group consisting of anne, bert, carl, and diana is about to select one out of five possible alternatives, a, b, c, d, e. the true utilities of the four individuals for the five alternatives are as follows:
a) U(6) UC) Ud) U(e) Anne 0.9 0.8 0.6 0.5 0.4 Bert 0.6 1.0 0.5 0.3 0.4 Carl 0.4 0.3 0.7 0.9 0.2 Diana 0.7 0.6 0.5 0.2 0.1 Which alternative will be selected if the following decision making methods are used: (i) the decision is based on the traditional voting procedure (each voter gets one vote). (ii) each person is asked for their top two choices, and the alternative that is chosen by the maximum number of people is selected. (iii) the group uses the Borda count with 5 points for the most preferred alternative, and 1 point for the least preferred alternative. (iv) the group follows a dot-voting scheme, where each person gets 10 "dots", and they assign the number of dots to each alternative that are roughly proportional to their Utility. (v) the group uses the "maximin rule" which prescribes that the group should prefer the alternative in which the worse-off person is as well-off as possible.
(vi) the sum of individual utilities is maximized for the group. Discuss the pros and cons of the group decision making methods listed above.

The original number is 57.

The two equations are x+y = 12 and (10y+x)−(10x+y) = 18.

Let the digit at the tens place be x and the digit at the unit place be y.

x+y = 12 .........(1)

Required Number = (10x+y).

Number obtained on reversing the digits = (10y+x).

According to the condition, we get

(10y+x)−(10x+y) = 18

→ 9y−9x = 18

→   y−x = 2     ..........(2)

Adding (1) and (2), we get

2y = 14

y =7

x = 12 - 7

x  = 5

Hence, the required number is 57.

The equations used to solve this is x+y = 12 and (10y+x)−(10x+y) = 18.

To know more about equations check the below link:

https://brainly.com/question/25976025

#SPJ1

The missing features of the Venn diagram include the following:

I=472, II=449 ,IV=459 ,V=218 , VI=456,

A Venn diagram is a circular illustration of how variables are interrelated to each other.

To solve for I;

Total number of students taking dance = 1031

Total number of students taking science and dance= 449

Total number of students taking all three courses= 218

Total number of students taking science and English = 459

Therefore, the number of students taking only science;

I =( II-V)+ (IV-V)

I= (449-218)+(459-218)

I = 231+241

I= 472

The number of students that took Science, Dance, or English =V= 218

The number of students took Dance and English, but not Science = VI = 456

The number of students took Science or didn't take Dance = IV = 459

The number of students took none of the courses = VIII = U

The number of students took Science or English, but not Dance = 459 students.

Learn more about Venn diagram here:

https://brainly.com/question/24713052

#SPJ1

Answer:

To solve the given system of equations, we can start by substituting the value of x in the second equation into the first equation. Since the second equation tells us that x = y - 2, we can substitute y - 2 for x in the first equation to get:

x = 17 - 4y

y - 2 = 17 - 4y

Then, we can combine like terms on the right-hand side to get:

x = 17 - 4y

-3y = 15

Finally, we can divide both sides by -3 to solve for y, and then substitute this value back into one of the original equations to solve for x:

x = 17 - 4y

y = -5

x = 17 - 4(-5) = 17 + 20 = 37

Therefore, the solution to the system of equations is x = 37 and y = -5.

Answer:

[tex]6^{\frac{1}{12}}[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt[3]{6} }{\sqrt[4]{6} } =\frac{6^{\frac{1}{3} } }{6^\frac{1}{4} }[/tex]

[tex]= 6^{\frac{1}{3}[/tex] ÷ [tex]6^{\frac{1}{4}}[/tex]

= [tex]6^{\frac{1}{3}-\frac{1}{4}}[/tex]

=[tex]6^{\frac{4}{12}-\frac{3}{12}}[/tex]

[tex]= 6^\frac{1}{12}[/tex]

Answer: 1: 9x

Step-by-step explanation:

2: 3b

3: 3m

4: 5a

5: 7x

6: 3a+5b

7: 9x-4

8: m-6b

9: 13a+3b+6c

10: 1+9b

11: 7p

12: 2a+1b-10

Answer: 44ft^2

Step-by-step explanation:

plug it into the equation, h=11, b=8

so A=1/2(11)(8) = 44ft^2

The distance between the satellite and the tracking station is 1220 miles

To find the distance between the satellite and the tracking station we need to apply cosine law:

                    [tex]c^{2} =a^{2} +b^{2} -2ab cos(\beta )----------(1)[/tex]

where:

c=length of side c

a=length of side a

b=length of side b

β=angle opposite c

we need to find the angle of β

computing the angle  β gives

[tex]\beta =\frac{3min}{120min} *360[/tex]

β=9°

Now substitute the β value ,a=4000,b=5000,in cosine law, and we get

[tex]x^{2} =4000^{2} +5000^{2} -2(4000)(5000)cos 9[/tex]

[tex]=(16+15-39.51)*10^{6 }\\=1.49*10^{6}[/tex]

x=1.22x10^3

x=1220 miles distance from the satellite to the tracking station.

To know more about the Distance of the points:

https://brainly.com/question/7243416

#SPJ4

The exponential form of the given sequence is - [tex]t_n[/tex] = [tex]t_(n-1)[/tex] + [tex]2^x[/tex] where x is a set of whole numbers and n is a set of natural numbers.

The given sequence is -  4, 5, 7, 11, 19, 35, 67, ...

the first term - [tex]t_1[/tex] is 4

Hence, we can write the sequence as follows-

4 + [tex]2^0[/tex] = 5

5+[tex](2)^1[/tex]=7

7+[tex](2)^2[/tex]=11

11+[tex](2)^3[/tex]=19

and so on.

Here, we are adding the previous term with the exponential form of 2.

thus, we can conclude that -

[tex]t_n[/tex] = [tex]t_(n-1)[/tex] + [tex]2^x[/tex]

where,  x is a set of whole numbers, and n is a set of natural numbers.

Read more about Sequences:

brainly.com/question/28417178

#SPJ4

The linear equation that representing the given model is 6x-3 = 15.

In the given question, we have to choose the equation represented by the model given below.

As we know that;

A linear equation represent the relationship between the two unknown variable. The equation of linear equation is of one degree.

The simplest linear equation shows the correlation between (x,y), which may then be used to make a table or a graph on the coordinate plane or to assess at a specific x or y value.

To write the equation that represented by the given model, we count the variable that are of the same type. Then we write them after counting.

As we can see that in the model have 6 triangles of x, 3 circles of -1 and 15 circles of 1. So the linear equation that representing the given model is 6x-3 = 15.

To learn more about linear equation link is here

brainly.com/question/11897796

#SPJ4

Answer:

9,510,223.49 galones!

Step-by-step explanation:

Primero, tienes que saber la cauntidad de los litros en un galon.

Hay 3.7854 litres en un galon

ahora, hacemos un ratio

1 galon = 3.7854 litres

? galones = 600,000 litres

Para encontrar la respuesta, divide 600,000 por 3.7854 para obtener la cauntidad de los galones

600,000 ÷ 3.7854 = 158,503.725 galones

158,503. 725 litres fluyen por segundo.

Hay 60 segundos en un minuto asi que, tenemos que multiplica nuestra respuesta por 60 para calcular nuestra respuesta final.

158,503. 725 × 60 = 9,510,223.49 galones!

The correct statements are:

a) The independent variable is the number of people.

b) The initial value (initial fee) for the picnic is $40.

d) As the number of people increases, the total cost of the picnic increases.

A general linear equation is given by:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know that the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is given by the formula:

m = (y - y')/x - x'

Now let's analyze the table:

The x-values are the ones in the left and the y-values are the ones on the right, now from the table we can use two points, let's use the first two:

(6, 52) and (9, 58).

