Answers
For the following quadratic equations:
14) the value that completes the square - 32415) the value that completes the square - 20.25.16) discriminant is negative (-8), equation has 2 complex solutions.17) discriminant is positive (25), the equation has 2 real solutions.18) solutions to the equation are 4 and -5.2519) solutions to the equation are r = 4 + √86 and r = 4 - √86How to solve the quadratic equations?14) To complete the square for the quadratic equation x² + 36x + c,
add the square of half the coefficient of x (36/2)² = 18² = 324.
Therefore, the value of c that completes the square is 324.
15) To complete the square for the quadratic equation x² + 9x + c,
add the square of half the coefficient of x (9/2)² = 4.5² = 20.25.
Therefore, the value of c that completes the square is 20.25.
16) For the equation -2n² + 8n - 9 = 0, the discriminant is b² - 4ac. Here, a = -2, b = 8, and c = -9.
Discriminant = (8)² - 4(-2)(-9) = 64 - 72 = -8.
Since the discriminant is negative (-8), the equation has two complex solutions.
17) For the equation -9m² + 5m = 0, the discriminant is b² - 4ac. Here, a = -9, b = 5, and c = 0.
Discriminant = (5)² - 4(-9)(0) = 25 - 0 = 25.
Since the discriminant is positive (25), the equation has two real solutions.
18) For the equation 4n² + 5n - 84 = 0, use the quadratic formula to solve it.
The quadratic formula is given by:
n = (-b ± √(b² - 4ac)) / (2a)
In this equation, a = 4, b = 5, and c = -84. Plugging these values into the quadratic formula:
n = (-5 ± √(5² - 4(4)(-84))) / (2(4))
n = (-5 ± √(25 + 1344)) / 8
n = (-5 ± √1369) / 8
n = (-5 ± 37) / 8
So, the two solutions to the equation are:
n = (-5 + 37) / 8 = 32 / 8 = 4
n = (-5 - 37) / 8 = -42 / 8 = -5.25
19) For the equation r² - 8r - 70 = 0, solve it by completing the square.
r² - 8r - 70 = 0
(r - 4)² - 16 - 70 = 0 (Adding and subtracting (8/2)² = 16 to complete the square)
(r - 4)² - 86 = 0
(r - 4)² = 86
Taking the square root of both sides:
r - 4 = ± √86
r = 4 ± √86
So, the solutions to the equation are:
r = 4 + √86
r = 4 - √86
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Related Questions
write rational number in number line -7 upon 2
Answers
Answer:
el numero 1
Step-by-step explanation:
Let f(x) E Z[x] with deg (f(x)) ≥ 1, and let f(x) be the polynomial in Z, [x], where p is prime integer, obtained from f(x) by reducing all the coefficients of f(x) modulo p. Assume that deg (F(x)) = deg(f(x)), then: If f(x) is reducible over Q. then f(x) is irreducible over Z O This option If f(x) is reducible over Zp, then f(x) is reducible over Q If f(x) is reducible over Zp, then f(x) is reducible over Q O This option None of choices
Answers
If f(x) is reducible over Zp, then f(x) is reducible over Q.
What is the probability of selecting a respondent who prefers public transportation or cycling from a survey of 500 commuters?If a polynomial f(x) with integer coefficients is reducible over Zp (the integers modulo p), where p is a prime number, then it is also reducible over Q (the rational numbers).
This result follows from the fact that if a polynomial is reducible over a smaller field (Zp), it must also be reducible over a larger field (Q).
Since Zp is a subset of Q, any factorization of the polynomial in Zp can also be used in Q. Therefore, if f(x) is reducible over Zp, it is also reducible over Q.
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A steam power plant operates on the ideal reheat-pipe steam Rankine cycle and generates 90 MW of net power. Steam enters the high pressure turbine at a pressure of 10 MPa and a temperature of 520° and exits at a pressure of 1 MPa. Some steam leaving the turbine at this pressure is used to heat the boiler feedwater in an open feedwater heater. After the remaining steam is heated to 480°, it is expanded in the low pressure turbine to a condenser pressure of 14 kPa. Calculate the mass flow rate of the steam passing through the boiler and the thermal efficiency of the cycle by showing the cycle in a T-s diagram with saturated liquid and saturated steam curves.
Answers
The mass flow rate is 0.56 kg/s
How to determine the mass flow rateThe formula for calculating the mass flow rate is expressed as;
m = W / (hf - hg)
Such that the parameters are expressed as;
m is the mass flow rate (kg/s)W is the net power output (W)hf is the enthalpy of the feedwater (kJ/kg)hg is the enthalpy of the steam at the turbine exit (kJ/kg)Substitute the values, we get;
m = 90 MW / (2418 - 2257)
Subtract the values, we have;
m = 90/161
Divide the values, we get;
m= 0.56 kg/s
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pythagorean theorem
Answers
Answer:
The pythagorean theorem is a theorem which states that the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
Pythagorean theorem
in the right angle triangles there is a relationship that governs the length of the three sides. if we knows the length of any two sides, the third side may be calculated by the use of the Pythagorean theorem.
This theorem states that the square on the hypotenuse of a right angled triangle is equal to the sum of the squares on the remaining two sides.
we only use Pythagorean theorem to find the length of the missing side of a right angled triangle only.
What is the value of x?
Answers
Answer:
106
Step-by-step explanation:
reflection
The matrix A has eigenvalues X₁ = 3 and X₂ = 4 with associated eigenvectors 2 V₁ = and v2 [A] Use this information to find the solution to the initial value - [³] Y' = AY where Y (0) = [ (0)] - [8] - [ 2₂ ] 1 problem = Give your answer as x(t) and y(t). y
Answers
The solution to the initial value problem is:
x(t) = [tex](1/4) * e^{(3t)} - (1/4) * e^{(4t)}[/tex] and y(t) = [tex]e^{(3t)} + (1/6) * e^{(4t)}[/tex]
To find the solution to the initial value problem Y' = AY, where A is the matrix with eigenvalues and eigenvectors given, we can use the eigenvalue-eigenvector method.
Let's denote the eigenvectors as v₁ and v₂:
v₁ = [2]
[8]
v₂ = [-3]
[2]
The general solution to the system of linear differential equations can be written as:
Y(t) = [tex]c_1 * e^{(X_1t)} * v_1 + c_2 * e^{(X_2t)} * v_2[/tex]
where c₁ and c₂ are constants.
Substituting the given eigenvalues and eigenvectors:
Y(t) = c₁ * [tex]e^{(3t)[/tex] * [2] + c₂ * [tex]e^(4t)[/tex] * [-3]
[8] [2]
Simplifying further:
Y(t) = [2c₁ * [tex]e^{(3t)[/tex] - 3c₂ * [tex]e^{(4t)[/tex]]
[8c₁ * [tex]e^{(3t)[/tex] + 2c₂ * [tex]e^{(4t)[/tex]]
To find the specific solution that satisfies the initial condition Y(0) = [0] and [8], we can substitute t = 0 into the general solution:
Y(0) = [2c₁ - 3c₂]
[8c₁ + 2c₂]
Equating this to the initial condition:
[2c₁ - 3c₂] = [0]
[8c₁ + 2c₂] [2]
Solving this system of equations will give us the values of c₁ and c₂:
2c₁ - 3c₂ = 0 ----(1)
8c₁ + 2c₂ = 2 ----(2)
Multiplying equation (1) by 4 and adding it to equation (2), we get:
16c₁ = 2
Solving for c₁, we find:
c₁ = 1/8
Substituting c₁ back into equation (1), we can solve for c₂:
2(1/8) - 3c₂ = 0
1/4 - 3c₂ = 0
3c₂ = 1/4
c₂ = 1/12
Therefore, the specific solution to the initial value problem is:
x(t) = [tex](1/8) * e^{(3t)} * 2 + (1/12) * e^{(4t) }* (-3)[/tex]
y(t) = [tex](1/8) * e^{(3t)} * 8 + (1/12) * e^{(4t)} * 2[/tex]
Simplifying further:
x(t) = [tex](1/4) * e^{(3t)} - (1/4) * e^{(4t)}[/tex]
y(t) = [tex]e^{(3t)} + (1/6) * e^{(4t)}[/tex]
Therefore, the solution to the initial value problem is x(t) = [tex](1/4) * e^{(3t)} - (1/4) * e^{(4t)}[/tex] and y(t) = [tex]e^{(3t)} + (1/6) * e^{(4t)}[/tex].
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Translate each equation into slope-intercept form. Then, state the slope and y-intercept . 4y=2x+20
Answers
Answer:
The slope-intercept form of the equation: y = 0.5x + 5
The slope: m = 0.5
The y-intercept: b = 5
Step-by-step explanation:
Slope-intercept form is y = mx + b, where m is the slope and b is y-intecept
4y = 2x + 20 {divide both sides by 4}
y = 0.5x + 5 ⇒ m = 0.5 and b = 5
plz help me please please
Answers
Answer:
5%
Step-by-step explanation:
Answer:
5% increase
Step-by-step explanation:
30/600 equals .05 or 5%
A payment of $970 scheduled to be paid today and a second payment of $1,260 to be paid in seven months from today are to be replaced by a single equivalent payment. What total payment made today would place the payee in the same financial position as the scheduled payments if money can earn 6.25%? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
Answers
Therefore, the total payment made today by the payee is $2,149.01
Payment calculation.
To total payment made today would place the payee in the same financial position as the scheduled payments if money can earn 6.25% we will use the formula below.
PV = FV /(1 + Rr)^n
r =6.25%
FV = $1,260
PV = $ 1,260 / (1+ 0.0625) ^(7/12)
PV = $ 1,179.01
The value of the second payment is $ 1,179.01.
Lets find the total payment. We can represent the total payment by X.
X - $ 970 = $ 1,179.01.
To isolate X, we will add $ 970 to both sides.
X = $ 970 + $ 1,179.01.
X = $2,149.01
Therefore, the total payment made today by the payee is $2,149.01
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Last year the records of a convenience store chain showed the mean amount spent by a customer was $52. A sample of 36 transactions made this month revealed the mean amount spent was $50 with a standard deviation of $11. At the 0.10 significance level, test the claim that the mean amount spent by a customer has significantly decreased since last year.
Answers
There insufficient evidence to support the claim that the mean amount spent by a customer has significantly decreased since last year.
Step 1: State the hypotheses:
- Null hypothesis (H0): The mean amount spent by a customer is equal to or greater than last year's mean ($52).
- Alternative hypothesis (H1): The mean amount spent by a customer is significantly less than last year's mean ($52).
Step 2: Set the significance level:
The significance level (α) is given as 0.10. This represents a 10% chance of rejecting the null hypothesis when it is true.
Step 3: Formulate the decision rule:
Since the alternative hypothesis is stating a decrease in the mean amount spent, we will conduct a one-tailed t-test and reject the null hypothesis if the test statistic falls in the critical region corresponding to the left tail of the t-distribution.
Step 4: Calculate the test statistic:
We need to calculate the t-statistic using the formula:
t = (sample mean - population mean) / (sample standard deviation / √(sample size))
Given data:
Population mean (μ) = $52
Sample mean (X) = $50
Sample standard deviation (s) = $11
Sample size (n) = 36
Plugging in the values:
t = ($50 - $52) / ($11 / √(36))
t = -2 / ($11 / 6)
t ≈ -1.0909
Step 5: Determine the critical value and make a decision:
Since the significance level is 0.10 and the test is one-tailed to the left, we need to find the critical t-value at a 0.10 significance level with degrees of freedom equal to (n - 1) = (36 - 1) = 35.
so, the critical t-value is -1.3104.
Since the calculated t-statistic (-1.0909) does not fall in the critical region (t < -1.3104), we do not have enough evidence to reject the null hypothesis.
Step 6: State the conclusion:
Based on the data and the hypothesis test, at the 0.10 significance level, there is insufficient evidence to support the claim that the mean amount spent by a customer has significantly decreased since last year.
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A survey asked, "How many tattoos do you currently have on your body?" Of the 1233 males surveyed, 190 responded that they had at least one tattoo. Of the 1033 females surveyed,128
responded that they had at least one tattoo. Construct a 99% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval.
Let p1 represent the proportion of males with tattoos and p2 represent the proportion of females with tattoos. Find the 99% confidence interval for p1−p2.
The lower bound ___ your response here.
The upper bound is ___ (Round to three decimal places as needed.)
Interpret the interval.
A.There is 99% confidence that the difference of the proportions is in the interval. Conclude that there is insufficient evidence of a significant difference in the proportion of males and females that have at least one tattoo.
B.There is a 99% probability that the difference of the proportions is in the interval. Conclude that there is insufficient evidence of a significant difference in the proportion of males and females that have at least one tattoo.
C.There is a 99% probability that the difference of the proportions is in the interval. Conclude that there is a significant difference in the proportion of males and females that have at least one tattoo.
