Answers
The relative frequency is 8/25.
Describe Relative Frequency?Relative frequency is a statistical concept that refers to the proportion of times that an event occurs in a given sample or population. It is calculated by dividing the number of times the event occurs by the total number of observations in the sample or population.
Relative frequency is an important concept in probability theory and statistics because it provides a way to estimate the probability of an event occurring based on the observed data. As the sample size increases, the relative frequency becomes a more accurate estimate of the true probability of the event.
Relative frequency is also used in hypothesis testing, where it is used to test whether a particular hypothesis is supported by the data. In this case, the observed relative frequency is compared to the expected relative frequency under the null hypothesis to determine whether the difference between the two is statistically significant.
The total number of spins is 75 and the number of times the spinner landed on 3 is 24.
Therefore, the relative frequency for the event "spin a 3" is:
24/75 = 8/25
So, the relative frequency is 8/25.
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The total number of spins is 75 and the number of times the spinner landed on 3 is 24.
The "spin a 3" occurrence has a relative frequency of [tex]\frac{8}{25}[/tex].
Describe Relative Frequency?A statistical concept known as "relative frequency" describes the percentage of times an event happens in a given sample or population. It is calculated by dividing the total number of observations in the sample or group by the frequency of the event.
Because it offers a method to calculate the probability of an event occurring based on the observed data, relative frequency is a crucial concept in probability theory and statistics. The relative frequency becomes a more precise indicator of the actual probability of the event as sample size rises.
In order to determine whether a specific hypothesis is backed by the data, relative frequency is also used in hypothesis testing. To determine
whether the difference between the two is statistically significant, the observed relative frequency is in this instance compared to the expected relative frequency under the null hypothesis.
There were 75 total spins, and 3 appeared 24 times during those rotations.
As a consequence, the proportional frequency of "spin a 3" is as follows:
[tex]\frac{24}{75} =\frac{8}{25}[/tex]
So, the relative frequency is [tex]\frac{8}{25}[/tex].
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Related Questions
help me pleasee will mark brilliantep
Answers
Since
AB/DC = AC /CE - Given; and
AB || CD - Given
Where BCA = DEC = 90°
Therefore, ΔABC ~ ΔCDE - Side-Side-Similarity.
What does the theorem of Side-Side- Similarity state?The theorem of Side-Side-Similarity (SSS) states that if in two triangles, the lengths of corresponding sides are proportional, then the triangles are similar. More specifically, if triangle ABC is similar to triangle DEF, then AB/DE = BC/EF = AC/DF.
This theorem is one of the three criteria for similarity of triangles, the other two being Angle-Angle (AA) similarity and Side-Angle-Side (SAS) similarity.
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Adam plans to choose a video game from a section of the store where everything is 75% off. He writes the expression d−0.75d to find the sale price of the game if the original price is d dollars. Rena correctly writes another expression, 0.25d , that will also find the sale price of the game if the original price is d dollars. Drag each description to explain each part of both expressions.
Answers
In 1st part expression there is a subtraction of 75% of 0.75d from orignal price and in 2nd expression the discount of 75% of the orignal price.
What do you mean by an expression?In mathematics, an expression is a combination of symbols, numbers, and operators (such as +, −, ×, ÷, etc.) that represent a quantity or a mathematical operation.
Expressions can be simple or complex, and they can involve variables, constants, and functions. Expressions can be evaluated or simplified to obtain a numerical or symbolic result.
d: This represents the original price of the video game in dollars.
0.75d: This represents the price of the video game after the 75% discount has been applied. It is equivalent to subtracting 75% of the original price (0.75 times d) from the original price (d).
0.25d: This represents the amount of the original price that is discounted by 75%. It is equivalent to subtracting the sale price (d - 0.75d) from the original price (d), since the discount is 75% or 0.75 of the original price (d).
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In 1980 a value of home is 81600 since then it's value has increased by 12 percentage each year what is the appoxmate value of the home in the 1987 round to the nearest hundred dollars
Answers
The approximate value of the home in 1987 is approximately $161,872.
The formula to calculate the approximate value of a home in 1987 is:
V1987 = 81600 x (1 + 0.12)^7
V1987 = 81600 x 1.987
V1987 = 161872
Therefore, the approximate value of the home in 1987 is approximately 161,872.
To arrive at this answer, we first started with the value of the home in 1980, which was 81,600. We then multiplied this value by 1.12, which is the 12% increase every year, to the seventh power. This resulted in a value of 1.987. We then multiplied this value by the original value of the home in 1980, which gave us the approximate value of the home in 1987. We then rounded the answer to the nearest hundred dollars, which resulted in the answer of 161,872.
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Do the values in the table represent a linear function? if so what is the function rule?
Answers
The values in the table represent a linear function with the function rule y = 3x + 6, where x is the input value and y is the output value.
To determine if the values in the table represent a linear function, we can check if there is a constant rate of change between the input and output values. This means that for every increase or decrease in the input value, there is a constant increase or decrease in the output value.
Looking at the input and output values in the table, we can see that for every increase of 1 in the input value, the output value increases by 3. This constant rate of change indicates that the values in the table represent a linear function.
To find the function rule, we can use the slope-intercept form of the equation for a linear function, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, we can find the slope by dividing the change in output values by the change in input values:
slope = change in output / change in input = 3/1 = 3
Therefore, the slope of the function is 3. To find the y-intercept, we can use one of the points in the table. For example, we can use the first row, which gives an input value of 0 and an output value of 6:
y = mx + b
6 = 3(0) + b
b = 6
Therefore, the y-intercept of the function is 6. Combining the slope and y-intercept, we can write the function rule as:
y = 3x + 6
This means that for any input value x, the output value y is equal to three times x plus six.
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c) the united states has a population of about 320 million. if our homicide deaths were proportional to that of honduras, how many deaths would we expect in the united states due to homicides? round to the nearest person.
Answers
The United States has a population of about 320 million, so if homicides were proportional to Honduras' rate of homicide, we would expect about 12,800 deaths due to homicides in the United States.
This is calculated by taking the population of the United States (320 million) and multiplying it by the Honduras' homicide rate of 40 per 100,000 people.
To calculate this, we first need to find Honduras' homicide rate. The World Bank has this information, which states that the rate is 40 per 100,000 people. We then need to take the population of the United States (320 million) and multiply it by the rate.
This equals 128 million homicides per 100,000 people in the United States. This comes out to 12,800 deaths due to homicides in the United States. Round this to the nearest person, and you get 12,800.
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which transformation carries the rhombus below onto itself?
1. a rotation of 180 clockwise about (-2,-2)
2. a rotation of 90 counterclockwise about (-2,-2)
3. a reflection over the line y=x+10
4. a reflection over the line y=-x-6
Answers
Therefore, the answer is option 4: a reflection over the line y=-x-6.
What is transformation?In mathematics, a transformation is a process that changes the position, size, or shape of a geometric object in some way. Transformations are often used in geometry and other branches of mathematics to study the properties of shapes and their relationships to each other.
Here,
To determine which transformation carries the rhombus onto itself, we need to identify the symmetries of the rhombus. A rhombus has two types of symmetry: rotational symmetry and reflectional symmetry.
Option 1: a rotation of 180 degrees clockwise about (-2,-2)
This transformation takes each point of the rhombus and rotates it 180 degrees clockwise about the point (-2,-2). Since the rhombus has rotational symmetry of order 2 (i.e., a rotation of 180 degrees carries the rhombus onto itself), this transformation carries the rhombus onto itself.
Option 2: a rotation of 90 degrees counterclockwise about (-2,-2)
This transformation takes each point of the rhombus and rotates it 90 degrees counterclockwise about the point (-2,-2). Since the rhombus does not have rotational symmetry of order 4 (i.e., a rotation of 90 degrees does not carry the rhombus onto itself), this transformation does not carry the rhombus onto itself.
Option 3: a reflection over the line y=x+10
This transformation reflects each point of the rhombus over the line y=x+10. Since the rhombus does not have reflectional symmetry over this line, this transformation does not carry the rhombus onto itself.
Option 4: a reflection over the line y=-x-6
This transformation reflects each point of the rhombus over the line y=-x-6. Since the rhombus has reflectional symmetry over this line, this transformation carries the rhombus onto itself.
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let f(x)=3|x-7|+11. write a function g whose graph is a vertical shrink of the graph of f by a factor of 1/2
Answers
Thus, the function g(x) is:
g(x) = (1/2)f(x)
Substituting the expression for f(x), we get:
g(x) = (1/2)[3|x-7| + 11]
Now, we simplify this expression by distributing the 1/2 coefficient:
g(x) = (3/2)|x-7| + 11/2
So the function g(x) is g(x) = (3/2)|x-7| + 11/2.
