You roll a six sided die. You are given $8 if a 6 comes up, $2 if a 3, 4, 5 comes up, and
nothing otherwise. Find the expected value of the entries.
Expected Value Table for rolling a six-sided die
Answers
We want to get the expected value for the given experiment. We will see that the expected value is $2.33
For an experiment with outcomes {x₁, ..., xₙ} each one with probability {p₁, ..., pₙ} the expected value is defined as:
EV = x₁*p₁ + ... + xₙ*pₙ
Here we have 3 outcomes:
x₁ = winning $8x₂ = winning $2x₃ = winning $0.For x₁ we need to roll a 6, this is a probability of 1 out of 6, then:
p₁ = 1/6
For x₂ we need to roll a 3, 4, or 5 (3 out of 6), then:
p₂ = 3/6
For x₃ we need to roll a 1 or a 2 (2 out of 6) so the probability is:
p₃ = 2/6
Then the expected value is:
EV = $8*(1/6) + $2*(3/6) + $0*(2/6) = $2.33
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Related Questions
this is for 8th grade pls answer .
Answers
Step-by-step explanation:
We have that
[tex](x + \frac{1}{x} ) {}^{2} = 3[/tex]
We are trying to find the number value so that we can apply in the later equation.
Qe first simplify.
Remeber that
[tex](a + b) {}^{2} = a {}^{2} + 2ab + {b}^{2} [/tex]
Also remeber that
[tex] \frac{1}{x} = {x}^{ - 1} [/tex]
so
[tex](x + x {}^{ - 1} ) {}^{2} = {x}^{2} + 2x {}^{0} + {x}^{ - 2} = 3[/tex]
We then simply remeber that x^0=1 so
[tex] {x}^{2} + 2 + \frac{1}{ {x}^{2} } = 3[/tex]
Multiply both sides by x^2.
[tex] {x}^{4} + 2 {x}^{2} + 1 = 3 {x}^{2} [/tex]
Subtract both sides by 3x^2
[tex] {x}^{4} - {x}^{2} + 1 = 0[/tex]
Notice that x^4= (x^2)^2.
So our reformed equation is
[tex]( {x}^{2} ) {}^{2} - {x}^{2} + 1 = 0[/tex]
Let a variable , w equal x^2. This means that we subsitute variable, w in for x^2.
[tex]w {}^{2} - w + 1 = 0[/tex]
Now we use the quadratic formula
[tex] w = \frac{ - b + \sqrt{b {}^{2} - 4ac } }{2a} [/tex]
and
[tex]w = - b - \frac { \sqrt{b {}^{2} - 4ac } }{2a} [/tex]
Let a=1 b=-1 and c=1.
[tex]w = \frac{1 + \sqrt{1 - 4(1)} }{2} [/tex]
[tex]w = \frac{1 - \sqrt{1 - 4} }{2} [/tex]
Now, we get
[tex]w = \frac{1}{2} + \frac{i \sqrt{3} }{2} [/tex]
and
[tex]w = \frac{1}{2} - \frac{ i\sqrt{3} }{2} [/tex]
Now since we set both of these to the x^2 we solve for x.
and
[tex] {x}^{2} = \frac{1}{2} + \frac{i \sqrt{3} }{2} [/tex]
and
[tex] {x}^{2} = \frac{1}{2} - \frac{i \sqrt{3} }{2} [/tex]
We can represent both of these as complex number in the form of a+bi. Next we can convert this into trig form which is
[tex] {x}^{2} = 1( \cos(60) + i \: \sin(60) [/tex]
and
[tex] {x}^{2} = 1( \cos(300) + i \: sin(300))[/tex]
Next we take the sqr root of 1 which is 1, and divide the degree by two.
[tex] {x} = 1( \cos(30) + i \: sin \: 30)[/tex]
and
[tex]x = 1( \cos(150) + i \: sin(150)[/tex]
We are asked for the 2nd root so just add 180 degrees to this and we have
[tex]x = 1 \cos(210) + i \: sin \: 210)[/tex]
and
[tex]x = 1( \cos(330) + i \: sin(330)[/tex]
which both simplified to
[tex]x = - \frac{ \sqrt{3} }{2} - \frac{1}{2} i[/tex]
and
[tex]x = \frac{ \sqrt{3} }{2} - \frac{1}{2} i[/tex]
Now we must find
x^18+x^12+x^6+1.
We just use demovire Theorem. Which is a complex number raised to the nth root is
[tex] {r}^{n} (cos(nx) + i \: sin(nx)[/tex]
So let plug in our first root.
[tex]1( \cos(330 \times 18)) + i \: sin \: (330 \times 18))) + 1( \cos(12 \times 330)) + i \: sin(12 \times 330) + 1( \cos(6 \times 330) + i \: sin(6 \times 330))) + 1[/tex]
To save time we multiply the angle and use rules of terminals angle and we get
[tex]1( \cos(180) + i \sin(180) ) + 1( \cos(0) + i \: sin \:( 0) + 1( \cos(180) + i \: sin(180) + 1[/tex]
And we get
[tex] - 1 + 1 + - 1 + 1 = 0[/tex]
So one of the answer is x=0
And the other, let see
[tex]1 \cos(210 \times 18) + i \: \sin(210 \times 18) + 1 \: cos(210 \times 12) + i \: sin(210 \times 12) + 1 \cos(210 \times 6) + \:i sin(210 \times 6) + 1[/tex]
[tex] \cos(180) + i \: sin(180) + 1 \cos(0) + i\sin(0) +1( \cos(0) + i \sin(0) + 1[/tex]
We get
[tex] - 1 + 1 + 1 + 1 = 2[/tex]
So our answer are 2.
So the answer to the second part is
0 and 2.
A hen costs $4 and chicks are sold at 3 for $2. A farmer paid $100 exactly for 80 of these birds. How many of each type did he buy?
Answers
Answer:
Above is the answer, coupled with a detailed step-by-step explanation. Thank you!
Find an equation of a degree 3 polynomial (in factored form) with the given zeros of f(x): -5, -3,1.
Assume the leading coefficient is 1.
Answers
Answer:
f(x) = x^3 + 7x^2 + 7x -15
Step-by-step explanation:
f(x) = (x+5)(x+3)(x-1)
f(x) = (x^2 + 3x + 5x + 15)(x-1)
f(x) = (x^2 + 8x + 15)(x-1)
f(x) = x^3 + 8x^2 + 15x -x^2 -8x -15
simplify
f(x) = x^3 + 7x^2 + 7x -15
Answer:
[tex]f(x) = (x + 5)\, (x + 3)\, (x - 1)[/tex].
Step-by-step explanation:
By the factor theorem, if a constant [tex]a[/tex] is zero of the polynomial [tex]f(x)[/tex], [tex](x - a)[/tex] would be a factor of this polynomial. (Notice how [tex]x = a[/tex] would indeed set the value of [tex](x - a)\![/tex] to [tex]0[/tex].)
For instance, since [tex](-5)[/tex] is a zero of the polynomial [tex]f(x)[/tex], [tex](x - (-5))[/tex] would be a factor of [tex]f(x)\![/tex]. Simplify this expression to get [tex](x + 5)[/tex].
Likewise, the zero [tex](-3)[/tex] would correspond to the factor [tex](x + 3)[/tex], while the zero [tex]1[/tex] would correspond to the factor [tex](x - 1)[/tex].
All three of these factors above are linear, and the degree of the variable [tex]x[/tex] in each factor is [tex]1[/tex]. Multiplying three such linear factors would give a polynomial of degree [tex]3[/tex].
Given the three factors, the expression of [tex]f(x)[/tex] in factored form would be:
[tex]f(x) = m\, (x + 5)\, (x + 3)\, (x - 1)[/tex] for some constant [tex]m[/tex].
When this expression is expanded, the constant [tex]m[/tex] would be the coefficient of the [tex]x^{3}[/tex] term (the leading term.) In other words, [tex]m\![/tex] is the leading coefficient of [tex]f(x)[/tex]. This question has required this coefficient to be [tex]1[/tex]. Thus, [tex]m = 1[/tex]. The expression of [tex]f(x)\![/tex] in factored form would be:
[tex]f(x) = (x + 5)\, (x + 3)\, (x - 1)[/tex].
I NEED ASAP ON THIS MATH PROBLEM
Answers
Ok done. Thank to me :>
I NEED HELPP WITH THIS
Answers
Answer:
Look at the screenshots
Step-by-step explanation:
what is 5x to the power of 2 times 4x to the power of 3 divided by 4
Answers
Answer:
5x^5
Step-by-step explanation:
5x^2*4x^3/4
Divide
5x^2*1x^3
Multiply and Calculate
5x^5
answer: [tex]25x^{3}[/tex]
steps to solve:
→ let's write this out as an equation instead of in word form. 5x to the power of 2 times 4x to the power of 3 divided by 4 is [tex]\frac{5^{2} * 4x^{3}}{4}[/tex].
→ first, calculate the power of [tex]5x^{2}[/tex]. [tex]5x^{2} = 25[/tex], so now we have [tex]\frac{25^{2} * 4x^{3}}{4}[/tex]
→ now, multiply the monomials. [tex]25 * 4x^{3} = 100x^{3}[/tex].
→ [tex]\frac{100x^{3}}{4}[/tex]. we need to cross out the common factor, which is 4. 100 divided by 4 is 25. we're now left with [tex]25x^{3}[/tex].
so, [tex]25x^{3}[/tex] is the answer
PLEASE HELP!! find the value of x. attached image.
Answers
Answer:
x = 4
Step-by-step explanation:
The angle markings at the bottom of the triangle mean they are congruent. Since they are the only two congruent to each other, that means this triangle is an isosceles triangle.
In an isosceles triangle, not only are the bottom angles congruent, their opposing sides are congruent as well. In this instance, that means 9x - 8 = 28. Knowing that we can solve for x.
[tex]9x-8=28\\\\9x-8+8=28+8\\\\9x=36\\\\\frac{9x}{9}=\frac{36}{9}\\\\x=4[/tex]
Answer:
x = 4Step-by-step explanation:
9x - 8 = 28 ( converse of isosceles triangle )
(If two angles of a triangle are congruent , then the sides opposite to these angles are congruent.)
[tex]9x - 8 = 28 \\ 9x - 8 = 28 + 8 \\ 9x = 36 \\ \frac{9x}{9} = \frac{36}{9} \\ x = 4 \\ [/tex]
A bicycle store costs $2550 per month to operate. The store pays an average of $45 per bike. The average selling price of each bicycle is $75. How many bicycles must
the store sell each month to break even?
Answers
Answer:
3750
Step-by-step explanation:
2250/45=50
50x75=3750
Find a degree 3 polynomial with real coefficients having zeros 4 and 4i and a lead coefficient of 1. Write P
in expanded form. Be sure to write the full equation, including P(x) = .
Answers
Answer:
P(x)= x^3 - 4x^2 + 16x - 64
Step-by-step explanation:
First, let’s find all of the zeroes. If the question is asking for a degree 3 polynomial, than there has to be more than 2 zeroes. The complex conjugates theorem states that if a+bi is a zero, than a-bi has to be a zero as well. So if 4i is a zero, than -4i has to be a zero as well. By looking at the zeroes, you can write them as a linear factorization.
(x-4)(x+4i)(x-4i)
If you foil all of it, you will get x^3 - 4x^2 + 16x - 64.
You went 160 miles in 20 hours. What is the constant of proportionality that relates the y, the distance in miles to x, the time in hours?
Answers
Answer:
X = Y times 8
Step-by-step explanation:
You need to figure out how many miles you can go in an hour.
160/x and 20/1
20x=160
x=8
You can go 8 miles in 1 hour.
Therefore, if X is 1 and Y is 1
1 = 8
1 hour equals 8 miles
can someone help me with these? it's a study guide and I lost the notes I took for these
Answers
Step-by-step explanation:
[tex]thanks \: you \: the \: point \\ pls \: follow \: me[/tex]
What is the value of x?
Answers
We know that the triangle is an isosceles triangle because the base angles are the same.
=> 4x - 1 = x + 5=> 4x - x = 1 + 5=> 3x = 6=> x = 6/3 = 2Conclusion:Therefore, the answer is 'x = 2'
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Help me this hard im stuck
Answers
Answer:
B, C
Step-by-step explanation:
The long sides of a rectangle measure 5 ft 6 in, and the short sides are 3 ft 4 in. What is the perimeter?
Answers
Answer:
17 ft 8 in
Step-by-step explanation:
Solve for x
-7x - 8 = 10x +4
Answers
Answer: put 14
Step-by-step explanation:
BRAINLIEST FOR CORRECT ANSWER
Two friends rent an apartment together. They agree that one person will pay 3 times what the other person pays. If the rent is $850, then what equation could be used to determine how much each person pays?
Answers
Answer:
n+3n=$850 n is one person and 3n is the other represented by n
Step-by-step explanation:
This can be shown as, where x is equal to the pay of what the other person pays:
Again, one friend will pay 3 times what one person pays.
3x + x = 850
Which can be simplified to:
4x = 850
Where 850 is the total rent to be payed.
To find out how much one person pays, you can solve the equation for x.
4x = 850
x = $212.5
e. Find the slope of the line that passes through the points (1, 3) and (9,7),
Answers
Answer:
0.5
Step-by-step explanation:
→ Find the difference in y
7 - 3 = 4
→ Find the difference in x
9 - 1 = 8
→ Divide the results
4 ÷ 8 = 0.5
Answer:
The slope is 1/2 (m=1/2)
Step-by-step explanation:
Use the slope formula: [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] to solve for the slope. y2 is 7, y1 is 3, x2 is 1, x1 is 9. [tex]\frac{7-3}{9-1}=\frac{4}{8} = \frac{1}{2}[/tex]
Find the value of y.
Answers
The value of the variable 'y' will be square root 21 that is √21.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The ratio of the corresponding sides of a similar triangle remains constant. Then the equation is given as,
y / 3 = 7 / y
Simplify the equation, then we have
y / 3 = 7 / y
y² = 21
y = √21
The value of the variable 'y' will be square root 21 that is √21.
More about the triangle link is given below.
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A worker earns $30 every 4 hours. How much would the worker earn in 19 hours?
Answers
Step-by-step explanation:
30/4 = 7.5 per hour
now,
7.5 × 19 = 142.5
$142.5
Answer:
$142.50
Step-by-step explanation:
30 divide by 4 = 7.5
So each hour the worker would earn $7.50
7.5 x 19= The worker will earn 142.50 after working 19 hours.
winter coat was originally priced at 140$ and went on sale for 91$ by what percentage was the price of the winter coat reduced?
Answers
Answer:
35%
Step-by-step explanation:
Find out what percent 91 is of 140
91÷140 = 0.65
Then find out how much was reduced by subracting 0.65 from 1
1 - 0.65 =0.35
The coat was reduced by 35%
There are 40 slices of pizza at the party that are shared equally between 8 people. Peter ate 3 slices of pizza before he came to the party. How many slices of pizza did Peter eat in all?
Answers
Answer:
that depends if it's taken in consideration the pizzas that he ate were from the 40 slices or not
Answer:
he ate 5 slices
Step-by-step explanation:
40/8=5 you would thinks you are timeing the answerPLS I RLLY NEED HELP
Water flows out of a tank at the rate of 400 ml per minute. How long
will it take for 7.2 liters of water to flow out of the tank?
Answers
Answer:
18 minutes
Step-by-step explanation:
7.2 litres is 7200ml
each minute 400ml leaves the tank
so the question being asked is how many 400's are there in 7200...
7200 divided by 400 is 18.
NO LINKS PLS
The ratio of sugar to flour used in a pudding recipe is 2:1. Which figure shows equivalent ratios?
A graph is drawn. The title is Pudding Recipe. The axis label is Sugar in cups. The x axis values are 0, 2, 4, 6, 8, 10, 12. The y-axis label is Flour in cups. The y axis values are 0, 1, 2, 3, 4, 5, 6. Points are plotted on the ordered pairs 1,2 and 2,4 and 3,6.
A graph is drawn. The title is Pudding Recipe. The axis label is Sugar in cups. The x axis values are 0, 2, 4, 6, 8, 10, 12. The y axis label is Flour in cups. The y axis values are 0, 1, 2, 3, 4, 5, 6. Points are plotted on the ordered pairs 2,2 and 4,3 and 6,4.
A graph is drawn. The title is Pudding Recipe. The x axis label is Sugar in cups. The x axis values are 0, 2, 4, 6, 8, 10, 12. The y axis label is Flour in cups. The y axis values are 0, 1, 2, 3, 4, 5, 6. Points are plotted on the ordered pairs 2,1 and 4,2 and 6,3.
A graph is drawn. The title is Pudding Recipe. The axis label is Sugar in cups. The x axis values are 0, 2, 4, 6, 8, 10, 12. The y axis label is Flour in cups. The y axis values are 0, 1, 2, 3, 4, 5, 6. Points are plotted on the ordered pairs 2,2 and 4,4 and 6,6.
Answers
Answer:
Answer #3
Step-by-step explanation:
The ratio of sugar to flour is 2:1, so the x values need to be twice as big as the y values in the points.
Determine whether the following sequence is arithmetic,
geometric, or neither.
1. 4, 1, 2
2. 4, 20, 100
3.212 106,53
Answers
=================================================
Explanation:
The sequence {4,1,2} is neither because both arithmetic sequences and geometric sequence are either always increasing or always decreasing. We start off decreasing when going from 4 to 1, but increase to 2.
----------
The sequence {4,20,100} is geometric because we multiply each term by 5 to get the next term. That means the common ratio is 5. Notice how this sequence is increasing.
---------
The sequence {212,106,53} is also geometric. This time the common ratio is 1/2 = 0.5; this sequence is decreasing.
What can readers learn from ""A Flight Through the Sky""?
Answers
Readers can learn various information related to an airplane flight.
Fly through the sky is a children's song in which different aspects of an airplane flight are described in a simple and direct way. Some of the aspects that a person can learn by reading the lyrics of the song are:
Technical aspects of flight and aircraft. Its wheels are inflated with air. Its engine runs on fuel. Its wings are made of aluminum. All passengers must wear seat belts during take off.
Learn more about airplane in: https://brainly.com/question/15415980
Does anybody know what Savvas is? cause I don't know the answer to 6.4 x 3.7 can anybody help.
Answers
Answer: I'm not sure what Savvas is, but the answer to your second question is 23.68.
Step-by-step explanation: This can be solved using the stacking method of multiplication, like so:
6.4
x3.7
You would multiply this equation as if there are no decimals, (first doing 7x4, and then 7x6 + 2, then adding a zero to your ones place at the bottom, and doing 3x4, the 3x6 + 1), to get 2348. You then would add the decimals in by moving over 2 places to the left.
1
x 1.0 -
=
10
1
-
10 x 1.0
Answers
Step-by-step explanation:
the question doesn't make sense and you need to rephrase the question.
1 ton is equal to 2,000 pounds. How many pounds are in 5 tons, 230 pounds?
Answers
Answer: 10230
Step-by-step explanation:
The amount in pound is 1230 pounds.
What is Unitary Method ?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
1 ton is equal to 2,000 pounds.
So, 5 tons and 230 pounds
= 5 x 2000 + 230
= 1000 + 230
= 1230 pounds.
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if you have 6 apples and you give 2 apples to Ciara how many apples do you have? (hint you don't have friends)
Answers
Answer:
4
Step-by-step explanation:
6 - 2 = 4
Answer:
4
Step-by-step explanation:
Ciara is not my friend but she's my sister
Help please! Due today
Answers
Answer:
First triangle: 54.46 degrees
Step-by-step explanation:
For the first problem, solve for the third side, then the third angle, and then subtract from 180.
20^2 + 28^2 = c^2
400 + 784 = c^2
1184 = c^2
34.41 = third side
Find the third angle:
sin(90)/34.41 = sin(x)/20
20 * sin(90)/34.41 = sin(x)
35.54 is the third angle.
180 - 35.54 - 90 = 54.46. The angle with the question mark is 54.46. Do the other 2 problems the same way.