Answer: 7
Step-by-step explanation:
[tex]g(3)=5 \implies f(g(3))=f(5)=2(5)-3=7[/tex]
Find an equation of the plane tangent to the following surface at the given point. 7xy +yz +4xz - 48 = 0; (2,2,2) The equation of the tangent plane at (2,2,2) is ... = 0.Find an equation of the plane tangent to the following surface at the given point. yze^xz + 7 = 0; (0, - 7,1) An equation of the tangent plane at (0, - 7,1) is ... = 0. Find an equation of the plane tangent to the following surface at the given point. z = 4 - 4x^2 - 2y^2; (2,3,-30) z = ...?Find an equation for the plane that is tangent to the surfacez = In (x^2 + y^3) at the point P(0,1,0). The equation of the plane is ... = 0
Therefore , the solution of the given problem of equation comes out to be x−3y−4z=0.
The equation is what?When the equals symbol (=) is used to signify equality, a mathematical equation appears to be a formula that connects two statements. In algebra, a factual assertion called an equation shows that several mathematical variables are equal. An equal sign separates the amounts doc d + 6 and 12 in the formula obd + 6 = 12, for instance. The relationship between the syllables to each side of each letter can be expression mathematically. Frequently, the symbol and the message are identical.
Here,
First, we rewrite the surface equation as
f(x, y, z) = x² - y²+2z²
y²+22=0
Thus, our role is as follows:
f(x, y, z) = x² - y²+2z²
We employ the Del, or gradients operator, to determine the normal at any given location in vector space:
Vf(x, Y, Z) = x - y + z
When partially differentiating, keep in mind that we only differentiate with respect to the variable in issue and regard the other factors as constants.
Consequently, (x)(2)+(y)(6)+(z)(2)=(1)(2)+(3)(6)+(2) (-8)
2x−6y−8z=2−18+16
2x−6y−8z=0
x−3y−4z=0
Therefore , the solution of the given problem of equation comes out to be x−3y−4z=0.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ4
Round 50276 to the nearest hundred
Answer:
50276 rounded to the nearest hundred is 50300.
Rounding to the nearest hundred means finding the number that is closest to the original number, but ends in two zeroes. In this case 50300 is the nearest number ending in two zeroes to 50276.
Answer:50300
Step-by-step explanation:
In 50276, the number 2 is in the hundreds place. If the number in the tens place if equal or bigger to 0 round up to get 50300.
John was 5 years old when his pet dog, Spot, was born.
Use your equation to calculate how old John will be when Spot has his 4th birthday. Write only the final answer the number.
Step-by-step explanation:
S = age of Spot
J(S) = the age of John, when Spot is S years old.
J(S) = S + 5
J(0) when Spot was born = 0 + 5 = 5
J(4) when Spot has 4th birthday = 4 + 5 = 9
John will be 9 years old.
A piece of a cow’s leg bone with a volume of 10 cm3 has a mass of 18 g. What is the density of the bone please answer
Part B: Starting from the origin, explain how to plot the following three points accurately: (2, −2) (−2, 1.5) (−1, fraction 2 over 4) HELP PLEASEEEE
1. (2,-2). From the origin, go 2 units to the right and two units down
2) (-2,1.5) From the origin, go 2 units to the left and 1.5 units up
3) (-1,[tex]\frac{2}{4}[/tex]) From the origin, go 1 unit to the left and half a unit up
Compare the shapes and angle measures of ABC and DEF.
Given triangles, ΔDEF and ΔABC are Similar triangles.
Similar Triangles:A set of triangles that are the same in shape but different in size is known as the Similar Triangles. In other words, triangles that resemble one another but may not be exactly the same size are said to be comparable triangles. Congruent triangles and similar triangles generally differ from one another. When two triangles are similar triangles then the corresponding angles are equal.
Here we have
ΔDEF and ΔABC
From the given figures
=> ∠D = ∠A
=> ∠E = ∠B
=> ∠F = ∠C
Therefore,
Given triangles, ΔDEF and ΔABC are Similar triangles.
Learn more about Similar triangles at
https://brainly.com/question/25882965
#SPJ1
Sheleah and her family are planning a trip from Los Angeles, California to Melbourne, Australla. Whille booking her
family's plane tickets, she notices on the itinerary that the airline is offering a sixteen hour straight flight from Los
Angeles to Melbourne on a Boeing 747-8 Intercontinental Jet. In an effort to learn more about the capabilities of the Jet,
Sheleah does a little research and stumbles upon the following graph and facts about the Jet's fuel consumption.
Boeing 747-8 Intercontinental Jet
Jet Fuel Available (gallons)
70,000
60,000
50,000
40,000
30,000
20,000
10,000
63,500
2
55,562.5
3
4
47,625
39,687.5
31,750
23,812.5
9
7
8
10
Flight Time (hours)
11
12
15,875
13
14
7,937.5
15
17
The Boeing 747-8 Intercontinental Jet can carry approximately 63,500 gallons of jet fuel, making it possible for the Jet to
travel 14,430 kilometers before needing to refuel.
Create a linear model that represents the amount of fuel on the plane, In gallons, as a function of the flight time, In hours.
Show all of your work.
PLEASE HELP I NEED TO FINISH BY TONIGHT
The linear model that represents the amount of fuel on the plane is F(h) = 63,500 - 7937.50h
What is the linear function ?A linear function is a function that has a single variable raised to the power of 1. A linear function increases or decreases by a constant value . As the flight time increases , the amount of fuel declines . Thus, the linear function would be a decreasing function .
The form of the linear function is:
Total fuel left = capacity of the plane - (fuel consumed peer hour x number of hours )
Total fuel left = 63,500 - [(63500 - 55562.5) x h]
F(h) = 63,500 - 7937.50h
To learn more about linear functions, please check: https://brainly.com/question/26434260
#SPJ1
here are two plants (A and B) in an industry. To reduce pollution, the government has imposed environmental standards forcing each plant to cut emissions by 60%. At the emissions standard, the marginal social benefit of pollution for Plant A is $500 and the marginal social benefit of pollution for Plant B is $125. The same level of pollution can be achieved at a lower cost by
To achieve the same level of pollution at a lower cost, the government could adjust the environmental standards for each plant based on their respective marginal social benefits of pollution.
The government's environmental standards require Plant A and Plant B to reduce their emissions by 60%. The marginal social benefit of pollution for Plant A is $500 and the marginal social benefit of pollution for Plant B is $125. This means that the benefit of reducing one unit of pollution for Plant A is $500, while for Plant B is $125.
This information suggests that Plant A has a higher marginal social benefit of pollution than Plant B. Since the government's standards require both plants to reduce emissions by the same percentage, Plant A will have to reduce a greater amount of pollution than Plant B to reach the same level of emissions. This means that the cost of reducing pollution for Plant A will be higher than the cost of reducing pollution for Plant B.
To achieve the same level of pollution at a lower cost, the government could adjust the environmental standards for each plant based on their respective marginal social benefits of pollution. For example, if Plant A has a marginal social benefit of $500 and Plant B has a marginal social benefit of $125, the government could require Plant A to reduce its emissions by 50% and Plant B to reduce its emissions by 70%. This would achieve the same level of pollution while minimizing the cost of reducing pollution for both plants.
Thus, To achieve the same level of pollution at a lower cost, the government could adjust the environmental standards for each plant based on their respective marginal social benefits of pollution.
To learn more about cost-minimizing,
Visit; brainly.com/question/15060322
#SPJ4
Let's Scream for Ice Cream serves 333 scoops of ice cream in its signature cone. Each scoop is a sphere with a radius of 444 centimeters. To the nearest cubic centimeter, what is the total volume of ice cream served per cone
Volume of the sphere to the nearest cubic cm will be 803.84 cm^3
A sphere has a spherical, symmetrical form. It is a three-dimensional solid with equal distances between each surface point and the center. On the basis of its radius, it has a surface area and a volume. There are no faces, corners, or edges on it.
The collection of all points in three-dimensional Euclidean space that are separated by a certain amount of space, or "radius," is known as a sphere (the "center"). The diameter is equal to twice the radius, and antipodes are pairs of locations on the sphere that are on opposing sides of a diameter.
Volume of sphere[tex]=\frac{4}{3} \pi r^3[/tex]
As we have the value of radius = r=4 cm
We have the value of total scoops = 3 mm
So, by putting the value in the above expression of the volume of the sphere, we will get it as:
[tex]V =\frac{4}{3} \times 3.14(4)^3 \times 3 \\=3.14 \times 256 \\=803.84 \mathrm{~cm}^3[/tex]
For more questions on Volume of sphere
https://brainly.com/question/1832322
#SPJ4
The correct question should be:
Let's Scream for Ice Cream serves 3 scoops of ice cream in its signature cone. Each scoop is a sphere with a radius of 4 centimeters. To the nearest cubic centimeter, what is the total volume of ice cream served per cone?
The equation, 687.5 = 550(1 0.05t), represents the amount of money earned on a simple interest savings account. what does the value 550 represent?
The value 550 represents the initial deposit into the savings account.The equation 687.5 = 550(1 + 0.05t) is an equation in the form of A = P(1 + rt), which represents simple interest.
The equation 687.5 = 550(1 + 0.05t) is an equation in the form of A = P(1 + rt), which represents simple interest. The equation states that the amount A (687.5) is equal to the product of the initial deposit P (550) and the sum of one and the interest rate (0.05) multiplied by the time t (t is unknown). Thus, the value of 550 represents the initial deposit into the savings account.
The value 550 represents the initial deposit into the savings account.
The equation 687.5 = 550(1 + 0.05t) is an equation in the form of A = P(1 + rt), which represents simple interest.
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
What’s the missing value on the table? Will gift brainliest PLS.
Answer:
B) 23
Step-by-step explanation:
We need to find the pattern of the table. As seen on the other parts of the table, the pattern is 2x + 3. Here, x is the input. So, we substitute 10 for x, giving us:
2 * 10 + 3 = 20 + 3 = 23
So, the missing value in the table is B) 23.
Hope this helped!
Answer:
B. 23
Step-by-step explanation:
The length of the larger tabletop is 12 feet. What is its width, x?
The width of the tabletop is t feet when its length is 12 feet.
What is length and width?In contrast to width, which is used to describe how wide an object is, length simply states how long something is.
The term "width" is also used to refer to "breadth." It is the distance measured across a specific shape or object, such as a rectangle, whose lengths form right angles with the sides.
In contrast to the measurement of the area of the rectangle, which is a product of two units, the length and width. Length and width are two fundamental one-dimensional units. Today, a variety of length units are in use. The metre in SI units of measurement is the most fundamental of all.
Given that:
The length of a larger tabletop is 2 more than 2 times its width
l = 2(w) + 2
The length is 12
12 = 2(w) + 2
12 - 2 = 2w
10 = 2w
w = 10/2
w = 5
Thus, the width of the tabletop is t feet when its length is 12 feet.
Learn more about length and width
https://brainly.com/question/17156323
#SPJ1
Full question:
The width of a larger tabletop is 2 more than 2 times its length. The length of the larger tabletop is 12 feet. What is its width, x?
The points (1, r) and (5, 1) lie on a line with slope 2. Find the missing coordinate r.
Answer:
r=-7
Step-by-step explanation:
Let (x1,y1) be (1,r)and (x2,y2) be (5,1)
Slope m=2
[tex]slope = \frac{rise}{run} = \frac{y2 - y1}{ x2 - x1 } \\ = \frac{1 - r}{5 - 1} = 2 \\ 1 - r = 8 \\ r = - 7[/tex]
Find m∠S in rhombus RSTU
Answer:
In a rhombus, opposite angles are equal, therefore:
m∠S = m∠U = a + 62 degrees
And
m∠R = 2a - 80 degrees
The opposite angles of a rhombus are supplementary, meaning they add up to 180 degrees. So,
m∠S + m∠R = 180 degrees
Therefore,
a + 62 + 2a - 80 = 180
Solving for a, we get:
a = 59
So,
m∠S = a + 62 = 59 + 62 = 121 degrees
if you buy a concert ticket in advance the cost is $120. if you wait until the day of the concert, they cost $150. what is the percent change in the price,
Answer:
Step-by-step explanation:
Add 25% of 120 to 120
and you get 150 so boom there it is
Answer : 25% difference
answering which of the following questions will require divergent thinking? group of answer choices how many months constitute a year? what is the capital of nevada state? how many quarts make up a gallon? what are the various uses of a coffee mug?
This question will require divergent thinking.
The other questions are convergent thinking questions because they require a single, correct answer. However, the question "What are the various uses of a coffee mug?" requires divergent thinking because there is no single, correct answer. Instead, this question requires the respondent to think creatively and come up with a variety of possible uses for a coffee mug.
The question “What are the various uses of a coffee mug?” requires divergent thinking as it requires creative thinking and the generation of a variety of possible uses for a coffee mug.
learn more about divergent here
https://brainly.com/question/29475684
#SPJ4
“What if you have negative exponents in the denominator? How do you change it into positive exponents?”
