(Beautiful Mind) There is an interesting scene in A Beautiful Mind in which John Nash's character discovers his equilibrium concept. The setup is that there are four men and five women at a bar, and each man must simultaneously walk over to a woman. One of the women, who is blonde, is considered to be more desirable than the other four, who are all brunettes. Although the men all prefer the blonde to the brunettes, if they all go for the blonde they will "block each other" (according to the logic of the movie) and end up unsuccessful; moreover, after going for the blonde, they cannot then go to a brunette because the brunette would be offended at being someone's second choice and would turn down the man. Nash's character then realizes that what ought to happen is for each of the four men to choose a brunette. Let's try to put this situation in a game theoretic model by using a to denote the payoff a man would receive if another man goes for the same woman he does (here there are assumptions that it is possible to "block each other" on brunettes and that being "blocked" on a brunette gives the same payoff as being "blocked" on a blonde, although this is not important for the problem). We'll use b to refer to a man's payoff if he is the only man to go for a woman and that woman is a brunette. We'll use c to refer to a man's payoff if he is the only man to go for a woman and that woman is blonde. The natural restrictions on payoffs are a < b < c. Is there a pure strategy Nash equilibrium where each man ends up with a brunette? What are the pure strategy Nash equilbria? How do these answers change if the blonde turns down everyone (meaning that the payoff to going to the blonde is a, regardless of how many men choose her)? [Hint: classify situations based on how many men go to the blond woman.]

Answer:

1: x = 6

2: There is no solution. Sorry. (because the ending equation will be 0 = 7)

3: I can't see the other part of the equation, I need to see what the fraction is in order to solve it. If you can retake the picture, I can edit my response :)

Step-by-step explanation:

#1: 3(x-1) is pretty much just 3x-3. Simple.

Now, your equation becomes 3x-3 = 2x+9.

Arrange them so that the like terms are together.

Since you will be taking the 2x from 2x+9 over to the other side, it becomes 3x-2x-3 = 9.

Now, bring the 3 over to the side with the 9.

x = 6.

#2: Same as before, -2(x+1) is (-2x) - 2.

So, -2x-2 = -2x+5.

As I said before, you need to group the like terms together.

-2x and -2x go together, and -2 and 5 go together.

-2x+2x=5+2

0=7.

There is no solution.

#3: Like the other two, 4(x-1) is 4x-4. As for the other part, I cannot see the fraction before (x-8).

Answer:

2:40

Step-by-step explanation:

Add 85 minutes to 45 minutes and then add that to 12:30

Answer:

y=9

Step-by-step explanation:

12/y=4/3

3×12/y=3×4/3

36/y=4

y×36/y= 4×y

36=4y

36/4=4y/4

9=y

Answer:

Where is the number I need to round to?

(Please don't give me a bad rating i'm trying to help :) )

Answer:

quadratic equation

Step-by-step explanation:

Answer:

the equation shown here is a quadratic equation

Answer:

36

Step-by-step explanation:

To find the area of a triangle, multipy the base and height of a triangle, then divide it in half

8x9=72/2=36

Answer:

Prism B has a larger base area

Step-by-step explanation:

Given

Base dimensions:

Prism A:

Lengths: 6cm, 8cm and 10cm

Prism B:

Lengths: 5cm and 5cm

Required [Missing from the question]

Which prism has a larger base area

For prism A

First, we check if the base dimension form a right-angled triangle using Pythagoras theorem.

The longest side is the hypotenuse; So:

[tex]10^2 = 8^2 + 6^2[/tex]

[tex]100 = 64 + 36[/tex]

[tex]100 = 100[/tex]

The above shows that the base dimension forms a right-angled triangle.

The base area is then calculated by;

Area = 0.5 * Products of two sides (other than the hypotenuse)

[tex]Area = 0.5 * 8cm * 6cm[/tex]

[tex]Area = 24cm^2[/tex]

For Prism B

[tex]Lengths = 5cm\ and\ 5cm[/tex]

So, the area is:

[tex]Area = 5cm * 5cm[/tex]

[tex]Area = 25cm^2[/tex]

By comparison, prism B has a larger base area because [tex]25cm^2 > 24cm^2[/tex]

Answer:

Write abt a poem you like or something

Step-by-step explanation:

Answer:

#1

#2

#3

#4

9514 1404 393

Answer:

  (d)  (-3, 1)

Step-by-step explanation:

We assume a typo in the problem statement, and that the equations are supposed to be ...

