The expected winnings for this game is calculated by multiplying the value of each possible outcome by their probability, providing an overall expected value of $1.33. This indicates that over a long period of repeated games, the average winnings per game would be $1.33.
Explanation:In this question, we're dealing with calculating the expected value in a game of probability. The game involves rolling a dice with outcomes ranging from 1 to 6 and the associated payoffs for roll outcomes of 4, 5, and 6 are $1, $2, and $5 respectively.
We calculate the expected winnings (value) for a single round of the game by multiplying all possible outcomes by their respective probabilities, then summing these products. In this case, symbols represent the payout (in $) and P represents the probability of each outcome.
(6) $5*P(1/6) = $0.83 (5) $2*P(1/6) = $0.33 (4) $1*P(1/6) = $0.17 (1-3) $0*P(1/2) = $0.00Adding up these expected outcomes gives us our overall expected winnings: $0.83 + $0.33 + $0.17 + $0.00 = $1.33 per game
If you play this game repeatedly, over the long term, you'd expect to win around $1.33 on average each game. Note that the exact winnings in a single instance of the game could be $0, $1, $2, or $5, and this value simply provides an average expected outcome over time.
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Stephen has a dog that weighs 5 times as much as ian’s dog. the total weight of both dogs is 72 pounds. how much does stephen’s dog weigh?
The weight of Stephen's dog such that Stephen has a dog that weighs 5 times as much as Ian's dog will be 60 pounds.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Let's assume the weight of Stephen's dog is "s" while Ion's dog is "i".
As per the given,
Stephen has a dog that weighs 5 times as much as Ian's dog.
s = 5i
Total weight, s + i = 72
Substitute, i = 72 - s into s = 5i
s = 5(72 - s)
s = 360 - 5s
s + 5s = 360
6s = 360
s = 60 pounds.
Hence "The weight of Stephen's dog such that Stephen has a dog that weighs 5 times as much as Ian's dog will be 60 pounds".
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The ratio of the number of cats to the number of dogs in an animal shelter was 2:3. After 120 cats were adopted, the ratio of the number of cats to the number of dogs became 3:7. Find the total number of cats and dogs in the animal shelter in the end?
how much is 2/7 of 1 and 3/4
Answer:
0.5 or half of it (1/2)
how do you solve this?
The function f(x)=400(1.5)xf(x)=400(1.5)x models an insect population after x months. How does the average rate of change between Months 2 and 4 compare to the average rate of change between Months 0 and 2?
The average rate of change is 2.25 times as fast.
The average rate of change is 2 times as fast.
The average rate of change is 3.125 times as fast.
The average rate of change is 1.5 times as fast.
Answer:
The answer is 2.25 times as fast. I just did this one
Step-by-step explanation:
Which situations can be represented by a linear function?
Select each correct answer.
Every day, the number of bacteria in the dish is 3 times what it was the previous day.
Every year, Luisa puts $10 into her savings account.
A country's population increases by 0.8% each year.
The barrel leaks 0.5 L of water each day.
The barrel leaks 0.5 L of water each day.
Every year, Luisa puts $10 into her savings account.
Linear functions represent situations with a constant rate of change. Saving $10 every year and a barrel leaking 0.5 L of water each day are examples of linear relationships due to this constant change.
Situations that can be represented by a linear function are those where the rate of change remains constant. Let's analyze the given situations according to this condition:
Every year, Luisa puts $10 into her savings account. This describes a constant rate of change, with $10 being added each year, which can be represented by a linear function.The barrel leaks 0.5 L of water each day. Here, the change in water level is constant (0.5 L per day), also indicative of a linear relationship.These two scenarios fit the criteria for being linear because they involve a constant rate of change over time. On the other hand, scenarios like the exponential growth of bacteria or percentage-based population growth are not linear since the rate of change is not constant; these would be represented by exponential functions.
The length of a social media interaction is normally distributed with a mean of 3 minutes and a standard deviation of 0.4 minutes.
What is the probability that an interaction lasts longer than 4 minutes?
1)0.0045254
2)0.043351
3)0.0095254
4)0.006209
Answer: 4) 0.0062097
Step-by-step explanation:
Given : The length of a social media interaction is normally distributed with a mean of [tex]\mu=3[/tex] minutes and a standard deviation of [tex]\sigma=0[/tex] minutes.
Using the formula , [tex]z=\dfrac{x-\mu}{\sigma}[/tex], the z-value corresponding to x=4 will be :-
[tex]z=\dfrac{4-3}{0.4}=2.5[/tex]
Using the standard normal distribution table for z-value , the probability that an interaction lasts longer than 4 minutes will be :-
[tex]P(z>2.5)=1-P(z\leq2.5)=1-0.9937903=0.0062097[/tex]
Hence, the probability that an interaction lasts longer than 4 minutes = 0.0062097
Divide. Write each quotient in simplest form.
2/3 ÷ 2 = _____ Show step-by-step solution.
A line contains the points (−26, −37) and (−32, −61) .
What is the slope of the line in simplified form?
Answer:
the answer should be 4, you left the - off of the 61
Step-by-step explanation:
Which function has a removable discontinuity?
a. g(x)=(2x-1)/(x)
b. p(x)=(x+2)/(x²-x-2)
c. f(x)=(5x)/(x-x²)
d. h(x)=(x²-x+2)/(x+1) ...?
The function [tex]\( f(x) = \frac{5x}{x-x^2} \)[/tex] has a removable discontinuity at ( x = 0 ) after canceling the common factor [tex]\( x \).[/tex]
A removable discontinuity occurs at a point where a function is not defined due to a factor in the denominator that could be canceled out with a factor in the numerator.
Let's analyze each function to determine if any of them have a removable discontinuity.
[tex]a. \( g(x) = \frac{2x-1}{x} \)[/tex]
- The denominator ( x ) is zero at ( x = 0 ).
- The numerator ( 2x-1 ) is non-zero at ( x = 0 ).
- Since there is no common factor in the numerator and denominator that could cancel out, the discontinuity at ( x = 0 ) is not removable.
[tex]b. \( p(x) = \frac{x+2}{x^2-x-2} \)[/tex]
- The denominator [tex]\( x^2-x-2 \) factors as \( (x-2)(x+1) \).[/tex]
- The function becomes [tex]\( p(x) = \frac{x+2}{(x-2)(x+1)} \).[/tex]
- The denominator is zero at ( x = 2 ) and ( x = -1 ).
- The numerator ( x+2 ) is zero at ( x = -2 ).
- There is no common factor between the numerator and the denominator that could be canceled out. So, the discontinuities at [tex]\( x = 2 \) and \( x = -1 \)[/tex] are not removable.
[tex]c. \( f(x) = \frac{5x}{x-x^2} \)[/tex]
- The denominator [tex]\( x-x^2 \) factors as \( x(1-x) \).[/tex]
- The function becomes [tex]\( f(x) = \frac{5x}{x(1-x)} = \frac{5x}{x-x^2} \).[/tex]
- The denominator is zero at x = 0 and x = 1 .
- The numerator ( 5x ) is zero at ( x = 0 ).
- There is a common factor of ( x ) in the numerator and denominator which could be canceled out, making the discontinuity at ( x = 0 ) removable.
- After canceling the common factor ( x ), the function becomes [tex]\( \frac{5}{1-x} \),[/tex] which is defined at ( x = 0 ).
[tex]d. \( h(x) = \frac{x^2 - x + 2}{x + 1} \)[/tex]
- The denominator ( x + 1 ) is zero at ( x = -1 ).
- The numerator [tex]\( x^2 - x + 2 \) is not zero at \( x = -1 \).[/tex]
- There is no common factor in the numerator and denominator that could be canceled out, so the discontinuity at ( x = -1 ) is not removable.
Conclusion
The function [tex]\( f(x) = \frac{5x}{x-x^2} \)[/tex] has a removable discontinuity at ( x = 0 ), because the discontinuity can be removed by canceling the common factor ( x ) in the numerator and the denominator.
So, the correct answer is:
[tex]c. \( f(x) = \frac{5x}{x-x^2} \)[/tex]
Is 5 a prime composite or neither
Answer:
Prime
Step-by-step explanation:
Its factors are:1 and itself.
ALL prime numbers have the same 2 factors: 1 and itself.
There are total of 84 students in the robotics club and the science club. The science club has 12 more students than the robotics club. How many students are in the science club?
By setting up an equation and solving for the number of students in each club, we find there are 48 students in the science club.
To solve the problem, we can set up an equation based on the information given. Let the number of students in the robotics club be represented by x.
According to the problem, the science club has 12 more students than the robotics club, so the science club has x + 12 students. We also know that there are a total of 84 students in both clubs combined. Therefore, we can set up the following equation:
x + (x + 12) = 84
Combining like terms, we have:
2x + 12 = 84
Subtracting 12 from both sides gives us:
2x = 72
Dividing both sides by 2 gives us:
x = 36
So, there are 36 students in the robotics club. To find the number of students in the science club, we add 12 to the number of students in the robotics club:
36 + 12 = 48
Therefore, there are 48 students in the science club.
how are the variables related on the graph?
A. As speed decreases, height stays constant
B. As speed deceases , height increases
C. As speed increases , height decreases
D. As speed increases , height increases
Answer:
The answer to this question is
As speed increases the height Increases
Step-by-step explanation:
Because increases mean going up so when the speed is going up the height of the speed also increases so that's why when the speed increases also the height increases
I hope this works
YW!
The correct explanation of the graph will be;
''As speed increases, height is decreases.''
Option D is true.
What is an mathematical expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The graph is shown in figure for the relation of height and speed.
Since, The graph is shows when the speed of any object increase, then its height will also be increase.
Thus,
The correct explanation of the graph will be;
''As speed increases, height is decreases.''
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The drawing of a building, shown below, has a scale of 1 in to 30 ft. what is the actual height, in ft, of the building
Your medical bill is $2345. Your health insurance covers 70% after a $120 deductible. What amount of the bill will you pay?
Answer:
It is $787.50.
The function q(w)=3+5(w−1) represents the number of quarters in a bowl on week w.
What does the value 5 represent in this situation?
A. Five quarters are added to the bowl every week.
B. The value of the quarters in the bowl on Week 1 was $5.
C. Quarters were added to the bowl for 5 weeks.
D. There were 5 quarters in the bowl on Week 1.
The statement "Five quarters are added to the bowl every week" is a correct option (A) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The function q(w)=3+5(w−1) represents the number of quarters in a bowl on week w.
q(w) = 3 + 5(w−1)
q(w) = 5w - 5 + 3
q(w) = 5w - 2
y = mx + c
m = 5
Here 5 means five quarters are added to the bowl every week.
Thus, the statement "Five quarters are added to the bowl every week" is a correct option (A) is correct.
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If a line crosses the y-axis at (0, -3) and has a slope of 3, what is the equation of the line?
f a computer costs $600.00 and the sales tax rate is 7.5 percent, what is the total cost of the computer?
As per linear equation, the total cost of the computer is $645.00.
What is a linear equation?"A linear equation is an equation in which the highest power of the variable is always 1."
Given, the cost of computer is $600.00.
The sales tax rate is 7.5%.
Therefore, the total cost of the computer is
= $[tex][600.00 + \frac{(7.5)(600.00)}{100}][/tex]
= $[tex][600.00 + 45.00][/tex]
= $[tex]645.00[/tex]
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How many steps does it take to complete 0.1 km?
Answer:1250
Step-by-step explanation:
What method can researchers employ in order to counter bias in their sampling?
a. snowball sampling
b. weighting
c. convenience sample
d. non-random surveying
Researchers can use b) weighting to counter bias in their sampling, which adjusts sample representation to match a desired population. While convenience sampling offers easy data collection, it lacks generalizability, and weighting is necessary to enhance the validity of findings.
To counter bias in their sampling, researchers can employ a method known as b) weighting. This technique adjusts the representation of samples to match a desired population, countering potential biases that may arise from non-random sampling methods such as convenience sampling. It is important to distinguish between non-random sampling methods that are potentially biased and strategies that are used to ensure data accuracy and representativeness.
Convenience sampling, also referred to as availability sampling or haphazard sampling, is a nonprobability sampling strategy where researchers collect data from individuals or elements that are most easily accessible. This approach is useful in exploratory research or student projects where probability sampling is too costly or difficult but does not offer the rigor needed to make generalizations to larger populations. To overcome these limitations and enhance the validity of their findings, researchers may adjust their data using weighting to better reflect the population being studied.
The midpoint of a segment is (2,-5) and one of the end points is (3,6). Where is the other endpoint?
Which number is a perfect cube? a.21 b.49 c.343 d.600
Answer:
343
Step-by-step explanation:
7*7*7=343
The factor of the 343 will be 7, 7, and 7. Then the number 343 is a perfect cube of 7.
What is a perfect cube?The integers that are the threefold multiplication with the same number are known as perfect cubes.
To put it another way, a perfect cube is the combination of complex times multiplying a whole integer by itself.
A perfect cube is a quantity that may be stated as the composition of three different numbers.
A. The factor of the 21 will be 3 and 7. It can not be a perfect cube.
B. The factor of the 49 will be 7 and 7. It can not be a perfect cube.
C. The factor of the 343 will be 7, 7, and 7. It is a perfect cube.
D. The factor of the 600 will be 2, 2, 2, 3, 5, and 5. It can not be a perfect cube.
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If p(x) = x2 – 1 and q(x)=5(x-1), which expression is equivalent to (p – q)(x)?
5(x – 1) – x2 – 1
(5x – 1) – (x2 – 1)
(x2 – 1) – 5(x – 1)
(x2 – 1) – 5x – 1
find a value of the constant k such that the limit exists:
lim (x^2+4x+k)/(x+2) as x goes to -2 ...?
The solution set for the inequality - 3 (x - 4) > 6(x - 1), includes 3 as an element. True False
The solution set for the inequality - 3 (x - 4) > 6(x - 1) does not include 3 as an element which is inequality is false.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We have been given inequality as:
-3(x-4) > 6(x-1)
To determine the solution set for the inequality.
Substitute x = 3 in the given inequality for each value of x with 3 and simplify both sides.
⇒ -3(x-4) > 6(x-1)
⇒ -3(3-4) > 6(3-1)
⇒ -3(-1) > 6(2)
⇒ 3 > 12
Since inequality 3 > 12 is not true,
So, for x = 3, the given inequality is false. Therefore, 3 is not included in the solution set.
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What is the domain and range for the function below?
1/square root x+4
find the amount that results from each. $50 invested at 6% compounded monthly after a period of 3 years ...?
Final answer:
Using the compound interest formula, the total amount after three years for $50 invested at 6% compounded monthly is approximately $59.70.
Explanation:
To calculate the future value of $50 invested at 6% compounded monthly after a period of three years, we use the formula for compound interest:
FV = P × (1 + (r/n))³⁼ ×⁴
where:
FV is the future value of the investment,
P is the principal amount ($50),
r is the annual nominal interest rate (6% or 0.06),
n is the number of times the interest is compounded per year (12, for monthly compounding),
t is the time the money is invested for, in years (3 years).
Using these values, we calculate as follows:
FV = $50 × (1 + (0.06/12))³·×´ = $50 × (1 + 0.005)·¹·´
Now we calculate this raised to the power of 36 (3 years times 12 months):
FV = $50 × (1.005)³···¶ = $50 × 1.194052
Thus, FV ≈ $59.70
The total amount after three years would be approximately $59.70, assuming the interest is compounded monthly at a rate of 6%.
Which of the following values is equal to 1 micrometer?
A. 0.000001 meter
B. 0.001 meter
C. 1,000 meter
D. 1,000,000 meter
You can buy DVDs at a local store for $15.49 each. You can buy them at an online store for $13.99 each plus $6 for shipping. How many DVDs can you buy for the same amount at the two stores?
if h(x)=-1/2x+3, find h(-29)