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a) the Shapley-Shubik Index of the Conservative party is 3360/5040.

b) the Shapley-Shubik Index of the Labour party is 82.142

To calculate the Shapley-Shubik index for a party in a weighted voting system, we need to consider all possible orderings of the parties and determine the party's contribution to the winning coalition in each ordering. The Shapley-Shubik index represents the average contribution across all possible orderings.

(a) The Shapley-Shubik Index of the Conservative party is 3360/5040. Justify this calculation:

To calculate the Shapley-Shubik Index of the Conservative party, we consider all possible orderings of the parties and determine the Conservative party's contribution to the winning coalition in each ordering.

The total number of possible orderings of the parties is given by the factorial of the total number of parties: 7! = 5040.

In each ordering, we examine the cumulative votes of the parties in the order until the winning threshold of 326 votes is reached. The Conservative party, with 316 votes, does not reach the threshold alone.

However, if we consider the cumulative votes of the Conservative party and the Labour party (316 + 259 = 575), we reach the winning threshold. Therefore, the Conservative party's contribution to the winning coalition is 575 votes.

Since there are 6 other parties, we need to distribute the remaining votes among them. We can do this in 6! = 720 different ways.

The Shapley-Shubik Index is calculated by summing the contributions of the Conservative party across all possible orderings and dividing by the total number of orderings:

Shapley-Shubik Index of the Conservative party = (575 * 720) / 5040 = 3360 / 5040

Therefore, the Shapley-Shubik Index of the Conservative party is 3360/5040.

(b) To compute the Shapley-Shubik Index of the Labour party, we follow a similar approach:

The Labour party has 259 votes. We consider all possible orderings of the parties and determine the Labour party's contribution to the winning coalition in each ordering.

In each ordering, we examine the cumulative votes of the parties in the order until the winning threshold of 326 votes is reached. The Labour party alone does not reach the threshold.

However, if we consider the cumulative votes of the Labour party and the Conservative party (259 + 316 = 575), we reach the winning threshold. Therefore, the Labour party's contribution to the winning coalition is 575 votes.

Similar to the previous calculation, we distribute the remaining votes among the 6 other parties in 6! = 720 different ways.

The Shapley-Shubik Index of the Labour party is calculated by summing the contributions of the Labour party across all possible orderings and dividing by the total number of orderings:

Shapley-Shubik Index of the Labour party = (575 * 720) / 5040

= 82.142

Therefore, the Shapley-Shubik Index of the Labour party is 82.142.

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Given question is incomplete, the complete question is below

A (simplified representation of) the 2019 British parliament was as a weighted voting system [326 : 316,259,35,12,12,10,6]. The Conservative party had 316 votes, the Labour party had 259 votes, and various other parties had the remaining votes.

(a) The Shapley-Shubik Index of the Conservative party is 3360/5040. Justify this calculation.

(b) Compute the Shapley-Shubik Index of the Labour party.

Answer: 1,953

Step-by-step explanation:

23,440 divided by 12

Answer:

D. 105°

Step-by-step explanation:

Option b. (Ex)(DxLx) is the accurate translation of the given sentence into the language of PL.

The accurate translation of the sentence "Only lunatics drive on the autobahn" into the language of PL (Propositional Logic) can be represented as:

b. (Ex)(DxLx)

Let's break down the translation scheme:

Lx: x is a lunatic (Lunatics)

Dx: x drives on the autobahn (Drive on the autobahn)

The sentence states "Only lunatics drive on the autobahn," which implies that there are some individuals who drive on the autobahn and they are lunatics. This can be expressed using existential quantification (Ex) to indicate that there exists at least one individual who satisfies the condition. Therefore, option b. (Ex)(DxLx) accurately translates the given sentence.

Option a. (x)(DxLx) would mean "For all x, x drives on the autobahn implies x is a lunatic." This does not capture the meaning of the original sentence because it suggests that everyone who drives on the autobahn is a lunatic, which is not what the sentence implies.

Option c. (x)(LxDx) would mean "For all x, x is a lunatic implies x drives on the autobahn." Again, this does not capture the intended meaning of the original sentence as it suggests that all lunatics drive on the autobahn.

Option d. (Ex)(LxDx) would mean "There exists an x such that x is a lunatic and x drives on the autobahn." This translation does not capture the sense of the original sentence, which states that only lunatics drive on the autobahn, not that there exists at least one lunatic who drives on the autobahn.

Therefore, option b. (Ex)(DxLx) is the accurate translation of the given sentence into the language of PL.

