Does the transformation appear to be a rigid motion?

The solution of the exponents is shown below.

Exponents are mathematical shorthand for multiplying a number by itself a certain number

We have that;

5^n = 1

5^n = 5^0

n = 0

2) 2^-7/2^n = 2^2

2^-7 - n = 2^2

-7 - n = 2

-n = 2 + 7

n = -9

3) 6^5 * 6^n = 6^1

6^ 5 + n = 6^1

5 + n = 1

n = 1 - 5

n = -4

4) (8^n)^7 = 8^21

8^7n = 8^21

7n = 21

n = 3

5) 4^n = (1/4)

4^n = 4^-1

n = -1

In each of the cases, we have applied the laws of the exponents as we know them.

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The equation of the forms are matched as;

2⁻⁷/2ⁿ = 2², n = -9

6⁵ * 6ⁿ = 6. n = -4

(8ⁿ)⁷ = 8²¹, n = 3

4ⁿ = 1/4 , n = -1

Index forms are simply described as mathematical forms that are used to represent numbers of variables that are too large or small.

To multiply index forms, you need to add the exponents of the same bases.

To divide index forms, you need to subtract the exponents of the same bases.

From the information given, we have that;

2⁻⁷/2ⁿ = 2²

cross multiply the values

2⁻⁷ = 2²⁺ⁿ

Then,

-7 = 2 + n

n = -9

6⁵ * 6ⁿ = 6

take the exponents

5 + n= 1

n =- 4

(8ⁿ)⁷ = 8²¹

We have;

7n = 21

Make 'n' the subject

n = 3

4ⁿ = 1/4

4ⁿ = 4⁻¹

n =-1

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If someone asked me how it could be possible for an annual interest rate to be higher than 100%, I would explain that it is actually quite common in certain situations, particularly in the case of loans with very short terms or loans with high fees.

For example, let's say you borrowed $100 from a lender and agreed to pay back $110 in one week. The lender is essentially charging you 10% interest for the one-week loan period, but if you annualize that rate, it comes out to over 520%. This is because the lender is charging you a very high interest rate for a very short period of time.

Another example would be if you took out a payday loan, which typically have very high fees attached to them. For instance, you might borrow $500 and have to pay back $575 in two weeks. The interest rate on this loan might be calculated as the $75 fee divided by the $500 borrowed, which comes out to 15%. However, if you annualize that rate, it comes out to over 390%.

In both of these examples, the interest rate is very high because the loan term is very short and/or the fees are very high. It's important to note that borrowing at such high interest rates can be extremely costly and can lead to a cycle of debt, so it's generally recommended to avoid loans with high interest rates whenever possible.

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The areas of the sector in the circle are 18π, 3π, 10π and 5π

The orange sector

This is calculated as

Sector area = central angle/360 * πr²

Where

So, we have

Sector area = 180/360 * π * 6²

Sector area = 18π

The yellow sector

This is calculated as

Sector area = central angle/360 * πr²

Where

So, we have

Sector area = 30/360 * π * 6²

Sector area = 3π

The green sector

This is calculated as

Sector area = central angle/360 * πr²

Where

So, we have

Sector area = 100/360 * π * 6²

Sector area = 10π

The purple sector

This is calculated as

Sector area = central angle/360 * πr²

Where

So, we have

Sector area = 50/360 * π * 6²

Sector area = 5π

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The time till you hit the water, given your height above the water, would be 0.76 seconds.

The maximum height above the pool you would get is 15.39 feet.

We are given h ( t ) = - 16 t ² + 5t + 15

You hit the water at 0 so the formula is:

0 = - 16 t ² + 5t + 15

Using the quadratic equation, we can solve:

t = ( - b ± √ ( b ² - 4  ac ) ) / 2a

t = ( - 5 ± √ ( 5 ² - 4 ( - 16 ) ( 15 ) )) / 2 (- 16)

t = (- 5 ± √ 985 ) / -32

t = 0. 76 seconds

The vertex of the parabolic function would be:

= - b / 2a

= - 5 / ( 2 x - 16 )

=  0. 15625 seconds

Maximum height is therefore:

= -16 ( 0. 15625 ) ² + 5 ( 0. 15625 ) + 15

=  15.39 feet

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Answer:

  (c)  x ≤ 5 or x ≥ 7

Step-by-step explanation:

You want the solution to |x -6| ≥ 1.

The absolute value relation represents two relations, one for the domain x < 6, and one for the domain x ≥ 6.

In this domain, the inequality becomes ...

  -1 ≥ x -6

  5 ≥ x . . . . . . add 6

  x ≤ 5 . . . . . . . put x on the left

In this domain, the inequality is ...

  x -6 ≥ 1

  x ≥ 7

The disjoint solution sets are x ≤ 5 or x ≥ 7.

__

Additional comment

For |x -a| ≤ b, we can "unfold" this to the compound inequality ...

  -b ≤ (x -a) ≤ b

copying the inequality symbol to the left side, and writing the opposite of the constant there.

We can do the same thing with the inequality ...

  |x -a| ≥ b

but it doesn't really make sense as a compound inequality.

Instead, we have to write it as ...

  -b ≥ (x -a)   or   (x -a) ≥ b

in recognition of the fact that the solution spaces are disjoint.

Answer:

El coeficiente del término 23x^5 es 23.

Step-by-step explanation:

At point (-43,0), f has a maximum. At point (0,4), f has a minimum. At point (463,0), f has a maximum. At point (0,0), f may have a critical point. none of the given points are critical points of the function f (x, y) = xy + 33 - 48y.

Hi! To analyze the critical points of the function f(x, y) = xy + 33 - 48y, we first need to find the partial derivatives with respect to x and y:

fx = ∂f/∂x = y
fy = ∂f/∂y = x - 48

Now, we can analyze the given points:

1. (-43, 0)
At this point, fx = 0 and fy = -48. Since both partial derivatives are not equal to 0, this point is not a critical point.

2. (0, 4)
At this point, fx = 4 and fy = 0. Again, both partial derivatives are not equal to 0, so this is not a critical point.

3. (463, 0)
At this point, fx = 0 and fy = 463 - 48 = 415. Since both partial derivatives are not equal to 0, this is not a critical point.

4. (0, 0)
At this point, fx = 0 and fy = -48. Since both partial derivatives are not equal to 0, this is not a critical point.

5. (0, -4)
At this point, fx = -4 and fy = -48. Again, both partial derivatives are not equal to 0, so this is not a critical point.

In summary, none of the given points are critical points of the function f(x, y) = xy + 33 - 48y.

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As a result, the function's absolute maximum and minimum values are 5 and -45, respectively, at x = -5 and x = 2, respectively.

Every element in a set (referred to as the domain) in mathematics is connected by a rule known as a function to exactly one component in some other set (called the range or codomain). In other terms, a role is a connection among 2 sets where every element in the domain matches exactly one member in the range. Using a formula or equation with a variable input, function notation is a common way to represent functions. As an illustration, the formula f(x) = 2x + 1 gives each true figure x the value 2x + 1.

given

We can apply the second derivative test to determine whether this critical point is a maximum or minimum. By taking f'(xderivative, )'s we arrive at:

f''(x) = -4

The critical point at x = 0 is a local maximum since f"(0) = -4 is a negative value.

Secondly, we must determine whether the interval's endpoints of -5 x 2 provide values that are higher or lower than the crucial point. By entering x = -5 and x = 2, we obtain:

[tex]f(-5) = 5-2(-5) (-5)^2 = 5 – 50 = -45[/tex]

[tex]f(2) = 5 - 2(2) (2)^2 = -3[/tex]

As a result, the function's absolute maximum and minimum values are 5 and -45, respectively, at x = -5 and x = 2, respectively.

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We can see here that the amount he or she will pay in taxes for their entire lifetime is: $344,000

Tax is a financial obligation that all people, businesses, and other types of entities must fulfill for a government organization.

Let us say that an average American makes $40,000  for his or her lifetime and works from age 22 to 65, and pays a combined federal and state income tax rate of 20%, the amount of taxes paid per year would be:

$40,000 x 0.20 = $8,000

Over a 43-year period (from age 22 to 65), the total amount of taxes paid would be: $8,000 x 43 = $344,000

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If the circumference of a circle is 50. 4 ft, its area is 202.24 sq ft. Correct  option is C: 202.24 sq ft.

The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle. We are given that the circumference is 50.4 ft, so we can solve for the radius:

50.4 = 2πr

r = 50.4 / (2π)

r ≈ 8.02 ft

Now we can use the formula for the area of a circle: A = πr²

A = 3.14 * (8.02)²

A ≈ 202.24 sq ft

Therefore, the answer is option C: 202.24 sq ft.

Alternatively, to find the area of a circle with a circumference of 50.4 ft, we will first find the radius using the formula for circumference (C = 2πr) and then use the formula for the area of a circle (A = πr²). Using π = 3.14:

Solve for the radius (r):
C = 2πr
50.4 = 2(3.14)r
r = 50.4 / (2 * 3.14)
r ≈ 8 ft

Calculate the area (A):
A = πr²
A = 3.14 * (8²)
A = 3.14 * 64
A ≈ 201.06 sq ft

The closest answer among the options provided is 202.24 sq ft. Correct  option is C: 202.24 sq ft.

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The missing numbers on the grids are given as follows:

2 and -6.

The amounts are obtained by a system of equations, for which the variables are given as follows:

x and y.

The top grid represents the sum of the measures, hence:

x + y = -4.

The bottom grid represents the subtraction of the measures, hence:

x - y = 8.

Adding the two equations, the value of x, representing the left grid, is given as follows:

2x = 4

x = 2.

Then the value of y, representing the right grid, is given as follows:

2 + y = -4

y = -6.

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Using the intersection of sets we find that A ∩ B = {1, 3}

A set is a collection of well ordered items.

Givent hat set A = {x| x is an od number greater than 0 and less than 10} and set B = {1, 2, 3, 4}, we desire to find A ∩ B. We proceed as follows.

First since set A = {x| x is an odd number greater than 0 and less than 10}, its elements are A = {1, 3, 5, 7, 9}

Also, set B =  {1, 2, 3, 4}

Since we require A ∩ B which is the intersection of both sets and is  the elements that both sets have in common. Since both sets have element 1 and 3 in common, we have that

A ∩ B = {1, 3}

So, A ∩ B = {1, 3}

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Polar coordinates for rectangular coordinates if x<0: r=√(x²+y²) and θ=tan⁻¹(y/x)+π if y≥0 or θ=tan⁻¹(y/x)−π if y<0, For x≥0: r=√(x²+y²) and θ=tan⁻¹(y/x) if y≥0 or θ=tan⁻¹(y/x)+2π if y<0.

The polar coordinates of a point with rectangular coordinates (x,y) depend on the sign of x.

If x<0, the polar coordinates are (r,θ) where r≥0 and −π/2≤θ<3π/2. If x≥0, the polar coordinates are (r,θ) where r≥0 and −π/2≤θ<3π/2.

If x<0, t

hen r=√(x²+y²) and

θ=tan⁻¹(y/x)+π if y≥0

or θ=tan⁻¹(y/x)−π if y<0.

The value of r is the distance from the origin to the point and θ is the angle between the positive x-axis and the line segment from the origin to the point.

If x≥0, then r=√(x²+y²) and θ=tan⁻¹(y/x) if y≥0 or θ=tan⁻¹(y/x)+2π if y<0.

In this case, θ is the angle between the positive x-axis and the line segment from the origin to the point, measured counterclockwise.

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The expression that is equivalent to the one Regina wrote is y + 27/4

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

y + 9 x 3/4

This means that

Expression = y + 9 x 3/4

When expanded, we have

Expression = y + 27/4

Using the above as a guide, we have the following:

The expression that is equivalent to the one Regina wrote is y + 27/4

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The distance is negative because it's a fall, so the cat falls 27.36 ft between t = 0.5 s and t = 1.4 s.

To find the distance the cat falls between t = 0.5 s and t = 1.4 s, we need to use the formula for velocity and distance.
we first need to find the position at each of these times using the given formula u(t) = -32t ft/s.

The formula for distance fallen is:
distance(t) = initial position + initial velocity × t + (1/2) × acceleration × t²

Since the cat falls with zero initial velocity and starts from the tree, we can simplify the formula:
distance(t) = (1/2) × acceleration × t²

First, let's find the velocity of the cat at t = 0.5 s and t = 1.4 s using Galileo's formula:
u(0.5) = -32(0.5) = -16 ft/s
and, u(1.4) = -32(1.4) = -44.8 ft/s

Now, we can use the formula for distance:
distance = (velocity at t = 0.5 s + velocity at t = 1.4 s) / 2 x (t = 1.4 s - t = 0.5 s)
⇒ distance = (-16 ft/s + (-44.8 ft/s)) / 2 x (1.4 s - 0.5 s)
⇒ distance = (-60.8 ft/s) / 2 x (0.9 s)
⇒ distance = -27.36 ft/s x s

Therefore, the cat falls 27.36 feet between t = 0.5 s and t = 1.4 s.

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Answer:

The total amount Joe spent on gasoline and oil can be determined by the expression: 2.85g + 3.15c. This expression represents the cost of g gallons of gasoline at $2.85 per gallon plus the cost of c cans of oil at $3.15 per can.

Step-by-step explanation:

The ratio of the corresponding dimensions of the smaller pyramid to the larger pyramid is 1/3.

Dimension is the measure of the distance or length of an obeject.

To calculate the ratio of the corresponding dimensions of the smaller pyramid to the larger pyramid, we use the formula below

Formula:

l/L = √(a/A) ........................ Equation 1

Where:

From the question,

Given:

Substitute these values into equation 1

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~5 - (-3)~~)^2 + (~~0 - (-6)~~)^2} \implies d=\sqrt{(5 +3)^2 + (0 +6)^2} \\\\\\ d=\sqrt{( 8 )^2 + ( 6 )^2} \implies d=\sqrt{ 64 + 36 } \implies d=\sqrt{ 100 }\implies d=10[/tex]

By setting up an inequality, the maximum number of vans that are needed to ferry 80 people are 7 vans.

To find the maximum number of vans needed to ferry 80 people using the given terms, let's set up an inequality. Let's use the variable "v" to represent the number of vans.

Since a van can ferry a maximum of 12 people, we can write the inequality as:

12v ≥ 80

Now, let's solve for "v":

Divide both sides of the inequality by 12.
v ≥ 80/12

Simplify the inequality.
v ≥ 6.67

Since we cannot have a fraction of a van, we need to round up to the nearest whole number:

v ≥ 7

Therefore, the maximum number of vans needed to ferry 80 people is 7 vans.

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Answer:

Step-by-step explanation:

as we alderdy have value of y,we can substuite it in the place of y

4x+8(2)=3x+7(2)+14

4x+16=3x+14+14

4x-3x=28-16

x=12

The total cubic centimeters of space the tissue box requires is 500 cubic centimeters, under the condition that the box is half full.

The volume of a cube is evaluated by multiplying its length by its width by its height. If all sides of a cube are equal,

we can use the formula

V = s³

here

s = length of one side of the cube.

If we let s be the length of one side of the cube and V be its volume,

V = s³

If we know that the tissue box is half full, then let us consider that half of its volume is occupied by tissues. Then

V' = 0.5 × V

Staging V = s³ in the equation

V' = 0.5 × s³

s = 10 cm (given)

V' = 0.5 × 1000 = 500 cubic centimeters

Hence, if Patrick's tissue box has a volume of 1000 cubic centimeters and it is half full, then the tissues occupy 500 cubic centimeters of space.

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The complete question is

Patrick buys a tissue box in the shape of a cube of side 10 centimeters. How many cubic centimeters of space do the tissues occupy if the box is half full? Show all work

Answer:

m=2

Step-by-step explanation:

The value of the volume of the cylinder is  706. 5 cm³

The formula for the volume of a cylinder is expressed as;

V = πr²h

Such that the parameters are;

Now, substitute the values into the formula, we get;

Volume, V = 3.14 × 5² × 9

Find the square value and substitute

Volume, V = 3.14 × 25 × 9

Multiply the values

volume, V = 706. 5 cm³

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The drive-thru is able to estimate their wait time more consistently will be A. Burger Quick, because it has a smaller IQR.

The interquartile range (IQR) is a measure of variability that represents the range of values in the middle 50% of scores in a distribution. It is used when the data is skewed and the median is a better measure of central tendency than the mean.

In this scenario, Burger Quick has an IQR of 14.5, while Fast Chicken has an IQR of 4.5.

The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3).

For Burger Quick, Q1 is 9.5 and Q3 is 24, so the IQR is 24 - 9.5 = 14.5. For

Fast Chicken, Q1 is 10 and Q3 is 14.5, so the IQR is 14.5 - 10 = 4.5.

Therefore, Burger Quick has a larger IQR than Fast Chicken, indicating that its data is more consistent and less spread out. This means that Burger Quick is better able to estimate its wait time consistently.

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The man needs to pay a total tax of Rs 69780 (3000 for social security and 66780 for yearly tax).

To find the tax, let's find the man's yearly income:

Yearly income = Monthly income x 12

Yearly income = 53000 x 12 = 636000

Next, let's find how much he deposits in civil investment fund and charity:

Amount deposited in civil investment fund = Yearly income x 20%

Amount deposited in civil investment fund = 636000 x 0.2 = 127200

Amount deposited in charity = Yearly income x 10%

Amount deposited in charity = 636000 x 0.1 = 63600

Now, let's calculate the total taxable income:

Total taxable income = Yearly income - Amount deposited in civil investment fund - Amount deposited in charity

Total taxable income = 636000 - 127200 - 63600 = 445200

Since the man's taxable income is above Rs 300000, he needs to pay 1% social security tax on Rs 300000:

Social security tax = 1% of 300000 = 3000

Now, let's calculate the yearly tax imposed at a rate of 15%:

Yearly tax = Total taxable income x 15%

Yearly tax = 445200 x 0.15 = 66780

Therefore, the man needs to pay a total tax of Rs 69780 (3000 for social security and 66780 for yearly tax).

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Answer:

  [tex]\displaystyle\textsf{a) }\binom{8}{4}\\\\\textsf{b) }\binom{-8}{4}[/tex]

Step-by-step explanation:

Given a translation vector ...

  [tex]\displaystyle \binom{g}{h}[/tex]

moves g to the right and h up, you want the vectors for 8 right, 4 up, and for 8 left, 4 up.

When we have g = units to the right, and we want 8 units to the right, we know that g = 8. Similarly, h = units up, and we want 4 units up, so h = 4.

Putting these values in the vector form, we have ...

a)   8 right, 4 up matches vector ...

  [tex]\displaystyle \boxed{\binom{8}{4}}[/tex]

b)  Left is the opposite of right, so 8 units left will be represented by ...

  g = -8

As before, 4 units up means h = 4.

  [tex]\displaystyle \boxed{\binom{-8}{4}}[/tex]

<95141404393>

The rate of change of revenue per unit is $8 when the unit cost is changing by $8 and the revenue is $4,000.

We are given that the unit cost (C) and unit revenue (R) are related by the equation C = R + 10621.

We want to find the rate of change of revenue per unit, dR/dx, when the unit cost (C) is changing by $8 per unit and the revenue (R) is $4,000.

1. Differentiate the given equation with respect to x: dC/dx = dR/dx

2. Plug in the given values: dC/dx = $8 (cost per unit is changing by $8) R = $4,000 (revenue per unit)

3. Solve for the cost per unit (C) using the equation

C = R + 10621

C = $4,000 + 10621

C = $14,621

4. Since dC/dx = dR/dx, and we know dC/dx = $8,

we can find the rate of change of revenue per unit (dR/dx) when the cost per unit is changing by $8: dR/dx = $8

Thus, the rate of change of revenue per unit is $8 when the unit cost is changing by $8 and the revenue is $4,000.

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The cost of the stock for the investor would be calculated as follows:

Cost of 1 share = $98.93
Number of shares purchased = 500

Total cost of the stock = Cost per share x Number of shares
Total cost of the stock = $98.93 x 500
Total cost of the stock = $49,465

The broker charges 2% of the cost of the stock, so the broker's fee would be calculated as:

Broker's fee = 2% x Total cost of the stock
Broker's fee = 2% x $49,465
Broker's fee = $989.30

Therefore, the total cost of the stock for the investor including the broker's fee would be:

Total cost of the stock + Broker's fee = $49,465 + $989.30
Total cost of the stock + Broker's fee = $50,454.30

So the cost of the stock for the investor including the broker's fee is $50,454.30.

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Answer: 161.2

Step-by-step explanation:

Plug into formula

6.9² = 13²+17.8²-2(17.8)(13) cos C      >simplify numbers

-438.23 = -2(17.8)(13) cos C               >Divide both sides by  -2(17.8)(13)

cos C=.947                                         > use   [tex]cos^{-1}[/tex] C  to solve for angle

<C=180-18.75 = 161.2                          > neded to subtract from 180 for this                    

                                                                one

Therefore, (70+72)/2 = **71 minutes** is the median time. B)42.5 minutes as a result. C,D)The range is determined by deducting the dataset's smallest value from highest value.

A)When the data are organized in order of magnitude, the median time is the middle value. The median in this situation is the average of the 14th and 15th values, which are 70 and 72, respectively. There are 28 data points in this situation. Therefore, (70+72)/2 = **71 minutes** is the median time.

b) The median of the lowest half of the data constitutes the lower quartile (Q1). We must arrange the data in descending order of magnitude before determining the median of the first half of the data in order to determine Q1.  is the average of the seventh and eighth values, which are 40 and 45, respectively, in the first half of the data, which consists of 14 values. Q1 = (40+45)/2 = **42.5 minutes as a result.

b) The median of the upper half of the data constitutes the upper quartile (C). We must first organise the data in descending order of magnitude before determining the median of the remaining data in order to determine Q3. Q3 is the average of the seventh and eighth values from the last, which are 90 and 105, respectively, in the second half of the data, which consists of 14 values. Q3 = (90+105)/2 = **97.5 minutes**3 as a result.

d) The range is determined by deducting the dataset's smallest value from highest value.

In this instance, Ben's practise time can be anywhere from **10 minutes** to **180 minutes**. Range then equals maximum value - minimum value, which in this case is 180 - 10 = **170 minutes**

e) Extreme values that are beyond the typical range of a dataset's values are known as outliers. We can use a criterion that states that any value that sits more than 1.5 times the interquartile range (IQR) below Q1 or above Q3 is regarded as an outlier to ascertain whether there are outliers in this dataset. When Q1 is subtracted from Q3, the result is the IQR: Q3 - Q1 = 97.5 - 42.5 = **55 minutes**3. By using this rule, we can see that the dataset contains the outliers **180** and **120** minutes.

The term "interquartile range" is IQR. It is a measure of variability that is based on quartilizing a dataset. The first quartile (Q1) is subtracted from the third quartile to determine the IQR. (Q3). It is a representation of the middle 50% of the data's range.

f) A box-and-whisker plot illustrates a dataset's quartiles, outliers, and range1. For Ben's practice, here's how to create a box-and-whisker plot:

- Create a number line with all the values Ben practised with.

- Draw a box spanning Q1 through Q3.

- Inside the box, at the location of Q2, draw a vertical line. (the median).

Draw whiskers from the box's two ends to all values that are not outliers.

- Place every outlier on the graph as a separate point, outside of any whiskers.

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