D.There is 99% confidence that the difference of the proportions is in the interval. Conclude that there is a significant difference in the proportion of males and females that have at least one tattoo.
Answers
There is insufficient evidence of a significant difference in the proportion of males and females that have at least one tattoo.
Therefore, the correct answer is A.
To construct a confidence interval for the difference in proportions, we can use the following formula:
CI = (p1 - p2) ± Z ×√[(p1×(1 - p1) / n1) + (p2 × (1 - p2) / n2)]
Where:
p1 and p2 are the sample proportions for males and females, respectively.
n1 and n2 are the sample sizes for males and females, respectively.
Z is the critical value corresponding to the desired confidence level.
From the given information, we have:
p1 = 190/1233
n1 = 1233
p2 = 128/1033
n2 = 1033
Confidence level = 99% (which corresponds to a critical value of Z)
Calculating the confidence interval:
CI = (190/1233 - 128/1033) ± Z× √[(190/1233× (1 - 190/1233) / 1233) + (128/1033 ×(1 - 128/1033) / 1033)]
Now, let's find the critical value Z for a 99% confidence level. Since the sample sizes are large, we can use the standard normal distribution. The critical value for a 99% confidence level is approximately 2.576.
CI = (0.154 - 0.124) ± 2.576× √[(0.154× (1 - 0.154) / 1233) + (0.124 × (1 - 0.124) / 1033)]
CI = 0.030 ± 2.576×√[0.000118 + 0.000124]
CI = 0.030 ± 2.576×√(0.000242)
CI = 0.030 ± 2.576×0.015556
CI = 0.030 ± 0.040085
CI ≈ (-0.010, 0.070)
The lower bound of the 99% confidence interval is approximately -0.010, and the upper bound is approximately 0.070.
Interpreting the interval, we can say:
A. There is 99% confidence that the difference of the proportions is in the interval. Conclude that there is insufficient evidence of a significant difference in the proportion of males and females that have at least one tattoo.
Therefore, the correct answer is A.
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Algebra pls help
Really
Answers
Answer: n=-14
Step-by-step explanation:
CONCEPT:
When the same-base exponents MULTIPLY= adding the exponents When the same-base exponents DIVIDE= subtracting the exponentsSOLVE:
The expression in the questions is [tex](x^{3} )(x^{-17})[/tex] which is MULTIPLYING, which means we should add the exponents together
[tex](x^{3} )(x^{-17})[/tex]=[tex]x^n[/tex] ⇔ Given
[tex]x^{3+(-17)}[/tex]=[tex]x^n[/tex] ⇔ Adding Exponents Together
[tex]x^{3-17}[/tex]=[tex]x^n[/tex] ⇔ Simplify
[tex]x^{-14}[/tex]=[tex]x^n[/tex] ⇔ Simplify
[tex]n[/tex]=[tex]-14[/tex] ⇔ Correspondingly
Hope this helps!! :)
Please let me know if you have any questions
Find mZN.
62°
K
N
Need help with this question?
Answers
Answer:
118degrees
Step-by-step explanation:
Assuming we are given the following and m<k and ,<N lies on the same straight line, hence;
m<K = 62 degrees
n<N = ?
Since are on the same straight line, hence;
m<N + m<K = 180
m<N + 62 = 180
m<N = 180 - 62
m<N = 118
Hence the measure of m<N is 118degrees
'
,
A size 8 kid's shoe measures 9 2/3 inches. If 5 size 8 shoes are lined end to end, then how many inches will they cover?
Answers
Answer:
its 77 1/3
just do the math with a calculator
Answer: 48 1/3
Step-by-step explanation:
I've done everything I can, please help
Answers
Answer:
D
Step-by-step explanation:
Answer:
4 is choice C. THis is because the y intercept is 1 and when you go up 2 units, and go right once, you go to another point (rise over run)
Step-by-step explanation:
Karlyn had an online business selling earrings. The materials to make a pair of earrings cost $15.00. Since it took her an hour to make each pair of earrings, she wanted to markup the price by $35 for her time and sell them for $50.00. What is the % markup for that pair of earrings?
Answers
The markup would be 133.33%
30is 200% of 15
5 is 33.33333333% of 15
33.33333333%+100+=133.33333333%
The markup is 133.33% or 133.33333333%
Are these proportional?
6/9 and 2/3
Answers
Answer:
yes.
Step-by-step explanation:
Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.
6/9 divided by 3/3= 2/3
proportional
Please help!!! I’ll mark you as brainliest!!!!!!
0.138613961 as a percent rounded to the nearest tenth
Answers
Answer:
13.9% Approximately
Can someone explain why the answer is False. Will Mark brainliest.
Answers
Answer:
Supplementary Angles are 180 degrees. A triangle has 180 degrees. One angle is already 90 degrees, so 2 more angles with 180 degrees is impossible.
Step-by-step explanation:
Factor the expression over the complex numbers. x2+20 Enter your answer in the box.
Answers
Answer:
2(x plus 20)
Step-by-step explanation:
this is the highest common factor
Given the points P(0,0,-2), Q(2,3,4), R(4, 6, 5), and S(6, 11, 10), find the following: (a) The area of triangle PQR. (b) An equation of the form ax + by + cz = d for the plane containing points P, Q, and R. (c) The volume of the parallelepiped with edges PO.PR, and Ps. (d) A point on the line through P and Q which is two units away from P.
Answers
(a) The area of triangle PQR is 9.165 units².
(b) The formula for a plane given three points is: 10x - 7y - 2z = 0
(c) The volume of the parallelepiped with edges PO, PR, and PS is 148 units³.
(d) A point on the line through P and Q which is two units away from P is (4/5, 6/5, 2/5).
(a) The area of triangle PQR is 9.165 units².
The formula for the area of a triangle given three points is:
Area = 1/2 | ((x2 − x1) × (y3 − y1)) − ((y2 − y1) × (x3 − x1)) |
The coordinates for P, Q, and R are: P (0, 0, -2)Q (2, 3, 4)R (4, 6, 5)
Substituting into the formula gives us:
Area = 1/2 | ((2 - 0) × (5 + 2)) − ((3 - 0) × (4 - 0)) |
Area = 9.165 units² (rounded to three decimal places)
(b) An equation of the form ax + by + cz = d for the plane containing points P, Q, and R is:
10x - 7y - 2z = 0
The formula for a plane given three points is: ax + by + cz = d
To find a, b, c, and d, we first need to find two vectors on the plane.
We can use PQ and PR.
PQ = Q - P = (2 - 0)i + (3 - 0)j + (4 + 2)k = 2i + 3j + 6k
PR = R - P = (4 - 0)i + (6 - 0)j + (5 + 2)k = 4i + 6j + 7k
Now we can find the normal vector by taking the cross product of PQ and PR:
PQ x PR = <3i - 26j - 12k>
So the equation of the plane is:3x - 26y - 12z = 0
We can simplify this by multiplying all terms by -2, which gives:10x - 7y - 2z = 0
(c) The volume of the parallelepiped with edges PO, PR, and PS is 148 units³.
The volume of a parallelepiped is given by the scalar triple product of three vectors.
We can use OP, PR, and PS.
OP = P - O = -i - j - 2k = < -1, -1, -2 >
PR = R - P = 4i + 6j + 7k = < 4, 6, 7 >
PS = S - P = 6i + 11j + 12k = < 6, 11, 12 >
The scalar triple product is:
OP ⋅ (PR x PS)OP ⋅ (PR x PS) = < -1, -1, -2 > ⋅ (< 54, -20, -10 >)OP ⋅ (PR x PS) = -148
The volume of the parallelepiped is 148 units³.
(d) A point on the line through P and Q which is two units away from P is (4/5, 6/5, 2/5).
The equation of the line through P and Q is:x = 2t, y = 3t, z = 4 + 6t
A point on the line that is two units away from P is given by:
t = 2/5
Substituting into the equations for x, y, and z gives:(4/5, 6/5, 2/5)
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Which of the graphs below represents the soltuion set for d - 4 > -3?
Answers
Answer:
The answer is d
Step-by-step explanation:
Which decimal is closest in value to the fraction below? 1/6
Answers
Answer:
0.1666...
Step by step explanation:
By using long division (with 6 as the divisor) the number sentence would keep on going with 40-36.
0.166666666
1.000000000
− 0
10
− 6
40
−36
40
−36
40
− 36
40
− 36
40
− 36
40
− 36
40
− 36
40
− 36
40 students where has their favorite shoe color
how many chose blue?
Answers
Answer:
8 students
Step-by-step explanation:
There are 20 boxes and there are a total of 40 students interviewed. So, each box is worth 2 students. Since blue has 4 boxes, 4*2 = 8 students chose blue as their favorite shoe color.
