Similarly, the conditional pdf of Y given X, fy|x(y|x), is found by dividing the joint pdf, fxy(x,y), by the marginal pdf of X, fx(x). Thus, fy|x(y|x) = fxy(x,y)/fx(x) = 3/11e-ly for 0 < x < y < ∞.
The marginal pdf of X, fx(x), is the probability density function of X. It is found by integrating the joint pdf, fxy(x,y), with respect to Y over all possible values of Y. Thus, fx(x) = ∫-∞∞fxy(x,y)dy = 11e-ly for 0 < x < ∞. The marginal pdf of Y, fy(y), is found in the same way, but by integrating with respect to X over all possible values of X. Thus, fy(y) =[tex]∫0yfxy(x,y)dx = 11e-lyy for 0 < y < ∞.[/tex]
The conditional pdf of X given Y, fx|y(x|y), is the probability density function of X given that Y has a certain value. It is found by dividing the joint pdf, fxy(x,y), by the marginal pdf of Y, fy(y).
Thus, fx|y(x|y) =[tex]fxy(x,y)/fy(y) = 3/11e-lyy for 0 < x < y < ∞.[/tex]
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explain the difference between cardinality and join type. describe why one-to-many cardinality is often handled using a one-to-one join.
The difference between cardinality and join type is that cardinality describes the relationship between two data tables, while join type is the specific method used to combine the two tables.
Cardinality defines the maximum number of records that can exist in one table for a relationship with another table. Cardinality can be either one-to-one, one-to-many, or many-to-many.
A one-to-many cardinality relationship is when one record in one table can be related to multiple records in another table. For example, a customer can have multiple orders. In this situation, a one-to-one join type is often used because it is the most efficient way to retrieve the related data. This is because one-to-one join type only requires that one record be searched, while a one-to-many join type would require that multiple records be searched in order to find the related records. Additionally, a one-to-one join type ensures that no duplicate records will be returned in the result.
In summary, cardinality describes the relationship between two tables while join type is the specific method used to combine the two tables. A one-to-many cardinality relationship is when one record in one table can be related to multiple records in another table. To efficiently retrieve the related data, a one-to-one join type is often used. This is because it only requires that one record be searched and it ensures that no duplicate records will be returned in the result.
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Use a calculator to find M Angle B to the nearest 10th.
Answer:
60.3°
Step-by-step explanation:
You want the measure of angle B in right triangle ABC with leg BC = 8 and leg AC = 14.
TangentThe tangent relation is ...
Tan = Opposite/Adjacent
Applying this to the given triangle, we have ...
tan(B) = 14/8
The arctangent function gives you the angle from the tangent.
B = arctan(14/8) ≈ 60.3°
The measure of angle B is about 60.3°.
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the australian sheep dog is a breed renowned for its intelligence and work ethic. it is estimated that 45% of adult australian sheep dogs weigh 65 pounds or more. a sample of 12 adult dogs is studied. what is the mean number of dogs who weigh 65 lb or more?
5.4 out of the 12 adult Australian sheep dogs in the sample weigh 65 pounds or more, on average.
We can start by calculating the likelihood that a single adult Australian sheep dog weighs 65 pounds or more using the provided estimate of 45%. If p represents the percentage of adult dogs weighing 65 pounds or more, the following is the result:
p = 0.45
Next, we may calculate the median number of dogs weighing 65 pounds or more using the sample size of 12. If X represents the proportion of dogs in the sample that weigh 65 pounds or more, X will follow a binomial distribution with n = 12 and p = 0.45 as its parameters.
The formula for X's mean or expected value is:
E(X) = np
When we change the values of n and p, we obtain:
E(X) = 12(0.45) = 5.4
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help me please!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A shape's perimeter is calculated by adding the lengths of all of its sides and edges. The V's direction is [tex](-5, -12)[/tex] .
What dimensions are expressed in linear units?The complete length of a shape's boundary is referred to as the perimeter in geometry. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.
We need to know the lengths of all the sides of Fard ZH in order to calculate its perimeter. We can see from the diagram that [tex]ZF = ZD + DF = 24 + 28 = 52[/tex] and [tex]FH = ZG = 30 and ZH = 36.[/tex]
As a result, Fard ZH's perimeter is as follows:
perimeter = [tex]= ZF + FH + ZH + ZG[/tex]
perimeter [tex]= 52 + 30 + 36 + 30[/tex]
perimeter [tex]= 148[/tex]
So the perimeter of Fard ZH is [tex]148[/tex] .