The negative exponents in the denominator change it into positive exponents are 1/(2⁻³) = 8, 1/(2x⁻³) = (1/2)x³ and 4/(2(3⁻³)) = (4/2)×3³ = 54
How do you change negative exponents in the denominator into positive exponents?
If you have a fraction with a negative exponent in the denominator, you can change it into a positive exponent by reversing the fraction and taking the reciprocal.
For example, if you have the fraction 1/(x⁻²) you can change it to x² by flipping the fraction and taking reciprocal: 1/(x⁻²) = 1/(1/x²) = x²
Note that when you have a negative exponent in the denominator, it means that the variable is in the denominator and the reciprocal can be taken to move the variable to the numerator, as shown above.
Thus, we can solve the given questions as follow:
1/(2⁻³) = 2³ = 8
1/(2x⁻³) = (1/2)x³
4/(2(3⁻³)) = (4/2)×3³ = (2)×3³ = 2 × 27 = 54
Learn more about negative exponents on:
brainly.com/question/10133763
#SPJ1
what is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curce y
The given curve is a second order, so it is a parabola. The area of the largest rectangle is 32 square units.
What is a curve?
A curve is a mathematical object that is similar to a line but does not have to be straight. A curve can be thought of intuitively as the trace left by a moving point.
Given curve is y = 12 - x².
The vertex of the parabola is on the y-axis. Thus y-axis is a symmetric line of the parabola.
Thus the x-coordinate of the vertices that are lying on the x-axis is the same but the opposite sign.
Thus the y-coordinate of the vertices that are lying on the x-axis is the same.
Thus the x-coordinate of the vertices that are lying on the curve is the same but the opposite sign.
Thus the y-coordinate of the vertices that are lying on the curve is the same.
The y - coordinate of the vertices that are lying on the curve is in form 12 - x².
Assume that the coordinate of the rectangle are A(a,0), B(-a,0), C(-a, 12 - a²), and D(a,12-a²).
The length of the rectangle is 2a.
The width of the rectangle is 12-a².
The area of the rectangle is A = 2a(12-a²).
A = 24a - 2a³
Differentiate with respect to a:
dA/da = 24 -6a² ....(i)
Equate dA/da with zero to find the critical point:
24 -6a² =0
6a² =24
a² = 4
a = ±2
Putting a=2 in A = 24a - 2a³:
A = 24×2 - 2×2³
A = 32
To learn more about the area of the largest rectangle, click on the below link:
https://brainly.com/question/7172514
#SPJ4
The given curve is a second order, so it is a parabola. The area of the largest rectangle is 32 square units.
What is a curve?A curve is a mathematical object that is similar to a line but does not have to be straight. A curve can be thought of intuitively as the trace left by a moving point.
Given curve is y = 12 - x²
The vertex of the parabola is on the y-axis. Thus y-axis is a symmetric line of the parabola.
Thus the x-coordinate of the vertices that are lying on the x-axis is the same but the opposite sign.
Thus the y-coordinate of the vertices that are lying on the x-axis is the same.
Thus the x-coordinate of the vertices that are lying on the curve is the same but the opposite sign.
Thus the y-coordinate of the vertices that are lying on the curve is the same.
The y - coordinate of the vertices that are lying on the curve is in form 12 - x².
Assume that the coordinate of the rectangle are A(a,0), B(-a,0), C(-a, 12 - a²), and D(a,12-a²).
The length of the rectangle is 2a.
The width of the rectangle is 12-a².
The area of the rectangle is A = 2a(12-a²).
A = 24a - 2a³
Differentiate with respect to a:
dA/da = 24 -6a² ....(i)
Equate dA/da with zero to find the critical point:
24 -6a² =0
6a² =24
a² = 4
a = ±2
Putting a=2 in A = 24a - 2a³:
A = 24×2 - 2×2³
A = 32
To learn more about the area of the largest rectangle visit:
brainly.com/question/7172514
#SPJ4
Complete question is: find the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y=12−x
2
WZ bisects RS at T. If RT = 15x + 5y, RS = 20x - 5y, WT = 40 and
ST=21, find the values of a and y.
The values of x and y are 1.8 units and 1.2 units respectively.
What is a perpendicular bisector?A perpendicular bisector is a line that bisects a line segment in two equal parts and makes an angle of 90° at the point of intersection. In other words, we can say that a perpendicular bisector divides a line segment at its midpoint making an angle of 90°.
Given that, RT = 15x + 5y, RS = 20x - 5y, WT = 40 and ST=21.
Here, RS=RT+ST
20x-5y=15x+5y+21
5x-10y=21 -------(I)
RT=ST
15x+5y=21 -------(II)
Multiply equation (II) by 2, we get
30x+10y=42 -------(III)
Add equation (I) and (III), we get
5x-10y+30x+10y=21+42
35x=63
x=63/35
x=9/5
x=1.8 units
Substitute x=1.8 in equation (I), we get
5(1.8)-10y=21
y=1.2 units
Therefore, the values of x and y are 1.8 units and 1.2 units respectively.
Learn more about the perpendicular bisector here:
https://brainly.com/question/24753075.
#SPJ1
how to graph 2x + y > -1
Answer:
Step-by-step explanation:
helppppppppp im
not good at geo
Answer:
Equal
Step-by-step explanation:
Since all angles are the same
So the border lines should also be equal
5 friends walked into a restaurant. they all had a different birthday. there was a round table with 5 seats around it. what is the probability that they sit down in correct age order either clockwise or counter clockwise?
1/12 OR 0.0083% PROBABILITY is that sit down in correct age order either clockwise.
What is probability ?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin.
The coin is fair, thus the outcomes "heads" and "tails" are equally likely; the likelihood of "heads" is equal to the likelihood of "tails"; and because there are no other conceivable outcomes, the likelihood of either "heads" or "tails" is 1/2 (which is also an acceptable spelling).
According to our question-
1/5 * 1/4 * 1/3 * 1/2 * 1/1 = 1/120
0.0083
learn more about probability click here:
brainly.com/question/13604758
#SPJ4
Line segment XY is dilated to create line segment X'Y' using point T as the center of dilation. What is YT? using point T as the center of dilation.3units6units12units15units
The value of TY using point T as the center of dilation = 12.
What is a line segment?A line segment in geometry is a section of a straight line that is enclosed by two clearly defined endpoints and contains all of the points on the line that lies inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.
Here, we have
Given: Line segment XY is dilated to create line segment X'Y' using point T as the center of dilation.
X'Y' and XY are parallels, which means X'Y' = means XY, there is a similarity between the two triangles, we can find YT by using the theorem of Thales,
TY' / TY =TX' / TX =X'Y' /XY,
TY' / TY = TX' / TX = 9/ TY =6/ 2+6=6/8
9/ TY = 6/8
TY= 12
Hence, the value of TY = 12.
To learn more about the line segment visit:
brainly.com/question/2437195
#SPJ1
Suppose the slope of a line is positive. Describe what happens to the graph of the line as you move from left to right.
As you move the graph of the line from left to right, the output value of the function increases.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change of the linear function.b is the intercept, representing the initial value of the linear function.The slope determines if the function is increasing or decreasing over it's domain, as follows:
Positive slope: increasing function.Negative slope: decreasing function.A positive slope means that the function increases when it moves from left to right, that is, when x increases.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
MARKING BRAINLIEST! please help asap
Answer: I think its -5
Step-by-step explanation:
How many permutations of three items can be selected from a group of six? (_____)
Use the letters A, B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F. (Enter your answers as a comma-separated list. Enter three unspaced capital letters for each permutation.)
(______)
A collection of six objects can be chosen from one of 120 possibilities. These six configurations comprise BDF, BFD, DBF, DFB, FBD, and FDB.
What is a permutation, exactly?A permutation is what? The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a mutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.
Out of the six things A, B, C, D, E, and F, rotations of items B, D, and F (a total of three items) must be listed.
Simply said, we must find every configuration for these three elements.
The three objects can be placed in three ways, which equals (3x2x1) ways, or six.
These six configurations are BDF, BFD, DBF, DFB, FBD, and FDB.
To know more about Permutations visit:
https://brainly.com/question/1216161
#SPJ4
What is a system of three equations that has infinitely many solutions?
The system of three equations x + y + z = 0, x + 2y + 3z = 0, and 4x + 5y + 6z = 0 has infinitely many solutions because the equations are dependent.
1. x + y + z = 0
2. x + 2y + 3z = 0
3. 4x + 5y + 6z = 0
These three equations form a system of equations that has infinitely many solutions because the coefficients of the variables satisfy the conditions for the equations to be dependent. This means that the equations are not independent, and therefore the system of three equations has infinitely many solutions.
