Ayo runs a fairground game.In each turn, a player rolls a fair dice numbered 1 - 6 and spins a fair spinner numbered 1 - 12.It costs a player £1.40 for a turn.A player can win £6 or £3 as in the diagrams:If 216 people are to play, how much profit can Ayo expect to make?
Answers
Using the definition of expected value, it is found that Ayo can be expected to make a profit of £55.8.
The expected value is given by the sum of each outcome multiplied by it's respective probability.
In this problem:
The player wins $6, that is, Ayo loses £6, if he rolls a 6 and spins a 1, hence the probability is \(\frac{1}{6} \times \frac{1}{12} = \frac{1}{72}\).The player wins $3, that is, Ayo loses £3, if he rolls a 3 on at least one of the spinner or the dice, hence, considering three cases(both and either the spinner of the dice), the probability is \(\frac{1}{6} \times \frac{1}{12} + \frac{1}{6} \times \frac{11}{12} + \frac{5}{6} \times \frac{1}{12} = \frac{1 + 11 + 5}{72} = \frac{17}{72}\)In the other cases, Ayo wins £1.40, with \(1 - \frac{18}{72} = \frac{54}{72}\) probability.Hence, his expected profit for a single game is:
\(E(X) = -6\frac{1}{72} - 3\frac{17}{72} + 1.4\frac{54}{72} = \frac{-6 - 3(17) + 54(1.4)}{72} = 0.2583\)
For 216 games, the expected value is:
\(E = 216(0.2583) = 55.8\)
Ayo can be expected to make a profit of £55.8.
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Related Questions
3n *power 2 +10n+7 how to factories and pls tell with solution
Answers
Answer:
(n + 1)(3n + 7)
Step-by-step explanation:
3n² + 10n + 7
Consider the factors of the product of the n² term and the constant term which sum to give the coefficient of the n- term.
product = 3 × 7 = 21 and sum = + 10
The factors are + 3 and + 7
Use these factors to split the n- term
3n² + 3n + 7n + 7 ( factor the first/second and third/fourth terms )
3n(n + 1) + 7(n + 1) ← factor out (n + 1) from each term
= (n + 1)(3n + 7) ← in factored form
Example: $2.21 + 8% tax = $2.3868, rounds to __________.
Answers
The equation in percentage given by, $2.21 + 8% tax = $2.3868 rounds to $2.4 to the nearest tenth.
Given an equation,
$2.21 + 8% tax = $2.3868
This is an equation which relates the cost including the percentage of tax.
When 2.21 is added to the tax amount, we get $2.3868.
2.21 + (0.08 × 2.21) = 2.3868
Here it is not mentioned up to what decimal we have to round the figure.
If 2.3868 is rounded to the nearest whole number, it becomes 2.
If 2.3868 is rounded to the tenth, it becomes 2.4.
If 2.3868 is rounded to the hundredth, it becomes 2.39.
Hence the rounded amount to the nearest tenth is $2.4.
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Molly's monthly income is $4,200 . She spends 30% of her income on living expenses, 7% on gas and car- related expenses , 7% on gas and the rest as spending money
How much money did molly have as spending money?
Answers
Answer:
$2,436
Step-by-step explanation:
I added the percentage together 30+7+7=42 and I multiplied 0.42 by $4,200 and then I got $1,764 which is the amount I spend on expenses each month. Last, I did 4,200-1,764 and got the answer
How many positives and negatives are in 10 + (-5)
Answers
Answer:
2
Step-by-step explanation:
Help me PLEASEEEE
find the the angles
Answers
consider data below 62 78 84 62 72 78 54 60 78 80, the mode is?
Answers
Answer:
The mode is 78, which appears the most times (3).
The mode of the given data 62, 78, 84, 62, 72, 78, 54, 60, 78, 80 is 78.
The mode is the data that occurs most frequently, in the data set listed below 62, 78, 84, 62, 72, 78, 54, 60, 78, 80. We can see that the number 78 appears three times, which is more than any other value in the set when we look at the data.
Note: If multiple values occur with the same highest frequency, but in this case, 78 is the only mode, the data set may have multiple modes.
Thus, the mode of 62, 78, 84, 62, 72, 78, 54, 60, 78, and 80 data set is 78.
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Which statement about triangle ABC is true?
Answers
Answer:
third statement. is right
Answer:
I'm think the answer is
A) since none of the sides are congruent, it is not a right triangle.
Ben and his n − 1 friends stand in a circle and play the following game: Ben throws a frisbee to one of the other people in the circle randomly, with each person being equally likely, and thereafter, the person holding the frisbee throws it to someone else in the circle, again uniformly at random. The game ends when someone throws the frisbee back to Ben.
(a) What is the expected number of times the frisbee is thrown through the course of the game?
(b) What is the expected number of people that never got the frisbee during the game?
Answers
(a) The expected number of times the frisbee is thrown through the course of the game is n-1. (b) The expected number of people that never got the frisbee during the game is 1.
