Out of all the given situations, all are fair gambles,
Any gamble is considered to be a fair gamble if the expectation of it is 0. Here, gamble means any situation which has a probabilistic uncertainty attached to it.
The expectation of any game is
E(X) = ∑xp(x)
In the first case
The probability to get a had or tails on flipping a coin is 1/2
Hence the expectation will be
E(X) = 0.5 X 10 + 0.5 X (-10)
= 5 - 5
= 0
Hence this is a fair gamble
In the next gamble, two coins are tosses
The probability to get 2 head is 1/4
The probability to get 2 tails is 1/4
The probability to get one head and one tail is 1/2
Hence,
E(X) = 0.25 X 10 + 0.25 X (-10) + 0.5 X 0
= 2.5 - 2.5
= 0
Hence this too is a fair gamble
Here,it is given that
Probability Gain
0.5 $100
0.25 - $200
0.25 $0
Therefore,
E(X) = 0.5 X 100 + 0.25 X (-200) + 0.25 X 0
= 50 - 50
= 0
Hence, all are fair gambles.
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Correct Question
which of the following is a fair gamble?
one coin toss: win $10 if heads, lose $10 if tails.
two coin tosses: win $10 if two heads, lose $10 if two tails, and no change of wealth otherwise.
a game in which you win $100 with a probability of 50%, lose $200 with a probability of 25%, and gain nothing with a probability of 25%.
all of the above are fair gambles.
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When b is 9 what is 24/b + 8? In my homework, it says it is not 10, 11, 10.6 or 10.666.
Answer:
10.7
Step-by-step explanation:
The only thing I can think of is 10.7. Because when you do this problem you get 10.6666666667. So I'm assuming you're to round it. There is no other way to solve the problem that wouldn't get you either 10.6666666667 or 10.7.
Answer:
10.66
Step-by-step explanation:
[tex]\frac{24}{9}[/tex] + [tex]\frac{8}{1}[/tex]
[tex]\frac{24}{9}[/tex] + [tex]\frac{72}{9}[/tex]
[tex]\frac{96}{9}[/tex]
10.666...
(13.4-0.896 and 8.6 + 9.16 pls help thx
The simplified terms are 12.504 and 17.76 when the terms are in decimal.
Given that,
The numbers are 13.4-0.896 and 8.6 + 9.16
We have to simplify the terms.
We know that,
When a full number and a fraction are combined, decimals are used. The "." symbol, often known as a decimal point, will be used to demarcate the entire number from the fraction in this instance.
Take the numbers,
13.4-0.896
Subtracting the terms
12.504
Take the numbers,
8.6 + 9.16
Adding the terms
17.76
Therefore, The simplified terms are 12.504 and 17.76 when the terms are in decimal.
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answer the question in the screenshot please?
The value of x and y in the vector matrix are 2 and 5
What is a vector Matrix?If a matrix has only one row or only one column it is called a vector.
A matrix having only one row is called a row vector.
A matrix having only one column is called a column vector.
The matrix for two equations
3 - x/4 = 5/2 ---------------------1
8 - 12/4 = y ----------------------2
From equation 1,
collect like terms
x/4 = 3-5/2
x/4 = 1/2
cross multiply
2x = 4
x = 4/2
x = 2
From equation 2,
8 - 3 = y
y = 5
In conclusion, the value of x = 2 and the value of y = 5
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Find the measures of the numbered angles.
Answer: <1=104 degrees, <2=76 degrees, <4=104 degrees, <5=104 degrees, <6= 76 degrees, <7= 76 degrees, <8= 104 degrees
Step-by-step explanation:
<76 & < 2 are vertical angles, which means they are congruent. <1 & <2 are supplements, meaning when you add them up they equal 180 degrees (180-76=104 degrees). <1 & <4 are vertical angles. Using the Alternating Exterior Angles Theorem (AIA), <2 & <7 are congurent. Using the same theorem, <1 & < 8 are congruent. <7 & <5 are supplements, and so is <8 & <6.
Given: AB || CE
Find: ED
Answer:
49
Step-by-step explanation:
18/42=21/ED
18 ED=882
ED=49
help me guys ..........
Answer:
here you go....
Step-by-step explanation:
Find the value of x.
a
x = [?]
x
In the given circle the length of the chord marked x is
We know that the length of the chord is bisected by the perpendicular from the center of the circle.
Therefore the length of the chord is 7 × 2 = 14 units.
Again from the chord properties of a circle we know that, chords that are equidistant from the center are equal.
Since both the chords are at a distance of 9 units hence both chord lengths
Hence the length of the other chord = 14 units.
∴ x = 14
The segment of a line that joins any two points on a circle's circumference is known as the chord. It must be emphasized that its longest chord is its diameter, which runs through the center of the circle.
The circle and its chord are depicted in the diagram below. In the center of the circle, equal-length chords subtend equal angles.
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What is the decimal value of 5/6? Show your work using long division.
Answer:
0.83 repeating 3
Step-by-step explanation:
5 goes in the box and 6 goes outside. you can't put 6 into 5 so you would put a 0 on the top and a decimal point. now you would write a 0 next to the 5 and you would do 6×8=48 and so put 8 next to the 0 and the decimal point. then subtract 50-48 which will be 2. Put another 0 next to the 50 and bring it down. you will have 20 which you do 6×3=18. and so put a 3 next to 0.8 and you will subtract 20-18=2. It will be repeating so put a line at the top of 3 to show that it's repeating.
What is the value of q in the solution to this system of equations?
2m - 5q = 8
4m + 2q = 64
Answer:
q = 4
Step-by-step explanation:
Step 1: Set up the equation
The system of equations can be solved algebraically by substitution or elimination.For substitution, solve one of the equations for m and plug it into the other equation in order to solve for q.For elimination, cancel the m terms in order to solve for q.Step 2: Solve for q
Substitution:2m - 5q = 84m + 2q = 644m = 64 - 2qm = [tex]\frac{64-2q}{2}[/tex]m = 16 - [tex]\frac{1}{2}[/tex]q2(16 - [tex]\frac{1}{2}[/tex]q) - 5q = 832 - q - 5q = 8-6q = -24q = 4Elimination:2m - 5q = 8 (multiply whole equation by -2 in order cancel m terms)4m + 2q = 64-2(2m - 5q = 8)-4m + 10q = -164m + 2q = 6412q = 48q = 4Convert 7/10 into a decimal
Answer please with proofs and statements
Proved that ΔABC ≅ ΔDEC
SAS rule of congruent states that if two sides and one angle of the triangle is equal to the two sides and one angle of the another triangle, then the both triangles are congruent
The line BE and AD intersect at point C
The measure of the angle BCA = The measure of the angle ECD
The length of the side BC = The length of the side EC
The length of the side AC = The length of the side DC
Consider the triangle ABC and triangle DEC
Two sides and one angle of the triangle ABC is equal to the two sides and one angle of the triangle DEC, according to SAS rule of congruent the triangle ABC and triangle DEC are congruent
Hence, proved that ΔABC ≅ ΔDEC
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helene was paid a total of $33.00 for the 6 hours she worked. she continues to be paid at the same rate. how long would it take her to earn $165.00 for working?
The number of hours that helena need to work to generate 165 dollars is
33 hours.
Helena has to work hours to earn $165. 33
Algebraic equations are equations with
unknown variables. The alphabet letters are used to represent algebraic equations.
Total $33.00 in her 6 hours she worked.
This question should find out how long it takes her to earn her $165.00 in that job.
let x hours be required work hours to earn $165.00 ..
This can be expressed in algebraic equations as:
x= 6× 165/33
x= 990/33
x= 30
Hence, helna have to work thirty hours to earn $165.00 ..
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Select the correct answer. The table shows the balance of an investment account at the beginning of each year the account was held. Assuming that no other deposits have been made to the account, which statement describes the account's growth?
Year/////Account Balance
1: $500.00
2: $510.00
3: $520.20
○The account is growing linearly at an annual interest rate of 4.04%.
○The account is growing exponentially at an annual interest rate of 4.04%. MUTAT
○The account is growing linearly at an annual interest rate of 2.00%.
○The account is growing exponentially at an annual interest rate of 2.00%.
The statement that describes the account growth is D. The account is growing exponentially at an annual interest rate of 2.00%.
How to calculate the growth?From the information, the table shows the balance of an investment account at the beginning of each year the account was held.
The percentage change for the second year will be:
= (510 - 500) / 500 × 100
= 10/500 × 100
= 2%
The percentage change for the third year will be:
= (520.20 - 510) / 510 × 100
= 10.20/510 × 100
= 2%
Therefore, there's. 2% growth.
The correct option is D.
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Answer:
D
Step-by-step explanation:
Can u help me please
The slope of the line as shown in the diagram is 4/3.
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount.
To calculate the slope from the diagram, we use the formula below.
Formula:
S = Δy/Δx........... Equation 1Where:
S = Slope.From the graph,
At x = 30, y = 20
And at x = 60, y = 60
Therefore,
Δy = 60-20 = 40Δx = 60-30 = 30Substitute these values into equation 1
S = 40/30S = 4/3Hence, the slope of the is 4/3.
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1. The floor of a building is 120 feet long
and 80 feet wide. A scale model of the
building has a length of 24 inches. What
is the width of the model?
Step-by-step explanation:
120 ft relate to 24 inches.
120/80 must be the same ratio as 24/model width.
120/80 = 3/2
so,
24/width = 3/2
48/width = 3
48 = 3width
width = 48/3 = 16 inches
Conider the polynomial function []
p
given by p(x)=5x38x2−3x1
A(x). Evaluate the function at x=−2
x
The polynomial function p(x) = 5[tex]x^{3}[/tex] +8[tex]x^{2}[/tex] - 3x +1 value at x = -2 is -1
given that
polynomial function p(x) = 5[tex]x^{3}[/tex] +8[tex]x^{2}[/tex] - 3x +1 at x=-2
To find the value of a function at x = -2, put in all the places of in the function.
Polynomial is made up of two words, poly, and nomial. "Poly" means many, and "nomial" means the term, and hence when they are combined, we can say that polynomials are "algebraic expressions with many terms".
Polynomial functions are expressions that may contain variables of varying degrees, coefficients, positive exponents, and constants.
Here,
p(x) = 5[tex]x^{3}[/tex] +8[tex]x^{2}[/tex] - 3x +1 put x =-2
p(-2) = 5[tex](-2)^{3}[/tex]+8[tex](-2)^{2}[/tex] - 3(-2)+1
p(-2) = 5(-8) + 8(4) + 6+1
p(-2) = -40+32+6+1
p(-2) = -40+39
p(-2) =-1
At So, the value of the function at x= -2 is -1
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(a) 11³ x 11=11
11³
||³ + x = || 2
Step-by-step explanation:
I suspect you mean
11³ × 11 = ?
11³ ÷ 11 = ?
11³ × 11 = 11⁴
11³ ÷ 11 = 11²
why ?
11³ = 11×11×11
11³ × 11 = 11×11×11 × 11 = 11×11×11×11 = 11⁴
11³ ÷ 11 = 11×11×11 / 11 = 11×11 × 1 = 11×11 = 11²
- 12 = 10n - 40n + 3
Answer:
[tex]\sf n=\cfrac{1}{2}[/tex]
Step-by-step explanation:
[tex]\sf -12=10n-40n+3[/tex]
[tex]\sf 10n-40n+3=-12[/tex]
Combine like terms:-
[tex]\sf \:(10n-40n)=-30n[/tex]
[tex]\sf -30n+3=-12[/tex]
Subtract 3 from both sides:-
[tex]\sf -30n+3-3=-12-3[/tex]
Simplify:-
[tex]\sf -30n=-15[/tex]
Divide both sides by -30:-
[tex]\sf \cfrac{-30n}{-30}=\cfrac{-15}{-30}[/tex]
Simplify:-
[tex]\sf n=\cfrac{1}{2}[/tex]
_________________
Hope this helps!
Have a great day! :)
Emily's family loves to work together in the garden. They have a slight preference for flowers, as 60\%60%60, percent of their plants are flowers and 40\%40%40, percent are vegetables. They have 505050 plants growing in the garden.
How many vegetable plants do they have?
If Emily's family loves to work together in the garden . The number of vegetable plants they have is :20.
How to determine the number of vegetable plants?Using this formula to determine the number of vegetable plants
Number of vegetable plants = Percentage of vegetable plants × Number of plants
Let plug in the formula
Number of vegetable plants = 40% × 50
Number of vegetable plants = 20
Therefore we can conclude that the number of vegetable plants is 20.
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The correct question is :
Emily's family loves to work together in the garden. They have a slight preference for flowers, as 60 percent of their plants are flowers and 40 percent are vegetables. They have 50 plants growing in the garden.
How many vegetable plants do they have?
Create the graph of this quadratic function below please!
x2+3x-108
Make sure to have the two roots and axis of symmetry AKA the vertex.
The graph of this quadratic function (x² + 3x - 108) is shown in the image attached below. Also, the two roots of this quadratic equation (x² + 3x - 108) are -12 and 9, while the axis of symmetry (vertex) is equal to -1.5.
What is a quadratic function?In Mathematics, a quadratic function is a mathematical expression which defines and represent the relationship that exists between two or more variable on a graph.
Mathematically, the graph of every quadratic functions is either an upward or downward parabola, which is typically a u-shaped curve. This ultimately implies that, the graph of a quadratic function would always form a parabolic curve. For this quadratic function, the graph is a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero.
Next, we would determine the axis of symmetry (vertex) of this quadratic function:
Axis of symmetry (vertex), Xmax = -b/2a
Axis of symmetry (vertex), Xmax = -3/2(1)
Axis of symmetry (vertex), Xmax = -1.5.
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Figure JKLMN is reflected across the y-axis to form figure J'K'L'M'N'.
What are the coordinates of the vertices of figure J'K'L'M'N'?
Decide if each statement describing figures JKLMN and J'K'L'M'N' is true or false. Choose True or False for each statement.
a. L' is located at (-3, 4).
b. M' is located 4 units left of the y-axis.
c. The y-coordinate of N' is the opposite of the y-coordinate of N.
d. J'K' = JK
e. M' is located at (-4, 1).
The co-ordinates of J'K'L'M'N' are (0,5), (-2,3), (-3,4), (-4,1), (-1,2)
What is Co-ordinate Geometry?
Coordinate geometry is a field of mathematics that assists in displaying geometric forms on a two-dimensional plane and learning the attributes of these figures.
Solution:
The co-ordinates of J'K'L'M'N' are (0,5), (-2,3), (-3,4), (-4,1), (-1,2)
From the figure it can be clearly observed that
a) L' is located at (-3,4) - True
b) M' is located 4 units left of the y - axis - True
c) The y - co ordinate of zN' is the opposite of the y - co ordinate of N - False
d) J'K' = JK - False
e) M' is located at (-4,1) - True
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(a) A(-1,4)and B(3,2) are the end points of a line segment AB. Determine (i) The gradient of AB. (ii) The coordinates of the midpoint of AB. (iii) The equation of the perpendicular bisector of AB.
The slope of the line is -1/2, the coordinates of midpoint is (1,3) and the equation of perpendicular bisector is y = 2x + 1
What is slope?The slope of a line is a measure of its steepness.
Given that, a line segment has end points = A(-1,4) and B(3,2)
(i) Slope = (y2 - y1)/(x2 - x1) = -1/2
(ii) Coordinates of the midpoint of a line = (Xm, Ym) = (x₁ + x₂)/2, (y₁ + y₂)/2
(Xm, Ym) = (-1+3)/2, (4+2)/2 = (1,3)
(iii) The slope of the two lines perpendicular to each other are negative reciprocal of each other, so, slope of the line perpendicular to the given line is = 2
Standard equation of a line = y = mx + c
Since the line is the perpendicular bisector of AB, it will pass through (1,3)
Solving for c,
3 = 2*1 + c
c = 1
Therefore, the equation of the of line perpendicular to AB is
y = 2x + 1
Hence, the slope of the line is -1/2, the coordinates of midpoint is (1,3) and the equation of perpendicular bisector is y = 2x + 1
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Factor: 4x + 18 =
I don't understand Pre-algebra
Answer:
2(2x+9)
Step-by-step explanation:
Just break each number up
2 X 2 = 4
2 X 9 = 18
2(2x+9)
Answer:
-4.5
......
......
9/g +2h +5 when g=3 and h=6
Answer:answer is 20
Step-by-step explanation:9/3=3 then add that to 2 times 6 which is 12+3=15 then 15+5+20
Lance recieved 10 more sweets than Randal and Rema recieved three times the amount that was given to Lance and handal. The total number of sweets that was shared is 120. How many did Rema recieve?
Answer:
Rema receives 90 sweets
Step-by-step explanation:
See attached image
Seema used compatible numbers to estimate the product of (–25. 31)(9. 61). What was her estimate? –250 –240 240 250.
Estimate product of (-25.31) (9.61) using compatible numbers is equal to -250.
As given in the question,
Given expression is equal to :
( -25.31 ) ( 9.61 )
Compatible numbers to calculate the estimate product we have,
Compatible number for ( -25.31 ) is equal to ( -25 ) .
-25 > -25.31 > -26
-25.31 is more nearer to -25 .
Now, 9 < 9.61 < 10
Compatible number for 9.61 is equal to 10 as 9.61 is more close to 10.
( -25.31 ) × ( 9.61 )
= ( -25 ) × (10)
= 250
Therefore, estimate product of (-25.31) (9.61) using compatible numbers is equal to -250.
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PLEASE HELP ME!!
A soccer team receives a discount on each jersey purchased. The original price of each jersey is x dollars. The team buys 18
jerseys for a total of (18x-36) dollars. What can you conclude about the discount?
If the team buys 18 jerseys for a total of (18x-36) dollars then we can conclude that the discount the team has received is $36.
According to the question,
We have the following information:
A soccer team receives a discount on each jersey purchased. The original price of each jersey is x dollars. The team buys 18 jerseys for a total of (18x-36) dollars.
Now, the original price of 18 jerseys will be 18x.
Now, when 36 is subtracted from 18x to find the total cost then it means that this is the discount from the original price.
Hence, if the team buys 18 jerseys for a total of (18x-36) dollars then we can conclude that the discount the team has received is $36.
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I need to write an equation the Aline’s with the stars so that the purple ball will fall on to the line and hit all the stars
Answer:
y = - [tex]\frac{3}{4}[/tex] x - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 12, 4 ) and (x₂, y₂ ) = (0, - 5 ) ← coordinates of 2 end stars
m = [tex]\frac{-5-4}{0-(-12)}[/tex] = [tex]\frac{-9}{0+12}[/tex] = [tex]\frac{-9}{12}[/tex] = - [tex]\frac{3}{4}[/tex]
the lowest star is on the y- axis at (0, - 5 ) ⇒ c = - 5
y = - [tex]\frac{3}{4}[/tex] x - 5
For her softball uniform,Meredith has a green,white,or striped jersey.She also has white or green shorts.If Meredith chooses a jersey and shorts randomly ,what is the probability that she will go to softball practice ima striped jersey and green shorts?
Answer: Give me brainliest or your mean.
Step-by-step explanation: 1/3 jersey 1/2 short. 1/3 x 1/2 = 1/6 possibility.
Find x and y please
10 points
The value of x is 15 and the value of y is 4 for the given triangle.
According to the question,
We have the following information:
We have a figure of triangle and a line parallel to the base is drawn. Some measurements of the sides are given.
Now, to find the values of x and y, we will use Basic Proportionality theorem which states that the ratio of the corresponding sides are equal.
For the larger triangle, we have:
12/y = 18/6
Using the cross multiplication method:
y = 12*6/18
y = 4
Now, using the same theorem for the smaller triangle:
12/y = x/5
12/4 = x/5
Using the cross multiplication method:
x = 15
Hence, the value of x is 15 and the value of y is 4 for the given triangle.
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