or 6. Based on the expected value, I should accept the $1000 bill.

Answers

Answer 1

Answer:

you should accept the $1,000 bill

Step-by-step explanation:

Given the information:

$500 for rolling 1 or 2$400 for rolling 3lose $300 for rolling 4,5,6

P (rolling 1 or 2) = 1/6 + 1/6 = 2/6 = 1/3

P (rolling a 3) = 1/6

P (rolling 4 or 5 or 6) = 3/6 = 1/2

Hence, the expected value for 1 time is:

E = (1/3)*500 + (1/6)*400 - (1/2)*300

E = $166 + $66 - $150

E = $82

Expected value is linear so if you roll the die 10 times, expected value is: 10*82 = $820

The expected value is $82, meaning you should accept the $1,000 bill


Related Questions

You are assigned a computer generated 4-digit password to access your new voice mail account. If the
digits can not be repeated, how many passwords are possible?
b
34 different passwords are possible
5,040 different passwords are possible
40 different passwords are possible
10,000 different passwords are possible
d

Answers

Answer:

5,040 different passwords are possible

Step-by-step explanation:

Assuming that 4-digit means using only numeric values.

This is a permutations problem.

n = number of values used with number values only this is 10

r = the number used in each case without repeating in this case 4

nPr = n! / (n - r)!

nPr = 10! / (10-4)!

nPr = 10! / 6!

The ! means factorial. For example 4! = 4 x 3 x 2 x 1 = 24

A quick hack for dividing factorials is to use cancelling.

10! / 6! = 10 x 9 x 8 x 7 (because 6 to 1 are cancelled by 6!)

= 5040

A 20% acid solution is mixed with 20 liters of a 45% acid solution. How much of a 30% acid solution will result?

Answers

Answer:

50 liters

Step-by-step explanation:

If x is the volume of 20% acid, then:

x (0.20) + 20 (0.45) = (x + 20) (0.30)

0.2x + 9 = 0.3x + 6

3 = 0.1x

x = 30

30 liters of 20% acid are needed, so there will be a total of 50 liters of 30% acid.

hannah made 0.7 of her free throws in a basketball game.abbrahmade 9/10 of her free throws.dinah made 3/4 of her free throws. who is the best shooter. EXPLAIN!!

Answers

Answer:

Abbrah is the best shooter.

Step-by-step explanation:

Hannah made 0.7 which is equal to 70 out of 100 shots.

Dinah made 3/4 which is equal to 75 out of 100 shots.

Abbrah made 9/10 shots which is equal to 90 out of 100 shots.

Answer:

Abbrah is the best shooter

Step-by-step explanation:

A sector with a radius of 8 cm has an area of 56pi cm2. What is the central angle measure of the sector in radians?

Answers

Answer:

[tex]\frac{7\pi}{4}[/tex].

Step-by-step explanation:

Given information:

Radius of circle = 8 cm

Area of sector = [tex]56\pi\text{ cm}^2[/tex]

Formula for area of sector is

[tex]A=\dfrac{1}{2}\theta r^2[/tex]

where, r is radius and [tex]\theta[/tex] is central angle in radian.

Substitute [tex]A=56\pi[/tex] and r=8 in the above formula.

[tex]56\pi=\dfrac{1}{2}\theta (8)^2[/tex]

[tex]56\pi=\dfrac{64}{2}\theta[/tex]

[tex]56\pi=32\theta[/tex]

[tex]\dfrac{56\pi}{32}=\theta[/tex]

[tex]\dfrac{7\pi}{4}=\theta[/tex]

Therefore, the measure of the sector in radians is [tex]\frac{7\pi}{4}[/tex].

what is the answer to -12= -2x-4x

Answers

Answer:

x = 2

Step-by-step explanation:

-12 = -2x - 4x

-12 = - 6x

x = -12/(-6) = 2

Answer:

Step-by-step explanation:

WILL MARK BRAINLIEST! If you buy 3 pounds of hamburg for $8.97, how much will it cost for 5 pounds of hamburg?