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HELP ME PLEASEEEEEEE CIRCUMFERENCE AND AREA OF A CIRCLE
Answers
Answer:
Formula for circumference: 2 x pie(3.14 or 22/7) x radius(half of diameter or already given radius). Area of a circle: pie(3.14 or 22/7) x radius squared
Radius: 3, 6 is diameter and half of that is 3.
3 x 3.14 x 2 = 18.84 <------ circumference
3.14 x 3^2
3.14 x 9 = 28.26 <------ area of the circle
Evaluate the expression when a=-2 and x=6. \
4x-a
Answers
Answer:
26
Step-by-step explanation:
Given
4x - a ← substitute a = - 2, x = 6 into the expression
= 4(6) - (- 2) [ note - (- ) is equivalent to + ]
= 24 + 2
= 26
the radius of a circle is 18.4 inches. the circle's circumference is about ___ inches.
use 3.14 for pi
Answers
Answer:
115.552 or 116 inches.
Step-by-step explanation:
Use the circumference of a circle formula which is C= 2piR. Where C is circumference and R is radius. So you get C=2(3.14×18.4) which gives you 115.552.
please helpppp
also just click the image for it to be bigger
Answers
0
Tickets to a movie cost $9.00 for adults and $5.50 for students. There were 150 tickets purchased for a total of $1,105.00. The following system of
equations models the situation, where a is the number of adult tickets purchased and s is the number of student tickets purchased. Write the
terms with the variables in alphabetical order.
9a + 5.5s = 1.105
a +5 = 150
Rewrite the second equation in the system so that the variable for the number of adult tickets purchased can be eliminated by subtraction.
Answers
Answer:
150a
Step-by-step explanation:
Now, the Group of Good would like to decide how they should infiltrate the gallery. The group wants to vote on different plans to sneak into the gallery; the plans are labelled a - e. While the group puts all of the plans together so everyone can see them, a tragedy occurs. Kenny gets a paper cut by Plan a! The cut is too deep! Saddened by their colleague’s sudden paper death, they decide that the leader should have more say in which plan is picked (in hopes to avoid more unnecessary death). Suppose the leader’s vote (from the last question) counts as 5 votes. The following preference schedule is produced:
Total Votes = 2 2 1 1
Choice 1 e c a b b
Choice 2 d a b d a
Choice 3 c d e c d
Choice 4 a b d e c
Choice 5 b e c a e
(a) If plurality voting is used, what plan should the group use? Does this plan have a majority
Total Votes = 2 2 1 1
Choice 1 e c a b b
Choice 2 d a b d a
Choice 3 c d e c d
Choice 4 a b d e c
Choice 5 b e c a e
(b) If Instant Runoff Voting is used, what plan should the group use? Show how you discovered your answer.
Total Votes = 2 2 1 1
Choice 1 e c a b b
Choice 2 d a b d a
Choice 3 c d e c d
Choice 4 a b d e c
Choice 5 b e c a e
(c)If the Borda Count method is used, what plan should the group use? Show how the winner is computed
What was the best part of this project? What was the worst part?
Answers
(a) If plurality voting is used, Plan E will be chosen.
b It has the most first-place votes, with 2 each from voters 1 and 5. No other plan has more than 1 first-place vote.
c If the Borda Count method is used, Plan C will be chosen.
How to explain the informationa The best part of this project was learning about different voting methods and how they can be used to choose a winner. The worst part of the project was the difficulty of calculating the Borda Count.
b If Instant Runoff Voting is used, Plan C will be chosen. In the first round of counting, Plan E is eliminated, as it has the fewest first-place votes. In the second round, Plan C is eliminated, as it has the fewest second-place votes. In the third round, Plan B is eliminated, as it has the fewest third-place votes. In the fourth round, Plan D is eliminated, as it has the fewest fourth-place votes. This leaves Plan A as the winner, as it has the most votes remaining.
c If the Borda Count method is used, Plan C will be chosen. Each voter's ballot is assigned a number of points equal to the number of candidates ranked lower than that candidate. For example, voter 1's ballot gives Plan E 5 points, Plan C 4 points, Plan A 3 points, Plan B 2 points, and Plan D 1 point. The total number of points for each candidate is then calculated. Plan C has the most points, with 16, so it is the winner.
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