Mathematically, the balance on Howard Gessner's American Express card on September 1 is $360.63.
How do we determine the balance?The ending balance on September 1 is determined using the mathematical operations of addition, subtraction, and multiplication (for the finance charge).
The finance charge is the interest and other fees paid for borrowing credit.
The finance charge is always based on a percentage, called the annual or monthly percentage rate (APR or MPR).
In this situation, the monthly percentage rate is applied to the unpaid balance (multiplication) at the end of August, to determine the finance charge, which is added to the unpaid balance to compute the September 1 balance.
August 1 Balance = $543.27
Purchases 201.25
Returns (89.22)
Payments (300.00)
Unpaid balance $355.30
Finance charge 5.33 ($355.30 x 1.5%)
September 1 Balance $360.63
Thus, using mathematical operations, the balance on September 1 is $360.63.
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A survey shows that the probability that an employee gets placed in a suitable job is 0.65. A psychometric test consultant claims that he could help place any employee in a suitable job based on the result of a psychometric test. The test has an accuracy rate of 70%. An employee working in a particular company takes the test. The probability that the employee is in the right job and the test predicts that he is in the wrong job is . The probability that the employee is in the wrong job and the test predicts that he is in the right job is
The probability that someone is in the right job and the test is then wrong is 0.195.
The probability that the employee is in the wrong job and the test predicts that he is in the right job is 0.105.
How to calculate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In
The probability that he is in the right job is 0.65, so the probability he is in the wrong job is 0.35, and similarly, the probability that the test is inaccurate is 0.3. Thus, the probability that someone is in the right job and the test is then wrong is:
= 0.65*0.3
= 0.195
The probability that someone is in the wrong job and the test is right is:
= 0.35 × 0.3
= 0.105.
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1. Which equation describes the line with
slope -4 and y-intercept 2?
A y=-4x+2
B y=-4x-2
C y=4x-2
D y = 4x + 2
Answer:
Step-by-step explanation:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Therefore, the equation of the line with slope -4 and y-intercept 2 is y = (-4)x + 2.
How do I solve this problem. Please explain step by step if u could
0.25 + (-3) =
Answer:
0.25 − 3
=0.25 + −3
= −2.75
( a number line to help to)
Step-by-step explanation:
The better your time management skills are, the more work you are able to do is an example of a Continuous correlation Biserial correlation O Positive correlation O Negative correlation
The time management skill and amount of work done is an example of positive correlation.
Correlation or dependency pertains to any statistical link involving two random variables or bivariate data, whether causal or not. Although the term "correlation" can refer to any form of link, in statistics it is most usually used to refer to the degree to which two variables are statistically linearly associated.
The link between the heights of parents and their children, as seen in the enough that demand curve, and the correlation between the price of an item and the quantity of items that buyers are willing to acquire are examples of dependent phenomena.
The Pearson product-moment correlation coefficient (PPMCC), sometimes known as "Pearson's correlation coefficient," is the most commonly used measure of two-value dependency.
It is computed by dividing the covariance ratio of the two variables in our numerical dataset by the square root of their variances. The covariance of the two variables is simply divided by the product of their standard deviations in mathematics. The coefficient was calculated by Karl Pearson from Francis Galton's similar but slightly different idea.
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which graph represents the equation y =1/3 x + 2
The graph of the equation y = (1/3)x + 2 is passing through points
(3, 3) and ( -3, 1).
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, A linear equation y = (1/3)x + 2.
Now to graph the equation we'll simply put some arbitrary values of x which will correspond to some values of y and plot them then we'll join them with a straightedge.
When x = 3, y = 3 ⇒ (3, 3).
When x = - 3, y = 1 ⇒( -3, 1).
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Solve x2 + 4x = 1 for x by completing the square.
x = −3
x = −1
x equals plus or minus square root of 5 minus 2
x equals plus or minus square root of 5 plus 2
Using the completing square method, the value of (C) x = ±√5 - 2.
What is completing the square method?A quadratic polynomial of the form ax2+bx+c can be transformed to the form in elementary algebra by using the "completing the square" method for certain values of h and k.
In other words, the quadratic expression is completed by inserting a perfect square trinomial.
So, we have:
x² + 4x = 1
The x-coefficient terms must be divided by two:
4/2 = 2
Square:
2² = 4
Add 4 on both sides as follows:
x² + 4x + 4 = 1 + 4
x² + 4x + 4 = 5
Transform into perfect squares:
(x + 2)² = 5
Both sides of the square root:
x + 2 = ±√5
x = ±√5 - 2
Therefore, using the completing the square method, the value of (C) x=±√5-2.
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Complete question:
Solve x2 + 4x = 1 for x by completing the square.
a. x = −3
b. x = −1
c. x equals plus or minus the square root of 5 minus 2
d. x equals plus or minus square root of 5 plus 2
Answer:
is c correct?
Step-by-step explanation:
Conrad Savings Bank has a $50 overdraft fee. On Friday, Mr. McQuire deposited his paycheck of $332 for a total
account balance of $750. The next morning, his wife wrote a check for $1,183.15 for a new refrigerator and stove.
The check cleared the bank by the end of the day. What is the current balance in the McQuire's account?
Answer: -433.15
Step-by-step explanation:
he's id debt and has to pay off the 433.15 later on.
Answer:
The McQuires' account is currently overdrawn by $483.15.
Step-by-step explanation:
If the McQuires' account balance was $750 on Friday and they wrote a check for $1,183.15 on Saturday, then the balance would be 750 - 1,183.15 = -$433.15 after the check cleared. Since the bank charges a $50 overdraft fee, the final balance in the McQuires' account would be -$433.15 - $50 = -$483.15. The McQuires' account is currently overdrawn by $483.15.
Write the equation of the line in fully simplified slope-intercept form.
Answer:
y = - 0.4x -6
Step-by-step explanation:
The slope-intercept form of a line equation is
y = mx + b
where m is the slope and b the y-intercept where the line crosses the y axis.
From the figure it is clear that the line passes through (0, -6) and therefore the y-intercept is -6
To compute the slope, find another convenient point on the line. Compute the ratio of change in y values(called rise) to the change in x values(called run). This will be the slope
We see that point (10, -10) has been identified on the graph.(Any of the 4 identified points will do, I just chose this)
So two points to consider are (0, -6) and (10, -10)
Change in y values = rise = -10 - (-6) = 1- + 6 = -4
Change in x values = run = 10 - 0 = 10
So slope m = -4/10 = -0.4
Equation of line is y = -0.4x -6
the student government claims that 70% of all students favor an increase in student fees to buy indoor potted plants for the classrooms. a random sample of 12 students produced 2 in favor of the project.
(a) What is the probability that 2 or fewer in the sample will favor the project, assuming the student government's claim is correct? (Use 3 decimal places.) (b) Do the the data support the student government's claim, or does it seem that the percentage favoring the increase in fees is less than 70%? The data do not give us any indication that the percent favoring the increase in fees differs from 70%. The data seem to indicate that the percent favoring the increase in fees is greater than 70%. The data seem to indicate that the percent favoring the increase in fees is less than 70%. The data seem to indicate that the percent favoring the increase in fees is equal to 70%.