Then the slope is:

a = (58 - 52)/9 -6 = 2

Then the line is something like:

y = 2*x + b

To find the value of b, we use the point (6, 52). This means that when x = 6, y must be equal to 52.

We will get:

52 = 2*6 + b

52 = 12 + b

52 - 12 = b = 40

Then the linear equation is:

y = 2*x + 40

Now let's see which statements are correct.

a) The independent variable is the number of people.

True, the "x" represents the number of people.

b) The initial value (initial fee) for the picnic is $40.

True, the y-intercept does not depend on the value of x, so we can say that you need to pay that indifferent of the number of people that goes.

c)The rate of change is $8.67 per person.

False, the rate of change is equal to the slope, in this case is $2 per person.

d) As the number of people increases, the total cost of the picnic increases.

True.

e)  If 4 people attended the picnic, the total cost would be $46.

To see if this is true or not, we just need to evaluate the function that we got in x = 4.

y = 2*4 + 40 = 48

So we can see that this is false.

Therefore, the correct statements are A, B, D

To learn more about linear equation refer here

brainly.com/question/11897796

#SPJ4

Number of marbles were not chosen = 62 marbles

Number of marbles were in the bag before the game = 86 marbles

Number pf blue marbles were chosen = 24

Number of blue marbles = 40

Number of white marbles = 46 marbles

Total number of marbles = 40 + 46

= 86 marbles

Of the 40 blue marbles, 3/5 fraction were chosen

Number of blue marbles chosen = 40 × (3/5)

= 24 marbles

Part a

Number of bag's marbles were not chosen = 86 - 24

= 62 marbles

Part b

Number of marbles were in the bag before the game = 86 marbles

Part c

Number of blue marbles were chosen = 40 × (3/5)

= 24 marbles

Therefore, the 62 marbles were not chosen. There were 86 marbles before the game and number of blue marbles were chosen is 24 marbles

Learn more about fraction here

brainly.com/question/8482939

#SPJ4

g give a derivation to show that the following argument is valid in tfl. be p ∨ q) → r, p → s, ¬s → ¬r

1. (p ∨ q) → r Premise

2. p → s Premise

3. ¬s → ¬r Premise

4. p Assumption

5. s Modus Ponens (2, 4)

6. ¬r Modus Ponens (3, 5)

7. ¬(p ∨ q) Assumption

8. ¬p Simplification (7)

9. ¬q Simplification (7)

10. r Addition (1, 9)

11. Contradiction (6, 10)

12. ¬¬(p ∨ q) Double Negation (7-11)

13. (p ∨ q) Simplify(12)

14. r Modus Ponens (1, 13)

15. p → r Hypothetical Syllogism (4-14)

Learn more about simplify here

https://brainly.com/question/17453188

#SPJ4

1. The equation of the inverse variation is, y = 272/x.

2. When x = 12, y = 68/3

When y = 30, x = 136/15.

An inverse variation is defined by the equation, y = k/x, where k is the constant of proportionality between the relationship of y and x.

1. Given that y varies inversely with x, substitute y = 34 and x = 8 into y = k/x, and find the value of the constant of proportionality, k:

34 =  k/8

34 × 8 = k

k = 272

To write the equation, substitute k = 272 into y = k/x:

y = 272/x

2. When x = 12, we have:

y = 272/12

Simplify

y = 68/3

When y = 30, we have:

30 = 272/x

30x = 272

30x/30 = 272/30

x = 136/15

Learn more about the equation of inverse variation on:

https://brainly.com/question/13998680

#SPJ1

The volume of the cone is approximately 134 ft cube.

The cone would fit in 4 times in the red beach ball.

The diameter of the red beach ball is 8 inches, then the cone has the same radius and a height of 8 inches .

Therefore, to know the number of times the beach ball will fit into the cone, we have to find the volume of each solid shape.

Therefore,

volume of the beach ball(sphere) = 4πr³

where

r = 8  /2 = 4 inches

volume of the beach ball(sphere) = 4 × π × 4³

volume of the beach ball(sphere) = 256π ft³

Therefore,

volume of the cone = 1 / 3 πr²h

where

volume of the cone = 1 / 3 × π × 4²  × 8

volume of the cone = 128π / 3

volume of the cone = 42.7π

volume of the cone = 134.078

volume of the cone ≈ 134 ft³

Therefore,

volume of beach ball / volume of cone = 256π / 42.7π = 5.99531615925

Therefore, the cone will fit 4 times into the red beach ball.

learn more on volume here: https://brainly.com/question/9994313

#SPJ1

The friend should change the multiplication of 9/4 to multiplication by the reciprocal of 9/4.

Option C is the correct answer.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

4(2/3) and 2(1/4)

Divide 4(2/3) by 2(1/4)

4(2/3) ÷ 2(1/4)

= 14/3 ÷ 9/4

Multiply the reciprocal of 9/4.

= 14/3 x 4/9

= 56/27

= 2(2/27)

Thus,

The value of the division of the fraction is 2(2/27).

Learn more about fractions here:

https://brainly.com/question/24370499

#SPJ1

A is negative semidefinite if and only if all the kth order principal minors of A are ≤ 0 if k is odd and ≥ 0 if k is even. The given statement is true.

What is a negative semidefinite matrix?

A Hermitian matrix with all of its eigenvalues being nonpositive is known as a negative semidefinite matrix. Using the Wolfram Language's NegativeSemidefiniteMatrixQ[m], a matrix may be checked to see if it is negative semidefinite.

The direction of space is inverted when the determinant is negative. If you give your fingers dimensions before transformation and they remain true after, it indicates that the orientation of space has not changed and the determinant is positive.

To learn more about negative semidefinite matrix visit:https://brainly.com/question/16969351

#SPJ4

A polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 3, 8 is x³ - 7x² + 36.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

Given,

As stated, the polynomial's leading coefficient is equal to 1.

The function's zeroes are also listed as -2, 3, and 6.

For root 3: ( x - 3)

for root 6: (x - 6)

As a result, the polynomial function is

f = 1(x+2)(x-3)(x-6) (x-6)

f = (x+2)(x² - 6x - 3x + 18)

f = (x+2)(x² - 9x + 18)

f = x³ - 9x² + 18x + 2x² - 18x + 36

f = x³ - 7x² + 36

A polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 3, 8 is x³ - 7x² + 36.

To learn more about polynomial function, visit:

https://brainly.com/question/21106451

#SPJ1

In standard form the equation of the line passing through the points,

(-3, -2) and (-1, 0). is

x - y = -1

Information given in the question include

points,  (-3, -2) and (-1, 0).

Standard form of linear equations is of the form Ax + By = C

The slope is represented as m, The slope by definition is the ratio change of the output values to the input values

the slope, m calculating using the points  (-3, -2) and (-1, 0).

m = (0 - (-2)) / (-1 - (-3))

m = (2) / (2)

m = 1

if the line passes through point X(-1, 0)

y - 0 = 1(x - (-1))

y = x + 1

x - y = -1

the intercept C = 1

The equation of the line is x - y = -1

Learn more about linear functions at:

https://brainly.com/question/29056744

#SPJ1

The point estimate of the difference between the two population means is -1.05.

Here, we are given the data representing the scores of the golf players in the 1st and final rounds.

a. The significance level is: α = 0.10

we can construct the following hypothesis test-

Null hypothesis H₀ ⇒ μd = 0

This implies that there is no difference between the population mean of the first round and final round.

Alternative hypothesis: Ha ⇒ μd ≠ 0

This implies that there is a difference between the population mean of the 1st round and final round.

Now, the test statistic will be-

[tex]t = (d-mean_{d})\sqrt{n}/ s_{d\\}[/tex]

we can use excel to calculate the test statistic.