The graph of g(x) will have the same shape as the graph of f(x), but it will be compressed vertically by a factor of 1/2, making it half as tall as the graph of f(x).
When Fredrick buys a cup of coffee he is given change of €1.65 when he should have received €1.50. Find percentage error
Answers
When Frederick purchases a cup of coffee, he gets handed €1.65 in change rather than the expected €1.50. The error percentage is 9.09%
Explain about the percentage error?The variation between the real value and the predicted value, in relation to the theoretical value, is known as percentage error.
When compared to the real number and expressed in percent format, percentage error seems to be the gap between the anticipated amount and the actual number. The equation is as follows:
To put it another way, you divide the deviation between the true answer and the answer you guessed by the true answer to get the percent.
Amount paid by Fredrick for cup of coffee: €1.65
Actual amount: €1.50.
percentage error = (amount paid - actual amount)/amount paid * 100 %
percentage error = (1.65 - 1.50)/1.65 * 100
percentage error = 9.09%
Thus, When Frederick purchases a cup of coffee, he gets handed €1.65 in change rather than the expected €1.50. The error percentage is 9.09%
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sylvia wants to go on a cruise in 4 years. she could earn 7.3 percent compounded monthly in a bank account if she were to deposit the money today. she needs to have 14,000 dollars in 4 years. how much will she have to deposit today? (round to the nearest dollar).
Answers
The amount Sylvia should deposit today: P = A / (1 + r/n)^(nt)Where:P = P = $ ___The principal amount is $9,463. So, Sylvia has to deposit $9,463 today.
Sylvia wants to go on a cruise in 4 years. She could earn 7.3% compounded monthly in a bank account if she were to deposit the money today. She needs to have $14,000 in 4 years. To determine the amount Sylvia should deposit today to earn $14,000 in 4 years with a 7.3% interest rate compounded monthly,
we can use the formula for compound interest:A = P(1 + r/n)^(nt)Where:A = the amount of money at the end of the time periodP = the principal, or initial amount of moneyr = the annual interest raten = the number of times interest is compounded per yeart = the time period, in yearsWe need to solve for P.
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Need HELP ASAP!!!! RIGHT NOW!!!! THIS INSTANT!!!!
The value of a brand new car is $10,000 and the value depreciates 18% every year. Write a function to represent the value of the car after t years, where the quarterly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per quarter, to the nearest hundredth of a percent.
Answers
The function representing the value of car is 10000 (1 - 0.045)[tex]^{(4t)}[/tex]. The percentage rate of change per quarter is 0.68%. The solution has been obtained by using the substitution method.
What is the substitution method?
The substitution approach is a widely used method in algebra for solving simultaneous linear equations. The name of the method implies that the value of one variable from one equation is changed in the second equation.
We are given that the value of car depreciates 18% every year.
Let f(t) represent the car's worth after t years.
So, we get the function as:
⇒ f(t) = 10000 (1 - 0.18/4)[tex]^{(4t)}[/tex]
⇒ f(t) = 10000 (1 - 0.045)[tex]^{(4t)}[/tex]
Now, the percentage rate of change per quarter is:
⇒ r = [tex](1-q)^{4}[/tex] - 1
Here, q = 0.045
On substituting the value, we get
⇒ r = [tex](1-0.045)^{4}[/tex] - 1
⇒ r = -0.68%
Hence, the required solutions have been obtained.
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meghan, a researcher at um, conducted a similar survey among michigan residents. she used a random sample of the same size as the study conducted by the pew research center and obtained the same value for the sample proportion. gloria is concerned that the computation of the margin of error for a confidence interval for the population proportion will be affected by the fact that the population size for all michigan residents is much smaller than that for all us adults. do you agree with gloria's concern?
Answers
Yes, Gloria's concern about the computation of the margin of error for a confidence interval for the population proportion being affected by the fact that the population size for all Michigan residents is much smaller than that for all US adults is true.
Sample
A subset of the population is known as a sample. A sample is a smaller group of individuals or things chosen from the population.
Error
The distinction between the estimated value of a population parameter and the true, but unknown, value of that parameter is referred to as an error. Sampling error is the difference between the sample statistic and the population parameter. Inference is less accurate if the sample is too small or if the sample is biased, and the resulting sample statistics may differ from the actual population parameters.