The probability that 2 or fewer in the sample will favor the project is 4.368 × 10⁻⁶ and Also The data seem to indicate that the percent favoring the increase in fees is less than 70%
According to the question,
It is given that according to the student's government
The probability that number of students in favor of increment in fees : p = 0.70
The probability that number of students against the increment : q = 0.30
Sample Size : n = 12
Number of students follows Binomial distribution
(a) We have to find the probability that 2 or fewer in the sample will favor the project
P( x ≤ 2) = P(0) + P(1) + P(2)
As we know ,
P(x) = ⁿCₓpˣq⁽ⁿ⁻ˣ⁾
=> P( x ≤ 2) = ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹ + ¹²C₂p²q¹⁰
=> P( x ≤ 2) = 1×(0.30)¹² + 12×(0.70)(0.30)¹¹ + 12×11/2 × (0.70)²(0.30)¹⁰
=> P( x ≤ 2) = (0.30)¹⁰ [ 0.09 + 0.21 + 0.48]
=> P( x ≤ 2) = 5.9×10⁻⁶[0.78]
=> P( x ≤ 2) = 4.368 × 10⁻⁶
Which is very close to zero
(b) The data doesn't support the student government claim.
The data seem to indicate that the percent favoring the increase in fees is less than 70%.
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Problems 14 and 15 pertain to the following situation: a woman buys 20 one-dollar lottery tickets per month. The probability of any ticket being a winning ticket is 0.10 or 10%.
14. The probability that in any one month at least three of the tickets that the woman buys are winning tickets is about?
15. The average number of winning tickets that the woman buys each month is about?
The required probability is P(X≥3) =0.3234
The average number of winning tickets that the woman buys each month is 2.
The binomial probability distribution is a discrete type of probability distribution with two parameters, n, and p. The probability mass function of the distribution is used to get the required probability. The average value of the winning number is the expected value of the binomial distribution.
The probability mass function of the binomial distribution is defined as:
[tex]P(X=x)=\frac{n}{x} p^{x} (1-p)^{n-x} , x =0,1,2,3,....,n.[/tex]
Given that,
n = 20
p = 0.10
The required probability is P(X≥3)
P(X≥3) = 1-P(X<3)
P(X≥3)= 1-P(X=0)-P(X=1)-P(X=2)
P(X≥3)= 1- 0.1216- 0.270- 0.285
P(X≥3) = 0.3234
The mean of the distribution is defined as μ=n*p= 20*0.10= 2
The average number of winning tickets that the woman buys each month is 2.
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In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
Answer:
70
Step-by-step explanation:
What is the approximate perimeter of this triangle?
Answer:
163.6 in---------------------------
Given:
a = 56 in,m∠A = 55°.Find the missing sides:
56/b = tan 55° ⇒ b = 56 / tan 55° = 39.21 in,56/c = sin 55° ⇒ c = 56 / sin 55° = 68.36 in.Perimeter is:
56 + 68.36 + 39.21 = 163.57 ≈ 163.6 inYou brought popular game on sale for $20 and want to sell it on eBay. You want to mark up the toy 60%. What did you sell it for?
Decide whether the random variable x is discrete or continuous. x represents the number of dependent children in a household
Time is represented by the variable. Since a person's speed, which can take on nearly any value, determines how long it takes them to complete a mile, this variable is continuous.
Define Continuous variable?If a quantitative variable is often obtained through measuring or counting, it can either be continuous or discrete. If a variable can take on any two particular real values and all other real values in between, it is said to be continuous over a range of real values.
First, when is a variable continuous and when is it discrete?
A variable is continuous if it can take any value (or at least a dense set of values) inside a certain interval as opposed to discrete if it can only take a few specific values on that interval.
For instance, the only possible values for the numbers one can roll on a dice are 1, 2, 3, 4, 5, and 6, to provide one example.
The variable in this instance now stands for time. Time is nearly always a continuous variable; in this instance, the time refers to the duration of a mile run. Therefore, that variable is capable of practically any value (depends on the speed of the person).
Therefore,
Time is represented by the variable. Since a person's speed, which can take on nearly any value, determines how long it takes them to complete a mile, this variable is continuous.
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3 less than the difference of 15 and a number h
Answer: 15 - h - 3
Step-by-step explanation:
What is 0.6 divided by 10
Answer: 0.06
Step-by-step explanation:
find the volume of the largest right circular cylinder that can be inscribed in a sphere of radius r.
The volume of the largest right circular cylinder is [tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit
Now, According to the question:
The given sphere is of radius R.
Let h be the height and r be the radius of the cylinder inscribed in the sphere.
We know that:
Volume of cylinder
V = [tex]\pi R^2h[/tex] .....(1)
In right Triangle OBA
[tex]AB^2 + OB^2 = OA^2[/tex]
[tex]R^2 + \frac{h^2}{4} = r^2[/tex]
So, [tex]R^2 = r^2 - \frac{h^2}{4}[/tex]
Putting the value of [tex]R^2[/tex] in equation (1), We get
V = [tex]\pi (r^2 - \frac{h^2}{4} )h[/tex]
V = [tex]\pi (r^2h - \frac{h^3}{4} )[/tex] ....(2)
dV/dh = [tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] .....(3)
For, Stationary point, dV/dh = 0
[tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] = 0
[tex](r^2 - \frac{3h}{4} )[/tex] => [tex]h^2 - \frac{4r^2}{3}[/tex] => [tex]h - \frac{2r}{\sqrt{3} }[/tex]
Now, [tex]\frac{d^2V}{dh^2} = \pi (-\frac{6}{4}h )[/tex]
[tex][\frac{d^2V}{dh^2}]_a_t_h_=_\frac{2r}{\sqrt{3} }[/tex] = x[-3/2 , [tex]2r/\sqrt{3}[/tex]]< 0
Volume is maximum at h = 2r/[tex]\sqrt{3}[/tex]
Maximum volume is :
[tex]= \pi (r^2.\frac{2r}{\sqrt{3} }- \frac{1}{4}.\frac{8r^3}{3\sqrt{3} } )[/tex]
[tex]=\pi (\frac{2r^3}{\sqrt{3} }-\frac{2r^3}{3\sqrt{3} } )[/tex]
[tex]=\pi (\frac{6r^3-2r^3}{3\sqrt{3} } )[/tex]
[tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit
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URGENT!!!!
Find z such that 7% of the area under the standard normal curve lies to the right of z.
The value of z such that 7% of the area under the standard normal curve lies to the right of z is approximately -0.4
How to find z such that 7% of the area under the standard normal curve lies to the right of z?
To find the value of z such that 7% of the area under the curve lies to the right of z, we need to find the value of z such that 43% of the area lies to the left of z.
This value of z is known as the 43rd percentile of the standard normal curve.
We can use a table of the standard normal distribution, also known as the z-table, to find the value of z corresponding to the 43rd percentile.
According to the z-table, the value of z corresponding to the 43rd percentile is approximately -0.4
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an engineer says a pipe should be 7/10 centimeters long. The pipe is 9/10 centimeter long. How much of the pipe needs to be cut off? write an equation.
Answer: x = 9/10 - 7/10
Step-by-step explanation:
Need Awnser asap
Right Awnser gets branliest
Answer:
x1,y16 is the rate of change
Step-by-step explanatI subtracted 13-32 which gives me 16, then I added 16 to 32 to be sure and it gave me 48 so the change on the Y axis is going up by 16 and x axis is going up by 1
Find the rate of change of the line that contains the two points (-1, -4) and (5, 4). Be sure to show all calculations and reduce your slope to a fraction in simplest form.
The rate of change of the line that contains the two points (-1, -4) and (5, 4) is 4/3.
What is the rate of change of the line?The rate of change for a line is the slope, the rise over run, or the change in over the change in.
The slope of line can be calculated using the formula, slope =(y2-y1)/(x2-x1).
The given coordinate points are (-1, -4) and (5, 4).
Now, slope = (4-(-4))/(5-(-1))
= (4+4)/(5+1)
= 8/6
= 4/3
Therefore, the slope of a line is 4/3.
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Your class council determined that its profit from the upcoming homecoming dance is directly
related to the ticket price for the dance. Looking at past dances, the council determined that the
profit p can be modeled by the function p(t) = -1212 + 480t + 30, where t represents the price of
each ticket. What should be the price of a ticket to the homecoming dance to maximize the
council's profit?
The price of a ticket to the homecoming dance to maximize the council's profit is 4830.
Define vertex?A vertex is a location in geometry where two or more curves, lines, or edges converge. As a result of this definition, vertices are the intersection of two lines that create an angle as well as the corners of polygons and polyhedra.A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.The vertex of an angle is the point around which it is measured, and the vertex angle is the angle that corresponds to a particular vertex.A face is a flat surface, an edge is a straight line connecting two faces, and a vertex is the corner of the shape.Given: a= -12, b = 480Vertex t= -b/2at= -480/2(-12) = 20Therefore, $20 per ticket.p(20) = -12(20) pow 2 + 480(20) + 30= 4830To learn more about vertex refer to:
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Answer:
$2 each ticket
Step-by-step explanation:
I don't really know how it's 2, but it's in the vertex of the graph. I just got my test back which the answer was 2. I'm sorry if you expected reasoning but I only got an answer. You can make a table for the equation and then see that 2 results in the highest profit though. 2 being substituted for t equates to the greatest profit.
in a circle of 4 meters, what is the measure of the central angle (in degrees) subtended by an arc of length 5 meters
The measure of the central angle in degrees subtended by an arc of length 5 meter is 71.61 degrees
The radius of the circle = 4 meters
The circumference of the circle = 2πr
Where r is the radius of the circle
The value of π = 3.14
The circumference of the circle = 2π × 4
= 8π
The arc length = 5 meters
Consider the x as the central angle
The proportion of central angle and circumference will be
5/8π = x radiance / 2π
Cross multiply the terms
x × 8π = 5 × 2π
x = 10π / 8π
x = 5/4 radiance
Convert radiance to degrees
We know
1 radiance = 180/π degrees
5/4 radiance = 5/4 × 180/π degrees
= 71.61 degrees
Therefore, the central angle is 71.61 degrees
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u (x comma y )space equals space 5 (x plus y )u (x comma y )space equals space 5 y u (x comma y )space equals space 5 x u (x comma y )space equals space 5 x squared plus 5 y squared
To solve this system of differential equations using the series method, we can assume that the solution can be expressed as a power series in both x and y:
[tex]u(x,y) = a0 + a1x + a2y + a3xy + a4x^2 + a5y^2 + ...[/tex]
Substituting this expression into each of the differential equations and collecting the coefficients of each term gives us the following system of equations:
a0 + 5a0 = 0
a1 + 5a2 = 0
a2 + 5a1 = 0
a4 + 5a4 = 0
a5 + 5*a5 = 0
Solving this system of equations gives us the following values for the coefficients:
a0 = 0
a1 = 0
a2 = 0
a3 = 0
a4 = 0
a5 = 0
Therefore, the power series expansion of the solution is:
u(x,y) = 0
This means that the only solution to the differential equations is the trivial solution u(x,y) = 0.
Note that this method of solving differential equations using power series is only applicable if the differential equations are linear and homogeneous, which means that the coefficients of the terms in the differential equations do not depend on x and y, and the right-hand sides of the equations are all equal to 0. If the differential equations are nonlinear or inhomogeneous, other methods may be required to find their solutions.
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What is BC?
BC= units?
The value of BC = 25 using properties of triangle.
What are properties of triangle ?
Let us discuss here some of the properties of triangles.
1. A triangle has three sides and three angles.
2. The sum of the angles of a triangle is always 180 degrees.
3. The exterior angles of a triangle always add up to 360 degrees.
4. The sum of consecutive interior and exterior angle is supplementary.
Properties for isosceles:
Isosceles triangles are those triangles that have at least two sides of equal measure.
1. Two equal sides and two equal angles.
2. The two equal sides of an isosceles triangle are called the legs and the angle between them is called the vertex angle or apex angle.
3. The side opposite the vertex angle is called the base and base angles are equal.
Using 1st property,
in given triangle two angles are equal then opposite side will also be equal.
So, AB = AC
i.e. 4x+4 = 6x-14
4+14 = 6x-4x
18 = 2x
x = 9
Putting value of x in BC
BC = 2*9 +7
= 18+7
= 25.
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Find the Probability of, A King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.
The Probability of, a ace, jack of clubs, King or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards is 4/13.
As per the given data,
we need to find out the probability of, King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.
We know that,
Probability(Event) =Number of Favorable Outcomes/Total number of
Outcomes = x/n.
Total number of Outcomes is 52 (given)
So, we will calculate Number of Favorable Outcomes as follows:
The total no. of King in deck of card is 4
The total no. of queen in deck of card is 4.
The total no. of ace in deck of card is 4.
The total no. of jack in deck of card is 4.
Therefore, the number of favorable outcomes is 4+4+4+4= 16
Now, putting values in the above stated formula of probability, we get:
Probability= 16/52=4/13
Therefore, the probability of pulling a King, Ace, Jack of Clubs, or Queen of Diamonds from a 52-card standard deck that has been properly shuffled is 4/13.
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Using the above graphic, it takes about _____ years to transition from using no oil to consuming 100 million barrels per day whereas it takes about______ years to transition from using 100 million to 200 million barrels per day.
A. 60, 10
B. 10, 60
C. 120, 50
D. 50, 120
It takes about 120 years for the graph to reach 100 million barrels per day whereas it takes 50 years to go from 100 million to 200 million.
As per the question the left axis indicates the amount of oil in the earth in trillions of barrels.
The right axis indicates the global consumption rate of oil in millions of barrels per day.
To the left of the red vertical line are model results that approximate reality whereas to the right are model-based predictions of the future.
The bottom axis is time in years.
The graph attached at the end of the solution.
Let the number of years of transition from using no oil to consuming 100 million barrels per day be a.
Let the number of years of transition from using 100 million to 200 million barrels per day be b.
From the given graph, we can see that initial consumption rate is low, and it takes 120 years for the graph to reach 100 million barrels.
But it takes 50 years to go from 100 million to 200 million.
This is known as exponential growth.
Therefore, the value of a is 120 and the value of b is 50.
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Use the extended Euclidean algorithm to find the greatest common divisor of 3,984 and 588 and express it as a linear combination of 3,984 and 588.
Step 1: Find
q1
and
r1
so that
3,984 = 588 · q1 + r1,
where
0 ≤ r1 < 588.
The greatest common divisor is 12. The linear combination of 3984 and 588 is given by 12 = 61×588 - 9×3984.
The extended Euclidean algorithm is an algorithm to compute integers x and y such that: ax+by=gcd(a,b)The extended Euclidean algorithm can be viewed as the reciprocal of modular exponentiation.
By reversing the steps in the Euclidean algorithm, it is possible to find these integers x and y. The whole idea is to start with the GCD and recursively work our way backwards. This can be done by treating the numbers as variables until we end up with an expression that is a linear combination of our initial numbers.
First use Euclid's algorithm to find the GCD:
3984 = 588 ×6 + 456
588 = 456×1 +132
456= 132 ×3 + 60
132 = 60×2 +12
60 = 12×5+0
The last non-zero remainder is 12.
Thus, the greatest common divisor is 12.
Now we use the extended algorithm:
12 = 132 +(-2)×60
= 132 + (-2)×(456 + (-3)×132))
= (-2)×456 + 7×132
= (-2)×456 + 7×(588 +(-1)×456))
= 7×588 + (-9)×(3984 +(-6)×588))
= 61×588 + (-9)×3984
Thus, a = -9 and b = 61.
Thus, the linear combination of 3984 and 588 is given by 12 = 61×588 - 9×3984.
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If 1+3+5+7+…+49 =625, what is 2+4+6+8+…+50?
If 1+3+5+7+…+49 =625, then the value of 2+4+6+8+…+50 = 650.
What is arithmetic series?
A series of numbers called an arithmetic progression or sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Here, we have
Given: 1+3+5+7+…+49 =625
We have to find the value of 2+4+6+8+…+50.
Here, we calculate the sum of all even numbers and we get
2+4+6+8+…+50 = 650
Hence, if 1+3+5+7+…+49 =625, the value of 2+4+6+8+…+50 = 650.
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Say that we have three voters deciding among seven candidates, a, b, c, d, e, f, g. Their preference orderings are as follows.
1 2 3
(Best) c f g
a b b
e c c
g g d
b a e
d d f
(W orst) f e a
a. Find the top cycle.
b. For each candidate in the top cycle, write down an agenda (a sequence of majority rule
votes) that makes that candidate win (you can write the agenda as a tree).
c. Say that the voters use the Borda count system (each voter gives 6 points to their first
choice, 5 points to their second choice, and so on) to decide among the candidates. Which
candidate wins?
d. Is the Borda count winner also the Condorcet winner?
e. Which candidate does the worst in the Borda count?
f. Say that the person who does worst in the Borda count (your answer in part e. above) is
embarrassed about their poor performance, and tries to convince another candidate to drop
out so that they are no longer the worst person. If a candidate drops out, there would be
six candidates, and hence in the Borda count system, each voter gives 5 points to their first
choice, 4 to their second choice, and so forth. If a candidate drops out, is it possible for the
person who was originally the worst to no longer be the worst? If so, which candidate should
drop out? If not, please explain why not.
A. The top cycle in this case is a -> b -> c -> a.
B. The agenda that wins the candidate is:
First vote:
a vs b -> a wins
Second voice:
versus. c -> a wins
The agenda that Candidate B wins is:
First vote:
b vs c -> b wins
Second Voice:
b vs a -> b wins
The agenda that Candidate C wins is:
First vote:
c vs a -> c wins
Second Voice:
c vs b -> c wins
C. Using the Borda count system, the candidates' scores are as follows:
a:
18 points (6 points from voter 1, 4 points from voter 2, and 8 points from voter 3)
b:
18 points (4 points from voter 1, 6 points from voter 2, and 8 points from voter 3)
c:
18 points (6 points from voter 1, 8 points from voter 2, and 4 points from voter 3)
d:
12 points (8 points from voter 1, 4 points from voter 2, and 0 points from voter 3)
e:
12 points (4 points from voter 1, 8 points from voter 2, and 0 points from voter 3)
f:
12 points (8 points from voter 1, 0 points from voter 2, and 4 points from voter 3)
g:
6 points (4 points from voter 1, 0 points from voter 2, and 2 points from voter 3)
Therefore, candidates a, b, and c tie for first place with 18 points each.
D. No, the Borda count winner is not the Condorcet winner, because the Condorcet winner is the candidate who would win in a majority rule vote against every other candidate. In this case, candidate c is the Condorcet winner, because c beats a and b in majority rule votes.
E. The candidate with the worst score in the Borda count is g of 6 points.
F. If a candidate fails, the original worst candidate may no longer be the worst. In this case, if candidate g fails, the remaining candidates will have the following results:
a:
15 points (Voters 1 to 5 points, Voters 2 to 4 points, Voters 3 to 6 points)
b:
15 points (Voters 1 to 4 points, Voters 2 to 5 points, Voters 3 to 6 points)
c:
15 points (Voters 1 to 5 points, Voters 2 to 6 points, Voters 3 to 4 points)
Day:
10 points (voters 1 to 6 points, voters 2 to 4 points, voters 3 to 0 points)
e:
10 points (voters 1 to 4 points, voters 2 to 6 points, voters 3 to 0 points)
f:
10 points (voters 1 to 6 points, voters 2 to 0 points, voters 3 to 4 points)
In this case, g's 6-point score is not included in the calculation, so candidate g is no longer last.
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