The system of three equations x + y + z = 0, x + 2y + 3z = 0, and 4x + 5y + 6z = 0 has infinitely many solutions because the equations are dependent.
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
when isa travels to the usa for a holiday he leaves the uk at 1.00 pm local time and lands at 5.00 pm local time. on the return journey he leaves at 8.00 pm local time and lands at 10.00 am local time the next day. find the length of the flight in hours and the time difference between the uk and the part of the usa that isa visited
Isa took 4 hour when isa go from UK to USA and took 14 hour when she returns and time difference will be 10 hours
What is a definition distance?
the extent or amount of space between two things, points, lines, etc. the state or fact of being apart in space, as of one thing from another; remoteness
when isa travels to the usa for a holiday he leaves the uk at 1.00 pm local time and lands at 5.00 pm local time.
so isa took 4 hour
on the return journey he leaves at 8.00 pm local time and lands at 10.00 am local time the next day
isa tool 14 hour
find the length of the flight in hours and the time difference between the uk and the part of the usa that isa visited
length of flight is 18 hour
time difference will be 14-4 = 10 hour
learn more about time here
https://brainly.com/question/23973491
#SPJ4
eduardo had 4.5 cups of flour in a jar. he opened a bag of flour, poured in enough to fill the 12-cup jar completely, and still had some left over in the bag. let x represent how much flour was in the bag to start. which inequality describes the problem?
The amount of flour in the bag (x) plus the amount of flour in the jar (4.5 cups) must be greater than or equal to 12 cups.
x + 4.5 ≥ 12
Solve for x:
x ≥ 7.5
The problem states that Eduardo had 4.5 cups of flour in a jar, and then opened a bag of flour and poured it in until the jar was full. The question is how much flour was in the bag to start? To solve this problem, we can use an inequality. Let x represent the amount of flour in the bag to start. The equation we can use is x + 4.5 ≥ 12, which states that the amount of flour in the bag (x) plus the amount of flour in the jar (4.5 cups) must be greater than or equal to 12 cups. To solve for x, we can subtract 4.5 from both sides of the equation, which yields x ≥ 7.5. This means that the bag of flour must have contained at least 7.5 cups of flour for Eduardo to have enough to fill the jar.
Learn more about amount here
https://brainly.com/question/28970975
#SPJ4
Answer: 7.5 4.5>12
Step-by-step explanation:
I already had this one and got it right
A club is holding a raffle. ten thousand tickets have been sold for $2 each. there will be a 1st prize of $3000, 3 second prizes of $1000 each, 5 third prizes of $500 each, and 20 consolation prizes of $100 each. find the expected winnings of a single ticket
A single ticket's estimated earnings are around -$0.9442, which indicates that a consumer may expect to lose approximately $0.9442 for each ticket purchased.
To find the expected winnings of a single ticket, we need to calculate the weighted average of the winnings based on the probabilities of winning each prize.
The probabilities of winning each prize are as follows:
1st prize: 1 winner out of 10,000 tickets sold (probability = 1/10,000 = 0.0001)
2nd prize: 3 winners out of 10,000 tickets sold (probability = 3/10,000 = 0.0003)
3rd prize: 5 winners out of 10,000 tickets sold (probability = 5/10,000 = 0.0005)
Consolation prize: 20 winners out of 10,000 tickets sold (probability = 20/10,000 = 0.0020)
No prize: (1 - (probability of winning any prize)) = 1 - (0.0001 + 0.0003 + 0.0005 + 0.0020) = 0.9971
Now, let's calculate the expected winnings:
Expected winnings = (Probability of 1st prize × $3000) + (Probability of 2nd prize × $1000) + (Probability of 3rd prize × $500) + (Probability of consolation prize × $100) + (Probability of no prize × -$2)
Expected winnings = (0.0001 × $3000) + (0.0003 × $1000) + (0.0005 × $500) + (0.0020 × $100) + (0.9971 × -$2)
Expected winnings ≈ -$-0.9442
To learn more about the expected value;
https://brainly.com/question/28197299
#SPJ12
The complete question:
A club is holding a raffle. Ten thousand tickets have been sold for $2 each. There will be a 1st prize of $3000, 3 second prizes of $1000 each, 5 third prizes of $500 each and 20 consolation prizes of $100 each. Find the expected winnings of a single ticket.
x -2 98 498 998 2998
p .9971 .0020 .0005 .0003 .0001
