Lama paid $3,510 to Social Security and Medicare in 1990.
What is earnings ?
Earnings typically refer to the salary or wages received by an employee for their labor. It can also include bonuses, commission, and other forms of compensation.
Since Lama's earnings were below the threshold of $52,000, the 7.8% rate applied to all of her earnings. To calculate the amount she paid to Social Security and Medicare, multiply her earnings by the rate:
$45,000 x 7.8% = $3,510
So, Lama paid $3,510 to Social Security and Medicare in 1990.
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at what angle, in degrees south of east, is a line connecting your starting point to your final position?
The angle in degrees south of east, is a line connecting your starting point to your final position is 144.46°.
The displacement vector represents the displaced distance along with the direction of displacement. The initial point of the displacement is represented by a tail of a vector arrow whereas, the final point is represented by the arrowhead. Assume i walk 17.5 m straight west and then 24.0 m straight north. Let vectors A and B denotes the displacement. The total displacement, R is determined by adding both vector and direction is θ. So, [tex] \vec R = \vec A + \vec B[/tex]
[tex] \vec R = −17.5 \hat{i} + 24 \hat j[/tex]
The magnitude of the displacement vector is denoted by,
[tex]| \vec R |= \sqrt{{ (- 17.5)}^{2} + {24}^{2} } = \sqrt{882.25} = 29.70 \\ [/tex]
The angle of displacement is given by,
[tex]θ={tan}^{- 1} ( \frac{24}{ - 17.5}) [/tex]
From the above diagram, the displacement is at − 54.46° , which is in the west-north direction in the compass. Let the south of east angle be φ. Now, the angle south of east is φ = 180° - 90° - θ Hence required angle is 90° + 54.46° = 144.46°.
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Complete question:
Suppose you walk 17.5 m straight west and then 24.0 m straight north. At what angle, in degrees south of east, is a line connecting your starting point to your final.
A 20-minute TV program consists of two commercials, each 13 over 4 minutes long, and three equal-length entertainment segments. How long is each entertainment segment? Enter your answer as a decimal.
Each single entertainment segment is 4.5 minutes.
How to find how long is each entertainment segmentOut of the 20 minute show there are two blocks of time that are ads. The ads are each 13/4 minutes long.
13/4 = 13 ÷ 4 = 3.25
minutes.
Let's take away the time used for ads from the 20 minute total.
20 - 3.25 - 3.25
= 13.5
Without ads the show's actual runtime is 13.5 minutes.
Now we'll divide that 13.5 into three equal parts.
13.5 ÷ 3 = 4.5
Each of the three equal entertainment segments is 4.5 minutes long.
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Boyle’s law states that the pressure of compressed gas is inversely proportional to its volume. The pressure of a certain sample of gas is 16 kilopascals when its volume is 1,800 liters. What is the pressure, in kilopascals, when its volume is 900 liters?
The pressure of the gas at the volume of 900 litres will be 32 kilopascals.
What is Boyle's law?Boyle’s law states that the pressure of compressed gas is inversely proportional to its volume. It means that the product of the pressure and volume of the gas is constant when the temperature of the gas is constant.
Given that the pressure of a certain sample of gas is 16 kilopascals when its volume is 1,800 litres.
The pressure of the gas at the volume of 900 litres will be calculated as;-
P₁V₁ = P₂V₂
( 16 x 1800 ) = P₂ x 900
P₂ = ( 16 x 1800 ) / 900
P₂ = 16 x 2
P₂ = 32 Kilopascal
Hence, the pressure will be 32 kilopascals.
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A student bought a pair of sunglasses in the USA. He paid $35.50 in the USA. In England, an identical pair of sunglasses costs £26.99 The exchange rate is £1 = $1.42. How much more did he pay for them in England compared to the USA?
Answer:all you do is multiply 26.99*1.42
this equals 38.33 dollars
35.50 is less than 38.33
thus, USA is cheaper than England.
Step-by-step explanation:
What is 4.5pi minus pi/0.5?
Answer:
≈ 7.8598
Step-by-step explanation:
Let's round pi to 3.14159. First, we multiply 3.14159 by 4.5, which is around 14.13716. Then, we divide 3.14159 by 0.5, which is around 6.28318. So, 14.13716 - 6.28318 = 7.8598
9,37,39,13 Find the median and mean of the data set
Rearrange first
9,13,37,39
median=13+37÷2
=25
median is 25
mean=9+13+37+39÷4
=98÷4=24.5
Mean=24.5
Liliana wants to find the area of a polygon. First, she breaks apart the polygon into two trapezoids. What is Liliana's next step?
Liliana's next step is to find the area of each of the two trapezoids.
How to determine her next stepFrom the question, we have the following parameters that can be used in our computation:
Liliana wants to find the area of a polygon. First, she breaks apart the polygon into two trapezoids.Given that she has broken the polygon into two trapezoids, the next step ti so calculate the area of each trapezoid
This is done using
Area = 1/2 * (sum of parallel sides) * height
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Graph the inequality.
The graph of the inequality y ≤ 5x - 3 is given below.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
An inequality:
y ≤ 5x - 3.
The intercepts are (0.6, 0) and (0, -3)
The graph of the inequality is given in the attached image.
Therefore, the graph is given.
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models that are based on mathematic formula are called _____ models.
Symbolic models are those that are based on mathematical formulas.
By symbolic model, what do you mean?The goal of symbolic modelling is to help clients become more aware of their own "symbolic domain of experience," allowing them to create their own "metaphor landscape" and explore internal metaphors, which are believed by conceptual metaphor theory to influence behaviour.
What benefits do symbolic models offer?
One of the most significant and defining technologies of next-generation modelling methodologies is swiftly emerging as symbolic computation. It allows the freedom to easily create model equations, manage models more effectively, and reach the best outcomes more quickly.
Describe domain through an example.
the domain name example.com might be connected to the address 198.102. 434.8.
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a children's book publisher is interested in kid's opinions of their new book. a random sample of children are shown the book and the proportion of those kids who like the book is found. if the publisher changes from a sample size of 100 to a sample size of 1000, what affect will it have on the sampling distribution
If the publisher changes from a sample size of 100 to a sample size of 1000, the precision of the estimate will be more accurate and the publisher will have more confidence in the results.
Increasing the sample size from 100 to 1000 will result in a more precise estimate of the proportion of children who like the book. The larger sample size will lead to a narrower sampling distribution, meaning that the estimates of the proportion will be more tightly clustered around the true value. This increased precision can provide the publisher with more confidence in the results and a better understanding of the opinions of children on the new book.
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Create a two-way table from the diagram: Match the values with their correct places in the table:
Based on the information in the Venn diagram, we can infer that the table would be completed with the following data from left to right and from top to bottom: 6, 30, 36, 41, 22, 63, 47, 52, 99.
How to find the values that complete the table?To find the values that complete the table, we must analyze the sales diagram and the data it contains. In this case, it is showing two sets, one referenced with the word fish and the other with the word bird, each of them has different values and there is a set that relates them. Additionally, on the outside of these sets there is a value for a category that is not related to these sets.
In accordance with the above, we only have to look at the values and complete the table. Additionally, to find the totals we must add the values of each row or column.
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juan starts walking at 4 miles per hour. an hour and a half later, cathy starts jogging along the same route at 5 miles per hour. how long will it take cathy to catch up with juan?juan starts walking at 4 miles per hour. an hour and a half later, cathy starts jogging along the same route at 5 miles per hour. how long will it take cathy to catch up with juan?
Answer:
6 hours
Step-by-step explanation:
They meet at distance d from their starting point.
Juan walks at 4 mph for time t.
Cathy jogs at 5 mph for time t - 1.5 since she starts 1.5 hour later.
speed = distance/time
distance = speed × time
Juan
d = 4t
Cathy
d = 5(t - 1.5)
4t = 5t - 7.5
t = 7.5
They meet 6.5 hours after Juan started walking.
Cathy jogged for 1.5 hours less than Juan walked.
7.5 hours - 1.5 hours = 6 hours
Answer: 6 hours
5200 is invested into an account that pay’s simple Interest annually after 8 years there is £6,240 in the account at what rate dose the account pay simple interest?
On solving the provided question, we can say that we have been provided with, by Simple Interest SI = PRT/100 =>rate = 15% per yr
what is interest ?Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it. The majority of the time, interest is calculated as an annual percentage of the loan balance. This proportion is referred to as the loan's interest rate.
we have been provided with,
Interest = 6240
principal = 5200
time = 8 yrs
so, by SI = PRT/100
R = SI * 100/PT = 15%
rate = 15% per yr
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a metric ruler contains ten equally spaced increments between each labeled centimeter. when using this ruler to record the length of an object in centimeters, how many decimal places should be recorded?
When using a metric ruler with ten equally spaced increments between each labeled centimeter, the length of an object can be recorded to one decimal place.
A metric ruler is typically divided into centimeters (cm) and millimeters (mm). The ruler has ten equally spaced increments between each labeled centimeter, which means that each centimeter can be divided into ten equal parts. Each of these parts represents a millimeter, and they can be used to measure smaller lengths with more precision.
When using a metric ruler to record the length of an object in centimeters, the smallest division on the ruler that can be used to measure the length is a millimeter. The length of the object can be estimated to the nearest millimeter by aligning it with the closest division on the ruler.
To express the length of the object in centimeters, the number of millimeters must be divided by 10. The resulting value will represent the length of the object in centimeters, rounded to the nearest tenth of a centimeter. This means that the length of the object can be recorded to one decimal place.
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a student bought a smartwatch that tracks the number of steps she walks throughout the day. the table shows the number of steps recorded t minutes after 3:00 p.m. on the first day she wore the watch. t (min) 0 10 20 30 40 steps 3,288 4,609 5,772 6,686 7,128 (a) find the slopes of the secant lines corresponding to the given intervals of t.
The slopes of the secant line corresponding to the given intervals of t is 132.1, 116.3, 91.4 and 44.2 steps per minute.
To find the slope of a secant line between two points, we need to divide the difference in the y-values (number of steps) by the difference in the x-values (time in minutes).
For the interval from t = 0 to t = 10 minutes:
y1 = 3,288 steps
y2 = 4,609 steps
x1 = 0 minutes
x2 = 10 minutes
The slope of the secant line is:
(y2 - y1) / (x2 - x1) = (4,609 - 3,288) / (10 - 0)
= 1,321 / 10
= 132.1 steps per minute
For the interval from t = 10 to t = 20 minutes:
y1 = 4,609 steps
y2 = 5,772 steps
x1 = 10 minutes
x2 = 20 minutes
The slope of the secant line is:
(y2 - y1) / (x2 - x1) = (5,772 - 4,609) / (20 - 10)
= 1,163 / 10
= 116.3 steps per minute
Similarly, for interval t = 20 to t = 30 minutes
Slope = (6,686 - 5,772)/ (30 - 20) = 91.4 steps per minute
for interval t = 30 to t = 40 minutes
Slope = (7,128 - 6,686)/ (40 - 30) = 44.2 steps per minute
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if six numbers are chosen at random, with replacement, from the set of integers from 1 to 900, inclusive, what is the probability that the product of these six integers leaves a remainder of 4 when divided by 30? express your answer as a percent to the nearest thousandth.
Let's first find the total number of possible 6-number combinations from the set of integers 1 to 900, inclusive. This is simply 900^6.
Next, we need to find the number of 6-number combinations that leave a remainder of 4 when their product is divided by 30.
Since the remainder of a product of integers is equal to the product of the remainders of each integer when divided by the same number, we only need to focus on finding the number of combinations of integers from 1 to 900, inclusive, that leaves a remainder of 4 when divided by 30.
We can find this number by dividing 900 by 30 and rounding up to the nearest integer (since we're choosing with replacement, some numbers may be repeated), which gives us 30. So there are 30 possible integers that leave a remainder of 4 when divided by 30.
Since we're choosing 6 numbers from these 30 integers, the number of 6-number combinations that leave a remainder of 4 when their product is divided by 30 is simply 30^6.
Finally, to find the probability of this happening, we divide the number of favorable outcomes by the total number of possible outcomes, and express the answer as a percent:
(30^6) / (900^6) * 100 = 0.000008 * 100 = 0.0080 = 0.80% (rounded to the nearest thousandth)
So the answer is 0.80%
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the magnitude of a vector can be different in different coordinate systems.
Depending on the coordinate system used, a vector's magnitude can vary. A vector may be enhanced by the addition of a scalar. When one of a vector's components is nonzero, the vector can have a magnitude of zero.
What is magnitude of a vector ?
A vector's magnitude, represented by the symbol |v|, is used to determine a vector's length. The distance between the vector's beginning point and endpoint is what this amount essentially represents.
What does the vector coordinate system mean?
An ordered list of integers (a tuple) that represents a vector in terms of a specific ordered basis is known as a coordinate vector in the language of linear algebra.
The coordinates (5, 2, 1) in a three-dimensional Cartesian coordinate system with the axes as its basis serve as an accessible example.
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In the example, was more glass used to make the cone paperweight or the cylinder paperweight? How much more
There was more glass used to make the cylinder paperweight, and there was 16π cm³ more glass was used.
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
Given that, Two solid glass paperweights in the shape of a solid cone having height 6 cm and radius 4 cm, and a solid cylinder with height 3 cm and diameter of 8 cm, we need to find the volume of glass used to make each paperweight,
Volume of cylinder = π×radius²×height
Volume of cone = π×radius²×height / 3
Therefore,
Volume of the cylinder =
π × 4² × 3
= 48π cm³
Volume of cone = π × 4² × 6 / 3
= 96π / 3
= 32π cm³
Therefore, the volume of glass used in the cone paperweight is 32π cm³, and the volume of glass used in the cylinder paperweight is 48π cm³
And, 48π-32π = 16π
Since, the volume of cylindrical paperweight is more than conical paperweight, therefore, there was more glass used to make the cylinder paperweight, and there was 16π cm³ more glass was used.
Hence, there was more glass used to make the cylinder paperweight, and there was 16π cm³ more glass was used.
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The question was incomplete, so I solved for,
"Two solid glass paperweights are shown at the right. What is the volume of glass used to make each paperweight? Write the volumes in terms of pi"
In the example, was more glass used to make the cone paperweight or the cylinder paperweight? How much more?
according to a 2018 survey, 74 percent of employed young adults expect to bring work on a vacation trip. a random sample of 20 employed young adults will be selected. what is the probability that 8 of the selected young adults will expect to bring work on a vacation trip? responses (208)(0.26)8(0.74)12 20 choose 8, times 0.26 to the eighth power, times 0.74 to the twelfth power (208)(0.74)8(0.26)12 20 choose 8, times 0.74 to the eighth power, times 0.26 to the twelfth power (128)(0.26)8(0.74)12 12 choose 8, times 0.26 to the eighth power, times 0.74 to the twelfth power (128)(0.74)8(0.26)12 12 choose 8, times 0.74 to the eighth power, times 0.26 to the twelfth power (288)(0.26)8(0.74)12
There is a 0.00108 probability of choosing 8 candidates the option b from given choices.
The discrete probability distribution known as the binomial distribution only offers Success or Failure as the only two possible outcomes for an experiment. In a binomial distribution, the two parameters n and p are employed. The variables "n" and "p" indicate how many times the experiment is conducted and the probability of each possible outcome, respectively. Let X be the interesting random variable; in this instance, we can suppose that it follows the following distribution: x- Binomial (n = 20; p = 0.74).
For the Binomial distribution, the probability mass function is given as
: p(x) = ( ⁿc ₋ₓ)ˣ (1 - p)ⁿ⁻ˣ.
where ( ⁿc ₋ₓ)ˣ refers to a combination. In this instance, we want this probability.
P ( x = 8 ) = (²⁰c₋₈) × (0.74)⁸ (1-0.74)²⁰⁻⁸ = 0.00108.
The probability of choosing 8 young adults is 0.00108.
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complete Question
according to a 2018 survey, 74 percent of employed young adults expect to bring work on a vacation trip. a random sample of 20 employed young adults will be selected. what is the probability that 8 of the selected young adults will expect to bring work on a vacation trip?
a) (²⁰c₈)(0.26)⁸(0.74)¹²⁻²⁰ choose 8, times 0.26 to the eighth power, times 0.74 to the twelfth power
b) (²⁰c₈)(0.74)⁸(1-0.74)²⁰⁻⁸ choose 8, times 0.74 to the eighth power, times 0.26 to the twelfth power
c) (¹²c₈)(0.26)⁸(0.74)¹²⁻¹² choose 8, times 0.26 to the eighth power, times 0.74 to the twelfth power
d) (¹²c₈)(0.74)⁸(0.26)¹²⁻¹² choose 8, times 0.74 to the eighth power, times 0.26 to the twelfth power (288)(0.26)8(0.74)12
four students graphed the transformations below. Apply what you've learned to write a description of each transformation below as well as an algebraic rule.
The transformation rule descriptions are;
1) Reflection over the x-axis
(x, y) → (x, -y)
2) Reflection over the x-axis
(x, y) → (x, -y)
3) Reflection over the y-axis
(x, y) → (-x, y)
4) Reflection over the x-axis and then a reflection over the y-axis:
(x, y) → (-x, -y)
How to find the transformation rule?1) We clearly see that the transformed image is an exact mirror image of the original image which is a rhombus. Thus, the transformation is a reflection over the x-axis.
This is expressed as (x, y) → (x, -y)
2) We clearly see that the transformed image is an exact mirror image of the original image which is a triangle. Thus, the transformation is a reflection over the x-axis.
This is expressed as (x, y) → (x, -y)
3) We clearly see that the transformed image is an exact mirror image of the original image which is a rectangle. Thus, the transformation is a reflection over the y-axis.
This is expressed as (x, y) → (-x, y)
4) We clearly see that the transformed image is an exact mirror image of the original image which is a pentagon. Thus, the transformation is a reflection over the x-axis and then a reflection over the y-axis.
This is expressed as (x, y) → (-x, -y)
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find the volume of the composite solid. round your answer to the nearest tenth
Answer:
2488.46 ft³
Step-by-step explanation:
the composite solid consists of;
cone and cylinder
volume of a cone=⅓πrh
volume of a cylinder=πr²h
then sum up the volume
⅓×3.142×8×9= 75.408 ft³
3.142×8×8×12=2413.056
2413.056+75.408=
2488.46 ft³
Given f(x) = -3x^2+5 what is range of the function? A- all nonnegative integers. B-all nonnegative real numbers. C-all integers less than or equal to 5. D- all real numbers less than or equal to 5
The range of the function f (x) = - 3x² + 5 is,
⇒ (- ∞, 5]
⇒ All real numbers less than or equal to 5
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
The equation is,
⇒ f (x) = - 3x² + 5
Now, We an draw the graph of function f (x) = - 3x² + 5.
In graph the range is the defined as cover by up and down.
Hence, The range of the function f (x) = - 3x² + 5 is,
⇒ (- ∞, 5]
⇒ All real numbers less than or equal to 5
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Do the following lengths satisfy the Pythagorean Theorem? Lengths= 15 10 5
pls help plssssss
it would really help
Answer:
11.9
Step-by-step explanation:
Sin 58/ BC = Sin 90/ 14
BC = sin 58 × 14 / sin 90
BC = 11.9cm
3. Adam has created a fitness app that currently
has 1,250 downloads. If the number of
downloads for the app is doubling every month,
How many downloads will the app have after 10
months?
Answer:the fitness app will have 1,280,000 downloads after 10 months.
Step-by-step explanation:
To find the number of downloads after 10 months, we need to calculate the number of downloads after each month and add them up. Here's the formula to calculate the number of downloads after n months:
Number of downloads after n months = 1,250 * 2^n
Substituting n=10 in the formula, we get:
Number of downloads after 10 months = 1,250 * 2^10 = 1,250 * 1024 = 1,280,000
So, the fitness app will have 1,280,000 downloads after 10 months.
a scientist randomly divided a group of 100 lab rats into two groups of 50. one group was fed regular rat chow while the other was fed the same amount of rat chow with added ddt (an insecticide). both groups were housed in the same room with the same environmental conditions. at the end of the experiment, rats were weighed and the mean difference was calculated. what is the independent variable?
the answer is DDT
your welcome and have a great rest of your day
a hole of radius unit is bored through the center of a sphere of radius unit. find the exact value of the volume of the remaining portion of the sphere.
The volume of the remaining portion of the sphere is 2.096 cubic units.
Let's take the volume of the remaining portion of the sphere = V
The volume of the sphere = [tex]\frac{4}{3}[/tex] * π * [tex]r^3[/tex]
The volume of the sphere with radius 1 = 4/3 * π
The volume of the cylinder = π * [tex]r^2[/tex] * h
The volume of the cylinder with height 2 and radius 1 = π * [tex]r^2[/tex] * h = 2 * π.
The difference between the volume of the sphere and the cylinder is
V = 4/3 * π - 2 * π = 4/3 * π - 2 * π = 2/3 * π.
By taking π = 3.14
V = [tex]\frac{2}{3}[/tex] * 3.14
V= 2.096.
So, the volume of the remaining portion of the sphere is 2.096 cubic units.
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WHICH IS EQUIVALENT TO
The equivalent exponential function is ( 8 ) ^ ( 3x/4 ).
option A.
What is the equivalent of the exponential function?The equivalent of the exponential function is calculated by applying the following formula.
Generally, for an exponential function of (√a)³ = ( a ) ^ (2/3)
The given exponential function = ∛ (8) ^ (1/4)× , the equivalent function is determined as;
∛ (8) ^ (1/4)× = ( 8 ) ^ ( 1 / 4 ) ( 3x )
= ( 8 ) ^ ( 3x/4 )
Thus, the equivalent exponential function is determined by applying exponential rules.
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Sarah bought a piece of fabric that was 82.2 meters long. Then she cut 1.31 meters of it off to use in a sewing project. How much fabric is left?
Answer:
80.89 metres
Step-by-step explanation:
82.2 - 1.31 = 80.89
Answer:
80.89m
Step-by-step explanation:
Just calculate:
82.2 - 1.31 = 80.89m
scrabble in the game of scrabble, each player begins by drawing 7 tiles from a bag containing 100 tiles. th describe the sampling distribution
The sampling distribution of the A tile in this population is 0.04.
The sampling distribution is a probability distribution of an observed result from a sample that is used to draw inferences about a population. In the game of Scrabble, the sampling distribution is used to draw inferences about the population of 100 tiles. Specifically, the sampling distribution explains the likelihood of a certain tile being drawn. For example, if the population contains 4 A tiles and 96 other tiles, then the probability of drawing an A tile is 4/100 or 0.04. This probability is the sampling distribution of the A tile in the population of 100 tiles. The sampling distribution can also be represented by the formula P(X=x)=nx/n, where n is the total number of tiles and x is the number of tiles of a certain type. Therefore, in the example above, P(X=A)=4/100=0.04. Thus, the sampling distribution of the A tile in this population is 0.04.
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