Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. y = 5 3√x , y = 0, x = 1
Answers
The volume of the cylinder is
V = 2πr ∫ x h(x) dx.
Here the factor 2πr is the average circumference of the cylindrical shell, the factor h is its height, and the factor ∆r is its the thickness.
The formula sums the volume of a cylindrical shell over the radius of the cylinder, and the volume of a cylinder is given by V=2πrh V = 2 π r h where r is the radius and h is the height.
I first found what x=1 would be in terms of y.
y=(2)3=8
And in terms of y, the original equation becomes:
y=x3x=y13
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The volume of the cylinder is V = 2πr ∫ x h(x) dx.
Here the factor 2πr is the average circumference of the cylindrical shell, the factor h is its height, and the factor ∆r is its the thickness.
The formula sums the volume of a cylindrical shell over the radius of the cylinder, and the volume of a cylinder is given by V=2πrh V = 2 π r h where r is the radius and h is the height.
I first found what x=1 would be in terms of y.
y=(2)3=8
And in terms of y, the original equation becomes:
y=x3x=y13
See the image as the answer is given in the image down below.
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Related Questions
in a given year, approximately 30% of children and adolescents in the united states display serious psychological disturbances and need clinical treatment.
Answers
It can be concluded that in 2018, approximately 21.7% of children and adolescents in the United States displayed serious psychological disturbances and needed clinical treatment.
The percentage of children and adolescents in the United States displaying serious psychological disturbances is calculated by dividing the number of children and adolescents with serious psychological disturbances by the total number of children and adolescents in the United States. This can be expressed mathematically as:
% = (Number of children and adolescents with serious psychological disturbances / Total number of children and adolescents in US) x 100
Using estimates from 2018, approximately 48.5 million children and adolescents in the United States, and 10.5 million of them displaying serious psychological disturbances, the percentage of children and adolescents in the United States displaying serious psychological disturbances in 2018 can be calculated as:
% = (10.5 million / 48.5 million) x 100 = 21.7%
Therefore, it can be concluded that in 2018, approximately 21.7% of children and adolescents in the United States displayed serious psychological disturbances and needed clinical treatment.
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Determine constants and such that the given piecewise function is continuous for all .
F(x)= -6 if x < -1
Ax + 2. if -1 ≤ x ≤ 2
-x^2 + Bx + 14. if x > 2
Round your answers to one decimal place, if necessary.
Answers
Answer: To make the piecewise function continuous for all x, we need to make sure that the function values and the function slopes at the boundaries (-1 and 2) are the same for each piece.
For x = -1:
F(-1) = -6 (from the first piece)
F(-1) = A(-1) + 2 = -A + 2 (from the second piece)
So, to make the function continuous at x = -1, we need to set -6 = -A + 2, which gives us A = -8.
For x = 2:
F(2) = -x^2 + Bx + 14 (from the third piece)
F(2) = A(2) + 2 = 2A + 2 (from the second piece)
So, to make the function continuous at x = 2, we need to set -4 + 2B + 14 = 2A + 2, which gives us B = -5.
Now we can write the function with the constants that we found :
F(x) = -6 if x < -1
-8x + 2 if -1 ≤ x ≤ 2
-x^2 - 5x + 14 if x > 2
This function is continuous for all x and the values and slopes match at x = -1 and x = 2.
Step-by-step explanation:
Mick drew the following steps using parallel lines. What is the measure of z?
Answers
Answer:
Step-by-step explanation:
The top left angle = 52⁰ - also right angle = 52⁰. ( alternate angles of parallel l;ines).
So, x = 180 - 2(52) = 180-104
= 76 degrees.
Find the equation for the plane through Po(-4,-3,8) perpendicular to the following line.
x = -4+t, y=-3-3t, z= -4t, -∞
Answers
The equation of plane is x - 3y - 4z = 27.
What method can be used to determine the equation of a plane that is perpendicular to a vector?a plane produced by the application of vectors perpendicular to a normal. The implication of this is that, given a vector a, b, c, we may deduce that all planes perpendicular to it have the form ax+by+cz=d and that any surface with this form is a plane perpendicular to a, b, c.
The equation for a plane perpendicular to a given line with direction ratios a, b, and c> and passing through a point is a(x-x1) + b(y-y1) + c(z-z1) = 0. (x1, y1, z1).
The equation of the plane traveling through the points x, y, and z on a plane perpendicular to the line whose parametric equation is provided
Equation of a plane through the point (-4,-3,8) is
a(x - 4) + b(y - 3) + c(z + 8) = 0
Since it is perpendicular to the line :
x = -4+t, y=-3-3t, z= -4t,
t = x + 4 = -y - 3 / 3 = -z/4
therefore coefficients a, b, c must be proportional to 1, - 3 & (-4) respectively.
Therefore, putting the values of a, b & c in eq.(1), we get the required equation of the plane as ;
λ(x - 4) -3 λ(y - 3) - 4λ(z + 8) = 0 (λ is a constant)
⇒ x - 4 - 3y + 9 -4z - 32 = 0
⇒ x - 3y - 4z = 27
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Add 4x +1
To
5x+6
Write the following as an algebraic expression. Simply if possible
Answers
Answer:
9x + 7
Step-by-step explanation:
Add 4x + 1 to 5x + 6
in an algebraic expression is:
4x + 1 + 5x + 6
To simplify, combine like terms. This means add the x terms together and add the constants (plain number- - the 1 and 6) together.
4x + 1 + 5x + 6
= 4x + 5x + 1 + 6
= 9x + 7
Olivia earns $12 an hour at the grocery store. She kept track of her hours per week and how much she earned in the following table. Graph the values in the table on the coordinates plane shown. what will you label the x-axis?
Answers
Answer:
12 times y = x
Step-by-step explanation:
I see on you paper you want to do intervals of 2 so just take 12 and multiply it by the desired number. Equation: 12 x # = the y axis point. This is where #=x-axis and plugging it in the equation gives you the y point.
PLEASE HELP FOR 30 POINTS ITS A UNIT TEST!!!!!!!
The coordinates of the vertices of a polygon are shown on the graph below.
What is the name of the polygon?
hexagon
octagon
quadrilateral
triangle
Answers
Answer: Quadrilateral
Step-by-step explanation:
hexagon: 6 sides
octagon: 8 sides
quadrilateral: 4 sides
triangle: 3 sides
The quadrilateral is the only one that makes sense.
when the population mean and standard deviation are known, we can generally assume the following about the sample mean and standard deviation (check all that apply
Answers
When σ is known, hypothesis tests are performed for one population mean. The one-mean z-test, or simply z-test, is a hypothesis test carried out for a single population mean when the population standard deviation is known.
A data distribution's spread is measured by standard deviation. It calculates the average separation between each data point and the mean.
Whether we consider the data to be a population unto itself or a sample of a broader population affects the method we use to calculate standard deviation.
Statistics is the parent topic for the Population Mean notion. In a nutshell, statistics addresses the issues of gathering data as well as its analysis, interpretation, and presentation. The population mean formula calculates the average of all the values in the population or set of data.
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let f (x, y) be the statement x trusts y, where the domain of discourse for both x and y is all people. (a) use quantifiers to express each of the following propositions in symbols. (i) nobody trusts ralph. (ii) everybody trusts fred. (iii) somebody trusts everybody.
Answers
The required expressions are ¬ ∃x(F(x, Ralph)), ∀xF(x, Fred), and ∀x∃yF(x,y). Here, ¬ means negation, ∃ means existential quantifier, and ∀ means universal quantifier.
One or more variables that are defined on a particular domain are expressed by a predicate. By giving the variable a value or by quantifying it, it is possible to turn a predicate with variables into a proposition.
There are two quantifiers used in this they are (i) existential quantifier which is represented by ∃ and (ii) universal quantifier which is represented by ∀.
For, the proposition, "Nobody trusts Ralph", the quantifier is written as ¬ ∃x(F(x, Ralph)).
For the proposition, "Everybody trusts Fred", the quantifier is written as ∀xF(x, Fred).
For the proposition, "Somebody trust everybody", the quantifier is written as ∀x∃yF(x,y).
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a) Using the 2" zn rule, construct a frequency distribution for these data. Select the correct choice below and fill in the answer boxes to complete your choice.O A. Credit Card Balances Frequency $0 to less than $1,000 $1,000 to less than $2,000 $2,000 to less than $3,000 $3,000 to less than $4,000 $4,000 to less than $5,000 $5,000 to less than $6,000 O B. Credit Card Balances Frequency $0 to less than $1,200 $1,200 to less than $2,400 $2,400 to less than $3,600 $3,600 to less than $4,800 $4,800 to less than $6,000 Credit Card Balances$2,368 $5,789 $1,754 $5,927 $5,815 $349 $3,522 $3,888 $5,323 $1,039 $1,247 $2,429 $461 $1,464 $4,505 $2,667 $5,425 $669 $911 $750 $1,007 $1,706 $300 $410 $4,650 $3,770 $4,502 $4,056 $1,020 $158 $168 $4,565 $1,557 $924 $524 $1,669
Answers
If k is the number of classes and n is the number of observation then for class intervals, select the smallest k such that 2k >= n using statistics.
n = 36
2^5 = 32< 36
2^6 = 64 > 36
So k = 6
a) Frequency distribution: Answer A.
Class interval Frequency
0 to less than 1000 11
1000 to less than 2000 9
2000 to less than 3000 3
3000 to less than 4000 3
4000 to less than 5000 5
5000 to less than 6000 5
b) Relative frequency distribution: Answer B.
Class interval Relative frequency
0 to less than 1000 11 / 36 = 0.306
1000 to less than 2000 9 / 36 = 0.250
2000 to less than 3000 3 / 36 = 0.083
3000 to less than 4000 3 / 36 = 0.083
4000 to less than 5000 5 / 36 = 0.139
5000 to less than 6000 5 / 36 = 0.139
c) Cumulative relative frequency:
Class interval Cumulative Frequency
less than 1000 11
less than 2000 20
less than 3000 23
less than 4000 26
less than 5000 31
less than 6000 36
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#15 find the measure of angle P. I need help with this problem
Answers
The measure of ∠P is 96°.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
∠P and ∠R are alternate angles.
Alternate angles are equal.
So,
∠P = ∠R
2x = x + 48
2x - x = 48
x = 48
Now,
∠P = x + 48
∠P = 48 + 48
∠P = 96
Tus,
The value of ∠P is 96°.
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convert the system to an augmented matrix. type each element of the answer in the spaces provided. 2x y
Answers
The augmented matrix of the solution to the system of equations is x = 4 and y = -1/2.
The augmented matrix of the system of equations 2x + y = 8 and 3x - y = 7 can be written as follows:
|2x + y = 8 |
|3x - y = 7 |
This can be rewritten in matrix form as:
|2 1 | |x | | 8 |
|3 -1| |y | | 7 |
To solve this system of linear equations, we can use the Gauss-Jordan elimination method. First, we add the first row to the second row to eliminate the x coefficient from the second equation:
|2 1 | |x | | 8 |
|0 -2| |y | | 1 |
Then, we can divide the second row by -2 to get the coefficient of y to be 1:
|2 1 | |x | | 8 |
|0 1 | |y | |-1/2|
Finally, we can subtract the second row from the first row to eliminate the y coefficient from the first equation:
|2 0 | |x | | 8/2|
|0 1 | |y | |-1/2|
Therefore, the solution to the system of equations is x = 4 and y = -1/2.
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which if the following definitions is not correct? which if the following definitions is not correct? raw data is data that have been collected but are not processed, cleaned or analyzed. statistics is the branch of math that deals with collection, analysis and interpretation of large masses of data. you generally use some form of statistics to get to a useful data visualization. qualitative data is data that cannot be counted easily using numbers. social scientists often used qualitative data which includes text, observations, interviews, and open questions. the y-axis is the horizontal number line and the x-axis is the vertical number line in a chart.
Answers
Qualitative data is data that cannot be counted easily using numbers is not have the correct definitions.
Qualitative data is used to address the research questionnaire regarding whats and how many(s) or also for research procedures to quantify a problem. This data can be used to compare or count data on a numerical scale.
This type of research typically involves in-depth interviews, focus groups, or observations in order to collect data that is rich in detail and context. This data is used for Qualitative research which is very helpful when understanding social reality and the attributes, beliefs, and motivations of people.
The main importance of this kind of project come into the limelight when someone is trying to understand the reason behind one's beliefs or behaviors.
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Find f(-5) if f(x) = |x + 1|
Answers are 4, 5, or 6
Answers
Answer:
f(-5) = 4
Step-by-step explanation:
[tex]f(x)=|x+1|\\f(-5)=|-5+1|=|-4|=4[/tex]
Write an expression for a polynomial function whose graph intercepts the horizontal axis at -7,8 and 15
Answers
The polynomial function with the given intercepts of the hirzontal axis can be written as:
p(x) = (x + 7)*(x - 8)*(x - 15)
How to write the polynomial?We know that a polynomial of degree N whose leading coefficient is 1 and has the zeros {x₁, x₂, ...}
Then the polynomial can be written as:
p(x) = (x - x₁)*(x - x₂)*...
Here the zeros (also called intercepts of the horizontal axis, like on this case) are {-7, 8, 15}
Then wecan write the polynomial with these zeros as:
p(x) = (x - (-7))*(x - 8)*(x - 15)
p(x) = (x + 7)*(x - 8)*(x - 15)
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Which difference is 4.517?
Answers
The difference between 4.507 and 4.517 can be expressed as -0.010.
What is difference in mathematics?The concept that will be used here is substraction. The outcome of subtracting one integer from another is difference. While we frequently discuss differences in how objects appear, feel, or even taste, mathematics demonstrates how much two numbers vary from one another in terms of quantity. Difference is what is left behind after subtracting one number from another.
the outcome of subtraction of two numbers. the difference between two numbers. For instance: There is a 5 difference between 8 and 3.
We were to find the difference between 4.507 and 4.517 whichg implies the substraction between the values and can be done as
(4.507 - 4.517)= -0.010
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complete question:
What is the difference between 4.507 and 4.517
For the rectangular parking area of the shopping
center shown, which one of the following equations
says that the area is 30,000 yd² ?
A. x(4x +300) = 30,000
B. x+(4x +300)=30,00
Equation
(Type A, B, C, or D.)
says that the area is 30,000 yd².
CO
C. 2x + 2(4x + 300) = 30,000
D. x² (4x+300)² = 30,000²
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4x+300
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Answers
For the rectangular parking area of the shopping center shown, an equation which says that the area is 30,000 yd² is: A. x(2x + 200) = 30,000.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width of a rectangle.L represents the length of a rectangle.From the information provided about the rectangular parking area of the shopping center shown in the image attached below, we have the following dimensions:
Length = x
Width = 2x + 200
Substituting the given points into the area of rectangle formula, we have the following;
30,000 = x × (2x + 200)
30,000 = x(2x + 200) ⇒ (required equation).
30,000 = 2x² + 200x.
2x² + 200x - 30,000 = 0.
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Help I need to do corrections but they need to be turned in by 4pm today
Answers
Answer: I think it is -7 I'm not exactly sure but that's what I think please take someone else's answer just in case.
Step-by-step explanation:
10. Some people who have never smoked develop lung cancer. Does this disprove the evidence?
(1 point)
I
Answers
The fact that some people who smoked never develop lung cancer does not disprove the evidence.
Why can some people smoke and not develop lung cancer ?The fact that some people who have never smoked develop lung cancer does not disprove the evidence linking smoking to lung cancer.
Smoking is a major risk factor for lung cancer, and the overwhelming majority of people who are diagnosed with the disease are smokers or former smokers. However, it is important to note that other factors, such as exposure to radon and other pollutants, can also increase the risk of lung cancer, and that some people may be more genetically susceptible to the disease. So, it is possible for people who have never smoked to develop lung cancer as well.
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What is (f/g)(x)?
f(x) = -x
g(x) = -5x + 2
Write your answer as a polynomial or a rational function in simplest form.
Answers
The rational function in the simplest form of (f/g)(x) is x / 5x - 2.
How to solve functions?Composite functions are when the output of one function is used as the input of another. A typical example of a composite function is (f/g)(x).
Therefore, let's solve the rational function in the simplest form.
Hence,
f(x) = -x
g(x) = -5x + 2
(f/g)(x) = f(x) / g(x)
Therefore,
(f/g)(x) = - x / -5x + 2
Hence,
(f/g)(x) = - x / - (5x - 2)
Finally,
(f/g)(x) = x / 5x - 2
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Solve the system by elimination 8x+3y=4 2x+y=2 what is the solution
Answers
The solution for the system of equations 8x + 3y = 4 and 2x + y = 2 by elimination are x = -1, y = 4
How to evaluate for the solutions of the equations by eliminationwe shall write the equations as:
8x + 3y = 4...(1)
2x + y = 2...(2)
multiply equation (2) by 3 to get equation (3)
3(2x + y) = 3 × 2
6x + 3y = 6...(3)
subtract equation (1) from (3) to eliminate y
6x + 3y - 8x - 3y = 6 - 4
-2x = 2
divide through by -2
x = -1
put the value -1 for x in equation (2) to get y
2(-1) + y = 2
-2 + y = 2
y = 2 + 2 {add 2 to both sides}
y = 4
Therefore, the solution for the system of equations 8x + 3y = 4 and 2x + y = 2 by elimination are x = -1, y = 4.
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Cement cost $76 per cubic yard. What is the cost of cement for a sidewalk that is 4" thick, 3' wide, and 40' long.
Answers
If cement costs $76 per cubic yard, the total cost of cement for a sidewalk with a volume of 480 inches³ is $1,013.
How is the total cost determined?The total cost of cement for the sidewalk is determined using unit conversions and multiplication.
After determining the volume in inches and converting it to yards, the result is multiplied by the unit cost of cement per cubic yard.
Dimensions of the Sidewalk:
Length = 40 inches
Width = 3 inches
Thickness = 4 inches
Volume = 480 inches³ (40 x 3 x 4)
36 Inches = 1 Yard
480 cubic inches = 13.33 cubic yards
Cost of cement per cubic yard = $76
Cost of the sidewalk = $1,013 ($76 x 13.33)
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A sunflower is measured at the beginning of June and is 40cm tall. The sunflower
grows by 25% each month for three months. What height is the sunflower to the nearest
centimetre at the beginning of September?
Answers
Answer:
78cm 78.125
Step-by-step explanation:
Answer: 78.13
Step-by-step explanation:
you start with 40cm and find 25% of that and add it to 40cm. Or you can do 1.25x40=50 That would be July, so repeat to get 50x1.25=62.5 to get august, then again to get 62.5x1.25=78.13
2 x – 3 y = 7
–4 x + y = –5
What is the x -value of the solution to this system of equations?
Answers
Answer:
x = [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
2x - 3y = 7 → (1)
- 4x + y = - 5 → (2)
multiplying (2) by 3 and adding to (1) will eliminate y
- 12x + 3y = - 15 → (3)
add (1) and (3) term by term to eliminate y
- 10x + 0 = - 8
- 10x = - 8 ( divide both sides by - 10 )
x = [tex]\frac{-8}{-10}[/tex] = [tex]\frac{4}{5}[/tex] (= 0.8 )
The image includes the questions
Answers
Answer:
a.
b. 35/100 of 76 = 26 to 27 remained
c.
d. statistic
e. experiment
f. I don't think so
Step-by-step explanation:
4 Four boys and five girls went to the movies together. Between them they
had $120 to spend. Tickets cost $8 each. How much money did they have
to buy refreshments?
Answers
If an item that originally cost $18 is decreased to $12, what is the percentage of decrease in the item?
Answers
This is the answer
Will Mark brainliest
Write an equation in point slope form for the line that passes through the given point and is perpendicular to the graph of each equation.
(3, - 2) ; y = 2/3x + 4
Answers
An equation in point slope form for the line that passes through the given point and is perpendicular to the graph of each equation is y=2/3 x²+4x
How to find the equation?A mathematical equation is a formula that uses the equals sign ('=') to express the equality of two expressions. The meanings of the word equation and its cognates in other languages can vary slightly. For instance, an equation in English is any well-formed formula consisting of two expressions related by an equals sign, while an equation in French is defined as containing one or more variables.
step 1
y=2/3+4
y=2/3 x²+4x
y=m x+ b
step 2
y= y coordinate
m=slope
x=x coordinate
b=y intercept
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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
3.5π yards
7π yards
21.98π yards
49π yards
Answers
Circumference of circle = 7π yards
The correct option is B.
What is circle?A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.
Given,
Segment drawn from one point on the circle through the center to another point = diameter of circle = 7 yards
Circumference of the circle = π × Diameter
= 7π yards
Hence, 7π yards is the circumference of the circle
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Answer:
b
Step-by-step explanation:
consider the following input-output table. p q r s 1 1 1 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 the output column, s, was created from the student id 21444368 using the algorithm: if id digit n (left-to-right) is an even integer, place a 0 in s, row n (top-down) if id digit n (left-to-right) is an odd integer, place a 1 in s, row n (top-down) create a similar table, but with s reflecting the result of the algorithm applied to your student id (do this on scratch paper). on the quiz essay: record your student id, id
Answers
The output column, S, of the given input-output table was created from the student ID 21444368 using an algorithm where if the student ID digit is an even integer, a 0 is placed in the corresponding row of column S, and if the student ID digit is an odd integer, a 1 is placed in the corresponding row of column S.
Student ID: 81725225
P Q R S
1 1 1 0
1 1 0 1
1 0 1 1
0 1 0 0
0 0 1 1
0 1 1 0
0 0 0 1
Student ID: 81725225
P: The first digit of my student ID is 8 so it is an even integer, therefore I place a 0 in row 1 of column P.
Q: The second digit of my student ID is 1 so it is an odd integer, therefore I place a 1 in row 2 of column Q.
R: The third digit of my student ID is 7 so it is an odd integer, therefore I place a 1 in row 3 of column R.
S: The fourth digit of my student ID is 2 so it is an even integer, therefore I place a 0 in row 4 of column S.
The resulting table is:
P Q R S
1 1 1 0
1 1 0 1
1 0 1 1
0 1 0 0
0 0 1 1
0 1 1 0
0 0 0 1
The output column, S, of the given input-output table was created from the student ID 21444368 using an algorithm where if the student ID digit is an even integer, a 0 is placed in the corresponding row of column S, and if the student ID digit is an odd integer, a 1 is placed in the corresponding row of column S. The same algorithm was applied to my student ID 81725225, resulting in the table shown above.
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