(3) The vector that connects points A and B must be identified in order to determine the direction of V, and it can be written as follows:
[tex]V = (xB - xA, yB - yA)[/tex]
Where xA and yA represent point A's x and y coordinates, and xB and yB represent point B's x and y coordinates.
Plugging in the given values, we get:
[tex]V = (5 - 10, 2 - 14)[/tex]
[tex]V = (-5, -12)[/tex]
Therefore, The V's direction is [tex](-5, -12)[/tex] .
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FARMING A dairy farmer has 2650 dairy cows on his farm. If each dairy cow produces 2320 gallons of milk per year, how much milk does the dairy farm yield in one year? Write your answer in scientific notation.
Answer:
To calculate the total milk yield in one year, we need to multiply the number of dairy cows by the amount of milk each cow produces per year:
Total milk yield = 2650 dairy cows × 2320 gallons of milk per cow per year
Total milk yield = 6,188,000 gallons per year
To write this answer in scientific notation, we need to express the number 6,188,000 as a number between 1 and 10 multiplied by a power of 10. We can do this by moving the decimal point to the left until we have a number between 1 and 10, and counting the number of decimal places we moved. In this case, we need to move the decimal point 6 places to the left:
Total milk yield = 6.188 × 10^6 gallons per year
Therefore, the dairy farm yields 6.188 × 10^6 gallons of milk per year.
Help me pls I don’t know what it is
The bread recipe calls for 2 more cups of flour per cup of sugar than the cookie recipe.
========================================================
Explanation:
I'll use this shorthand
s = sugarf = flourSomething like "2 cups of sugar" will shorten to "2s".
The cookies need 3s for every 6f.
Therefore we get this ratio
3s : 6f
And we can divide both sides by 3 to end up with
s : 2f
Meaning "each cup of sugar needs 2 cups of flour".
--------------------
Meanwhile, the bread recipe calls for 2s for every 8f.
2s : 8f
2s/2 : 8f/2 .... divide both sides by 2
s : 4f
When making bread, each cup of sugar needs 4 cups of flour. In other words, the amount of flour is quadruple that of the sugar.
--------------------
Recap
Cookies have the ratio of s : 2fBread has the ratio of s : 4fThese ratios are reduced so that we have "s" on the left side without any numbers attached to it. In other words, we have 1s.
We can see that the bread needs 2 more cups of flour compared to the cookies (since 4f - 2f = 2f). It's important that we reduce those ratios so that we're talking about the same amount of sugar for each food item.
This is why choice B is the final answer.
--------------------
An example:
Each food item will use 1 cup of sugar.
The cookies need twice the amount of flour, so the cookies require 2 cups of flour (because of the ratio s:2f mentioned earlier).
The bread needs quadruple the amount of flour compared to sugar. Meaning the bread needs 4 cups of flour (because of the ratio s:4f).
Then subtract to get
(4 cups flour for bread) - (2 cups flour for cookies) = 2 cups flour
HELP!!!!!!!! For #19-20, solve for x. simplify all radicals.
Answer:
19. sqrt{305}
20. 3*sqrt{7}
Step-by-step explanation:
You use the Pythagorean theorem, which can be applied to right triangles. It states that x^2+y^2 = hypotenuse ^2, where x and y are the two sides other than the hypotenuse.
Step-by-step explanation:
hope this will gel help u
Can someone help me please
a bag contains 3 black ,4 red and 2 green balls if two balls are drawn at random what's the probability of getting exactly 2 balls
Answer:9 red
Step-by-step explanation:
PLEASE HELP!!
Solve and explain
Answer:
Step-by-step explanation:
holy mocacrise
Select the statements that are true for the graph of y=(x+2)^2+4
The true statements for the graph of y=(x+2)²2+4 are:, The vertex of the parabola is at the point (-2, 4)., The graph opens upwards, since the coefficient of the squared term is positive., The y-intercept of the graph is at the point (0, 9)., The x-coordinate of the vertex is -2, which is also the axis of symmetry of the parabola., The graph is a parabola, which is a U-shaped curve.