  [tex]2x -3y = -9\\-x +3y = 6[/tex]

Adding the two equations gives ...

  x = -3

Substituting for x in the second equation gives ...

  3 +3y = 6

  1 + y = 2 . . . . divide by 3

  y = 1 . . . . . . . subtract 1

The solution is (x, y) = (-3, 1).

Answer:

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Step-by-step explanation:

Answer:

The circumference is 16π or 50.2654 depending on whether they ask you for an exact value or in terms of pi.

Step-by-step explanation:

2r=d

2(8)=d

16=d

C=πd

C=π16

So, the circumference is 16π or 50.2654 depending on whether they ask you for an exact value or in terms of pi.

Answer:

50.2654

Step-by-step explanation:

Answer:

1350 m³

Step-by-step explanation:

To find the volume of a rectangular prism, we have to multiply its length, width, and height together.

The dimensions of this prism are 9, 10, and 15.

9 · 10 · 15 = 1350

The volume is 1350 meters³.

I hope this helps ^^

0%

Where rolling a pair of die, a pair is two so there is two die. Now we have to look at the sample space for the two dice.

1 2 3 4 5 6

1 l 2l 3l 4l 5l 6l 7l

2l 3l 4l 5l 6l 7l 8l

3l 4l 5l 6l 7l 8l 9l

4l 5l 6l 7l 8l 9l 10l

5l 6l 7l 8l 9l 10l 11l

6l 7l 8l 9l 10l 11l 12l

there is 36 outcomes in the sample space none of them include getting 15.

After considering the given data we conclude the x term of h(x) is [tex]44 + 5*2 = 26.[/tex]We can continue this process for the [tex]x^2[/tex] term, the [tex]x^3[/tex] term, and the [tex]x^4[/tex] term, using the appropriate terms from f(x) and g(x) and adding up the products and  the quotient q(x) is [tex]x^2 - x,[/tex] and the remainder r(x) is [tex]3x^2 + 8x + 5,[/tex]

To evaluate the product h(x) of the two polynomials f(x) and g(x) manually, we can apply a table [tex]T_3[/tex] to show line by line how each term is computed.
The table possess columns for the term from f(x), the term from g(x), and the product of the two terms. The rows of the table will correspond to the different powers of x, starting from [tex]x^0[/tex].
For instance , to compute the constant term of h(x), we need to multiply the constant terms of f(x) and g(x). The constant term of f(x) is 5, and the constant term of g(x) is 4, so the constant term of h(x) is 54 = 20.
Similarly, to compute the x term of h(x), we need to multiply the x term of f(x) (which is 4) by the constant term of g(x) (which is 4), and add it to the constant term of f(x) (which is 5) multiplied by the x term of g(x) (which is 2).
Therefore, the x term of h(x) is [tex]44 + 5*2 = 26.[/tex]We can continue this process for the [tex]x^2[/tex] term, the [tex]x^3[/tex] term, and the [tex]x^4[/tex] term, using the appropriate terms from f(x) and g(x) and adding up the products.

To evaluate the quotient q(x) and remainder r(x) when f(x) is divided by g(x), we can use polynomial long division.
We apply division the highest degree term of f(x) by the highest degree term of g(x) to get the first term of q(x).
Then we multiply g(x) by this term of q(x) and subtract the result from f(x) to get the first remainder. We repeat this process with the next highest degree term of the remainder until the degree of the remainder is less than the degree of g(x).
The coefficients of the terms in q(x) are the quotients obtained in each step of the division, and the coefficients of the terms in the remainder are the final remainder obtained after all the steps of the division.
For instance , to compute the quotient q(x) and remainder r(x) when [tex]f(x) = x^4 + 2x^3 + 3x^2 + 4x + 5[/tex] is divided by [tex]g(x) = x^2 + 2x + 4,[/tex]
we first divide [tex]x^4[/tex] by [tex]x^2[/tex] to get [tex]x^2[/tex] as the first term of q(x).
We then multiply g(x) by [tex]x^2[/tex] to get [tex]x^4 + 2x^3 + 4x^2,[/tex] and subtract this from f(x) to get[tex]-x^3 - x^2 + 4x + 5[/tex] as the first remainder.
We then divide [tex]-x^3[/tex] by [tex]x^2[/tex] to get -x as the second term of q(x).
We multiply g(x) by -x to get[tex]-x^3 - 2x^2 - 4x[/tex], and subtract this from the first remainder to get [tex]3x^2 + 8x + 5[/tex]as the final remainder.
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The given integral is: $$\int (-2x^2 + 500)dx$$

To solve the above integral, we integrate both terms separately. Using the integral formulas, $$\int x^n dx= \frac{x^{n+1}}{n+1}+ C$$$$\int kf(x)dx= k\int f(x)dx$$

where C is a constant of integration and k is a constant.

The integral $\int -2x^2 dx$ is:\begin{align*} \int -2x^2 dx &= -2\int x^2 dx\\&= -2\times \frac{x^{2+1}} {2+1} + C\\&= -\frac {2}{3}x^3+ C\end{align*}

The integral $\int 500 dx$ is:\begin{align*}\int 500 dx &= 500\int dx\\&= 500\times x + C\\&= 500x + C\end{align*}

Thus, the integral $\int (-2x^2 + 500) dx$ is:\begin{align*}\int (-2x^2 + 500) dx &= \int -2x^2 dx + \int 500 dx\\&= (-\frac {2}{3}x^3+ C_1) + (500x + C_2)\\&= -\frac {2}{3}x^3+ 500x + C\end{align*}

where C is a constant of integration and $C=C_1+C_2$.

Therefore, the exact value of the integral is $-\frac {2}{3}x^3+ 500x + C$.

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Answer:

For two fractions to be proportional, they must be equivalent. 32=1.5 and 188=2.25 , so these fractions are not proportional.

Step-by-step explanation:

Using a Normal distribution table , the value of the given probability is 0.0359

Find the row corresponding to the tenths digit of -1.8, which is -1.8 rounded to -1.9.

Find the column corresponding to the hundredths digit of -1.8, which is -1.8 rounded to -1.80.

The value in the intersection of the row and column is the probability of Z being less than -1.8.

Therefore, we find that the probability is approximately 0.03593

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Answer: $45

Step-by-step explanation:

Let the original price be x.

Since there was a discount of 20%, it means the person bought the frying pan at (100% - 20%) = 80% of the original price. This can then be formed into an equation as:

80% × x = $36

0.8 × x = $36

0.8x = $36

x = $36/0.8

x = $45

The original price was $45

Answer:

Step-by-step explanation:

1.  Not sure...

2. $ 1.44

3. $ 3.70

4. $11 per ticket

Answer:

Mean and IQR

Step-by-step explanation:

The measure of centre gives the central or the measure which gives the best mid term of a distribution. Based in the details of the box plot, the median is the value which divides the box in the box plot.

For company A:

Range = 25 to 80 with a median value at 30 ; this means the median does not give a good centre measure of the distribution ad it is very close to the minimum value. This goes for the Company B plot too; with values ranging from (35 to 90) and the median designated at 40.

Hence, the mean will be the best measure of centre rather Than the median in this case.

For the variability, the interquartile range would best suit the distribution. With the lower quartile and upper quartile both having reasonable width to the minimum and maximum value of the distribution.

Answer:

B

Step-by-step explanation:

Answer:

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

DC is the radius and its length is:

DC is the perpendicular bisector of EF.  Hence the half of the segment EF is the leg of a right triangle with the hypotenuse of EC = DC = 70 and other leg of 50 units.

Using the Pythagorean theorem, find the length of EF:

To find the partial sum S₁7 for the arithmetic sequence with a first term (a) of 3 and a common difference (d) of 2, we can use the formula for the sum of an arithmetic sequence. Therefore, the partial sum S₁7 for the arithmetic sequence with a first term of 3 and a common difference of 2 is 323.

The formula for the sum of an arithmetic sequence is given by:

Sn = (n/2)(2a + (n-1)d)

In this case, we want to find the partial sum S₁7, which means we need to substitute n = 17 into the formula.

Plugging in the values, we have:

S₁7 = (17/2)(2(3) + (17-1)(2))

Simplifying the equation inside the parentheses, we get:

S₁7 = (17/2)(6 + 16(2))

Simplifying further:

S₁7 = (17/2)(6 + 32)

S₁7 = (17/2)(38)

Finally, evaluating the expression, we have:

S₁7 = 17(19)

S₁7 = 323

Therefore, the partial sum S₁7 for the arithmetic sequence with a first term of 3 and a common difference of 2 is 323.

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Answer:

It would be D

Step-by-step explanation: