Answer:
y = 5.25 [tex](8)^{x}[/tex]
Step-by-step explanation:
the general form of an exponential function is
y = a [tex](b)^{x}[/tex]
to find a and b , substitute the coordinates of the given points into the equation.
using (2, 336 )
336 = a b² → (1)
using (3, 2688 )
2688 = a b³ → (2)
divide (2) by (1)
[tex]\frac{ab^3}{ab^2}[/tex] = [tex]\frac{2688}{336}[/tex] ( cancel ab on numerator/denominator of left side )
b = 8
substitute b = 8 into (1) and solve for a
336 = a × 8² = 64a ( divide both sides by 64 )
5.25 = a
then exponential function is
y = 5.25 [tex](8)^{x}[/tex]
taking into accoutn rules of precendent which of the following parathesized expressions is equivalent
Legal precedent means that a decision on a definite principle or question of law has already been made by a court of higher authority, such as a call or supreme court. below such a decision, lower courts defer to, or adhere to, that prior decision in similar cases.
The commitment of lower courts may be used as precedent for courts of similar jurisdiction, but higher courts are not bound by the resolution of lower courts.
The use of legal precedent helps secure court rulings remain consistent among similar cases. To this end, courts are bound to cling to prior decisions made by a higher court on a same legal matter.
Because a judge is bound by these previously made decisions, this is mentioned to as binding precedent. anew, following the principle of glare decisis, binding precedent promotes the maintenance of answers to legal questions already established.
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Water flows at a steady rate from a tap.
It takes 40 seconds to fill a 4 litre watering can from the tap
The rate at which the water is now flowing from the tap is 50 cubic centimeters per second.
What is Unit Rate?Unit rate is the amount of one quantity for a unit amount of the other quantity.
In other words it compares 1 unit of some quantity with different amount of another quantity.
Given that,
Time taken to fill the watering can of 4 liter = 40 seconds.
4 liter = 4000 cm³
Time taken to fill the watering can of 4000 cm³ = 40 seconds
Unit rate of flow of water = 4000 / 40 = 100 cm³ / sec
Now the rate at which water flows is halved.
Rate = 100 / 2 = 50 cm³ / sec
Hence the rate of the flow of water now is 50 cubic centimeters per second.
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The complete question is as follow :
Water flows at a steady rate from a tap it takes 40 seconds to fill a 4 liter watering can from the tap. The rate at which water flows is halved.
4litre=4000cm³
Find the rate at which the water is now flowing from the tap. Give your answer in cubic centimeters per second (cm³/s).
find parametric equations for the line. (use the parameter t.)the line through (5, 5, 0) and perpendicular to both i j and j kx(t), y(t), z(t)
The parametric equations for the line are:
x(t) = 5 + t, y(t) = 5 - t and z(t) = t
Given that the line through (5, 5, 0) and perpendicular to both i + j and j + k
We know that the symmetric form of the equation of the line is given by,
[tex]\frac{x-x_1}{a} =\frac{y-y_1}{b} =\frac{z-z_1}{c} =t[/tex]
Let us assume that x₁ = 5, y₁ = 5 and z₁ = 0
Evaluating the product of ( i + j) and ( j + k ) we get,
( i + j) × ( j + k )
= i - j + k
The value of a = 1, b = -1 and c = 1.
Substitute all the values in the above equation we get,
[tex]\frac{x-x_1}{a} =\frac{y-y_1}{b} =\frac{z-z_1}{c} =t[/tex]
[tex]\frac{x-5}{1} =\frac{y-5}{-1} =\frac{z-0}{1} =t[/tex]
so, the parametric form of the equation would be,
x(t) = x₁ + at
x(t) = 5 + (1)t
x(t) = 5 + t
y(t) = y₁ + bt
y(t) = 5 + (-1)t
y(t) = 5 - t
And z(t) = z₁ + ct
z(t) = 0 + (1)t
z(t) = t
Thus, the parametric equations: x(t) = 5 + t, y(t) = 5 - t and z(t) = t
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The complete question is:
Find parametric equations and symmetric equations for the line. (Use the parameter t.) The line through (5, 5, 0) and perpendicular to both i + j and j + k
x(t), y(t), z(t) = ?
which of the following properties is true for all normal density curves? 1.) they are symmetric 2.) the curve reaches its peak at the mean 3.) 95% of the area under the curve is within one standard deviation of the mean.
All normal density curves are symmetric and have a peak at the mean. 68% of the area under the curve is within one standard deviation of the mean and 95% of the area under the curve is within two standard deviations of the mean.
All normal density curves are symmetric. This means that the curve looks the same to the right and left of the mean (μ). The curve reaches its peak at the mean, which is the highest point on the curve. The area under the curve is equal to 1. The area under the curve that is within one standard deviation (σ) of the mean is equal to 0.68. This means that 68% of the area under the curve is within one standard deviation of the mean and 95% of the area under the curve is within two standard deviations of the mean.
The formula for calculating the area under the curve within one standard deviation of the mean is:
Area = 0.68 * 1
The formula for calculating the area under the curve within two standard deviations of the mean is:
Area = 0.95 * 1
These formulas can be used to calculate the area under the curve for any normal density curve.
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admission to the movies is x dollars, and a bag of popcorn costs $4. write an expression to represent total cost for two people to go to the movies three times and sharing a bag of popcorn each time.
Answer: The total cost for two people to go to the movies three times is 3x2 = 6x dollars.
The cost of a bag of popcorn is $4 and they share one bag of popcorn each time they go to the movie, so the total cost of popcorn is 4*3 = $12 dollars.
So the total cost for two people to go to the movies three times and sharing a bag of popcorn each time is 6x + $12
So an expression to represent the total cost for two people to go to the movies three times and sharing a bag of popcorn each time is 6x + $12.
Step-by-step explanation:
Convert 0.622 0.622 to a fraction in simplest form and a percent.
Answer: 311/500 and 62.22%
Step-by-step explanation:
Fraction: 0.622 = 622/1000 = 311/500
Percent: 0.6222 = 62.22 % (Move decimal 2 places down)
The decimal 0.622 in the form of simplest fraction as 311/500 and in percent is 62.2%.
To convert 0.622 to a fraction in simplest form, write it as follows:
0.622 = 622/1000
Now, simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
622/1000 = (311 × 2)/(500 × 2)
= 311/500
So, 0.622, when expressed as a fraction in simplest form, is 311/500.
To convert 0.622 to a percent, multiply it by 100:
0.622 × 100 = 62.2%
Therefore, 0.622 is equivalent to 311/500 or 62.2%.
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In the linear equation 4x-3y=6, the slope of the line is
A box contains only orange truffles, strawberry truffles and caramel truffles. The ratio of orange truffles to strawberry truffles is 3:4.
Gwyneth picks a truffle at random from the box. The probability that it is an orange truffle is
13/3
What is the probability that it is a caramel truffle?
Give your answer as a fraction in its simplest form.
The probability that it is a caramel truffle is 6/13.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Given, A box contains only orange truffles, strawberry truffles, and caramel truffles and the ratio of orange truffles to strawberry truffles is 3 : 4.
Also given, The probability that it is an orange truffle P(O) is 3/13,
Hence The probability that it is a strawberry truffle P(S) = 4/13.
Therefore, The probability that it is a caramel truffle P(C) is = 1 - 3/13 + 4/13.
= 1 - 7/13.
= 6/16.
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10
Solve for x.
8
6
X
will give brainliest!!!
Answer:
7.5
Step-by-step explanation:
Since the segments are parallel, the side segment lengths are proportional.
8/10 = 6/x
4/5 = 6/x
4x = 30
x = 7.5
True or False: The purchase cost of fixtures can become tax-deductible.
The purchase cost of fixtures can become tax deductible is referred to as a true statement.
What is Taxation?This is referred to as the imposition of compulsory levies on individuals or entities by governments in other to fund government spending and various public expenditures.
Office fixtures such as furniture would typically be considered a long-term asset because it isn't typically replaced on a yearly basis which is why they are not deductible from a business's taxable income. However in a scenario where the fixtures start going through the process of depreciation, amortization or depletion then it becomes tax deductible.
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one week a shop sold 32 ham, 46 tuna, and 18 cheese sandwiches. The next week, the shop sold 38 ham, 43 tuna, and 24 cheese sandwiches. How many more sandwiches did the shop sell the second week?
Step-by-step explanation:
To get the total amount of sandwiches sold in the first week, we would need to add up all of the ham, tuna, and cheese sandwiches.
32 + 46 + 18 = 96
The shop sold 96 sandwiches in the first week.
To find out how many more sandwiches the store sold in the second week, we will need to add up all of the sandwiches again.
38 + 43 + 24 = 105
The shop sold 105 sandwiches in the second week.
Taking 105, we can subtract 96 from it to get how many more sandwiches the shop sold in week 2.
105 - 96 = 9
The shop sold 9 more sandwiches in the second week.
Need help asap, please don’t ignore :(
Answer:c
Step-by-step explanation:
The slope forms a uniform solution in each square box as shown in the drawing
here, s is the value or answer.
SOLUTION -
[tex] \frac{1}{2} = \frac{3}{6} \\ 1 \\ \frac{1}{2} = \frac{1}{2} \\ = \frac{1}{m } = \frac{1}{2} \\ m = 2[/tex]
ANSWER - 24
MP.1 Make Sense and Persevere Alicia
measured 1/4 yard of the Blue Diamonds fabric and5/6
yard of the Yellow Bonnets fabric to make a quilt.
Rename each length of fabric. Use the number of
inches in a yard as a common denominator.
HINT: 1 yard = 3 feet; 1 foot = 12 inches
Alicia made a quilt using 9 inches of Blue Diamonds fabric and 30 inches of Yellow Bonnets fabric.
Describe the length.The end-to-end measurement or size is called the length. In other words, the larger of the two or three dimensions of a geometric shape or object. For example, the length and width of a rectangle define its dimensions. In the international size system, length is also a dimensional distance quantity.
Blue Diamond fabric is 1/4" x 36" or 9" quarter yards.
5/6 yards of yellow bonnet fabric equals 5/6 x 36 inches or 30 inches.
Alicia made the quilt using 9 inches of Blue Diamonds fabric and 30 inches of Yellow Bonnets fabric.
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55oz to ____ lb ____ o
how does sleep deprivation affect your ability to drive? a recent study measured the effects on 19 professional drivers. each driver participated in two experimental sessions: one after normal sleep and one after 27 hours of total sleep deprivation. the treatments were assigned in random order. in each session, performance was measured on a variety of tasks including a driving simulation. use key terms from this module to identify the following values for this study this experiment.
The independent variable in this study is sleep deprivation, as the study aims to investigate the effects of sleep deprivation on the ability to drive.
This study is an experimental study that measures the effects of sleep deprivation on the ability to drive. The sample size is 19 professional drivers, and the study uses a within-subjects design as each driver participated in two experimental sessions: one after normal sleep and one after 27 hours of total sleep deprivation. The treatments were assigned in random order, meaning that each driver has an equal chance of being assigned to either the sleep deprivation or normal sleep condition. The outcome variable in this study is performance on a variety of tasks, including a driving simulation. The independent variable in this study is sleep deprivation, as the study aims to investigate the effects of sleep deprivation on the ability to drive.
Thus, The independent variable in this study is sleep deprivation, as the study aims to investigate the effects of sleep deprivation on the ability to drive.
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(2x + 5y = 18)
Consider the system of equations
(3x + 1.5y = 9)
A : Graph to estimate the solution of the system.
Estimated Solution
B: Solve the system by substitution
The solution for the equations (2x + 5y = 18) and (3x + 1.5y = 9) will be x = 1.5 and y = 3.
What is a system of equations?A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."
Given that the system of the equations is (2x + 5y = 18) and (3x + 1.5y = 9). The equations by substitution method can be solved as,
(2x + 5y = 18)
(3x + 1.5y = 9)
Rewrite the equation (2x + 5y = 18) as,
x = ( 18 - 5y) / 2
Substitute the value of x in the second equation,
3x + 1.5y = 9
3 ( 18 - 5y) / 2 + 1.5y = 9
( 54 - 15 y) /2 + 1.5y = 9
54 - 15y + 3y = 18
-12y = -54 + 18
-12y = -36
y = 3
The value of x will be calculated as:-
2x + 5y = 18
2x + ( 5x 3 ) = 18
2x + 15 = 18
2x = 3
x = 1.5
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PLEASE HELP The flight of Jae and Miguel's rocket t seconds after launch is modeled by
h(t) = -5t² + 40t + 1, where h(t) is their rocket's height in meters.
What was their rocket's height in meters 0.5 seconds after launch? How many sec after launch did their rocket hit the ground? What was their rockets maximum height in meters??
The rocket was at a height of 19.75 meters after 0.5 seconds
The rocket hit the ground after 8.02 seconds
The maximum height is 81 m.
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
The height (h) of the rocket t seconds after launch is modeled by:
h(t) = -5t² + 40t + 1
a) After 0.5 seconds:
h(0.5) = -5(0.5)² + 40(0.5) + 1 = 19.75 meters
b) The rocket hit the ground when h(t) = 0, hence:
-5t² + 40t + 1 = 0
t = 8.02 s
c) The maximum height is at h'(t) = 0
h'(t) = -10t + 40
-10t + 40 = 0
10t = 40
t = 4 s
h(4) = -5(4)² + 40(4) + 1 = 81 meter
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the quotient of 9(7y - 15) and 110 - 6y ÷ 4
y = 7
The quotient of the expression,
9(7y - 15) / (110 - 6y ÷ 4) is 18(7y - 15) / (55 - y).
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
We have an expression,
9(7y - 15) / (110 - 6y ÷ 4)
Simplifying,
9(7y - 15) / (110 - 6y ÷ 4),
= 9(7y - 15) x 4 / (110 - 6y)
= 36(7y - 15) / (110 - 6y)
= 18(7y - 15) / (55 - y)
Therefore, the quotient is 18(7y - 15) / (55 - y).
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help pls A rational expression has been simplified below.
(x-2)(x+6)/7(x+6) = x-2/7
For what values of x are the two expressions equal?
O A. All real numbers except 2
OB. All real numbers
O C. All real numbers except -6
O D. All real numbers except -6 and 2
The values of x if the two expressions equal are all real numbers.
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given expression ,
(x-2) (x+6) / 7 (x+6) = x-2/ 7
So, in LHS x+6 can be cancelled
and we get,
=x-2/ 7
which is same as the RHS from the given expression .
So, As the both LHS and RHS are equal , if put any value Both remains same
Hence, The values of x if the two expressions equal are all real numbers.
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1) Identify the quadrant in which the point belongs. (-17,-87)
Answer:
It belongs in quadrant 3.
What is the circumference of the circle in terms of π?
circle with a segment drawn from one point on the circle through the center to another point on the circle labeled 7 yards
A. 3.5π yards
B. 7π yards
C. 21.98π yards
D. 49π yards
The circumference of the circle in terms of π is 7π yards. Option B
How to determine the circumference of the circleThe formula for calculating the circumference of a circle is expressed as;
C = 2πr
Given that the parameters are;
C is the circumference of the circleπ is the constant value 3.14 and 22/7r is the radius of the circleThe formula for calculating the radius of a circle is given as;
Radius = d/2
Where; d is the diameter of the circle
From the information given,
Diameter = 7 yards
Radius = 3.5 yards
Now, substitute the value
Circumference = 2× 3. 5 ×π
Multiply the values
Circumference = 7π yards
Thus, the value is 7π yards
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Answer: 7 yards
Step-by-step explanation:
Carter has 10 fewer marbles than April. Nicholas has 3 times as many marbles as April. If April has m marbles, which expression BEST represents how many marbles Carter and Nicholas have altogether?
Which one of these?
4m-10 is the expression represents the number of marbles Carter and Nicholas have altogether.
What is Expression?An expression is combination of variables, numbers and operators.
Let m be the number of marbles.
The number of marbles April has be m.
Given that Carter has 10 fewer marbles than April.
If Carter has 10 less than m, that's m - 10.
Nicholas has 3 times as many marbles as April.
3m
marbles Carter and Nicholas have altogether
m-10+3m
4m-10
Hence, 4m-10 is the expression represents the number of marbles Carter and Nicholas have altogether.
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A certain mailing service's first class mail rates are $0.37 for the first ounce and $0.11 for each additional ounce or fraction thereof up to 3.5 ounces. A model for the cost C (in dollars) of a first class mailing that weighs x ounces is given below. C(x) = 0.37 0 ≤ x ≤ 1 0.48 1 < x ≤ 2 0.59 2 < x ≤ 3 0.7 3 < x ≤ 3.5 A.) At what values is the function not continuous? B.) Find the cost of mailing a 1.6-ounce letter.
For the given function C(x) = 0.37 + (x - 1)0.11 the cost of mailing a 1.6-ounce letter is $0.436
The term function in math is defined as a relation between a set of inputs having one output each.
Here we have given that certain mailing service's first class mail rates are $0.37 for the first ounce and $0.11 for each additional ounce or fraction thereof up to 3.5 ounces.
Let us consider that the term C refers that cost in dollars of a first class mailing and x refers the weight in ounces.
The the function for the given situation is written as,
=> C(x) = 0.37 + (x - 1)0.11
Here we have given that we need to find the cost of mailing a 1.6-ounce letter which defines that the value of x is 1.6, then the cost is calculated as,
=> C(x) = 0.37 + (1.6 - 1) 0.11
=> C(x) = 0.37 + 0.066
=> C(x) = 0.436.
Complete Question:
A certain mailing service's first class mail rates are $0.37 for the first ounce and $0.11 for each additional ounce or fraction thereof up to 3.5 ounces. Find the function of the situation and the cost of mailing a 1.6-ounce letter.
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A factory received a shipment of 48 generators, and the vendor who sold the items knows there are 8 generators in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the generators in the sample are defective, he will refuse the shipment.
For each of the following, give your responses as reduced fractions.
If a sample of 8 generators is selected, find the probability that all in the sample are defective.
If a sample of 8 generators is selected, find the probability that none in the sample are defective.
Answer: The probability that all generators in a sample of 8 are defective can be calculated by finding the number of ways that 8 defective generators can be selected out of 48 total generators, divided by the total number of ways that any 8 generators can be selected out of 48 total generators.
The number of ways to select 8 defective generators out of 48 total generators is:
C(8,8)*C(40,0) = 1
The total number of ways to select 8 generators out of 48 total generators is:
C(48,8) = 1,907,725
The probability that all generators in a sample of 8 are defective is:
1/1,907,725
If a sample of 8 generators is selected, find the probability that none in the sample are defective.
The number of ways to select 8 non-defective generators out of 48 total generators is:
C(40,8) = 45,765
The total number of ways to select 8 generators out of 48 total generators is:
C(48,8) = 1,907,725
The probability that none in the sample are defective is:
45,765/1,907,725
Both of these are reduced fraction.
three wires are connected at point d, which is located 18 in. below the t-shaped pipe support abc. determine the tension in each wire when a 180-lb cylinder is suspended from point d as shown.
The tension in each wire when a 180-lb cylinder is suspended from point d is 52.8
The term tension is defined as the tensile load in the wire as it is continuously fed between the wire guides that are used to keep the wire straight between said guides.
While we looking into the following diagram we have identified that the following values are known.
Here the width is 180 lb.
And the distance between the two wires on all the sides is 22 inches, 24 inches and 18 inches.
Then the tension is calculated as,
=> (22 x 24 x 18)/180
=> 9504/180
=> 52.8
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y-1=x
Slope intercept for m
Answer:
Slope intercept form = y=mx+b
So
y-1=x
Add 1 to both sides
y=x+1
what is property
if VW+WY=ZY, and VW + WY=XZ, then XZ=ZY
The property if VW+WY=ZY, and VW + WY=XZ, then XZ=ZY is referred to as a transitive property.
What is a Transitive property?This states that “if two quantities are equal to the third quantity, then we can say that all the quantities are equal to each other”.
A good example of its application can be seen here which is if x = y, and y = 7, then x must equal 7 which when observed in what was given above corresponds with this type of property and is therefore the reason why it was chosen as the correct choice.
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PLS HELP Solve for x
In the equation [tex](1/4)^{x-2} = 16[/tex], The value of the exponent x is 0.
What is an exponent?A number's exponent tells you how long you will need to multiply it in order to get the result. For instance, because 8 is multiplied by itself 3 times, 8 8 8 can be written as 83.
Here, 3 is the "exponent" or "power," which indicates how many times the number 8 is multiplied by itself, and 8 is the "base," which stands for the number being multiplied.
The number of times a number must be multiplied by itself is what a power or exponent, in essence, indicates. The base in this situation can be any integer, fraction, or decimal. Any value, positive or negative, can be assigned to the exponent.
Given
[tex](1/4)^{x-2} = 16[/tex]
[tex](1/4^{x-2}) = 16[/tex]
1 = 16 × [tex]4^{x-2}[/tex]
1 = 16 × [tex](2^2)^{x-2}[/tex]
[tex]$1 = 16 \times \frac{ 2^{2x}}{2^4}[/tex]
[tex]$1 = \frac{ 16 \times2^{2x}}{2^4}[/tex]
[tex]$1 = \frac{ 16 \times2^{2x}}{16}[/tex]
[tex]$1 = 2^{2x}[/tex]
1 = 2²⁽⁰⁾ The only possible exponent that values in 1 is when exponent is 0
1 = 1
x = 0
Thus, In the equation [tex](1/4)^{x-2} = 16[/tex], The value of the exponent x is 0.
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If a bottle holding 3 L of milk contains 2 1/2% butterfat how much skin milk must be added to dilute the milk to 2% butterfat
Answer:
You do not need to add any skim milk.
Step-by-step explanation:
Step-by-step explanation:
percentages are represented by hundredths in calculations.
2 1/2% = 2.5% = 0.025
2% = 0.02
we are mixing the 3 L 2.5% milk with x L of 0% milk.
and we are ending up with (3 + x) L of 2% milk.
so, we have
3×0.025 + x×0 = (3 + x)×0.02 = 3×0.02 + 0.02x
3×0.005 = 0.02x
0.015 = 0.02x
x = 0.015/0.02 = 0.75
so, 0.75 L have to be added to dilute the milk to 2%.
the kappa iota sigma fraternity polled its members on the weekend party theme. the vote was as follows: six for toga, four for hayride, eight for beer bash, and two for masquerade. display the vote count in a pareto chart.
Pareto chart is a type of bar graph which often displays the data in descending order of frequency.
It is made up of vertical bars, with the height of each bar representing the frequency of occurrence for each category. The chart is named after Vilfredo Pareto, who used it to analyze economic data in the late 19th century.
For the given data, we calculate the cumulative frequency of the data by adding the frequencies of each category.
Toga: 6
Hayride: 6 + 4 = 10
Beer Bash: 10 + 8 = 18
Masquerade: 18 + 2 = 20
The Pareto chart is created by plotting the cumulative frequency against the categories. The chart is plotted with the categories on the x-axis and the cumulative frequency on the y-axis.
Toga: 6 (30%)
Hayride: 10 (50%)
Beer Bash: 18 (90%)
Masquerade: 20 (100%)
Hence, the Pareto chart for the given data is as follows:
Toga: 30%
Hayride: 20%
Beer Bash: 40%
Masquerade: 10%
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