What is graph?
In mathematics, a graph is a visual representation of a set of points, called vertices or nodes, that are connected by lines or curves, called edges. Graphs are used to model relationships between objects or to represent data in a visual way.
In the context of coordinate geometry, a graph is a visual representation of a function or relation, which shows the relationship between the input values (x-axis) and output values (y-axis). The graph is typically a set of points plotted on a Cartesian plane, where each point represents a unique input-output pair.
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Complete Question:
Select the statements that are true for the graph of y = (x+2)²2 + 4.
a) The vertex of the parabola is (-2, 4).
b) The parabola opens upward.
c) The y-intercept of the parabola is 4.
d) The x-intercepts of the parabola are (-4, 0) and (0, 0).
e) The axis of symmetry of the parabola is a vertical line through x = -2.
assume that respondents aged 70 or older are only one-third as likely to be in an internet sample as their actual incidence in the population. using the propensity scoring method, their responses would be
The propensity scoring method is a statistical technique used to adjust for differences in the characteristics of groups being compared in a study. In this case, we want to adjust for the fact that respondents aged 70 or older are underrepresented in an internet sample.
To do this, we can assign a propensity score to each individual in the sample based on their likelihood of being in the sample, given their age. We can then use this score to weight their responses to account for the underrepresentation of older individuals.
In this case, we know that respondents aged 70 or older are only one-third as likely to be in an internet sample as their actual incidence in the population. This means that we can assign a propensity score of 3 to each individual aged 70 or older in the sample, and a propensity score of 1 to everyone else.
Using these propensity scores, we can weight the responses of each individual in the sample. Responses from individuals with a propensity score of 3 would be weighted by a factor of 3, while responses from individuals with a propensity score of 1 would be weighted by a factor of 1.
By adjusting for the underrepresentation of older individuals in this way, we can obtain more accurate estimates of the characteristics of the population being studied, and reduce the potential for bias in our analysis.
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I’m a bit stuck can someone help me out
Answer: 7x - 7y + 21
Step-by-step explanation:
7( x - y + 3) = 7x - 7y + 21
Answer this question. I will give brainlist.
The given diagram represents a right circular cylinder with a base equation of (x - 0)² + (y - 0)² = 7², resulting in an ellipse with an equation of (x - 0)²/4² + (y - 0)²/5² = 1.
The given diagram represents a right circular cylinder with a height of 10 meters and a radius of 7 meters, which means the base of the cylinder is a circle with a radius of 7 meters. The equation of the circle is (x - 0)² + (y - 0)² = 7², where (0, 0) is the center of the circle.
The cylinder has been sliced by a plane that is parallel to the base and 4 meters from the center of the cylinder. This means the distance between the center of the cylinder and the plane is 4 meters.
Mathematically, the equation of the ellipse can be written as (x - 0)²/4² + (y - 0)²/5² = 1, where the center of the ellipse is (0, 0), and the semi-major axis is 5 meters and the semi-minor axis is 4 meters.
So, the given diagram described as a right circular cylinder with a base equation of (x - 0)² + (y - 0)² = 7², sliced by a plane parallel to the base and 4 meters from the center of the cylinder, resulting in an ellipse with an equation of (x - 0)²/4² + (y - 0)²/5² = 1.
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if it is unstable, please change support at a to make stable structure. use the method of joints to calculate the force bd in the truss shown. question 2 (50 pts) find the forces in members cd and ce using the method of section. the support reactions have already been determined.
To make a stable structure, the method of joints can be used to calculate the force BD in the truss shown.
This method uses the equations of equilibrium to determine the forces in the members of a truss. To calculate the force BD, one needs to sum the moments about point A and equate them to zero.
The moment is given by M = FxD, where F is the force, and D is the perpendicular distance from the point of interest to the line of action of the force. Therefore, the force BD can be calculated using the equation:
MAB = 0 = (BD)(2) - (AE)(5)
BD = 5AE/2
To find the forces in members CD and CE using the method of sections, one needs to cut through the truss along a line passing through points C and E.
Then, the force in member CD can be found by using the equation of equilibrium, where the sum of the forces in the x-direction and the sum of the forces in the y-direction must be equal to zero. Similarly, the force in member CE can also be calculated using the same method.
