We have a game like the one described in the question and we have to calculate the expected payoff, which is equal to the sum of the possible outcomes weighted by the probability of that outcome.
In this case we have two outcomes:
1) We get an odd number and we win $26 (W=26).
2) We get an even number and we get $0 (W=0).
To calculate the probabilities of each oucome we have to know the proportion of odd an even numbers in the list of 1 to 50. We have a total of 50 numbers, rom which 25 are odd numbers and 25 are even numbers, so the probability of each outcome can be calculated as the relative frequency of each category:
[tex]\begin{gathered} P_1=\text{ number of odds / total numbers}=\frac{25}{50}=0.5 \\ P_2=\text{ number of evens / total numbers}=\frac{25}{50}=0.5 \end{gathered}[/tex]Then, we can calculate the expected payoff as:
[tex]E=\sum ^n_{i=1}p_iW_i=p_1W_1+p_2W_2=0.5\cdot26+0.5\cdot0=13+0=13[/tex]p_i: probability of outcome i.
W_i: prize when outcome i happens.
Then, the expected payoff for this game is $13.
Answer: the expected payoff for this game is $13.
Determine if the following system of equations has no solutions , infinitely many solutions or exactly one solution .- Infinitely Many Solutions - One Solution - No Solutions
Let's begin by identifying key information given to us:
[tex]\begin{gathered} x+3y=8----1 \\ x-3y=-6---2 \\ A\text{dd equations 1 \& 2, we have:} \\ x+x+3y-3y=8-6 \\ 2x=2 \\ x=1 \\ \text{Substitute the value of ''x'' into equation 1, we have:} \\ 1+3y=8 \\ \text{Subtract ''1'' from both sides, we have:} \\ 1-1+3y=8-1 \\ 3y=7 \\ y=\frac{7}{3} \end{gathered}[/tex]Therefore, the system of equations has one solution
A rocket is launched straight up and it takes 83 seconds to hit the ground. How long did it take the rocket to get to the top of its path?
It would take 41.5 to get to the top of its path if the rocket is launched straight up and it takes 83 seconds to hit the ground by solving through finding speed.
Given that the time that rocket took to hit the ground is 83 seconds.
We are required to find the time that it took the rocket to get to the top of its path.
Suppose the height from the ground is h.
To cover the distance of 2h it would take 83 seconds.
We know that speed=Distance/time
Speed=2h/83
So, to cover the distance of h, the time will be :
Time=Distance/Speed
=h/2h/83
=(h*83)/2h
=83/2
=41.5
Hence it would take 41.5 to get to the top of its path if the rocket is launched straight up and it takes 83 seconds to hit the ground by solving through finding speed.
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simplify the equation
The simplified expression of the equation given as (x² - 16)/(x² -2x - 3) ≤ 4 is 3x² -8x + 4 ≥ 0
How to simplify the equation?From the question, we have the following parameters
(x² - 16)/(x² -2x - 3) ≤ 4
Multiply both sides of the expression by (x² -2x - 3)
So, we have the following representation
(x² -2x - 3) * (x² - 16)/(x² -2x - 3) ≤ 4 * (x² -2x - 3)
Evaluate the products in the above expression
So, we have the following equation
(x² - 16) ≤ 4 * (x² -2x - 3)
Open the brackets
This gives
x² - 16 ≤ 4x² -8x - 12
Collect the like terms in the above expression
So, we have the following equation
0 ≤ 3x² -8x +4
Rewrite the expression as
3x² -8x + 4 ≥ 0
Hence, the simplified expression of the equation is 3x² -8x + 4 ≥ 0
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A triangle has sides of length 7 centimeters, 5.6 centimeters, and 4.2 centimeters. What is the perimeter?
The perimeter of the triangle is 16.8 cm.
What is a triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane. According to the sides of a triangle rule, the lengths of any two sides of a triangle must add up to more than the length of the third side.So, the perimeter of the triangle:
Formula: P = a + b + cWhere a = 7, b = 5.6 and c = 4.2.Now, substitute the values in the formula as follows:
P = a + b + cP = 7 + 5.6 + 4.2P = 16.8Therefore, the perimeter of the triangle is 16.8 cm.
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Identify the function in which y varies directly with x.
Let the function in which "y" varies directly with "x" be y = kx where "k" is the proportionality constant and y ∝ x
As per the question statement, We are supposed to write any function in which "y" varies directly with "x" i.e., y ∝ x
Let's say y = kx be the function where "k" is the proportionality constant and y ∝ x.
Now let x = 3 and y = 6, so 6 = k*3
or k = 3
Hence for any value of "x" value of "y" would be k times the value of x and this is called the direct proportion relationship.
Hence, the function in which "y" varies directly with "x" be y = kx where "k" is the proportionality constant and y ∝ x
Function: An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable).Proportionality constant: The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant ratio is another term for the constant of proportionality.To learn more about function and proportionality constant, click on the link given below:
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What is it called when two numbers have a product of one
Answer: Reciprocals
Explanation isn't really needed but reciprocals are basically
Example:
3/4's reciprocal is 4/3 and multiplying 3/4 x 4/3 = 1
Write and solve a direct variation equation to find the answer
Direct Variation
If y varies directly with x, then they are related by the equation:
y = kx
Where k is a constant called the proportionality factor.
It's given that y = -38 when x = 19. Substituting those values in the equation, we can find the value of k:
-38 = k*19
Dividing by 19:
k = -38 / 19
k = -2
Now our model is complete:
y = -2x
Now it's required to find the value of x when y = -4. Substituting:
-4 = -2x
Dividing by -2:
x = -4 / (-2)
x = 2
Solve for X
3-4x+5=2(8-2x)
Value of x will be 0.
What is equation?A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. Based on the degree, there are three different sorts of equations. Equations that are linear, quadratic, and cubic. In mathematics, an equation is a relationship between two expressions that is expressed as an equality on each side of the equal to sign. An equation would be 3y = 16, for instance.
Given Data
3-4x+5=2(8-2x)
3 - 4x + 5 = 16 -4x
3 + 5 -16 = -4x+4x
-8 = 0
Value of x will be 0.
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y varies jointly as a and b , and inversely as the square root of c. y=54 , a = 3 , b=9 , and c=25. Find y when a=5 , b=6 , c=36
When a=5 , b=6 , c=36, the value of y will be 50.
Here, we are given that y varies jointly as a and b and inversely as the square root of c.
⇒ y ∝ ab/[tex]\sqrt{c}[/tex]
Let k be a constant, then we can say that-
y = kab/[tex]\sqrt{c}[/tex]
We are given that y = 54 , a = 3 , b = 9 , and c = 25.
substituting these values in the above equation, we can calculate the value of k as follows-
54 = (k*3*9)/[tex]\sqrt{25}[/tex]
54 = 27k/5
54*5 = 27k
270 = 27k
27k = 270
k = 270/27
k = 10
Now, when a=5 , b=6 , c=36, the value of y will be-
y = (10*5*6)/[tex]\sqrt{36}[/tex]
y = 300/6
y = 50
Thus, when a=5 , b=6 , c=36, the value of y will be 50.
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Which does NOT represent a valid argument?Anyone who buys a boat will go water skiing.Ivan bought a boat.Ivan will go water skiing.Everyone who went to the football gamecheered.Maria cheered.Maria went to the football game.If the Nationals win the playoffs, then I will behappy.O if I am happy, then I will have a party.If the Nationals win the playoffs, then I will have aparty.Everyone who studies Geometry will pass theSOL.Everyone who passes the SOL will be exemptfrom the exam.Everyone who studies Geometry will be exemptfrom the exam,
the statement that does not represent a valid arguement is,
Everyone who went to the football game cheered.
Maria cheered.
Maria went to the football game.
3/4=6/x proportionsolve for x
5) x = 8
Explanation:[tex]\frac{3}{4}=\frac{6}{x}[/tex]cross multply:
[tex]\begin{gathered} 3\times\text{ x = 4 }\times\text{ 6} \\ 3x\text{ = 24} \end{gathered}[/tex]divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3\text{ }}=\text{ }\frac{\text{24}}{3} \\ x\text{ = 8} \end{gathered}[/tex]Question 14<>The table summarizes results from 981 pedestrian deaths that were caused by automobileaccidents.Pedestrian DeathsDriver Pedestrian Intoxicated?Intoxicated?NoYesYes5584No248594If one of the pedestrian deaths is randomly selected, find the probability that the driver was notintoxicated but the pedestrian was. Please enter a decimal to 4 places.Calculator
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
If one of the pedestrian deaths is randomly selected.
Find the probability that the driver was not intoxicated but the pedestrians were.
We are expected to enter 4 decimal places.
Now, from the table, we can see clearly that:
[tex]\begin{gathered} \text{Probability ( the driver was not intox}icated\text{ but the pedestrians were)} \\ =\text{ }\frac{248}{981} \\ =\text{ 0.2528 ( 4 decimal places)} \end{gathered}[/tex]CONCLUSION:
The final answer is 0. 2528 ( 4 decimal places).
Hope you help me, I need help with the check part
1.- 3(x - 2) = 15
Solve for x 3(x - 2)/3 = 15/3
Simplifying x - 2 = 5
(x - 2) = 15/3
(x - 2) = 5
x - 2 = 5
x = 5 + 2
x = 7
Check. Substitute the value of x in the original equation and solve it
3(7 - 2) = 15
3(5) = 15
15 = 15 As the two value are the same, the solution of x is
correct.
2.- 4y + 9 - 7y = -6
Solve for y
Simplify like terms
4y - 7y + 9 = -6
- 3y + 9 = -6
-3y = -6 - 9
-3y = -15
-3y/-3 = -15/-3
y = 5
Check
4(5) + 9 - 7(5) = -6
20 + 9 - 35 = -6
29 - 35 = -6
-6 = -6 The solution is correct because both numbers are the same.
Find the difference of (4y2 - 2y - 5) and (y² - y + 8).4у2 - 3у - 133у2 - у - 135y2 - 3y + 33у2 - 3у + 3
We must find the difference between the following polynomials:
[tex]\begin{gathered} f_1(y)=4y^2-2y-5, \\ f_2(y)=y^2-y+8. \end{gathered}[/tex]The difference between the polynomials is obtained by subtracting the coefficient of terms with equal power of y:
[tex]\begin{gathered} f_1(y)-f_2(y) \\ =\left(4y^2-2y-5\right)-\left(y^2-y+8\right) \\ =\left(4y^2-y^2\right)+\left(-2y+y\right)+\left(-8-5\right) \\ =3y^2-y-13. \end{gathered}[/tex]Answer3y² - y - 13
Angelina can type 150 words in 5 minutes. At this rate, how many words can she type in 1 minute?
Answer:
30 words per minute
Step-by-step explanation:
Answer:
30 words
Step-by-step explanation:
her typing speed is 150 words for 5 minutes.
Since we know that she can type 5 times as much in 5 minutes than in 1 minute, we know that 150 words is 5 times as much as she would be able to type in 1 minute. The question that should be asked is "5 times what would equal 150?" The answer would be 30 words.
Shorter answer: 150 words / 5 minutes = 30 words/minute
Lisa is saving for college. The account is modeled by the function:
f(x) = 250(1.25)^x
,when x represents how many years she has saved.
Xavier is also saving college. His account is modeled by this table:
X g(x)
0 200
1 270
2 364.5
3 492.08
1. After 3 years, how much does Lisa's account have in it? (Round to the hundredths
decimal place.)
2.After 3 years, how much does Xavier’s account have in it?
3.What is the positive difference in their accounts after 3 years?
Using exponential functions, it is found that:
a) Lisa's account has $489 after 3 years.
b) Xavier's account has $493 after 3 years.
c) The difference is of $4.
An exponential function is what, exactly?According to the following principle, an exponential function is modelled where the following description of the parameters is given:
The value of the function at x = 0 is known as its initial value, or a.The function's rate of change is denoted by bLisa's function is already given, while for Xavier's, the parameters are given as follows:
a = 200
b = 270/200
= 1.35
g(x) = 200 × [tex]1.35^{x}[/tex]
In 3 years, the amounts in each account will be given by the numeric values of the functions as follows:
Lisa = f(3)
= 250 (1.25)³
= 489$
Xavier = f(3)
= 200 (1.35)³
= 493$
The positive difference is given by the subtraction of the greater amount by the lesser amount, hence:
493 - 489 = 4$
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can someone solve this?2 > -3t - 10and is it an open or closed circle?
Given data:
The given inequality is 2> -3t-10.
The given inequality can be written as,
[tex]\begin{gathered} 2>-3t-10 \\ 12>-3t \\ 4>-t \\ t>-4 \end{gathered}[/tex]Thus the value of t is (-4, ∞), and it is open interval.
A survey found that women's heights are normally distributed with mean 63.6 in. and standard deviation 3,8 in. The survey also found that men's heights are normally distributed with
mean 67.6 in. and standard deviation 3.6 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 56 in. and a maximum of 62 in.
Complete parts (a) and (b) below.
a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement park?
The percentage of men who meet the height requirement iS
(Round to two decimal places as needed.)
%.
Since most men
the height requirement, it is likely that most of the characters are
b. If the height requirements are changed to exclude only the tallest 50% of men and the shortest 5% of men, what are the new height requirements?
The new height requirements are a minimum of
in. and a maximum of in.
(Round to one decimal place as needed.)
The percentage of men meeting the height requirement is 5.93%.The new height requirements are a minimum of 61.7 inches and a maximum of 67.6 inches.
What is probability?Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty. The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities. A measure of how likely something is to happen is called a probability. It gauges how likely the occurrence is to occur. The probability equation reads as follows: P(E) = Number of Favorable Outcomes/Total Outcomes.
For mean deviation of women
σ = 3.8
μ = 63.6
For mean deviation of men
σ = 3.6
μ = 67.6
The probability for men
= 5.93%
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The formula a = m – n represents the actual cost, a, of an item with original price m after a coupon for n dollars off is applied. Solve the formula for the amount of the coupon.
The formula for amount of the coupon is given by n = m - a.
This question can be solved using simple Linear equation. A linear equation may be defined as an expression which can be written in the form y = ax + b where a, b are coefficients and x, and y are independent and dependent variables respectively. According to question we have a formula a = m - n where a is the actual cost, m is original price and n is coupon discount. The actual cost of an item will depend on the coupon discount as well as the original cost of the item. To find the coupon amount from the formula we rearrange the equation as
a = m - n
a - m = -n
=> n = m - a which will be the required formula.
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Kendall is investing in the stock market and has a maximum budget of $9,900 with which to purchase stock in two promising companies. Stock in the software company currently sells for $38 per share. Stock in the robotics company is currently trading at $49 per share.
The solution is 38x+49y<9,900 of investing in the stock market.
What is the Equation of inequality?The idea of inequality can be used to understand this query.
Let x represent the number of stocks purchased in software firms, and y represents the number of stocks purchased in robotics companies.
$38 was placed in one software company stock.
$ was placed in one robotics firm's stock.
Total investment in the equity of the software company = 38*x
Cost of robotics firm stock as a whole: 49*y
Therefore, the overall cost should be lower than 9,900.
As a result, the equation is
38x+49y<9,900.
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which expression is equivalent to. -2(5x + 3y)
A. 3y(5x - 2)
B 5x(-2+3y)
c -10x - 6y
-10x + 3y
The -2 multiplies each every term in the brackets. meaning -2 will multiply 5x and also 3y
[tex] = - 2(5x) - 2(3y) \\ = - 10x - 6y[/tex]
OPTION C MATCHES AS THE SOLUTION.
GOODLUCK
At the bicycle shop there are 23 bicycles and 18 tricycles. Each bicycle has 2 wheels, and each tricycle has three wheels. How many wheels are there at the bicycle shop?
Answer:
There are 100 wheelsStep-by-step explanation:
GivenNumber of bicycles = 23,Number of tricycles = 18Total number of wheels23*2 + 18*3 = 46 + 54 = 100A rectangular pool is surrounded by a walk 3 meters wide. The pool is 5 meters longer than its width. If the total area of the pool and walk is 270 square meters more than the area of the pool, find the dimensions of the pool.
The length and width of the rectangular pool are respectively; Length = 22 meters and Width = 17 meters
What is the area of the rectangle?Area of the pool which is a rectangle has the formula;
A = Length(L) * Width(w)
Let the width of the pool = x
Then the length will = (x + 5)
Since the walkway is 3 meters wide, It means that the overall dimensions will be (x + 6) by (x + 5 + 6) or (x + 11)
Total area - pool area = 270
Thus;
(x + 11) * (x + 6) - x(x + 5) = 270
x² + 11x + 6x + 66 - x² - 5x = 270
17x - 5x + 66 = 270
12x + 66 = 270
12x = 270 - 66
x = 204/12
x = 17
Length of pool = x + 5 = 17 + 5 = 22 meters
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At a fruit stand , apples sell for $ 1.20 per pound . One week , the stand sold $600 worth of apples and pears . The equation below describes the situation , where A is the number of pounds of apples and P is the number of pounds of pears . 0.8a + 1.2p = 600 Which graph represents the equation?
we can calculate two points in order to know what graph corresponds to the equation
when a=0
1.2p=600
p=600/1.2
p=500
the point is (0,500) red point
when b=0
0.8a=600
a=600/0.8
a=750
the point is (750,0) green point
the answer is B
shshshdggdgdgdggddgegegegegegs
We need to solve the following equation by completing the square:
[tex]x^2-4x-9=0[/tex]we first pass the 9 to sum in the right side
[tex]x^2-4x=9[/tex]now we add 4 in both sides of the equation, because (4/2)^2=4, obtaining
[tex]x^2-4x+4=9+4[/tex]simplifying
[tex](x-2)^2=13[/tex]then
[tex](x-2)=\pm\sqrt[]{13}[/tex]adding 2 in both sides of the equation we have that the solution is:
[tex]x=2\pm\sqrt[]{13}[/tex]How many weeks can Shanika withdraw money from her account
Step 1
Given;
[tex]\begin{gathered} Money\text{ in her account \$500} \\ Money\text{ that will be left is \$200} \\ She\text{ withdraws \$25 weekly} \end{gathered}[/tex]Hence the equation from the question will be;
[tex]\begin{gathered} 500-25x=200 \\ where\text{ x= number of weeks} \end{gathered}[/tex][tex]\begin{gathered} 500-200=25x \\ 300=25x \\ x=\frac{300}{25} \\ x=12 \end{gathered}[/tex]Hence, the answer will be;
[tex]12\text{ or less weeks}[/tex]Factor the polynomial below. To earn full credit please share all work/calculations/thinking. You may want to do this work by hand and then upload an image of that written work rather than try to type it all out. 12t^2+t-13
Given:
The polynomial is,
[tex]12t^2+t-13[/tex]Factor the polynomial,
[tex]\begin{gathered} 12t^2+t-13=12t^2-12t+13t-13 \\ =\mleft(12t^2-12t\mright)+\mleft(13t-13\mright) \\ =12t(t-1)+13(t-1) \\ =\mleft(t-1\mright)(12t+13) \end{gathered}[/tex]Answer:
[tex]12t^2+t-13=(t-1)(12t+13)[/tex]1 Type the correct answer in each box. Use numerals instead of words, Consider this quadratic equation, x2 + 2x + 7 = 21 The number of positive solutions to this equation is The approximate value of the greatest solution to the equation, rounded to Reset
Answer:
The number of positive solutions to this equation is;
[tex]1[/tex]The approximate value of the greatest solution to the equation is;
[tex]2.87[/tex]Explanation:
Given the equation;
[tex]x^2+2x+7=21[/tex]Let us subtract 21 from both sides;
[tex]\begin{gathered} x^2+2x+7-21=21-21 \\ x^2+2x-14=0 \end{gathered}[/tex]We can now solve for x using the quadratic formula;
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]from the equation;
[tex]\begin{gathered} a=1 \\ b=2 \\ c=-14 \end{gathered}[/tex]substituting;
[tex]\begin{gathered} x=\frac{-2\pm\sqrt[]{2^2-4(1)(-14)}}{2(1)} \\ x=\frac{-2\pm\sqrt[]{4+56}}{2} \\ x=\frac{-2\pm\sqrt[]{60}}{2} \end{gathered}[/tex]so, we have;
[tex]\begin{gathered} x=\frac{-2\pm\sqrt[]{60}}{2} \\ x=\frac{-2+\sqrt[]{60}}{2} \\ x=2.87 \\ \text{and} \\ x=\frac{-2-\sqrt[]{60}}{2} \\ x=-4.87 \end{gathered}[/tex]Therefore, the number of positive solutions to this equation is;
[tex]1[/tex]The approximate value of the greatest solution to the equation is;
[tex]2.87[/tex]Ordering Decima
A) Write each set of decimals in increasing order.
1)
14.78, 46.1, 25.5, 14.8, 32.32
2)
37.44, 9.32, 16.49, 9.67, 37.91
Increasing order :
1) 14.78 , 14.8 , 25.5 , 32.32 , 46.1
2) 9.32 , 9.67 , 16.49 , 37.44 , 37.91
What is ascending order ?
Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right. Increasing order is another name for ascending order.The base-10 number system is known as the decimal system.The accepted method for representing both integer and non-integer numbers is the decimal numeral system.It is the extension to non-integer numbers.Decimal notation is the term used to describe the method of representing numbers in the decimal system.To learn more about ascending order refer :
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help meeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
33
Step-by-step explanation:
you are scamming everyone. why?