Hence, from the above, we can conclude that yes the Gloria's concern about the computation of the margin of error for a confidence interval for the population proportion being affected by the fact that the population size for all Michigan residents is much smaller than that for all US adults is true.
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Solve this system. -3x-y=10, 3x+y=-8 Somone answer this ASAP i need to turn in tonight.
Answers
Thus, the system of equation have no solution, solved by the elimination method.
Explain about the elimination method:To create an equation from one variable using the elimination approach, you can either add as well as subtract the equations.
To eliminate a variable, add the equations when the coefficients from one variable are in opposition, and subtract the equations when the coefficients from one variable are in equality.
Given system of equations are-
-3x - y = 10 ...eq 1
3x + y = -8 ... eq 2
Add both eq.
-3x - y + 3x + y = 10 - 8
0 = 2
As both value of x and y are getting cancelled.
But, 0 ≠ 2
Thus, the system of equation have no solution, solved by the elimination method.
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Question 5(Multiple Choice Worth 2 points)
(Comparing Data LC)
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. There is no shaded bar above 60 to 69. A shaded bar stops at 4 above 70 to 79, at 4 above 80 to 89, at 6 above 90 to 99, at 6 above 100 to 109 and at 10 above 110 to 119. The graph is titled Temps in Beach Town.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Sunny Town is symmetric
IQR, because Beach Town is skewed
Range, because Sunny Town is skewed
Range, because Beach Town is symmetric
Answers
Range because it measures the difference between the highest and lowest values in a dataset, provides a clear measure of variability for both sets of data. It is not affected by skewness or symmetry, which makes it a useful measure of variability for comparing the temperature consistency between Beach Town and Sunny Town.
What is the range?
A function's range can be used to describe one of two related ideas: The function's codomain a representation of the action A binary relation f between two sets X and Y is a function if there is exactly one y in Y such that f connects x to y for every x in X.
Here, we have
Given: A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks for every unit up to 14.
We have to determine which measure of variability should be used for both sets of data to determine the location with the most consistent temperature.
We concluded that Range because it measures the difference between the highest and lowest values in a dataset, provides a clear measure of variability for both sets of data. It is not affected by skewness or symmetry, which makes it a useful measure of variability for comparing the temperature consistency between Beach Town and Sunny Town.
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please solve this, thankyou
Answers
Answer:
probability of getting a red ball= 6/11
Step-by-step explanation:
we know, to find a probability of a event
1st we have to get the total number of events that can occur,i.e
6+4=11
and
the total probability of getting a red ball is 6/11
which is the required answer..
The relative frequency for the event "spin a 3" is __?
Answers
Answer:0.04
Step-by-step explanation:
I’m stuck on this question
Answers
[tex]\cos( 50^o )=\cfrac{\stackrel{adjacent}{MN}}{\underset{hypotenuse}{MO}}[/tex]
keep in mind that the opposite side is the side "facing off" the angle, and the adjacent is the one "not" facing it off.
8x-4x+2y-4z+3z
I just need the answer
Answers
4x + 2y - z
Can someone please help me
Answers
A statement about the model that is true include the following: A. the number of customers visiting the bodega decrease by 25 for every inch of rainfall.
What is the slope-intercept form?In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represent the y-intercept or initial number.Based on the information provided above, an equation that models the situation is given by;
y = 90 + (-25)x
y = 90 - 25x
By comparison of the two equations, we have:
mx = -25x
Slope, m = -25.
In conclusion, the rate of change is -25 customers per inch of rain.
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Find the area of the kite
Answers
so we can look at this as two triangles, one on the upper part, it has a base of 5+5 and a height of 5, and another triangle on the lower part, it has a base of 5+5 and a height of 12, let's get their area and sum them up.
[tex]\stackrel{ \textit{upper part} }{\cfrac{1}{2}(\underset{b}{5+5})(\underset{h}{5})}~~ + ~~\stackrel{ \textit{lower part} }{\cfrac{1}{2}(\underset{b}{5+5})(\underset{h}{12})}\implies25+60\implies \text{\LARGE 85}[/tex]
11y + 3(2y - 4) slove
Answers
Answer:
Step-by-step explanation:
17y-12
11y+3(2y-4)
11y+6y-12
17y-12
I hope this helps!
The length of a rectangle is 7 centimeters less than three times its width. Its area is 40 square centimeters. Find the dimensions of the rectangle. Use the formula, areaequals length times width.
Answers
The length and the width of the rectangle are 1cm and 8/3cm
How to determine the dimensionsThe formula that is used to calculate the area of a rectangle is expressed with the equation;
A = lw
Given that the parameters are;
l is the length of the rectangle.w is the width of the rectangle.A is the area of the rectangle.From the information given, we have that;
Length = 3w - 7
Substitute the values, we have;
40 = (3w - 7)w
expand the bracket
40 = 3w² - 7w
3w² - 7w - 40 = 0
3w² + 15w - 8w - 40 = 0
3w(w + 5) - 8(w + 5) = 0
w = 8/3 or - 5
Length = 3(8/3) - 7 = 1
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Maths, please help, I'm very stuck.
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The scale of the map is 1:2, the distance from Averton to Charlbrough is 12 kilometers, and the distance in the map is 6.25 cm.
What is the scale on the map?We know that 25 kilometers are represented in the map using only 12.5 centimeters. Now, let's simplify this:
25 kilometers / 12. 5 cm = 2
This can be expressed as a scale of 1:2 in which each centimeter represents 2 kilometers.
What is the distance between Averton to Charlbrough?We know the distance on the map is 6 cm, let's now convert this to kilometers:
6cm x 2 = 12 kilometers
What is the distance on the map?We know the distance is 12.5, using this information let's find out the distance on the map.
12.5/ 2 =6.25 cm.
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A diver descends to a depth of –25. 6 feet relative to sea level. How many feet must the diver ascend to reach sea level? 0. 6 feet 25 feet 25. 6 feet 256 feet
Answers
A height of 25.6 feet above the earth is required of the diver. So , the correct choice is C ) 25.6.
Assumed: A diver descends 25.6 feet below sea level.
He would be at sea level at that point, therefore the distance would be 0.
As a result, he must ascend 25.6 feet from sea level to reach 0 feet.
In order to descend to the sea level, the diver must ascend 25.6 feet.
As a result, in order to return to sea level from the diver's current depth of 25.6 feet below it, they must climb 25.6 feet. 25.6 feet is the correct answer.
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simultaneous equation x=5, y=1
Answers
The answer to the given problem is x = 3 and y = 1.
Define simultaneous equationSimultaneous equations are a set of equations with multiple variables that must be solved at the same time. In other words, they are equations that have more than one unknown value, and their solutions must satisfy all the equations in the system. These equations are used to model many real-world situations, such as business and engineering problems.
Given equation;
x + y = 4 ...................... (1)
2x - 5y = 1 ..................... (2)
Multiplying by 5 equation (1) we get,
5(x + y = 4)
5x + 5y = 20 ................. (3)
Adding equation (2) and (3) we get,
2x - 5y = 1
5x + 5y = 20
7x = 21
x = 21/7
x = 3
Putting x=3 in equation(2), we get
2x - 5y = 1
2(3) - 5y = 1
6 -5y =-5y = 1 - 6
-5y = -5
y = -5/-5
y = 1
As a result, the equation's answer is x = 3 and y = 1.
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The complete question is:
x+ y = 4 ; 2x - 5y = 1 solve by simultaneous equation
Geometry!! Please answer
Answers
The surface area of this rectangular prism is equal to 158 ft².
How to calculate the surface area of a rectangular prism?In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:
SA = 2(WH + LW + LH)
Where:
SA represents the surface area of a rectangular prism.L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given parameters into the formula for the surface area of a rectangular prism, we have the following;
SA = 2(8 × 3 + 5 × 8 + 5 × 3)
SA = 2(24 + 40 + 15)
SA = 2(79)
SA = 158 ft².
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Muffy ordered 3 muffins and 2 lattes for $7. Sammy ordered 4 muffins and a latte for $6. create a system of equations.
Answers
Step-by-step explanation:
I added a photo of my solution
Answer:
3m+2L = 7
4m + L = 6
Step-by-step explanation:
Let m = cost of the muffins
Let L = cost of the lattes
3m+2L = 7
4m + L = 6
To solve
Multiply the second equation by -2 and add them together.
3m+2L = 7
-8m + -2L = -12
-------------------------
-5m = -5
Divide by -5
-5m/-5 = -5/-5
m = 1
Then
4(1) +L = 6
L = 6-4
L =2
The solution is
muffins cost 1 dollar and lattes cost 2 dollars.
really need help please ASAP The graph of a function is shown below.
Use the graph of the function to find its average rate of change from x=0 to x=3
Simplify your answer as much as possible.
accualy in math one but they dont have 9th grade on hear.
Answers
As a result, the function's average rate of change from x = 0 to x = 3 is 4/3 as the average rate of change of the function from x = 0 to x = 3.
what is function ?A function is a rule in mathematics that links every element of one set, known as the domain, to a certain element of some other set, known as the range. A function is just a relationship between the values of the input and the output, where the outcome specifically depends on the input. A function can be depicted in a number of different ways, including as an equation, a chart, or a list of values. For instance, the function f(x) = 2x multiplies the input value x by two to get the output value f. (x). The range of this function is indeed the set of all real numbers, and its domain is any set of real numbers.
given
To determine (3, f(3)) on the function graph the average rate of change of the function from x = 0 to x = 3.
According to the graph, the point (0, f(0)) is on the y-axis and has a y-coordinate of 2, while the point (3, f(3)) is on the line that connects the points (2, 0) and (4, 6) and has a slope of m = 3. As a result, we have:
f(0) = 2 and f(3) = 6
We can determine the slope of the line connecting these two points using the slope formula:
m = (f(3) - f(0)) / (3 - 0) = (6 - 2) / 3 = 4/3
As a result, the function's average rate of change from x = 0 to x = 3 is 4/3 as the average rate of change of the function from x = 0 to x = 3.
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Find m (photo below)
Answers
Applying the linear pair theorem, the measures of the angles in degrees are:
m<ABD = 112°; m<DBC = 68°
What is the Linear Pair Theorem?The Linear Pair Theorem, also known as the Linear Pair Postulate, is a basic postulate in geometry that describes the relationship between two adjacent angles that form a straight line.
According to the Linear Pair Theorem, if two angles are adjacent and form a straight line, then they are supplementary. In other words, their measures add up to 180 degrees.
Therefore, according to the linear pair theorem, we have:
m<ABD + m<DBC = 180°
Substitute:
7x + 196 + 9x + 176 = 180
16x + 372 = 180
16x = 180 - 372
16x = -192
x = -192/16
x = -12
m<ABD = 7x + 196 = 7(-12) + 196 = 112°
m<DBC = 9x + 176 = 9(-12) + 176 = 68°
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What percentage of males prefer football? *
Male
Female
Total
15%
48%
20%
13%
Baseball Basketball Football
13
23
36
15
16
31
20
13
33
Total
48
52
100
Answers
The percentage of males who prefer football to baseball and basketball is 20%.
What is the percentage?The percentage refers to the quotient or ratios between two values or quantities.
In this situation, the percentage of males who prefer football to baseball or basketball is expressed as the number of football fans over the total number of the three sports fans.
To compute the percentage, the quotient is multiplied by 100.
Baseball Basketball Football Total
Male 13 15 20 48
Female 23 16 13 52
Total 36 31 33 100
Percentage of males who prefer football = 20% (20/100 x 100)
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Let Y1 and Y2 have joint pdf
f(y1,y2)=3y1
, if 0≤y2≤y1≤1
0, otherwise.
a) Find the marginal density function for Y2.
b) For what values of y2 is the conditional density f(y1|y2)
defined?
Answers
a. The marginal density function for Y2 is fY2(y2) = 3y2², where 0 ≤ y2 ≤ 10.
b. For y2 ≤ y1 ≤ 10 of y2 is the conditional density f(y1|y2) is defined
(a) To find the marginal density function for Y2, we integrate the joint pdf over all possible values of Y1:
fY2(y2) = ∫fY1,Y2(y1,y2) dy1, where the integral is taken over the range where 0 ≤ y2 ≤ y1 ≤ 10, otherwise 0.
fY2(y2) = ∫₀¹⁰3y1 dy1 = 1.5y² |₀y2 = 1.5y2², where 0 ≤ y2 ≤ 10.
So the marginal density function for Y2 is:
fY2(y2) = 3y2², where 0 ≤ y2 ≤ 10.
(b) The conditional density f(y1|y2) is defined as:
f(y1|y2) = fY1,Y2(y1,y2) / fY2(y2), where fY2(y2) > 0.
So the conditional density is defined for all y1 such that 0 ≤ y2 ≤ y1 ≤ 10 and 0 ≤ y2 ≤ 10, i.e.,
y2 ≤ y1 ≤ 10.
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