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Clark and bruce went to taco hut for lunch. Clark bought 4 burriots and 5 tacos. Which cost him $13. Bruce bought 5 burritos and 3 tacos, which cost him $13. Determine how much a burriot cost at taco hut
A burrito costs $2 at Taco Hut. Let's use "b" to represent the cost of a burrito and "t" to represent the cost of a taco.
From the problem, we know that:
4b + 5t = 13 (for Clark)
5b + 3t = 13 (for Bruce)
We want to determine the cost of a burrito, so we can solve for "b" using the second equation:
[tex]5b + 3t = 13\\5b = 13 - 3\\b = (13 - 3t)/5[/tex]
Now we can substitute this expression for "b" into the first equation:
[tex]4b + 5t = 13\\4[(13 - 3t)/5] + 5t = 13\\52/5 - 12t/5 + 5t = 13\\52 - 12t + 25t = 65\\13t = 13\\t = 1[/tex]
So we know that a taco costs $1. Now we can substitute this value into either of the original equations to solve for "b":
[tex]5b + 3t = 13\\5b + 3(1) = 13\\5b = 10\\b = 2[/tex]
Therefore, a burrito costs $2 at Taco Hut.
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what extraneous solution arises when solving for the point of intersection of the line f(x)=-1/2x+6 and the square root function f(x)= √x-4
The extraneous solution which arises when solving for the point of intersection of the line and the square root function is 20.
What is an extraneous solution?
An extraneous solution in mathematics is a solution that develops during the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.
We are given two equations as f(x) = [tex]\frac{-1}{2}[/tex]x + 6 and f(x) = √x - 4.
Now, on equating both the equations, we get
⇒ [tex]\frac{-1}{2}[/tex]x + 6 = √x - 4
On squaring both sides, we get,
⇒ [tex](\frac{-1}{2}x + 6)^{2}[/tex]= x - 4
⇒ [tex]\frac{1}{4}x^{2}[/tex] + 36 - 6x = x - 4
⇒ [tex]\frac{1}{4}x^{2}[/tex] + 40 = 7x
⇒ [tex]\frac{1}{4}x^{2}[/tex] -7x + 40 = 0
⇒ [tex]x^{2}[/tex] -28x + 160 = 0
⇒ x = 20 , 8
For point of intersection, we will substitute x = 20 in both the equations.
So, we get
⇒ f(x) = [tex]\frac{-1}{2}[/tex] (20) + 6
⇒ f(x) = -10 + 6
⇒ f(x) = -4
Similarly,
⇒ f(x) = √20 - 4
⇒ f(x) = √16
⇒ f(x) = 4
Since both the solutions are not same so this is an extraneous solution.
Hence, the extraneous solution which arises is 10.
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How many ways can you make chance. 45 cents
Answer:
There are several ways to make 45 cents using different coins:
Nine nickels
Four dimes and one nickel
Three dimes and six nickels
Two dimes and one quarter
One dime, two nickels, and three pennies
One quarter and two dimes
One quarter, one dime, and four nickels
One quarter, three nickels, and five pennies
45 pennies
So there are 9 ways to make 45 cents.
I Hope This Helps!
if the sun rotates once every 24.5 days at the equator, once every 24.8 days at latitude 15 degrees, and once every 34.3 days at the poles, what is the average number of days the sun takes to rotate once based on these three numbers?
Answer:
Step-by-step explanation:
To find the average number of days it takes for the sun to rotate once, we can add the three rotation periods and divide by 3:
Average rotation period = (24.5 + 24.8 + 34.3) / 3
Average rotation period = 83.6 / 3
Average rotation period = 27.87 days (rounded to two decimal places)
Therefore, the average number of days it takes for the sun to rotate once based on the given information is approximately 27.87 days.
the skewness coefficient can be used to multiple select question. compare standard deviations. compare two samples with different measurement units. compare means. compare one sample to a known reference distribution.
The skewness coefficient is a measure of asymmetry in a distribution that can be used to compare means and compare one sample to a known reference distribution, but it is not typically used to compare standard deviations or compare two samples with different measurement units.
The skewness coefficient is a measure of the degree of asymmetry in a probability distribution. It indicates the direction and degree of skewness in a distribution, and can be used to compare means and compare one sample to a known reference distribution.