(a) In this game, each time the frisbee is thrown, it moves to a different person in the circle, excluding Ben. Since there are n-1 people in the circle other than Ben, the frisbee is expected to be thrown n-1 times before it reaches Ben again. (b) Since the game ends when someone throws the frisbee back to Ben, there will always be one person who never gets the frisbee throughout the game. Therefore, the expected number of people that never got the frisbee during the game is 1.
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what is the domain of this function
A. (1,2,3,4,9,16)
B. (2,4,9,16)
C. (1,2)
D. (1,2,3,4)
Answers
Answer:
D
Step-by-step explanation:
multiple regression analysis is applied when analyzing the relationship between __________.
Answers
Multiple regression analysis is applied when analyzing the relationship between one dependent variable and two or more independent variables. The goal is to determine the extent to which the independent variables predict the dependent variable.
Multiple regression analysis is a statistical technique used to explore and quantify the relationship between a dependent variable and multiple independent variables. It allows researchers to examine how changes in one or more independent variables impact the dependent variable, while controlling for the effects of other variables. By estimating the coefficients for each independent variable, the analysis provides insights into the strength, direction, and significance of their relationships with the dependent variable. This method is commonly employed in various fields, such as economics, social sciences, and business, to understand complex relationships and make predictions based on the interplay of multiple factors.
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Why is [3, ∞) the range of the function.
Answers
The interval [3, ∞) represents the range of the function as it is the interval containing the output values, which are the values of y on the graph of the function.
How to obtain the domain and range of a function?The domain of a function is defined as the set containing all the values assumed by the independent variable x of the function, which are also all the input values assumed by the function.The range of a function is defined as the set containing all the values assumed by the dependent variable y of the function, which are also all the output values assumed by the function.For this problem, we have that the values of y on the graph of the function are of 3 or higher, hence the interval representing the range is given as follows:
[3, ∞)
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5: You should (......) before the beginning of each paragraph when you are reading.
answers:
1: history
2: terror
3:apology
4:Pause
Answers
Answer:
4:Pause
Step-by-step explanation:
Before starting the reading of each paragraph you should pause as it does not create misunderstanding between the people also each and every paragraph should be clear to everyone so the chances of doubt would be minimum
Therefore according to the given options the fourth option is correct
Hello!
The answer is pause.
All the other options are nouns, but it's clear that we need a verb.
So, the answer is pause.
Hope it helps! :)
Do ask me if you have any query.
~An excited gal
\(MagicalNature\)
Please help me, I will give brainliest if possible!
Pythagoras
1. if the radius of the smaller circle is 3, find its area
2. Find the area of the yellow ring
3. Find the area of the white ring
Answers
Answer:
A / Area = 28.36
Same for 2 and 3 Area = π \(r^{2}\)
Step-by-step explanation:
Radius:
The radius we know is:
r = 3
Area:
Area = π\(r^{2}\)
Also, Area = 3.14 × \(3^{2}\)
Area will equal, 28.36
In this formula we will be used to calculate the required areas of the circle:
Area = π\(r^{2}\)
Thus the answer is:
A / Area = 28.36
Same for 2 and 3 Area = π \(r^{2}\)
Which equation shows a proportional relationship between x and y?
A. y = 9
B. y = 3x + 1
C. y = −3x − 2
D. y = 4x
NO LINKS
Answers
B. y=3x+1
Step-by-step explanation:
#Hopeee Itttt Helppsssssss!
A proportion relationship is a direct relationship between two variables thus y = 4x will be the proportional relationship between x and y thus option (D) will be correct.
What are the ratio and proportion?The ratio is the division of the two numbers.
Proportion is the relation of a variable with another. It could be direct or inverse.
A proportional relationship is given as,
A ∝ B
Removing proportionality
A = kB
Here, k is the constant of proportionality.
As per the given in last option,
y = 4x
x = (1/4)y
Removing constant.
x ∝ y
Hence "A proportion relationship is a direct relationship between two variables thus y = 4x will be the proportional relationship between x and y".
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Find the slope!! Please helpp
Answers
Answer:
slope = 1/2
Step-by-step explanation:
the line is rising 1 box for every 2 boxes it goes over
Answer: Y=1/2x+3 (1/2 should be your slope)
Step-by-step explanation:
what word are you reminded of when you hear the word radian? discuss this with your team and make a conjecture about how this might relate to a way to measure angles. be prepared to share your ideas with the class.
Answers
Radians are a unit of measurement for angles used in mathematics and physics. They are defined as the ratio between the length of an arc of a circle and the radius of that circle.
One of the most important benefits of using radians to measure angles is that they simplify calculations involving angles, making them easier to work with.
Additionally, they allow for a more elegant and unified approach to mathematical and physical problems involving angles. So, in short, the word "radian" might be associated with concepts such as circles, arcs, and the measurement of angles in mathematics and physics.
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Professional ballet dancers in NYC train an average of 48 hours per week. A random sample of 35 dancers was selected and it was found that the average practice per week was 54 hours. Which of the following is a true statement about this scenario? If a different random sample of 35 dancers were selected, the average practice per week in that sample would have to be also 54 hours. Both 48 and 54 are parameters Both 48 and 54 are statistics 48 is a parameter and 54 is a statistic. The recorded sample average of 54 hours per week is clearly a mistake. It must be 48 hours just like the population mean.
Answers
The recorded sample average of 54 hours per week is clearly a mistake. It must be 48 hours just like the population mean.
In this scenario, the statement that the recorded sample average of 54 hours per week is a mistake and should be 48 hours is true. The given information states that professional ballet dancers in NYC train an average of 48 hours per week. However, when a random sample of 35 dancers was selected, it was found that the average practice per week in that sample was 54 hours.
Since the sample average of 54 hours deviates from the known population mean of 48 hours, it suggests that there might have been an error or an unusual occurrence in the data collection or recording process. It is highly unlikely for the average practice per week in a random sample to exceed the known population mean by such a significant margin.
Therefore, it can be concluded that the recorded sample average of 54 hours per week is an outlier or mistake, and it should align with the population mean of 48 hours.
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- Caramel apples cost $2. There is a 50¢ charge
for nuts or chips. Tori wants a caramel apple
with nuts. Chelsea wants both nuts and chips
on her apple. Max wants his caramel apple
plain. How much will the three apples cost?
Answers
So if 3x=21, how would i find the value of 22-4x?
Answers
Answer:
-6
Step-by-step explanation:
x= 21/3
x=7
using this value,
22-4x= 22-4*7
=22-28
=-6
The short-run aggregate supply curve is based on the assumption that firms and workers have established nominal wages, with the expectation that ______.
Answers
Answer:
The price level will stay constant.
Emily Casper earns a weekly salary of $785. How much will she make after:
a, two weeks?
b, four weeks?
c, one year?
Answers
Answer:
Two weeks: $1570
Four weeks: $3140
One year: 9420
Step-by-step explanation:
B 3140
C 9420
Find the slope of the line: y+5 = -3/4x
Answers
Answer:
y = -3/4x - 5
Slope: -3/4
y-intercept: -5
Assume that the situation can be expressed as a linear cost function. Find the cost function in this case.
marginal cost $20; 170 items cost $5500 to produce.
The linear cost function is C(x)=
Answers
The linear cost function is C(x) is (2100 + 20x).
What is Cost function?
The cost function calculates the absolute lowest cost of generating a specified level of output at some fixed factor prices. A firm's economic potential is described by the cost function.
As given,
Marginal cost $20; 170 items cost $5500 to produce.
Evaluate the Fixed cost:
Fixed cost = 5500 - 20 × 170
= 5500 - 3400
= 2100
Now,
cost function = fixed cost + x × (marginal cost)
Substitute values respectively,
cost function = 2100 + 20x.
Hence, the linear cost function is C(x) is (2100 + 20x).
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y - 12 = 89
y - 12 +____
=89 + 12
y=?
Answers
Answer:101
Step-by-step explanation:
Ella has $50,000 is a saving account. The savings collect interest at an 8% annual rate that compounds every year. How much money will be in Ellas account after 5 years?
Answers
Answer:
210000$
Step-by-step explanation:
1st we find the SI which will be P*R*T/100=50000*8*5/100
=32000
32000 will be added per year
32000*5=160000 for 5 years
160000+50000=210000$
What percent of the people are between 20 and 37 years old
Answers
Oliver flew home from vacation with a heavy bag. With the first airline he flew, Oliver had to pay $29 to check his bag, plus $12 for every pound that his bag was over the weight limit. The next flight was with another airline that had the same weight limit. Oliver had to pay $11 per pound that his bag was over the weight limit, in addition to the checked bag fee of $30. By coincidence, the fees ended up being the same with both airlines. How far over the weight limit was the bag? How large was each airline's fee?
The bag was ------ pounds over the weight limit, and each airline's fee was $ -----
Answers
Answer: 17x + 17 = 19x + 15
17 - 15 = 19x - 17x
2 = 2x
x = 1 kg over the limit
"How large was each airline's fee?"
17(1) + 17 = $34
19(1) + 15 = $34
Step-by-step explanation: thank you for letting me answers
two coins are tossed together What is the probability of obtaining
(1)exactly one tail
(2)at least one head
(3)no tails?
Answers
1) 2/4
2) 3/4
3) 1/4
Find the missing number?
Answers
Answer:
$4.60 and $18.40
Step-by-step explanation:
The total cost of one milk carton is $2.30. I got this by dividing $9.20 by 4. If you multiply $2.30 by 2, you get $4.60. If you multiply $2.30 by 8, you'll get $18.40.
John has a bag of different colored marbles. He has 6 red marbles, 3 blue marblos, 7 yellow marbles, and 5 green marbles. If John reaches into the bag and randomly pulls out a marble, what is the
probability that the marble will be blue? (If necessary, round to the nearest tenth )
Answers
Answer:
3/21, 14.29%, or 14.29
Step-by-step explanation:
John has 21 total marbles, which includes 3 blue ones.
(That's 3 over 21)
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