i need the answers for these 2 questions plss help me

No, 3 is not greater than 5. This is because 5 is larger than 3.

From the question, we have the following parameters that can be used in our computation:

3 and 5

No, 3 is not greater than 5. This is because 5 is larger than 3.

In other words, 5 is further to the right on the number line than 3.

We can also say that 5 is the greater number and 3 is the lesser number.

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The true statement is B. Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1), by comparing the probabilities and interpreting the likelihood.

From the given information,

Probability of the batting average of player 1 = 4/7

Probability of the batting average of player 2 = 5/8

Probability of the batting average of player 3 = 3/6 = 1/2

We have to find the likelihood of each player.

LCM (7, 8, 6) = 56

Probability of player 1 = (4 × 8) / (7 × 8) = 32/56

Probability of player 2 = (5 × 7) / (8 × 7) = 35/56

Probability of player 1 = (1 × 28 ) / (2 × 28) = 28/56

Here the likelihood is greatest for player 2, then player 1 and the least likelihood is for player 3.

Hence the correct option is B.

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For a continuous random variable X, which is uniformly distributed on an interval [4,9], the probability density function of [tex]f_Y( y)[/tex] is equals to

[tex]f_Y( y) =\begin{cases} \frac{2y}{5},\quad 2≤ x ≤ 3 \\ 0, \quad \: otherwise\ \ \end{cases}[/tex]. So, option(5) is correct.

We have a continuous random variable X is uniformly distributed on the interval [4,9]. The PDF is a probability that a random variable acquire a value exactly same or equal to the random variable but in case of CDF, this probability values is less than or equal to the random variable. The probability density function for X is defined as [tex]f_X(x) = \frac{1}{b - a} [/tex] so, we can write it as [tex]f_X ( x) =\begin{cases} \frac{1}{5},\quad 4≤ x ≤ 9 \\ 0, \quad otherwise \\ \end{cases}[/tex].

We have to determine the probability density function [tex]f_Y(y)[/tex]. For this first we have to calculate the cumulative distribution function for f(x) is written as [tex]F_X(x) = \int_{4}^{x} f(x) dx [/tex]

[tex]= \int_{4}^{x} \frac{1}{5} dx [/tex]

[tex]= \frac{1}{5} [ x]_{4}^{x} [/tex]

[tex]F_X(x) = \frac{x - 4}{5}[/tex]

Now, we have, [tex] Y = \sqrt{X}[/tex]

when X = 4 => Y = 2 and X = 9 => Y = 3

Also, X = Y²

Differentiating X = Y² with respect to Y

=> dX = 2Y dY

=> dX/dY = 2Y

Now, pdf of Y is written as [tex]f_Y(y) = f_X(x)|\frac{dX}{dY}| [/tex]

[tex] = \frac{ 1}{5} × 2y[/tex]

[tex]= \frac{ 2y}{5}[/tex]

So, [tex]f_Y( y) =\begin{cases} \frac{2y}{5},\quad 2≤ x ≤ 3 \\ 0, \quad \: otherwise \ \ \end{cases}[/tex]. Hence, required value is [tex]f_Y( y) =\begin{cases} \frac{2y}{5},\quad 2≤ x ≤ 3 \\ 0, \quad \: otherwise \ \ \end{cases}[/tex].

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Complete question:

The above figure complete the question.

Neither of the segments is the perpendicular bisector of the other.

To determine which segment is the perpendicular bisector of the other, we need to find the equations of the lines containing each segment and then check if one of the lines is perpendicular to the other and passes through the midpoint of the other segment.

Let's start by finding the midpoint of segment AT. The coordinates of A and T are not given, but we don't actually need them to find the midpoint.

So, the midpoint M of segment AT is:

M = ((AT_x1 + AT_x2)/2, (AT_y1 + AT_y2)/2)

We don't know the actual values of AT_x1, AT_x2, AT_y1, and AT_y2, but we can find their expressions in terms of x using the segment lengths and the coordinates of the endpoints. We have:

AT_x2 - AT_x1 = BT_x2 - AT_x1 = (x + 5) - (2x + 3) = -x + 2

AT_y2 - AT_y1 = BT_y2 - AT_y1 = (BT - AT) = (x + 5) - (2x + 3) = x + 2

Therefore,

AT_x1 = AT_x2 + x - 2

AT_y1 = AT_y2 - x - 2

Now, we can substitute x=2 and the expressions for AT_x1 and AT_y1 into the midpoint formula to find the coordinates of M:

M = ((AT_x1 + AT_x2)/2, (AT_y1 + AT_y2)/2) = ((AT_x2 + 2 - AT_x2)/2, (AT_y2 - 2 - AT_y2)/2) = (1, -1)

So, the midpoint of segment AT is M(1, -1).

Next, let's find the equations of the lines containing segments AT and DT. We can use the point-slope form of the equation of a line, which states that the equation of a line passing through a point (x1, y1) with slope m is y - y1 = m(x - x1).

For segment AT, we have:

m_AT = (AT_y2 - AT_y1)/(AT_x2 - AT_x1) = (x + 2)/(x - 1)

Let's substitute x=2 to find the slope of the line containing segment AT:

m_AT = (2 + 2)/(2 - 1) = 4

So, the equation of the line containing segment AT is:

y - AT_y1 = m_AT(x - AT_x1)

y - (22 + 3) = 4(x - 22 - 1)

y - 7 = 4(x - 5)

y = 4x - 13

For segment DT, we have:

m_DT = tan(m∠ATD) = tan(41x + 8)

Let's substitute x=2 and simplify:

m_DT = tan(82 + 8) = tan(90) = undefined

This means that the line containing segment DT is vertical and its equation is x = DT_x1 = 4*2 + 1 = 9.

Now, we need to check if one of these lines is perpendicular to the other and passes through the midpoint of the other segment.

First, let's check if the line containing segment AT is perpendicular to the line containing segment DT.  We have:

m_AT * m_DT = 4 * undefined = undefined

Since undefined is not equal to -1, the lines are not perpendicular, and we can rule out the possibility that the line containing segment AT is the perpendicular bisector of segment DT.

Next, let's check if the line containing segment DT is perpendicular to the line containing segment AT. We have:

m_AT = 4

So, the slope of the line perpendicular to the line containing segment AT is -1/4. We can use the point-slope form of the equation of a line again:

y - M_y = -1/4(x - M_x)

y - (-1) = -1/4(x - 1)

y + 1 = -1/4x + 1/4

y = -1/4x + 3/4

Now, we need to check if this line passes through point D, an endpoint of segment DT. We can substitute the coordinates of D into the equation of the line and check if the equation holds true:

DT_y1 = 4*2 + 1 = 9

DT_x1 = 9

9 = -1/4*9 + 3/4

9 = -9/4 + 3/4

9 = -6/4

This is not true, so the line containing segment DT does not pass through point D. Therefore, we can conclude that the line containing segment DT is not the perpendicular bisector of segment AT.

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Answer:

c and a

Step-by-step explanation:

Answer:

Step-by-step explanation:

I think it’s b

The graph that correctly displays the data is this: C. bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44.

A graph plots values to show the relationship between two variables often depicted by the x and y axes. The correct graph to display this data is a bar graph with the title "Favorite Sport" and the x-axis labeled "Sport" and the y-axis labeled "Number of Students."

The first bar should be labeled "Basketball" and go to a value of 17, the second bar should be labeled "Baseball" and go to a value of 12, the third bar should be labeled "Soccer" and go to a value of 27, and the fourth bar should be labeled "Tennis" and go to a value of 44.

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The interval over which both functions are positive is (4, ∞).

In Mathematics and Geometry, the general form of a logarithm function is represented by the following mathematical equation:

f(x) = alog(±x + h) + k

Where:

Based on the given logarithm function g(z) = log₂(z + 3) - 2, we can reasonably infer and logically deduce that it is a vertical translation of this logarithmic function f(z) = log₂(z + 3).

Additionally, the logarithm function g(z) has a vertical asymptote at z = -3 and would be positive on the interval (-3, ∞). This ultimately implies that, an intersection of the intervals over which each function is positive is given by;

Intersection of intervals = (4, ∞) ∪ (-3, ∞).

Positive interval = (4, ∞).

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Answer:

$10,244.14 after 12 years

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(n*t)

A = the final amount of the investment

P = the principal amount ($4200 in this case)

r = the annual interest rate (8% or 0.08 as a decimal)

n = the number of times the interest is compounded per year (once annually in this case)

t = the number of years the money is invested (12 years in this case)

Substituting the given values into the formula, we get:

A = 4200(1 + 0.08/1)^(1*12)

A = 4200(1.08)^12

A = 4200(2.44140625)

A = $10,244.14 (rounded to the nearest cent)

The axis of symmetry is located at a distance of 6.67 feet from one side of the smile and the height of the smile at the axis of symmetry is 0.891 feet.

The equation of the Amazon Smile logo is given by:

h(x) = -0.03x² + 0.4x

To find the axis of symmetry, we need to use the formula:

x = -b / 2a

where a and b are the coefficients of the quadratic equation ax²  + bx + c = 0.

a = -0.03 and b = 0.4.

x = -0.4 / 2(-0.03) = 6.67 feet

Therefore, the axis of symmetry is located at a distance of 6.67 feet from one side of the smile.

To find the height of the smile at the axis of symmetry, we need to substitute x = 6.67 into the given equation:

h(6.67) = -0.03(6.67)² + 0.4(6.67) = 0.891 feet

Therefore, the axis of symmetry is located at a distance of 6.67 feet from one side of the smile and the height of the smile at the axis of symmetry is 0.891 feet.

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Answer:

(0, [tex]\frac{1}{2}[/tex] ) , (1, [tex]\frac{5}{4}[/tex] ) , (2, 2 )

Step-by-step explanation:

to determine which points are contained in the graph.

substitute the x- coordinate of each point into the equation and if the value obtained is equal to the y- coordinate of the point then it is contained in the graph.

(0, [tex]\frac{1}{2}[/tex] )

y = [tex]\frac{3}{4}[/tex] (0) + [tex]\frac{1}{2}[/tex] = 0 + [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{2}[/tex] = y- coordinate ← contained in graph

(1, [tex]\frac{5}{4}[/tex] )

y = [tex]\frac{3}{4}[/tex] ( 1) + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{4}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{4}[/tex] + [tex]\frac{2}{4}[/tex] = [tex]\frac{5}{4}[/tex] = y- coordinate ← contained in graph

([tex]\frac{1}{2}[/tex], 0 )

y = [tex]\frac{3}{4}[/tex] ([tex]\frac{1}{2}[/tex] ) + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex] + [tex]\frac{4}{8}[/tex] = [tex]\frac{7}{8}[/tex] ≠ y- coordinate ← not contained in graph

(2, 2 )

y = [tex]\frac{3}{4}[/tex] (2) + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2 = y- coordinate ← contained in graph

Answer:

arc length ≈ 37.7

Step-by-step explanation:

the arc length is calculated as

arc = circumference of circle × fraction of circle

    = 2πr × [tex]\frac{135}{360}[/tex] ( r is the radius )

   = 2π × 16 × [tex]\frac{3}{8}[/tex]

   = 32π × [tex]\frac{3}{8}[/tex]

  = 4π × 3

  = 12π

  ≈ 37.7 ( to the nearest tenth )

Answer:

l = 2w - 3

2(2w - 3) + 2w = 27

4w - 6 + 2w = 27

6w - 6 = 27

6w = 33, so w = 5.5 feet and l = 8 feet

Answer:

Width: 5.5 feet

Length: 8 feet

Step-by-step explanation:

Let's begin by assigning variables to stand in for the rectangle's width and length.

Let x represent the rectangle's width.

The length is three feet shorter than double the width, according to the problem. As a result, the length may be written as:

2x - 3

The lengths of all the sides make up a rectangle's perimeter, which in this instance is:

2w + 2l

By substituting the width and length measurements we discovered:

2x + 2(2x - 3)

Simplifying:

2x + 4x - 6 = 27

6x = 33

x = 5.5

The rectangle is 5.5 feet wide as a result.

We may change x into the expression we discovered earlier to figure out the length:

2(5.5) - 3 = 8

The rectangle is 8 feet long as a result.

As a result, the rectangle's measurements are:

Width: 5.5 feet

Length: 8 feet

Using the given percentage we can see that the minimum and maximum numbers are:

N-  = 967

N+ = 1,150

The total number of students is 3,650, and we know that the average percentage is 29% ± 2.5%

The minimum value is what we get when we use the minus sign:

29% - 2.5% = 26.5%

The 26.5%  of 3,650 is:

N- = (0.265)* 3,650 = 967

The maximum value is what we get when we use the plus sign:

29% + 2.5% = 31.5%

The 31.5% of  3,650 is:

N+ = (0.315)*3,650 = 1,150

These are the two values.

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The rational numbers in the list of options are √4+√16, 2* √4 and √49 • √81

The examples of rational numbers among the given options are:

The other options are not rational numbers:

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Answer:

32 degrees

Step-by-step explanation:

Recall the three main trig functions: sine, cosine, and tangent.

When using sine, we divide the opposite side from the angle by the hypothenuse.

When using cosine, we divide the adjacent side of the angle by the hypothenuse.

When using tangent, we divide the opposite side from the angle by the adjacent side to the angle.

Since we are given the opposite and adjacent sides, we'll use tangent.

We set up the equation like normal:

tan x [tex]= \frac{13}{21}[/tex]

Now, when finding the angle measurement using trig, we must use the opposing trig function, arcsine, arccosine, and arctangent. The opposing trig function is arctangent. We have to move arctangent to the other side, so that it can be used with the fraction, so:

[tex]x = arctan(\frac{13}{21} )[/tex]

(You would also write arctan, as tan with an exponent of -1) Now, just punch the right side of the equation into a calculator. The nearest degree is 32.

Therefore, the answer is 32 degrees. If you got something different, make sure your calculator is in degrees, not radians! (They are usually abbreviated as DEG and RAD.)

A government structure that is authoritarian or dictatorial in nature would be threatened by debate over public policy.

In such a system, the government exercises complete control over decision-making and any opposition or dissent is not tolerated.

Open debate and discussion over public policy would challenge the authority of the government and its ability to maintain control over the population.

Democracies, on the other hand, thrive on healthy debate and discussion over public policy, as it allows for diverse perspectives and ideas to be heard and considered.

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The null hypothesis is that the proportion of students who have traveled abroad is still 12%, while the alternative hypothesis is that the proportion has increased and is now greater than 12%.

The appropriate null hypothesis is that the proportion of students at UW-Platteville who have traveled abroad remains the same as before the implementation of the study abroad program. The alternative hypothesis is that the proportion of students who have traveled abroad has increased after the implementation of the program.

Mathematically:

H0: p = 0.12

Ha: p > 0.12

where p is the true proportion of students at UW-Platteville who have traveled abroad.

To test this hypothesis, we can use a one-tailed z-test for proportions. Using the given sample information, we can calculate the test statistic as:

z = (0.35 - 0.12) / sqrt((0.12 * 0.88) / 100) = 3.87

where 0.88 is the complement of 0.12, and sqrt denotes the square root. The critical value for a one-tailed test at the 0.05 level of significance is 1.645.

Since the test statistic (3.87) is greater than the critical value (1.645), we reject the null hypothesis and conclude that there is sufficient evidence at the 0.05 level to support the claim that the proportion of students who have traveled abroad has increased after the implementation of the study abroad program.

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The possible lengths of each side of the garden is given by the inequality relation 0 ≤ x ≤ 12

Given data ,

Let's assume that the square garden has sides of length x.

To surround the garden, we will need fencing of length equal to the perimeter of the square, which is 4x

The total amount of fencing is at most 52 feet

So , the inequality is

4x ≤ 52

Dividing both sides by 4, we get:

x ≤ 13

Therefore, the possible length of each side of the garden is less than or equal to 13 feet

And , each side of garden should be more than 0 , so

x > 0

Hence , the full inequality representing the possible length of each side of the garden would be 0 < x ≤ 13

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Therefore , the solution of the given problem of equation comes out to be the value of an is 12 when b is 147. Therefore, 12 is the right response.

In intricate algorithms, variable words are typically employed to demonstrate consistency between two opposing arguments. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider the specifics of the above x + 7 suggestions. improving in this case provides b + 7 while constructing y + 7 before integrating.

Here,

The following values can be used to put up a proportion if the relationship between variables a and b is proportional:

=>  a / b = 4 / 49

The value of a when b is 147 can therefore be calculated using this ratio:

=>  a / 147 = 4 / 49

By cross-multiplying, we can isolate a:

=>  a = (4 / 49) * 147

Now that we know the value of a, we can:

=> a = 12

Therefore, the value of an is 12 when b is 147. Therefore, 12 is the right response.

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The surface area of a tissue box is a measure of the total area that the surface of the box occupies. Out of the options given, A - Square meters and E - Square centimetres are both square units and could be used to measure the surface area of a tissue box.

Explain surface area

The surface area is the total area that covers the outer surface of a three-dimensional object. It is calculated by adding the areas of all the faces or surfaces of the object.

Explain area

The area is the measure of the size of a two-dimensional surface or region. It is expressed in units of square units (e.g., square meters, square inches).

According to the given information

The surface area of a tissue box is a measure of the total area that the surface of the box occupies. Since area is measured in square units, the correct unit of measurement for the surface area of a tissue box would be a square unit. Out of the options given, A - Square meters and E - Square centimeters are both square units and could be used to measure the surface area of a tissue box.

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They form a parallelogram because opposite sides of the given points have an equal slope.

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

To prove that the four points (2,1), (-1,-5), (1,5), and (-2,-1) are the vertices of a parallelogram, we need to show that opposite sides are parallel.

First, we can find the slope of the line connecting (2,1) and (-1,-5):

m1 = (1 - (-5)) / (2 - (-1)) = 6/3 = 2

Next, we can find the slope of the line connecting (1,5) and (-2,-1):

m2 = (5 - (-1)) / (1 - (-2)) = 6/3 = 2

Since the slopes are the same, the line segments connecting these points are parallel.

Now, we can find the slope of the line connecting (2,1) and (1,5):

m3 = (5 - 1) / (1 - 2) = -4

Next, we can find the slope of the line connecting (-1,-5) and (-2,-1):

m4 = (-1 - (-5)) / (-2 - (-1)) = 4/3

Since the slopes are different, the line segments connecting these points are not parallel.

However, we can also see that the line connecting (1,5) and (-1,-5) has the same slope as the line connecting (-2,-1) and (2,1), which is:

m5 = (5 - (-5)) / (1 - (-1)) = 10/2 = 5

Therefore, the line segments connecting (1,5) and (-1,-5), and (-2,-1) and (2,1) are parallel.

Since opposite sides are parallel, the four points (2,1), (-1,-5), (1,5), and (-2,-1) form a parallelogram.

Therefore, they form a parallelogram because opposite sides of the given points have an equal slope.

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If Kelly has 3 bags containing 8 pieces each, and Lori has 8 bags containing 6 pieces each, then Lori have 24 candies more than Kelly.

If Kelly has 3 bags which contains 8 pieces of candy in each bag,

then Total number of candies with Kelly is = 3×8 = 24 candies,

If Lori has 8 bags which contains 6 pieces of candy in each bag,

then Total number of candies with Lori is = 8×6 = 48 candies,

So, to find how much more candy Lori has than Kelly, we need to subtract the number of pieces of candy Kelly has from the number Lori has;

The equation to find the difference in candies is written;

⇒ Difference = (total candies with Lori) - (total candies with Kelly),

⇒ Difference = 48 - 24 = 24 candies;

Therefore, Lori has 24 more pieces of candy than Kelly.

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Answer:

The definition of LCD is Least Common Denominator.

Step-by-step explanation:

Question 2:

LCD of 7/8 and 3/4 is 8

Question 3 :

7/8 - 3/4

7/8 - 6/8

1/8

Hope this helps :) !!

Answer:

Step-by-step explanation: First of all, the full form of LCD is "Lowest Common Denominator"

LCD is the least common denominator that can be used for all types of fractions.

For example, if we have the fractions 1/2 and 2/3, we can write:

1/2 as 2/4,3/6 or 4/8

           and

2/3 as 4/6,6/9 or 8/12

Hence, the least common denominator of 1/2 and 2/3 is 6, since it is present in the denominators of all the fractions.

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The box plot, as the median can be easily estimated from the big set of data, is the graphical representation that's most suitable for the data for gummy vitamins sold globally.

The distribution of data is shown using a boxplot, which is a standardised method based on a five-number summary ("minimum," first quartile ("Q1"), median ("Q3"), and "maximum").

For the case of -

A total of 100 distinct gummy vitamins that are offered worldwide were counted for their milligrammes of vitamin C content.

The box plot, as the median can be easily estimated from the big set of data, is the graphical representation that's most suitable for the data for gummy vitamins sold globally.

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Answer:

6.4

Step-by-step explanation:

The line plot of the data points is added as an attachment

Part A:

A line plot or dot plot would be an appropriate graphical representation for this data set. A line plot would show each data point on a number line with an X above the value,

This graph would be appropriate for displaying this data because the data set is relatively small and the values are discrete (whole numbers), making it easy to see the frequency and distribution of the data points.

Part B:

To create a line plot or dot plot for this data set, you would first need to create a number line that spans the range of values in the data set.

In this case, the range of values is from 91 to 125, so the number line would include all values between these two numbers.

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Answer:

  5.0

Step-by-step explanation:

You want the Beaufort scale number corresponding to 9.4 m/s, given the formula ...

  v = 0.83B^(3/2)

Put the given speed in the formula and solve for B.

  9.4 = 0.83B^(3/2)

  9.4/0.83 = B^(3/2)

  B = (9.4/0.83)^(2/3) ≈ 5.043

The wind speed is about 5.0 on the Beaufort scale.

Answer:

1. Neither would yield the lower tax.

2. (not sure yet about how much)

3. and there is not really a marriage penalty.

For the given problem, The correct answer will be option 2: The IQR of 13 is the most accurate to use, since the data is skewed.

The Interquartile Range (IQR) is a measure of variability that compares the 25th percentile (Q1) to the 75th percentile (Q3) of a dataset (Q3). It is frequently used to describe the distribution or variability of data that may contain outliers or is not regularly distributed.

The data in the histogram is not evenly distributed in this example because there are many donations at the higher end of the scale (16 to 20), resulting in a positively skewed distribution. Using a range of 20, which indicates the difference between the greatest and lowest value in the dataset, may not adequately depict the data's variability since it is significantly impacted by outliers at the extremes.

For the given dataset, IQR can be calculated as:

Arrange the dataset in ascending order:

[tex]5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20[/tex]

Find the median (Q2), i.e. the middle value of given dataset:

Median (Q2) = 15

Find the lower quartile (Q1), which is the median of the lower half of the dataset:

[tex]Q1 = Median of (5, 5, 6, 8, 10) = 6[/tex]

Find the upper quartile (Q3) i.e. median of the upper half of dataset:

[tex]Q3 = Median \;of (15, 18, 20, 20, 20, 20, 20) = 19[/tex]

[tex]IQR = Q3 - Q1 = 19 - 6 = 13[/tex]

Utilizing the IQR of 13, which represents the range between the 25th percentile (Q1 = 6) and the 75th percentile (Q3 = 19), would provide a more accurate measure of variability that is less impacted by outliers at the higher end of the data. It would also offer a better indication of the organization's typical donations because it captures the middle 50% of the data.

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