Answers

Answer:

14.95

Step-by-step explanation:

every 1 pound is 2.99 so you would do 2.99 * 5

Answer:

$14.95

Step-by-step explanation:

To find the slope or the cost per pound of hamburger you divide 8.97 by 5 in order to find out it costs 2.99 per hamburger. You then, multiply 2.99 by 5 to gather that to buy 5 pounds of hamburger it would cost $14.95.

What is the reciprocal of 3/4?
2
4/3
3/4
1/4 lb
none of the above

Answers

The reciprocal of 3/4 is 4/3.

Hope it will be helpful to u

The answer is 4/3. The reciprocal is just that opposite which is flipped around.

Which description of the graph of the linear inequality y ≥ 7x – 4 is correct????The graph will be a dashed line with a y-intercept of negative four and a slope of seven. The graph will be shaded below the line.
The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.
The graph will be a solid line with a y-intercept of seven and a slope of negative four. The graph will be shaded below the line.
The graph will be a dashed line with a y-intercept of seven and a slope of negative four. The graph will be shaded above the line.

Answers

Answer:

It's the second description

Step-by-step explanation:

It's one of the inequality symbols for greater/less than or equal to, which means the line is solid. Then, y is greater than or equal to 7x-4 which means it will be shaded above the line.

Answer:

The correct answer is the 2nd option

Step-by-step explanation:

The graph of the function f(x) is shown
Which graph represents the function 4(2x)?

Answers

Answer:

[tex]8x[/tex]

Step-by-step explanation:

[tex]4 \: time \: 2x = 8x[/tex]

What is the domain of the following parabola? (5 points)
3
-2
-1/
x
1
xs1
All real numbers
ys2

Answers

Answer:

Step-by-step explanation:

The domain of this quadratic is "all real numbers."  The function is defined for all x.  

Point L was plotted at (-4, 1), then L was transformed creating point L’ at (-1, -4).Which transformation rule could have been used to plot L’?
Reflection across the x-axis
a 180 degree rotation about the origin
A 270 degree rotation counterclockwise rotations about the origin
A translation using the rule (x,y) -->(x+3, y -5)

Answers

Answer:

you would go down 2 from the point

Step-by-step explanation:


What is the inverse function of f(x) = 4x + 3?

Answers

Answer:

f(x)=(x-3)/4

Step-by-step explanation:

To find the inverse of a function, I like to flip the x and the y, and then try to isolate the y. In this case:

x=4y+3

x-3=4y

y=(x-3)/4

Hope this helps!

f-1(x)=x-3/4 that is the answer hope it helps

On Monday, a restaurant made $545 by selling 109 hamburgers.
If they sold 95 hamburgers on Tuesday, how much money did they make?
(Show your work below.)

Answers

Answer:

$475

Step-by-step explanation:

$545 / 109 = $5

$5 is the one hamburgers price

$5 x 95 = $475

$475 on Tuesday

math question screen shot below

Answers

Answer:

a.3 m/s

Step-by-step explanation:

90 divided by 30

plz give brainliesttt

A 10-foot ladder is to be placed Against the side of the building. The base of the latter must be placed in an angle of 72° With the level ground for a secure footing. Find, to the nearest inch, how far the base of the latter should be from the side of the building and how far up the side of the building the latter will reach.

Answers

Answer:

Distance of foot of ladder from building: 37.2 inches

Distance of top of ladder from building's base: 114 inches

Step-by-step explanation:

Please refer to the figure attached in the answer area.

A right angled triangle [tex]\triangle ABC[/tex] is formed by the ladder with the building where hypotenuse is the length of ladder.

Hypotenuse, AC = 10 foot

Also, we are given that angle made by the base of ladder with the ground is [tex]72^\circ[/tex].

We have to find AB and BC.

[tex]\angle BAC = 72^\circ[/tex]

Using trigonometric functions:

[tex]cos \theta= \dfrac{Base}{Hypotenuse}\\cos 72^\circ= \dfrac{AB}{AC}\\\Rightarrow 0.309 = \dfrac{AB}{AC}\\\Rightarrow AB = 10 \times 0.309\\$\approx$ 3.1 foot\\$\approx$ 37.2 inches[/tex]

[tex]sin \theta = \dfrac{Perpendicular}{Hypotenuse}\\\Rightarrow sin72^\circ = \dfrac{BC}{AC}\\\Rightarrow 0.95 = \dfrac{BC}{AC}\\\Rightarrow AB = 10 \times 0.95\\$\approx$ 9.5 foot\\$\approx$ 114 inches[/tex]

Distance of foot of ladder from building: 37.2 inches

Distance of top of ladder from building's base: 114 inches

There are 6 yellow card, 3 blue cards, 4 pink cards and 7 purple cards in a hat. What is the probability of selecting a purple card, then another purple card? Give answers as reduced fraction and percent.

Answers

Answer:

7/20 = 0.35

Step-by-step explanation:

How many 9’s are there between 1 and a 100?

Answers

Answer:

11

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

You've got 9

19

29

39

49

59

69

79

89

And then all of the numbers in the 90s

90, 91, 92, 93, 94, 95, 96, 97, 98, 99

99 counts as two

In ΔIJK, the measure of ∠K=90°, the measure of ∠J=76°, and JK = 3.6 feet. Find the length of IJ to the nearest tenth of a foot.

Answers

This is my answer
Hope it help!

hi what is the answer

Answers

Answer:

A= 36π mm²

Step-by-step explanation:

Area of circle = πr² where radius= 6mm

A = π(6)²

A= 36π mm²

write an equation that represent the line. ASAP !!!!!! 40 POINTS + BRAINLIEST

Answers

Answer:

y = (3/2)x + 3

Step-by-step explanation:

slope is rise over run so 3 up and, 2 right

y-intercept is at (3,0)

I need help ples.
What is the volume of composite solid?

Answers

Answer:

58 13/32 ft. cubed

Step-by-step explanation:

Horizontal Shape: 6 x 5/2 x 7/4 = 26 1/4 ft.

Vertical Shape: 7/2 x 21/4 x 7/4 = 32 5/32 ft.

Total Volume: 26 1/4 + 32 5/32 = 58 13/32 ft. cubed

If this helped can I get brainliest :)

An aquarium in the shape of a rectangular prism has a bottom, no top, two square sides, and two sides
the same height as the square sides but twice their length. The total area of the five sides 15 2,592 in?.
Find the volume of the aquarium. Complete the explanation of your reasoning.
Let x represent the length and height of the square sides. Then the longer sides and the bottom measure
2x by x. The total area of the five sides, in terms of x, is A =____
So, the total area of the five sides,
A, is 2,592 in2. Solving for x we get x =____
The tank's volume is ____
in squared?

Answers

Answer:

volume = 11,664 units cubed

Step-by-step explanation:

2[tex]x^{2}[/tex] times 3 = bottom and sides

[tex]x^{2}[/tex] times 2 = ends

A = 6[tex]x^{2}[/tex] + 2[tex]x^{2}[/tex] = 8[tex]x^{2}[/tex]

2592 = A

2592/8 = 8[tex]x^{2}[/tex]/8

324 = [tex]x^{2}[/tex]

take square root of both sides

18 = x

so volume = length times width times height

2(18) times 18 times 18 = 11664

11664 units cubed

PLEASE HELP!!!! attached photo

Answers

Answer:

(-1, -2.5)

Step-by-step explanation:

The midpoint formula is just basicallyadding both  of the x values and then dividing the sum of them by 2, after that you will be adding both y values and then dividing them by 2, then you will get the midpoint x and y coordinate values. You can look up midpoint formula on google to see how it's actually written. You have to make sure to add correctly when you are using the negative numbers, because they can actually turn the equations into subtraction. Keep in mind, it can beconfusing sometimes when you are working with positive and negative numbers together. So make sure to just double check your work and also to make sure you added correctly.

Brainliest please, I need a few more :D

Which is the coldest temperature? Explain how you determined this using the number line.

Answers

Answer:

The coldest temperature would be -4 °F, because it is the farthest number on the left side of zero on the number line.

please help im having trouble with these problems​

Answers

Answer:

B I think

Step-by-step explanation:

How is the distributive property used when multiplying two binomials

Answers

Answer:

Step-by-step explanation:

When multiplying a binomial times a binomial, each term of the first binomial must be multiplied by each term of the second binomial. Like terms are then combined.

When multiplying two binomials, four multiplications must take place. These multiplications can occur in any order, as long as each of the first two terms is multiplied by each of the second two terms.

There are numerous ways to set up the multiplication of two binomials. The two basic formats, horizontal line-up and vertical line-up, are similar to what we saw in adding and subtracting polynomials. Let's investigate the simple product (x + 2)(x + 4) with a variety of set-ups. Start with the first term of the first binomial (the blue x).

• Distribute (multiply) this term times EACH of the terms in the second binomial (x + 4).

• Then take the second term in the first binomial (including its sign: +2) and distribute (multiply) this term times EACH of the terms in the second binomial (x + 4).

• Add the results, combining like terms when needed.

• This method will work with all polynomials, not just binomials times binomials.

Answer:

Distributive.

Step-by-step explanation:

I did the quiz.

5(7 + 3x) - 12 how to simplify​

Answers

To solve this we need to use this formula:

a(b+c)=ab+ac

5(7+3x)-12=35+15x-12=15x+23

Answer:

Step-by-step explanation:

Multiply the 5 to the 7 and 3x--> 35 + 15x -12. Then add 12 to the -12, making it 0 (inverse operations), and add 12 to the 35 making it 47 + 15x. :) Then you would simply divide the 15 by 15x (making the variable by itself). your answer for x should be 47/15. :> If I helped, please mark brainliest!!

What is 3 1/2 times 2 4/5​

Answers

Answer:

9 4/5

Step-by-step explanation:

You can rewrite them into decimal. It would be 3.5 times 2.8 and you get 9.8 or 9 4/5

Answer:

49 /5  = 9.8

Step-by-step explanation:

what is the quotient of the equation Below in simplest form? State any restrictions on the variable

Answers

Answer:

A

Step-by-step explanation:

Factor the numerators/ denominators where possible, that is

[tex]\frac{-(x-5)}{(x+4)(x-1)}[/tex] ÷ [tex]\frac{(x-5)(x+3)}{(x+4)(x+1)}[/tex]

Leave the first fraction, change division to multiplication and turn the second fraction upside down.

= [tex]\frac{-(x-5)}{(x+4)(x-1)}[/tex] × [tex]\frac{(x+4)(x+1)}{(x-5)(x+3)}[/tex]

Cancel the factors (x - 5) and (x + 4) from numerator/denominator

= [tex]\frac{-1}{(x-1)}[/tex] × [tex]\frac{(x+1)}{(x+3)}[/tex]

= [tex]\frac{-(x+1)}{(x-1)(x+3)}[/tex] , x ≠ 1, x ≠ - 3

What is the first quartile, Qı, of the data set?
{23, 28, 28, 36, 56, 60, 61, 65, 70}
Enter your answer in the box.
Q1
---

Answers

Answer:

28

Step-by-step explanation:

take the median of the data set which is 56 and then take the median of the numbers before 56

28 is the median Q1 is 28

Answer:

28

Step-by-step explanation:

First step is to find the median of the data set.

The median is the middle value of the data arranged in ascending order. If there is not an exact value then it the average of the values either side of the middle.

23  28  28  36  56  60  61  65  70

                          ↑ median

The first quartile [tex]Q_{1}[/tex] is the middle value on the left side of the median.

23  28  28  36

          ↑

[tex]Q_{1}[/tex] = [tex]\frac{28+28}{2}[/tex] = [tex]\frac{56}{2}[/tex] = 28

 

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