A positive skewness coefficient indicates that the distribution has a longer tail on the right side and that the mean is greater than the median, while a negative skewness coefficient indicates that the distribution has a longer tail on the left side and that the mean is less than the median.
The skewness coefficient can be useful in detecting departures from normality and in identifying outliers that might affect statistical inference.
However, the skewness coefficient is not typically used to compare standard deviations or to compare two samples with different measurement units.
Comparing standard deviations involves analyzing the variability in the data, whereas comparing means and comparing one sample to a known reference distribution involves analyzing the central tendency of the data.
Additionally, comparing two samples with different measurement units requires converting the measurements to a common scale, which is not related to skewness.
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the perimeter of the bottom of a rectangular swimming pool is 60 meters. the area is 221 square meters. what are the dimensions of the pool?
The dimensions of the pool are either (21.55, 16.45) or (28.45, 7.55).
The perimeter of the bottom of a rectangular swimming pool is 60 meters, and the area is 221 square meters.
To find the dimensions of the pool, we can use the formula P = 2(l + w) where P is the perimeter and l and w are the length and width of the pool respectively. We can rearrange this formula to solve for either l or w, so we'll solve for l.
2(l + w) = 60
2l + 2w = 60
2l = 60 - 2w
l = (60 - 2w)/2
Now, we can use the formula A = l*w to solve for w.
221 = l*w
221 = (60 - 2w)/2 * w
221 = (60w - 2w^2)/2
442 = 60w - 2w^2
2w^2 - 60w + 442 = 0
Using the quadratic formula, we get w = 16.45 or 7.55.
Now that we know the width, we can use the formula l = (60 - 2w)/2 to find the length. For w = 16.45, l = 21.55, and for w = 7.55, l = 28.45.
Therefore, the dimensions of the pool are either (21.55, 16.45) or (28.45, 7.55).
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Popular chocolate bar Toblerone is packaged in a triangular prism. Its cross-section is an equilateral triangle of side 3.6 cm and a perpendicular height of 3.1 cm. The length of the bar is 21 cm.
a. State the number of faces, vertices, and edges for this triangular prism.
b. Find the volume of the packaging. Show all your workings and include units in your final answer.
How do you solve the equation x=1.8x+32
One way to do this is to subtract 1.8x from both sides of the equation, which gives:
x - 1.8x = 32
Simplifying the left-hand side, we get:
-0.8x = 32
To solve for x, we can divide both sides of the equation by -0.8:
x = 32 / (-0.8)
Simplifying, we get:
x = -40
4. Mrs. Green made lunch for her
family. She made turkey sandwiches
and cheese sandwiches. She also
made coconut cookies and oatmeal
cookies. Which list shows all the
possible combinations if a person
picked one sandwich at random and
one cookie at random?
All of these are the combinations that might be made if a person chose a sandwich and a biscuit at random.
What do you mean by probability?The possibilities of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.
Turkey & cheese sandwiches and two varieties of cookies are available (coconut and oatmeal). As a result, there seem to be 2 x 2 = 4 different sandwich and biscuit combinations from which to pick.
The following four pairings are possible:
sandwich with turkey and a coconut biscuit
Oatmeal cookies and a turkey sandwich
Coconut cookies and a cheese sandwich
Oatmeal cookies with a cheese sandwich
So all of these are the combinations that might be made if a person chose a sandwich and a biscuit at random.
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Roberto plays on the school baseball team. In the last 10 games, Roberto was at bat 44 times. While at bat, Roberto got 11 hits and struck out 33 times. What is the experimental probability that Roberto will get a hit during his next time at bat?
The experimental probability that Roberto will get a hit during his next time at bat is 0.25 or 25%.
The experimental probability of an event is calculated by dividing the number of times the event occurred by the total number of trials.
In this case, the event is "getting a hit" and the number of times it occurred is 11. The total number of trials is 44, which represents the number of times Roberto was at bat.
Experimental probability of getting a hit = Number of times Roberto got a hit / Total number of times at bat
Experimental probability of getting a hit = 11 / 44
Experimental probability of getting a hit = 0.25 or 25%
Therefore, the experimental probability that Roberto will get a hit during his next time at bat is 0.25 or 25%.
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What is value of x?
Enter your answer in the box.
X =
B
8
A
X+4
12
2x + 1
C
Next ►
We can deduce that X + 4 = 8 by looking at the top row & second column. The X value is therefore 4.
The word "column" has what meaning?an arrangement of written or printed items on a page that are vertical. a vertical part of a printed page divided into two or more equal columns of numbers.
X + 4 corresponds to a value in the second column and top row.
The third row's value is equal to the first column's value plus two.
(Third row, second column) The value is 12 at the bottom right corner.
First row and the first column, top left, represents value as B.
It reads 8, first row, second column, in the upper right corner.
C is the value located on the bottom left (third row, first column).
We can deduce that X + 4 equals 8 from top row & second column. Hence, we can find X:
X plus 4 = 8
When we take 4 away from both sides, you get:
X = 4
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at steady state, the throughput time for one loaf is 3 hours 30 minutes. how much total wip is in the system, in loaves
At steady state, the total WIP in the system is equal to the throughput time divided by the time it takes to make one loaf. Thus, the total WIP in the system is 3.5 loaves.
The total WIP in a system is the sum of all of the work that is in progress. At steady state, the total WIP in the system can be calculated by dividing the throughput time (the time it takes for one loaf to be processed from start to finish) by the time it takes to make one loaf.
In this example, the throughput time is 3 hours 30 minutes and it takes 1 hour to make one loaf. Therefore, the total WIP in the system is 3.5 loaves. This means that at any given time, there are 3.5 loaves in progress in the system.
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the marks on a statistics midterm test are normally distributed with a mean of 78 and a standard deviation of 6. what is the probability that a class of 36 has an average midterm mark that is more than 77.83?
The probability that a class of 36 has an average midterm mark that is more than 77.83 is 0.0766. This is because the mean of the normally distributed marks is 78 and the standard deviation is 6. Using the standard normal distribution formula, we can calculate the probability that the average mark of 36 students is more than 77.83.
Standard Normal Distribution Formula: P(x > a) = 1 - P(x < a)
P(x > 77.83) = 1 - P(x < 77.83)
P(x > 77.83) = 1 - 0.9234
P(x > 77.83) = 0.0766
rahquez and trinidad both leave the park at the same time, but in opposite directions. if trinidad travels 6 mph faster than rahquez and after 8 hours they are 288 miles apart, how fast is each traveling?
The propensity scoring method is a statistical technique used to adjust for differences in the characteristics of groups being compared in a study. In this case, we want to adjust for the fact that respondents aged 70 or older are underrepresented in an internet sample.
To do this, we can assign a propensity score to each individual in the sample based on their likelihood of being in the sample, given their age. We can then use this score to weight their responses to account for the underrepresentation of older individuals.
In this case, we know that respondents aged 70 or older are only one-third as likely to be in an internet sample as their actual incidence in the population. This means that we can assign a propensity score of 3 to each individual aged 70 or older in the sample, and a propensity score of 1 to everyone else.
Using these propensity scores, we can weight the responses of each individual in the sample. Responses from individuals with a propensity score of 3 would be weighted by a factor of 3, while responses from individuals with a propensity score of 1 would be weighted by a factor of 1.
By adjusting for the underrepresentation of older individuals in this way, we can obtain more accurate estimates of the characteristics of the population being studied, and reduce the potential for bias in our analysis.
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fatouma is lifting wieghts over a 10 week training period . every week , she lifts 2 kg more than she lift the previous week . during the tenth week she lifts 120 kg . what mass did she lift during the week
Fatouma lifted 1 kg during the first week and 120 kg during the tenth week. Fatouma lifted 120 kg in 10 weeks, increasing by 2 kg each week.
What is linear equation ?Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0
Say the mass Fatouma lifted during the first week "x". According to the problem, she increases the weight she lifts by 2 kg every week. So, the mass of second week is "x + 2" kg, during the third week is "x + 4" kg, and so on.
Since there are 10 weeks of training, the mass she lifted during the 10th week is:
x + (10 - 1) × 2 = x + 18
We also know that during the 10th week, she lifted 120 kg. So, we can set up an equation:
x + 18 = 120
Solving for x, we get:
x = 102
Thus, Fatouma lifted 102 kg during the first week of training.
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