A 6-sided die is loaded in such a way where odd outcomes occur 2/9 of the time, and even outcomes happen the other
1/9 of the time. What is this die's expected value?
A. 3.25
B. 4
C. 3.5
D. 3.33

Answers

Answer 1

Answer:

3.33, or 3 1/3

Step-by-step explanation:

Expected value:

[tex](9 \times \frac{2}{9} ) + (12 \times \frac{1}{9} ) = 2 + \frac{4}{3} = 2 + 1 \frac{1}{3} = 3 \frac{1}{3} [/tex]


Related Questions

What is the volume of a regular pyramid having a base area of 24 inches and height of 6 inches

Answers

Answer:

V= 48 in^2

Step-by-step explanation:

Formula

Since the base has a known area, we do not need the full volume formula. This formula is

V = B * h / 3

B is the area of the base and h is the height measured from the top of the pyramid to the base meeting the base at right angles.

Givens

B = 24 in^2

h = 6 in

Solution

V = B * h / 3

V = 24 * 6/3

V= 48 in^2

Which of the following best describes the graph below?

Answers

The correct option is option D: This is the graph of one to one function.

Function is a relationship between two sets X and Y where set X is domain and set Y is codomain.

If we draw a vertical line and it crosses the graph only once at all locations, the relation is a function and this relation will be one-one.

by checking all the options

Option A: If we draw a vertical line parallel to y-axis in this at any location then it crosses the graph only once. So it is a function with one-one relation. Therefore option A is incorrect.

Option B: Linear function is a function in which highest degree of variable is 1 and it also describes the straight line. From the graph, it is clear that it is not a straight line. Therefore option B is incorrect.

Option C: If we draw a vertical line parallel to y-axis in this at any location then it crosses the graph only once. So, it is surely a function. Therefore option C is incorrect.

Option D: If we draw a vertical line parallel to y-axis in this at any location then it crosses the graph only once. So, it is surely a one-one function. Therefore option D is correct.

The correct option is option D: This is the graph of one-to-one function.

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Transform each graph as specified below.
(a) The graph of y= f(x) is shown. Draw the graph of y=1/2f(x).

(b) The graph of y=g(x) is shown. Draw the graph of y=g(1/2x)

Answers

Answer:

x f(x)

0 0

-2 -4

4 -2

You need to draw y = 2 f (x-1)

So you need to choose x so that x-1 = 0, -2, 4 then you can use the above values

New function

x-1 = 0, x = 1, y = 2 f (x-1) = 2 f(0) = 2 x 0 = 0

x-1 = -2 x = -1 y = 2 f (x-1) = 2 f(-2) = 2 x -4 = -8

x-1 = 4 x = 5 y = 2 f (x-1) = 2 f (4) = 2 x -2 = -4

So 3 points on the new graph are (1, 0) (-1, -8) and (5, -4)

Basically going from y = f(x) to y = f(x-a) where a is a constant positive number you translate (move) y = f(x) a units to the right.

y = f(x) to y = 2 f(x), you dilate f(x) with center (0,0) factor 2, so (a,b) > (2a, 2b)

So basically here you are doing both things.

So if (a,b) is on y = f(x) then after the translation (a,b) > (a+1, b) then after the dilation (a+1,b) > (2a+2, 2b)

Our graph for A was the same, but my B was a bit different. I hope this helps regardless. :)

Suppose you start with a full tank of gas (20 gallons) in your truck. After driving 3 hours, you now have 2 gallons left. If x is the number of hours you have been driving, then y is the number of gallons left in the tank. At what rate is the gas left in the tank changing? State your answer as a reduced fraction. Find an equation of a line in the form y = mx + b that describes the amount of gas in your tank.

Answers

The rate of the gas left in the tank will be -6 and the equation will be given as y = -6x + 20.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

Suppose you start with a full tank of gas (20 gallons) in your truck. After driving 3 hours, you now have 2 gallons left. If x is the number of hours you have been driving, then y is the number of gallons left in the tank.

The rate of gas will be calculated as:-

Suppose the hours are represented by x and the gallons are represented by y.

The rate of the gas will be the slope so the slope will be calculated as:-

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

[tex]m = \dfrac{2-20}{3-0}[/tex]

[tex]m =\dfrac{-18}{3}[/tex]

m = -6

The equation will be given as:-

y = mx + c

y  = -6x + 20

Therefore the rate of the gas left in the tank will be -6 and the equation will be given as y = -6x + 20.

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A game consists of rolling a colored die with three red sides, two green sides, and one blue side. A roll of a red loses. A roll of green pays $2.00. A roll of blue pays $5.00. The charge to play the game is $2.00. What is the expected value of the game?

Answers

The expected value of the game is $2.00.

To Find: The fair price to pay to play the game of rolling a colored die with three red sides, two green sides, and one blue side

Now the question arises how to find the Fair Price

We are told that in the game of rolling the colored die;

A roll of a red loses.

A roll of blue pays 5.00 and A roll of green pays 2.00.

Now, the best game to get the fairest price is to play; RRRGGB  i.e (RED, RED, RED, GREEN, GREEN,BLUE)

Fair price = 2(3/6) + 6(1/6) + 0(2/6)

Fair price = $2

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Alejandro kicks a football. The graph below shows the height of the football hh in meters after tt seconds. What is the football’s greatest height?

Answers

Answer:

The answer will be 30.625 m

The graphs below have the same shapes. What is the equation for the red graph? g(x)= A g(x) = 2^x + 5 B 2^x - 5 C. g{x} = 2^x+5 D G(x) = 2^x-5

Answers

This isn’t an answer, but if you attached the graph to the question I would be more than happy to help. The question isn’t possible to answer without the graph.

Find the radius of this sphere The calculate the volume of the sphere?

Answers

Answer: r = 121.92 cm

              Volume = 4/3 x 3.14 x [tex]121.92^{3}[/tex]

              7587404.65

Step-by-step explanation:

The radius is given. It's the distance from the center of the sphere to the end. The radius is 4 ft. 1 ft is 30.48cm so 4ft is 121.92cm  

(radius) r = 121.92 cm

Volume = 4/3 x 3.14 x [tex]121.92^{3}[/tex]

             = 4/3 x 3.14 x 1812278.18

             = 4/3 x 5690553.49

             = 7587404.65

Work out the bearing of D from C.
(Hint: bearings are written with three digits.)

Answers

Answer:

050°

Step-by-step explanation:

The bearing of D from C is the angle between the north pole and the line joining C and D when moving in a clockwise direction.

From the diagram, the angle is 050°

Attached is a document that I need help on, please help!!!

Answers

The ratio of the median weekly earnings is 3 : 5

The ratio of the median weekly earnings

From the graph, we have the median weekly earnings to be:

High school diploma = $750Bachelor's degree = $1250

So, the ratio is:

Ratio = $750 : $1250

Simplify

Ratio = 3 : 5

Hence, the ratio of the median weekly earnings is 3 : 5

The ratio of the area of the red rectangle to the blue rectangle in graph A?

In (a), we have:

Ratio = 3 : 5

The scale on the horizontal axis is given as:

1 unit per grid mark

Both rectangles have a width of 1 unit.

So, we have:

Ratio = 3 * 1: 5 * 1

Simplify

Ratio = 3 : 5

Hence, the ratio of the area of the red rectangle to the blue rectangle in graph A is 3 : 5

The ratio of the area of the red rectangle to the blue rectangle in graph B?

In (a), we have:

Ratio = 3 : 5

The scale on the horizontal axis is given as:

1 unit per grid mark

The red rectangle has a width of 3 units, while the blue has 5 units as its width

So, we have:

Ratio = 3 * 3 : 5 * 5

Simplify

Ratio = 9 : 25

Hence, the ratio of the area of the red rectangle to the blue rectangle in graph B is 9 : 25

The ratio of the volume of the red cube to the blue cube in graph C?

In (a), we have:

Ratio = 3 : 5

The scale on the horizontal axis is given as:

1 unit per grid mark

The red rectangle has a width of 3 units, while the blue has 5 units as its width.

Since the base are squares, we have:

Ratio = 3 * 3  * 3 : 5 * 5 * 5

Simplify

Ratio = 27 : 125

Hence, the ratio of the volume of the red cube to the blue cube in graph C is 27 : 125

The most misleading graph

The most misleading graph is graph B.

This is so because the blue rectangle and the red rectangle do not have the same width when plotted on the same scale

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Please help me

14.7 ÷ 4.2

Answers

Answer:

how many times does 4.2 go into 14.7

1. 4.2

2. 8.4

3. 12.6

14.7-12.6=2.1 or one half of 4.2

3.5

Hope This Helps!!!

If 6^(2x)=4 find 36^(6x-2) could anyone help me please?

Answers

Answer:

3.160

Step-by-step explanation:

You can solve for x using logarithm.

Rewrite in logarithm form

[tex]log_{6}4=2x\\\\x=\frac{log_64}{2}\\x=\frac{\frac{log4}{log6}}{2}\\x=\frac{log4}{log6} * \frac{1}{2}\\x=\frac{log4}{log6 * 2}\\x\approx0.386852807\\36^{6(0.386852807)-2} \approx3.160[/tex]

Consider the function shown on the graph.

Answers

Answer:

C.) y = 3(x - 3)(x - 7)

For the function:

x intercept: (3, 0), (7, 0)vertex point: (5, -12)point: (8, 15)

Writing equation:

y = a(x - h)² + k

15 = a(8 - 5)² - 12

15 = 9a - 12

9a = 15 + 12

9a = 27

a = 3

So the equation is:

y = 3(x - 5)² - 12

y = 3(x² - 10x + 25) - 12

y = 3x² - 30x + 63

y = 3(x - 3)(x - 7)

About 10% of the population has a particular genetic mutation. 1000 people are randomly selected.

Find the mean for the number of people with the genetic mutation in such groups of 1000. Round your answer to two decimal places.

Answers

Answer:

The standard deviation for the number of people with the genetic mutation in such groups of 1000 is 9.49.

Step-by-step explanation:

Standard deviation: It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.

The given parameters are:

Proportion, p = 10%

Sample size, n = 1000

The standard deviation is calculated as:

σ=[tex]\sqrt{np(1-p}[/tex]

So, we have:

σ=[tex]\sqrt{1000*10%*(1-10%)}[/tex]*(1-10%)

Evaluate:

σ= 9.49

Hence, the standard deviation for the number of people with the genetic mutation in such groups of 1000 is 9.49.

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Discrete Math please help

Answers

Considering the given operations, the discrete sets are given as follows:

A = {1,3,5,6,7,8,9}.B = {2,3,6,9,10}.

What is operation A - B?

It is the operation of elements that are in set A but not in set B, hence, since A - B = {1, 5, 7, 8}, we have that:

A = {1,5,7,8}

What is operation B - A?

It is the operation of elements that are in set B but not in set A, hence, since B - A = {2,10}, we have that:

B = {2,10}

What is the intersection operation?

It contains the elements that are in both sets, hence, since [tex](A \cap B) = \{3,6,9\}[/tex], we have that the sets are completed as follows:

A = {1,3,5,6,7,8,9}.B = {2,3,6,9,10}.

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Carmen drew this figure to represent the dividend of a division expression.

A number line going from negative 4 to positive 12. An arrow goes from 0 to 9.

What number is represented by the arrow?

Answers

The number represented by the arrow is 9 if each unit is represented by 1 option fourth is correct.

What is a number line?

It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a number line shown in the picture.

As we can see each unit is represented by 1.

So after 2 there will be 3 and after 4 there will be 5 and so on.

So after 8, there will be 9 which is represented by the arrow.

Thus, the number represented by the arrow is 9 if each unit is represented by 1 option fourth is correct.

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Answer: 9

Step-by-step explanation:

The number line going from - 4 to + 12 represents the range of possible values for the dividend of the division expression. The arrow going from 0 to 9 indicates the actual value of the dividend. Therefore, the number represented by the arrow is 9.

find 2^x=4x, find x ​

Answers

Whatever... I'll try to solve the first two problems.

[tex]2^x=4x\\4x=e^{\ln 2^x}\\4x=e^{x\ln 2}\\\dfrac{1}{4x}=e^{-x \ln 2}\\-\dfrac{\ln 2}{4}=-x\ln 2e^{-x \ln 2}\\-x\ln 2=W\left(-\dfrac{\ln 2}{4}\right)\\x=-\dfrac{W\left(-\dfrac{\ln 2}{4}\right)}{\ln 2}[/tex]

1.

[tex]x=\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5\ldots}}}}}}\qquad\left( x\geq0\right)\\\\x=\sqrt{13+\sqrt{5+x}}\\\\x^2=13+\sqrt{5+x}\\\sqrt{5+x}=x^2-13\\\\D:5+x\geq0 \wedge x^2-13\geq 0\wedge x\geq 0\\D:x\geq-5 \wedge x^2\geq13\wedge x\geq 0\\D:x\geq \sqrt{13} \vee x\leq-\sqrt{13}\wedge x\geq0 \\D:x\in[\sqrt{13},\infty)\\\\ 5+x=x^4-26x^2+169\\x^4-26x^2-x+164=0\\\vdots\\(x - 4) (x^3 + 4 x^2 - 10 x - 41) = 0\\x-4=0\\x=4[/tex]

One solution is [tex]x=4[/tex], and [tex]4\in D[/tex], therefore[tex]\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5\ldots}}}}}}=4[/tex].

We can ignore other possible solutions of the polynomial equation, because the expression can not be equal to two different values simultaneously.

its about efficiency in systems

Answers

.......................

Please answer all four of the questions I would really appreciate it <3

Answers

D

B

A

C

These are the answers in order.

Answer:

1)A because 3 < 3.9 < 4

2)C because 8.2<8.23<8.3

3) D because 6.1>5.9

4)B because 3.6<3.625<3.7

Hope it helps!

The graphs below have the same shape. The equation of the blue graph is F(x) = x^3. What is the equation of the red graph?

Answers

Answer:

g(x) = x³ - 2

(option B)

Step-by-step explanation:

because the shape of the graph has not changed, we know that there was no direct change to x

(this would have looked like 2x³ instead of x³)

and because the graph was not shifted along the x-axis (left or right), we know that the change did not happen inside the parenthesis

(this would have looked like (x³ - 3) instead of (x³) )

we know that the only change that has happened to this graph was a downward shift along the y-axis  which can be expressed as

g(x) = x³ - 2

The equation of the red graph will be g(x) = x³ - 2.Option B is correct.

What is the equation?

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

We know that there was no immediate change to x since the graph's form has not altered. Instead of , this would have appeared as 2x³.

Thus we can be confident that the change did not occur inside the parenthesis since the graph was not moved down the x-axis.

We may infer that this graph's sole modification was a downward shift along the y-axis, which is written as;

g(x) = x³ - 2

The graph is also attached in the attachment.

The equation of the red graph will be g(x) = x³ - 2.

Hence option B is correct.

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A football team has attempted 6 running plays. The change in field position resulting from each play is shown in the table. Running Play Outcomes Play 1 –3 yards Play 2 2 yards Play 3 –1 yard Play 4 –2 yards Play 5 –3 yards Play 6 1 yard What is the average change in field position per running play? –6 yards per play –1 yard per play 0 yards per play 1 yard per play Mark this and return

Answers

Answer:

Step-by-step explanation:

-3 +2 +-1 +-2 +-3 +1 = -6 yards total

-6 / 6 =  -1 yard per play average

Can someone help me? I’ll give brainliest to whoever gets it right first

Answers

Answer:

the measure of line AD is 8

Step-by-step explanation:

lines AD and BC are equal, due to the markings on the lines
this means that if line BC is 8, than line AD is also 8

Suppose a population parameter is 0.8, and many large samples are taken
from the population. If the sample proportions are normally distributed, with
95% of the sample proportions falling between 0.684 and 0.916, what is the
standard deviation of the sample proportions?

Answers

Using the Empirical Rule, it is found that standard deviation of the sample proportions is of 0.058.

What does the Empirical Rule state?

It states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of  the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.

0.684 and 0.916 is within 2 standard deviations of the mean(below and above), hence there are 4 standard deviations between these measures, so:

4s = (0.916 - 0.684)

s = (0.916 - 0.684)/4

s = 0.058.

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Simplify this equation 10 ^-8

Answers

1
———
10^8

1

100000000

Which of the following is the best buy?

a 6 oz box of rice for $0.90
a 12 oz box of rice for $1.93
a 16 oz bag of rice for $2.42
a 9 oz box of rice $1.25

Answers

The best buy is a 9 oz box of rice $1.25. (option d)

What is the best buy?

In order to determine the best buy, the unit cost of each option has to be determined. The best buy is the option with the lowest unit cost. The unit cost can be determined by dividing the total cost by the total quantity.

Unit cost = total cost / total oz

$0.90 / 6 = $0.15

$1.93 / 12 = $0.16

$2.42 / 16 = 0.151

$1.25 / 9 = 0.14

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What is the length of CD? In this diagram, AABC~ AEDC.

Answers

The length of CD will be option C. 3

From given diagram, triangle ABC and EDC meet at a common vertex C.

So, triangle ABC and EDC both are congruent to each other.

Applying the similarity property of congruence, ratio of the congruent triangles' corresponding sides will be equal.

Therefore,

AB/ED = AC/EC = BC/CD

AC/EC = BC/CD

18/6 = (12 - x)/x

Simplifying the expression,

We get

18x = 6(12 - x)

Multiplicating the terms in right hand side,

18x = 72 - 6x

Solving 6x on both sides,

we get

18x + 6x = 72 - 6x + 6x

24x = 72

Dividing both the sides by 24, we get

24x/24 = 72/24

x = 3

Hence, the length of CD is 3.

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fy= 2x² + 2x + 1
y = 2x + 3
What is the solution to this system of equations?
o (-1, 3) and (0,4)
o (0, 1) and (1,5)
○ (0, 1) only
o (-1, 1) and (1, 5)

Answers

The answer is (-1,1) and (1,5)

Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown below:

A coordinate grid is shown from negative 5 to 0 to 5 on both x- and y-axes. A polygon ABCD has A at ordered pair 2, 3, B at ordered pair 4, 4, C at ordered pair 3, 1, D at ordered pair 2, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 1, 3, B prime at ordered pair negative 3, 4, C prime at ordered pair negative 2, 1, D prime at ordered pair negative 1, 1.

Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD?

Answers

Using translation concepts, the sequence that is used to obtain the translated image is:

Reflection over the y-axis.Shift right of one unit.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

For all the vertices, the transformations follow the given pattern:

(x,y) -> (-x,y) -> (-x + 1, y).

In the step (x,y) -> (-x,y), the function is reflected over the y-axis. Then, in step (-x,y) ->  (-x + 1, y), the function is shifted right one unit.

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A building casts a shadow of 40 feet on the ground. A wooden figure of a man is placed on the building and casts a shadow an additional 10 feet beyond the building's shadow. What is the height of the man?\

Answers

The height of the man from the given question is; 37.5 ft

How to solve trigonometric ratios?

This question will form a triangle where;

Height of building = 30 ft

Height of man = h ft

Initial height of shadow = 40 ft

Additional height of shadow = 10 ft

Using similarity theorem, we have;

h/30 = (40 + 10)/40

h/30 = 5/4

h = (30 * 5)/4

h = 37.5 ft

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Translate to an equation then solve the equation. Seven times the difference of some number and 2 amounts to the quotient of 196 and 14. (Type the question using x as the variable. Do not simplify.) x= ____

Answers

Create the equation, then solve for x

Answer:

x = 4

Step-by-step explanation:

7 * ( x-2) = 196/14

7x -14 = 14

7x = 28

x = 4

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