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The calculated t-value is greater than 1.734, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

An engine additive is being tested to see whether it can effectively increase gas mileage for a number of vehicles. Twenty assorted vehicles had their gas mileage, in miles per gallon, measured. Then, the engine additive was placed into each of the engines, and the gas mileage was measured again. Let µd be the true mean difference in the gas mileage before and after the engine additive is placed into the engines. We want to test the hypothesis that the engine additive has no effect. The null hypothesis is: H0: µd = 0The alternative hypothesis is: Ha: µd > 0 (one-tailed test)Assuming that the difference in gas mileage before and after the engine additive is approximately normally distributed, we can use a one-sample t-test. The test statistic is given by: $$t=\frac{\bar{x}-\mu}{s/\sqrt{n}}$$Where, $\bar{x}$ is the sample mean difference in gas mileage, μ is the hypothesized population mean difference, s is the sample standard deviation of the differences, and n is the sample size. We can use a significance level of α = 0.05.To determine the critical value of the t-distribution, we need to find the degrees of freedom (df). Since we have a sample size of n = 20, we have n - 1 = 19 degrees of freedom. Using a t-distribution table with 19 degrees of freedom and a significance level of 0.05 for a one-tailed test, we get a critical value of t = 1.734. If the calculated t-value is greater than 1.734, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

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Answer:

the answer is 1,412

Step-by-step explanation:

all you do is add all the numbers together

Answer: a = 2^12  b= 2^12  c=2^20

d= 2^12   e= 2^64   f= 2^12   g= 2^22   h= 2^40

Step-by-step explanation:

Answer:

x²+8x+9=0

Comparing above equation with ax²+bx +c

we get

a=1

b=8

c=9

quadratic equation is

[tex]x = \frac{ - 8± \sqrt{ {8}^{2} - 4×1×9} }{2*1} [/tex]

[tex]x = \frac{ -8± \sqrt{ 64-36} }{2} [/tex]

2x+8=±[tex] \sqrt{ {28}}[/tex]

taking + ve

2x=[tex] \sqrt{ {28}}[/tex]-8

x=[tex] 2\sqrt{ {7}}[/tex]-8/2

x=[tex] \sqrt{ {7}}[/tex]-4

taking -ve

2x=-[tex] \sqrt{ {28}}[/tex]-8

x=-[tex] 2\sqrt{ {7}}[/tex]-8/2

x=-[tex] \sqrt{ {7}}[/tex]-4

As given

General equation

On comparing

(i)  When using three classifiers with a majority decision, the probability of correctly classifying the new object is 0.973.

(ii) The probability of correct classification increases as the number of classifiers increases

(i) All three classifiers make the correct classification: p * p * p = 0.7 * 0.7 * 0.7 = 0.343.

Two classifiers make the correct classification and one classifier makes an error:

(p * p * q) + (p * q * p) + (q * p * p) = 3 * (0.7 * 0.7 * 0.3) = 0.441.

One classifier makes the correct classification and two classifiers make errors:

(p * q * q) + (q * p * q) + (q * q * p) = 3 * (0.7 * 0.3 * 0.3)

= 0.189.

The probability of the new object being correctly classified is the sum of these probabilities:

0.343 + 0.441 + 0.189

= 0.973.

(ii)  The probability of correct classification increases as the number of classifiers increases. This is because the probability of a majority decision being correct is the probability that at least two of the classifiers make the correct decision. The more classifiers there are, the more likely it is that at least two of them will make the correct decision.

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Answer:

trapazoid

Step-by-step explanation:

.....

Required correct option is Since the two confidence intervals overlap, neither gender appears to be substantially more successful in their challenges.

a) In order to find the 99% confidence interval for the percentage of successful challenges, the formula is given below: Lower limit of CI: upper limit of CI: The confidence interval for the percentage of successful challenges is (19.68%, 34.97%).b) In part (a), we found the confidence interval for the percentage of successful challenges among women playing singles matches. 99% confidence interval for the percentage of successful challenges made by the men playing singles matches is 21.7%± 4.93%.Here, the two confidence intervals overlap, therefore, neither gender appears to be substantially more successful in their challenges.Therefore, option (C) is the correct answer.

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Answer:

12x^2 + 30x+12    

Step-by-step explanation:

3x+6) (4x+2)

3x          6

12x^2       24x              4x

6x           12                   2

use a punnet square type deal here.

12x^2 + 24x + 6x + 12

12x^2 + 30x+12    

And so your answer should be: 12x^2 + 30x+12  

Answer:

x = 10[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{20}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 20[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 10[tex]\sqrt{3}[/tex]

The congruent 10 - labeled color spinner isn't attached and could not be found.

However, we could solve the problem hypothetically.

Answer:

Kindly check explanation

Step-by-step explanation:

The events here are independent events :

Probability = required outcome / Total possible outcomes

Total possible outcomes = number of divisions on spinner = 10

Required outcome = number of specified color

Therefore, Probability that first spin lands on yellow :

Number of yellow divisions on spinner / total number of divisions

Let number of yellow divisions = 3

Therefore. Probability that first spin lands in yellow = 3 / 10

Probability that second spin lands on green :

Number of green divisions on spinner / total number of divisions

Let number of green divisions = 2

Therefore. Probability that first spin lands on green = 2 / 10

P(first) * P(second)

3/10 * 2/10 = 3/10 * 1/5 = 3/50

Recall ; this is an hypothetical situation and not the original problem.

The probability that the first spin will land on yellow and the second spin will land on green is; 2/5

The spinner is missing but from online search, it is discovered that from the 10 congruent sections labeled, the colors are as follows;

Yellow - 2 sections

Green - 2 sections

Red - 3 sections

Blue - 3 sections

Thus, probability of getting yellow on first spin is;

P(yellow on first spin) = 2/10

Probability of getting green on second spin is;

P(green on second spin) = 2/10

Thus, probability that the first spin will land on yellow and the second spin will land on green is;

P(1st on yellow and 2nd on green) = 2/10 + 2/10

P(1st on yellow and 2nd on green) = 2/5

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Before the price change, the optimal consumption choice (A) is determined by equalizing the marginal utilities of x and y.

Using the utility function U(x, y) = xy, and considering prices of Px = 1 and Py = 2, along with an income of 40, we find that the utility equalization condition leads to y = x/2.

With the budget constraint of x + 2y = 40, we solve for x = 20 and y = 10, giving the optimal consumption choice (20, 10) labeled as point A on the graph.

After the price change, with the price of y falling to 1, the consumer aims to maintain the same utility level. Setting MUX/Px = MUY/Py, we find x = y, and using the budget constraint x + y = 40, we get x = y = 20, resulting in the optimal consumption choice (20, 20) labeled as point B.

The substitution effect is illustrated by a movement from A to B along the budget constraint. The new optimal consumption choice (C) after the price change is determined by the new budget constraint x + y = 40, where x = 30 and y = 10, labeled as point C on the graph.

The income effect is depicted by the parallel shift of the budget constraint line outward from the origin.

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Answer:

The system of this equation is ( -1, 10) which is Option A.

Step-by-step explanation:

Solve for y in the first equation.

[tex]y = - 5x + 5 \\ - 2y = - x - 21[/tex]

Replace all occurrences of yy with -5x+5 in each equation.

[tex]10x - 10 = - x - 21 \\ y = - 5x + 5[/tex]

Solve for x in the first equation.

[tex]x = - 1 \\ y = - 5x + 5[/tex]

Replace all occurrences of x with -1 in each equation.

[tex]y = 10 \\ x = - 1[/tex]

The solution to the system is the complete set of ordered pairs that are valid solutions.

(−1, 10)

Hence, the system of this equation is (-1, 10).

Option A.

Answer:

Function notation means to replace y= into f(x)=. So I think that it would be f(x) = 40 +12d.

Step-by-step explanation:

The probability of Sunshine Delight winning given that it is raining is approximately 0.79. The probability that a document is spam if it contains the word "llwws" is approximately 0.50.

In the case of Sunshine Delight winning, given that it is raining, the probability is directly provided as 0.79.

For the probability of a document being spam if it contains the word "llwws," the information shows that the probability of the word "llwws" appearing in a spam document is 0.50. However, without further information about the overall prevalence of spam and non-spam documents, we cannot directly determine the probability that a document containing "llwws" is spam. Additional context about the overall occurrence of spam and non-spam documents is required to calculate the requested probability.

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Answer:

$86.94

Step-by-step explanation:

All we need to do is subtract his weekly play from his pay after taxes and his other taxes.

   $625

   $499.61

_ $38.45

____________

   $86.94

Have a nice day, fam. Spread The Love.

Answer:

71

93.5

x=15.5

Step-by-step explanation:

(2x+40)+(5x+16)+(x)=180

you have to put all the measures together and equal it to 180. when it comes to triangles, all the angles added together are equal to 180.

now solve the equation and you should get this:

x=15.5

the next step is to solve the give equations separately:

2(15.5)+40=71

5(15.5)+16=93.5

(15.5)=15.5

now to check the work, you have to add all the measures that were just calculated:

71+93.5+15.5=180 so check!

Answer:

808 over 25 as a faraction

Step-by-step explanation

a quarter of 65 is 16 4 over 25

16 4 over 25 times 2 808 over 25 as a fraction

The value of K is given as follows:

K = 1/12.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For a distribution, we have that the sum of all the probabilities in the distribution must be of 1.

This means that the cumulative distribution at the least value is of 1, hence the equation is given as follows:

17/12 - 5K = 1

Then the value of K is obtained as follows:

5K = 17/12 - 1

5K = 17/12 - 12/12

5K = 5/12

K = 1/12.

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Answer:

I'm not too sure what you mean but since there was no image I tried to look up how to tell if angles are corresponding based on angle degree and the most I got was the angles will be equal but only if there is a transversal cur but none of the answers equal each other

Step-by-step explanation:

so what advice I can give you is corresponding angles are usually the same degree but on a different level. like on the first parallel line there is an angle and on the second (or whatever) there is another angle (on the same side of the first) -meaning they will both be on the right or the left- and yeah there you go

if you have any questions comment and I'll try my best to help

Answer:

C and D.

Step-by-step explanation:

For C, 4 * 2x = 8x and 4*1 = 4.

For D, 5x+3x = 8x and 2+2 = 4.

Answer:

A)  8( x + 2 ) is the only equal expression.