Gavin tosses an unbiased coin. He receives Php 100 if the appears and pays Php 40 if a til appears. Find the expected value of his gain.
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In probability theory, the expected value of a random variable is a measure of the center of the distribution of the variable. It is a crucial concept that appears in various statistical problems. The expected value of a discrete random
variable can be calculated by the following formula: E(X) = ∑ x P(X = x), where E(X) is the expected value of the random variable X, x is a possible value of X, and P(X = x) is the probability that X takes the value x. Now let's calculate the expected value of Gavin's gain. Gavin tosses an unbiased coin, which means that the probability of getting head is 0.5 and the probability of getting tail is also 0.5. If Gavin gets head, he receives Php 100, and if he gets tail, he pays Php 40. Therefore, the random variable X that represents Gavin's gain can take two possible values: 60 and -40. We can calculate the expected value of X by plugging in the values of x and P(X = x) into the formula above: E(X) = 60*0.5 + (-40)*0.5 = 10. Therefore, the expected value of Gavin's gain is Php 10.
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Related Questions
Algebra 1 - I am confused on how to solve the problem. Please help
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h(-1) is undefined in the real number system since the square root of a negative number is not a real number.
What is the real number?
Real numbers are a set of numbers that include all rational and irrational numbers. They can be represented on the number line and are often used to represent physical quantities such as distance, time, and temperature.
To find h(-1), we substitute -1 for x in the given equation for h(x) and simplify:
h(x) = (√x+5)/(6x-2)
h(-1) = (√(-1)+5)/(6(-1)-2) [Substitute x=-1]
= (√(-1) is not a real number, since the square root of a negative number is not real]
Therefore, h(-1) is undefined in the real number system since the square root of a negative number is not a real number.
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the value of x-y+xy if x=1 y=1 is
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Answer:
1
Step-by-step explanation:
x-y+xy=1-1+1*1=0+1=1
Answer:
1
Step-by-step explanation:
X=1
Y=1
here,
x-y+xy=1-1+1×1
or,x-y+xy=0+1=1
Staysafe❤
Find the inverse of f(x)=−32x+72.
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Answer: \(f^{-1}(x)=-\frac{x-72}{32}\)
Step-by-step explanation:
To find the inverse function, you want to switch x with y and y with x, then solve for y.
y=-32x+72 [switch x with y and y with x]
x=-32y+72 [subtract both sides by 72]
x-72=-32y [divide both sides by -32]
\(y=-\frac{x-72}{32}\)
Now, we have found the inverse function.
The perimeter of a rectangular building is 1200 feet. The width of the building is 2 feet less than three times the length. What is the width of the building?
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Given:
The perimeter of a rectangular building is 1200 feet.
The width of the building is 2 feet less than three times the length.
To find:
Width of the building.
Solution:
Let length of the building be x.
Then, width = 3x-2
We know that,
\(Perimeter=2(length +width)\)
\(1200=2(x+3x-2)\)
\(1200=2(4x-2)\)
\(1200=8x-4\)
Add 4 on both sides
\(1204=8x\)
Divide both sides by 8.
\(\dfrac{1204}{8}=x\)
\(150.5=x\)
Now,
\(Width=3x-2\)
\(Width=3(150.5)-2\)
\(Width=451.5-2\)
\(Width=449.5\)
Therefore, the width of the building is 449.5 feet.
Determine the relationship between the two triangles and whether or not they can be proven to be congruent.
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solve for r
7(r+1)=20.3
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7r + 7 = 20.3
Minus 7 from both sides
7r = 13.3
Divide both by 7
R = 1.9
Find the equation of the linear function represented by the table below in slope- intercept form. X o 1 2 3 4 у -5 1 7 13 19
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Answer:
4x+4
Step-by-step explanation:
true or false f o r space s e t s space a space a n d space b comma space i f space a subset of or equal to b comma space t h e n space a intersection b space equals space a true false
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False. If A is a subset of or equal to B, it does not necessarily mean that A intersection B equals A. The intersection of two sets A and B is defined as the set of elements that belong to both A and B.
If A is a subset of B, then every element of A also belongs to B. Therefore, the intersection of A and B must include all the elements of A. However, it may also include additional elements that belong to B but not to A.
For example, let A = {1, 2} and B = {1, 2, 3}. A is a subset of B since every element of A also belongs to B. However, the intersection of A and B is {1, 2}, which is not equal to A.
In summary, if A is a subset of or equal to B, it is possible for A intersection B to equal A, but it is not always true. The intersection can also include additional elements from B that do not belong to A.
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Solve the proportion. * X-3 5 8. X= (Type an integer or a an integer or a simplified fraction.)
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We want to solve the proportion:
\(\frac{x-3}{x}=\frac{5}{8}\)For doing so, we remember that solving a proportion equivals to find the variable x. We will multiply means and extremes:
\(\begin{gathered} 8(x-3)=5\cdot x \\ 8x-24=5x \\ \text{Now, we solve for x:} \\ 8x-5x=24 \\ 3x=24 \\ x=\frac{24}{3}=8 \end{gathered}\)This means that the value of x is 8, which is the solution of the proportion.
how many 15 kilocalories to calories?
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15 Kilocalorie (international) (kcal) = 15000 Calorie (cal)
Kilocalorie (international) :The kilocalorie, sometimes call kilogram calorie is a measurement unit of energy. It is defined as the amount of energy needed to raise the temperature of one kilogram of water by one degree Celsius. The symbol of kilocalorie is kcal. The kilocalorie is commonly used in measuring the calorific, heating, or metabolizing value of foods. It is equal to 1000 calories, or approximately 4.2 kilojoules.
Calorie :The calorie is a pre-SI metric unit of energy. Its symbol is cal, and first defined as a unit of heat by Nicolas Clément in 1824. The calorie is commonly used in the field of chemistry, and in many countries it is commonly used as a unit of food energy. There are two defined for the calorie, gram calorie (approximately equals 4.2 joules) and kilogram calorie (approximately equals 4.2 kilojoules).
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What is the opposite of -63
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Answer:
63
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all u have to to do is coint up
Help please zjyjytbrbbrbrb
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PLEASE HELP! i don’t understand this :(((
Answers
Answer:
b : ( 3, 0, -1 )
Step-by-step explanation:
you need to sub the range into the equation to find their domains
Explain the difference between (-12) and -12
Answers
Answer:
0 or none
Step-by-step explanation:
jump the number line
"Evalúa 2x¹ +5 cuando x =3"
Answers
Answer: 11
Step-by-step explanation:
Just go through the order of operations. (PEMDAS)
Evaluate the exponent first,
X=3
3^1=3
then multiply 2 and 3, which gives you 6
then finally add 5
this gives you the answer of 11
Find an equation of the line parallel to y=2x-6 that passes through the point (3,-8) if possible write the equation in slope intercept form
Answers
Given the equation:
\(\text{ y = 2x -6}\)The equation is at Slope-Intercept Form: y = mx + b and the m in the equation represents the slope of the line. Therefore, the slope of the line that represents the equation y = 2x - 6 is 2.
It's been given that the equation of the line that we are looking for is parallel to y = 2x - 6 and passes through the point (3, -8). Thus, we will adapt the slope of the equation and determine the y-intercept by substituting the coordinates in the slope-intercept formula y = mx + b.
We get,
\(\text{ y = mx + b}\)At slope, m = 2 and x,y = 3, -8:
\(-8\text{ = (2)(3) + b}\)\(-8\text{ = 6 + b}\)\(\text{ b = -8 - 6 = -14}\)Let's substitute m = 2 and b = -14 to y = mx + b to complete the formula:
\(\text{ y = mx + b}\)\(\text{ y = (2)x + (-14)}\)\(\text{ y = 2x - 14}\)Therefore, the equation of the line parallel to y = 2x - 6 and passes through (3, -8) is
y = 2x - 14.
The figure is a triangle that is divided into two parts. Angle A and angle E are right angles and the measure of angle F is 30 degrees. What is the measure of angle C? Complete the steps below to solve the problem using equations.
Part A
Let the variable g represent the measurement of angle G. Write and equation that you can use to solve for g.
Part B
What is the measurement of angle G?
Part C
Let the variable c represent the measurement of angle C. Use the measurement of angle G to write an equation that you can use to solve for c.
Part D
What is the measurement of angle C?
Answers
Answer:
Part A) g + 30 + 90 = 180
Part B) G = 60 degrees
Part C) c + 60 = 180
Part D) C = 120 degrees
Step-by-step explanation:
Part A: If angle F is 30 degrees and E is 90, then we can easily find G using the fact that the sum of a triangle is 180 degrees.
g + f + e = 180
g + 30 + 90 = 180
Part B: g + 30 + 90 = 180
g + 120 = 180
g = 60
Part C: Since G and C are on the same line and just separated by another line, we can use supplementary angles to find C.
c + g = 180
c + 60 = 180
Part D: c + 60 = 180
c = 120
Answer:
A:The sum of the angle measurements in a triangle is 180°. If e, f, and g are the measurements of angles E, F, and G, respectively, e + f + g = 180°.
Angle E is a right angle, so e is 90°. From the given information, f is 30°. Substitute the values of e and f in the equation to solve for g : 90° + 30° + g = 180°.
B:Solve the equation from Part A to find the measurement of angle G:
90° + 30° + g
180° – 90° – 30°
Angle G measures 60°.
C: Angle C and angle G are supplementary angles. The sum of supplementary angles is 180°. If c and g are the measurements of angles C and G, respectively, then c + g = 180°.
The value of g is 60°. Substitute 60° in the equation to get an equation in terms of c:
c + 60° = 180°.
D:Solve the equation from Part C to find the measurement of angle C:
c + 60°
= 180°
c
= 180° – 60°
c
= 120°.
Angle C measures 120°.
the exact answer from edmentum
Step-by-step explanation:
Arturo's family hires 3 painters. Each painter charges $50 per hour. Arturo's family represents the charge for x hours of painting in different ways. Check all that apply to this situation
A. 150x
B. 50x+50x+50x
C. 50x
D. 150
please don’t guess random answers, thank you. 20 points for answering!
Answers
Answer:
D
Step-by-step explanation:
So if Arturo's family hires 3 painters for $50 an hour each, how much do they spend?
X= Charge for number of number of hours
Now let's say that each of the painters worked only one hour each.
That would be take a long time to add up so you multiply.
$50 x 3
In other words it's $50 + $50 + $50.
$50 x 3 = $150
Now X stands for the amount of money paid to each artist. In this case, X= $50. So we already figured out X. X is $50. It is a mistake to add the X at the end of the answer because X is already there in a numerical form. So the answer is D, $150.
=================================================
Explanation:
One painter charges $50 an hour. If they work for x hours, then they charge a total of 50x dollars.
For instance, let's say the painter works for x = 7 hours. This means s/he charges 50*x = 50*7 = 350 dollars overall.
That's for one painter. If we involve 3 painters, then the total bill comes to 50x+50x+50x = 150x dollars
We could also say 3*50x = 150x, since 3*(cost of one painter) = total cost for three painters.
This is why choices A and B are the two answers.
Choice C would be the answer if you only hired one painter. But instead, you hired three of them, so we can rule out choice C.
Choice D only works if x = 1 is plugged into 150x to get 150*x = 150*1 = 150. However, you don't want to limit yourself to this x value only. It's better to stick with 150x instead to be more general. That way you can find the cost for say x = 2 hours which is 150*x = 150*2 = 300 dollars. I'll let you try other x values.
The length of segment XY is 9 cm. Which statements regarding triangle XYZ are correct? Select two options.
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The statements that are true regarding triangle XYZ are XZ = 9√2 and YZ = 9
Which statements regarding triangle XYZ are correct?from the question, we have the following parameters that can be used in our computation:
XY = 9 cm
Also, we have the right triangle
The acute angle in the triangle is 45 degrees
This means that
XY = YZ = 9
It also means that
XZ = XY√2
So, we have
XZ = 9√2
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If a and b are whole numbers such that a x b = 2027, find the value of a + b. Explain your answer.
Answers
Answer:
2028
Step-by-step explanation:
2027 is a prime number, so a = 2027 and b = 1, then a + b = 2028
what are three reasons why it is not possible to define a simple analytical scheme that can be applied to all types of evidence?
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The complexity, reliability, and context of the evidence collected are some of the reasons why it is not possible to define a simple analytical scheme that can be applied to all types of evidence.
There are several reasons why it is not possible to define a simple analytical scheme that can be applied to all types of evidence.
Firstly, different types of evidence require different analytical techniques, as they have varying degrees of complexity. For example, analyzing DNA evidence requires a different set of analytical tools compared to analyzing physical evidence like fingerprints or footprints.
Secondly, the reliability of the evidence also plays a significant role in the analytical scheme. Some types of evidence may be more subjective than others, and the interpretation of the results may be open to bias or misinterpretation. In such cases, a simple analytical scheme may not provide accurate or reliable results.
Finally, the context in which the evidence is collected also plays a crucial role in determining the analytical scheme. The location, timing, and circumstances of the evidence collection may affect the reliability and accuracy of the results. Therefore, a simple analytical scheme may not be able to accommodate all the variables and nuances of the evidence collected in different contexts.
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please help me!!!!!!!!
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Answer:
Step-by-step explanation:
Option a,c,e,f,i,j are quadratic equations. (Because its degree is 2)
Option b,d,g are linear equations. (Because its degree is 1)
Just option h is not quadratics nor linear.
If you need to ask any questions, please let me know.What is the value of e?
Answers
e equals 129
The answer is 129
The second and third terms of a G.P is 6 times the fourth term. Find the possible values of the common ratio.
Answers
Answer:
-1/3 or 1/2.
Step-by-step explanation:
Second term = ar, the third = ar^2 and the fourth = ar^3.
So we have the equation:
ar + ar^2 = 6ar^3
r + r^2 = 6r^3
6r^3 - r^2 - r = 0
r(6r^2 - r - 1) = 0
(3r + 1 )(2r -1) = 0
r = -1/3, 1/2.
Need help please thanks!
Answers
Answer:
Step-by-step explanation:
<B = 360 - <A
<B = 360 - 170
<B = 190
There are two angles present, depending on which way you look at it. One is larger than 180 (the one we found) and the other is slightly less than 180 (the one you gave us).
Leslie joins a fitness club that has an initial fee of $20 plus a monthly fee of $15,
write it as a function of x below.
f(x)=
Answers
Answer:
20 + 15x
Step-by-step explanation:
The initial fee is $20, and the monthly fee is $15. x is the amount of months, so f(x) = 20 + 15x
what is the next term for this sequence: 5,7,3,9,1,11,?
Answers
Answer:
-1
Step-by-step explanation:
each time it moves by the next even number. (Difference between 5 and 7 is 2, difference between 7 and 3 is 4, difference between 3 and 9 is 6, etc.)
PLEASE help me with this!
Answers
The easiest way is to find a point within the shaded region and test out the equation.
Work out the surface area of a circle with radius 7.5cm.
Take pi to be 3.142
Answers
Answer:
C = 47.12388 cm
Step-by-step explanation:
The circumference of a circle is given by
C = 2 * pi * r where r is the radius and pi = 3.142
C = 2 * 3.142 * 7.5
C = 47.12388 cm
Answer:
The circumference of circle is 47.13cm.
Step-by-step explanation:
Given :-
A circle with radius 7.5cm. And value of pie is 3.142.We have to find: -
The circumference of a circle.Formula Used: -
Circumference of circle = 2πrSolution:-
Circumference of circle = 2πrSubstitute the value of pie and radius(r).
Circumference of circle= 2 × 3.142 × 7.5cmMultiply.
Circumference of circle = 47.13cm.Therefore, the circumference of circle is 47.13cm.
Tienes 12 personas Todas pesan exactamente lo mismo Menos 1 persona que pesa un poco más o un poco menos Dispones de una balanza y puedes pesar 3 veces Quien es el que pesa distinto
Answers
Answer:
El que pesa distinto es aquel que causa un desnivel en la balanza.
Step-by-step explanation:
Sabemos que una balanza tiene dos lados en los cuales podemos poner peso, si la balanza está equilibrada, ambos lados están a la misma altura, de lo contrario, habrá un desnivel entre ambos lados.
Puesto que solo podemos emplear la balanza 3 veces, debemos crear tres grupos de cuatro personas, que dentro de cada una cada mitad, conformada por dos personas, es colocada en un lado de la balanza. Si la balanza está equilibrada, entonces todo ese grupo está integrado por personas del mismo peso, pero si esta desequilibrada, una persona de alguno de los dos subgrupos.
En ese caso, se procede a sacar a dos personas, una por cada lado de la balanza, si el desbalance desaparece, entonces alguna de las dos personas que salió tiene un peso distinto, pero si el desbalance persiste, entonces es causante del desbalance se encuentra en aún en la balanza.
En conclusión, el que pesa distinto es aquel que causa un desnivel en la balanza.