This will give us: 0.10 < P < 0.20

b. the main margin of error is 90% confidence level. This means that there is no significant difference, hence - 1.05.

Learn more about hypothesis testing here-

https://brainly.com/question/15980493

#SPJ4

Your question was incomplete. Check for the missing figure below.

The value of Safeco stock given the required return growth rate and the dividend of the stock is $89.60.

The value of the stock can be determined using the constant growth dividend model. According to the model, the value of the stock is a function of the growth rate, dividend and the required return of the stock.

Value of the stock = [dividend x (1 + g)] / (r - g)

where

r = required return

g = growth rate

Value of the stock = [1.60 x (1.12) / (0.14 - 0.12)

Value of the stock = 1.792 / 0.02

Value of the stock = $89.60

Learn more about stock on:

https://brainly.com/question/14742629

#SPJ1

Answer:

c.

Step-by-step explanation:

as this can take on any value (with as many digits after the decimal point as necessary) between certain interval limits.

all the others are usually either pure integers (and every real number in between them is not valid) or at most have finite fractions (like 1/2 or 1/4 points for scores, and between these no value is valid).

The option that represents the arithmetic series is;

Option C: sum from k equals 0 to 4 of negative 12 plus 7 times k

An arithmetic series is defined as an arithmetic sequence, whereby each term of the series is gotten from the previous term by the addition or subtraction of a common term.

The series is given as;

-12 + (-5) + 2 + 9 + 16

By careful observation, we see that each term in the series is gotten from the previous term by the addition of 7.

The series here is therefore an example of arithmetic sequence.

The equation of the series when the first term is -12 can therefore be written as; -12 + 7·k

Where;

-12 is the first term

7 is the common difference

n is the number of terms

k = n - 1

When k = 0, we have;

-12 + 7·k

= -12 + 7 × 0

= -12

When k = 1, we have;

-12 + 7·k

= -12 + 7 × 1

= -5

When k = 2, we have;

-12 + 7·k

= -12 + 7 × 2

= 2

When k = 3, we have;

-12 + 7·k

= -12 + 7 × 3

= 9

When k = 4, we have;

-12 + 7·k

= -12 + 7 × 4

= 16

Therefore, we conclude that  using values of k that range from k = 0 to k = 4, the expression that represents the series is therefore the option C

Read more about Arithmetic Sequence at; https://brainly.com/question/6561461

#SPJ1

Answer:

-------------------------------------

Given expression:

Distribute and simplify:

Answer:

No.

Step-by-step explanation:

A function have only one output (y) for each x.  This is not true with this graph.  For example: the point (6,1) and ( 6,5) are both on the graph.  The input 6 has more than 1 output. It has the output of 1 and 5.  Since it has more than one output, it is not a function.

The weight of meteorite A and B are 21 and 168 tons respectively.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, The weight of meteorite A is 8 times the weight of meteorite B. And the sum of their weights is 189 tons,

To find their weights we need to establish an equation, relating their weights,

Let weight of meteoroid B be x, then weight of meteoroid A will be 8x,

Establishing the equation,

8x+x = 189

9x = 189

x = 21

8x = 21x8 = 168

Hence, The weight of meteorite A and B are 21 and 168 tons respectively.

For more references on equations, click;

https://brainly.com/question/29657992

#SPJ1

The expression using the common factor is 1/12xy(x² + 5y)

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

1/12 x^3 y + 5/12 xy^2

Rewrite properly

So, we have

1/12x³y + 5/12xy²

Factor out 1/12 from the expression

So, we have the following representation

1/12(x³y + 5xy²)

Factor out x from the expression

So, we have the following representation

1/12x(x²y + 5y²)

Factor out y from the expression

So, we have the following representation

1/12xy(x² + 5y)

Hence, the expression is (c) 1/12xy(x² + 5y)

Read more about common factor:

brainly.com/question/25266652

#SPJ1

Answer:The expression using the common factor is 1/12xy(x² + 5y)

Step-by-step explanation: