Let X and Y be two independent random variables. Suppose that X ~ Unif({0, 1,...,n}) and Y~ Ber(p), i.e. P(X= k) = 1 n+1' ke {0, 1,..., n}, and P(Y= 1) = 1 - P(Y= 0) = p. (a) [3 pts] Find the pmf and

The problem involves fair flow allocation with hard-constrained links. By solving equations and considering constraints, the proportional fairness solution results in flow rates of (4/1, 4/1, 2/1, 2/1) with corresponding prices for links (p1, p2, p3) being (2, 2, 0).

By inspection, we find that the maximum-minimum flow allocation is (3/1, 3/1, 3/1, 3/1).

To achieve proportional fairness, we introduce price variables (p1, p2, p3) for each link and solve the following equations:

x1 = p1 + p2 + p3

x2 = p1 + p2

x3 = p1

x4 = p2 + p3

x1 + x2 + x3 ≤ 1, with equality if p1 > 0

x1 + x2 + x4 ≤ 1, with equality if p2 > 0

x1 + x4 ≤ 1, with equality if p3 > 0

From the equations, it is clear that x1 + x4 < 1, which implies p3 = 0. Additionally, since links 1 and 2 are full, we have x3 = x4. Using x3 = p1 and x4 = p3, we find p1 = p2.

Finally, we can solve 2p1 + 2p1 + p1 = 1 to obtain p1 = p2 = 2. Thus, the solution is x_pf = (4/1, 4/1, 2/1, 2/1). Flows 1 and 2 use paths with a price of p1 + p2 = 4 and have a rate of 4/1 each, while flows 3 and 4 use paths with a price of p1 = p2 = 2 and have a rate of 2/1 each.

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Complete question:

Consider a fair flow allocation problem with hard-constrained links. By inspection, the maximum-minimum flow allocation is found to be (3/1, 3/1, 3/1, 3/1). Seeking a solution for proportional fairness, where the price for each link is denoted as (p1, p2, p3), solve the given equations and constraints to determine the flow rates and prices that satisfy the system. Explain the steps involved in finding the solution and provide the resulting flow rates and corresponding link prices.

Answer:

15 Weeks

Step-by-step explanation:

$11,000 - $5,000 = $6,000 This is how much he needs to pay.

$6,000 ÷ $200 = 30 This is how many weeks he needs to work to get the $6,000

The questions is asking how many weeks does he have to work to get %50, Therefore 30 x .50 = 15 which is your answer.

Hope this helps!!!

-Conrad

Therefore the minimum cost of a rectangular box of volume is x = 4.641588834 cents.

A cuboid is a six-faced solid known as a hexahedron in geometry. Four-sided quadrilaterals make up its faces. A cuboid is a hexahedron, a solid with six faces, and the word "cuboid" means "like a cube" in the sense that a cuboid can become a cube by changing the length of its edges or the angle between its faces and edges. Four-sided quadrilaterals make up its faces. A cuboid can be made to look more like a cube by varying the lengths of its edges or the angles between its faces and edges. A cuboid's volume is equal to the sum of its length, breadth, and height. The opposite faces of a cuboid on a rectangular cuboid are equal, and all the angles are at right angles.

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Ben has bbb dollars, Cam has 777 fewer dollars than Ben, So Cam's have b-7 dollars.

Based on the given conditions,

Here b represents the number of dollars Ben has,

Given expression is,

Cam has 7 fewer dollars than Ben,

So, the number of dollars cam has = The number of Ben's dollar - 7

= b - 7

Hence, the expression that represents cam's dollar is,

= b -7

Therefore,

Cam has 7 fewer dollars than Ben, then the Cam's have b-7 dollars.

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Answer:

45??!

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

If there were 15 bunnies 5 were females so there is 10 men and if each female had 5 babies each then that would be 25 babies plus the 10 men should be 35

Answer:

y=x-5

Step-by-step explanation:

Answer:

3/4 ÷ 1/8 = 6

Step-by-step explanation:

first you would have to figure out how to make them even factors.

6/8 ÷ 1/8

Then you would divide, and get 6.

The solution to the equation is x = -2 or x = 5

The equation is given as

3x^2-9x=30

Rewrite properly as

3x^2 - 9x = 30

Divide through by 3

So, the equation becomes

x^2 - 3x = 10

Rewrite the equation

So, the equation becomes

x^2 - 3x - 10 = 0

Expand the equation

So, the equation becomes

x^2  + 2x - 5x - 10 = 0

Factorize the equation

So, the equation becomes

x(x  + 2) - 5(x + 2) = 0

This gives

(x + 2)(x - 5) = 0

Evaluate

x = -2 or x = 5

Hence, the solution to the equation is x = -2 or x = 5

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Answer:

y ≤ 1/3x - 4

Step-by-step explanation:

it could not be options 3 or 4 because the y-intercept is -4, not +4

I picked a point in the shaded area to see which inequality, the first or the second, would make it true; the point I used was (3, -4)

1st option:  y ≥ 1/3x - 4        Is this true? -4 ≥ 1/3(3)  No, -4 is not GE 1

2nd option: y ≤ 1/3x - 4        Is this true? -4 ≤ 1/3(3)  Yes, -4 is LE 1  

Betrys needs another 400 grams of diced potatoes to make her vegetable stew for 8 people.

We know that Betrys is cooking for 8 people, and we know that a recipe for 2 people needs 10 ounces.

8 people is 4 times 2 people, then for 8 people you need 4 times 10 ounces, this is 4*10 oz = 40 ounces.

Now we can apply a change of units, remember that:

1 oz = 28 grams

Then the total amount she needs is:

40 oz = 40*28 g = 1,120 g

So she needs in total 1,120 grams, and in the balance, she already has 720 grams, so the amount that she needs is given by the subtraction:

1,120 g - 720g = 400

Betrys needs another 400 grams of diced potatoes to make her vegetable stew for 8 people.

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Answer: -25

Step-by-step explanation:

14-43+4

In conclusion, the probability that exactly 7 out of 17 cars will not have engine failure given that 24.1% of car engines will fail if they have not had routine maintenance in the past five years is 0.1918.

The probability that exactly 7 out of 17 cars will not have engine failure given that 24.1% of car engines will fail if they have not had routine maintenance in the past five years is 0.1918. This probability can be determined by using the binomial probability formula, which states that the probability of x successes in n trials is equal to

\(nCr * p^x * (1-p)^(n-x),\) where n is the number of trials, r is the number of successes, p is the probability of success, and x is the number of successes in the trials.

In this case, the number of trials (n) is 17, the number of successes (r) is 7, the probability of success (p) is 0.241, and the number of successes in the trials (x) is 7. Substituting these values into the equation, the probability that exactly 7 out of 17 cars will not have engine failure is \(17C7 * (0.241)^7 * (0.759)^(17-7) = 0.1918.\)

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Answer:

The required equation is:

Step-by-step explanation:

I think that's the answer

The linear function rule to model the distance in feet 'd' that the car has traveled any number of seconds 't' after passing the timing device. can be represented as d = f(t) = 117t

A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables but does not have exponents to the variables or the exponent of the variable is 1.

Given that car is moving at a constant speed.

Distance travelled by car = 936 feet

Time taken to travel the distance = 8 seconds

Speed = Distance / Time

           = 936 / 8

           = 117 feet per second

So the car will be moving at a speed of 117 feet per second at any time t.

Distance of car at any time is,

Distance = Speed × Time

d = 117 × t

d = f(t) = 117t

Hence the linear function which models the relationship between d and t is d = f(t) = 117t.

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The distance along the unit circle between any two successive 8th roots of 1 is c) π/4.

To find the distance along the unit circle between any two successive 8th roots of 1, we can consider the concept of angular displacement.

Each 8th root of 1 represents a point on the unit circle that is evenly spaced by an angle of 2π/8 = π/4 radians.

Starting from the point corresponding to 1 on the unit circle, we can move π/4 radians to reach the first 8th root of 1. Moving π/4 radians further will bring us to the second 8th root of 1, and so on.

Since we are moving by π/4 radians for each successive 8th root of 1, the distance between any two successive 8th roots of 1 is π/4 radians.

Therefore, the correct answer is option c. π/4.

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Answer:

AB ≈ 5.59 m

Step-by-step explanation:

The arc AB is calculated as

AB = circumference of circle × fraction of circle

      = 2πr × \(\frac{40}{360}\) ( r is the radius )

      = 2π × 8 × \(\frac{1}{9}\)

      = 16π ÷ 9 ≈ 5.59 m ( to the nearest hundredth )

Answer:

5.59

Step-by-step explanation:

I had the same one

Answer:

A

Step-by-step explanation:

If A is an m × n matrix. The following are true regarding it: 1. The number of pivot positions in A is called the rank of A.2. A pivot column of A is a column that contains a pivot position.3. A pivot position of A is a location in A that corresponds to a leading 1 in the reduced echelon form of A.4. Free variables of a linear system are variables corresponding to the non-pivot columns of A.

The rank of a matrix is the number of pivot positions in the matrix after it has been reduced to a reduced echelon form. In the reduction procedure, the rows and columns of the matrix are manipulated to convert the matrix into a reduced echelon form.

A pivot column of matrix A is one that contains at least one pivot position, according to the definition. These are columns that have a leading 1 in a reduced echelon form. These columns contain the variables in the equation system that correspond to the pivot rows.

In matrix A, a pivot position is the location of a leading 1 in the matrix's reduced echelon form. The reduced echelon form of a matrix is the one in which the matrix has been transformed so that it satisfies certain criteria for ease of use.

The variables that do not correspond to pivot columns in matrix A are referred to as free variables. These variables are not bound to specific values in a solution to the associated equation system. They can take on any value and therefore provide an infinite number of solutions.

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The formula for the surface area of a cube in terms of its volume is \(SA(V) = 6V^(2/3)\), and the domain of SA(V) is [0, ∞).

Let S represent the surface area of a cube, and let V represent its volume

. The formula for the surface area of a cube in terms of its volume is \(SA(V) = 6V^(2/3).\)

The domain of SA(V) is all nonnegative real numbers, since the volume and surface area of a cube cannot be negative.

Volume of cube (V) = s³ where s is the length of any side of the cube.

Surface area of a cube (S) = 6s²

=\(6(V^(2/3))\)

Formula for the surface area of a cube in terms of its volume is given as:

\(SA(V) = 6V^(2/3)\)

State the domain of SA(V):

The domain of SA(V) is all nonnegative real numbers, since the volume and surface area of a cube cannot be negative.

In interval notation, the domain is [0, ∞).

Therefore, the formula for the surface area of a cube in terms of its volume is\(SA(V) = 6V^(2/3)\), and the domain of SA(V) is [0, ∞).

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Answer:

Answer:

21.15  550 divided by 26 = 21.15.

Step-by-step explanation:

I did the work on my paper. =)

Answer:

A

Step-by-step explanation:

i have seen this before so yea

Answer:

The answer is A, y=-5/2x-3

Step-by-step explanation:

We know that the y intercept is -3, so we just need to use the rise/run technique to find the slope, which ends up being -5/2 when simplified.

a) The expression for the magnitude of the electric field at the upper right corner of the square is E = (k_e * 4) / (a^2 * 2) + (k_e * 5) / a^2

b)The expression for the total electric force exerted on the charge q is given by:

F = q * [(k_e * 4) / (a^2 * 2) + (k_e * 5) / a^2]

(a) To find the expression for the magnitude of the electric field at the upper right corner of the square, we need to consider the contributions from charges A and C.

The electric field due to a point charge is given by the equation:

E = k_e * (q / r^2)

where E is the electric field, k_e is the electrostatic constant, q is the charge, and r is the distance from the charge.

For the upper right corner, the distance from charge A is a√2, and the distance from charge C is a.

Therefore, the expression for the magnitude of the electric field at the upper right corner is:

E = (k_e * A) / (a√2)^2 + (k_e * C) / a^2

Substituting the given values A = 4 and C = 5, we have:

E = (k_e * 4) / (a^2 * 2) + (k_e * 5) / a^2

(b) The expression for the total electric force exerted on the charge q is given by:

F = q * E

where F is the force and q is the charge. Substituting the expression for the electric field from part (a), we have:

F = q * [(k_e * 4) / (a^2 * 2) + (k_e * 5) / a^2]

(c) If each of the four charges were negative with the same magnitude, the answers to parts (a) and (b) would change as follows:

The force would be the same magnitude but opposite direction as the force in part (b).

The electric field would be the same magnitude but opposite direction as the field in part (a).

In other words, the signs of both the electric field and force would be reversed. The magnitudes, however, would remain the same.

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Answer:

1047.2 cubic inches

Step-by-step explanation:

V = 4(pi)(r³/3)

V = 4(pi)(125/3)

V = 523.6 cubic inches (1 ball)

V = 2(523.6) = 1047.2 cubic inches (total)

Answer:

37.69911184

Step-by-step explanation:

because circumference is equal to pi multiplied by diameter, you will not get the circumference with the radius times pi. in order to get the diameter, you multiply the radius by 2, because the diameter is the length across the circle. So the diameter of this circle is equal to 12. so simply multiply that number by pi (3.14) and there is your answer. Hope i helped.

Answer:

D

Step-by-step explanation:

Somehting bknbye3uehnfhnjun Español uno, como sulfhídrica

Answer:

.44444444

Step-by-step explanation:

πr²=full circumference

18/π(9)²=x/2π

Carlos harvests cassavas at a constant rate. He needs 353535 minutes to harvest a total of 151515 cassavas.

The ratio of the change in dependent values or outputs to the change in independent values or inputs is known as the rate of change. The change, which also refers to the function's slope, represents the shift in values between two points on a coordinate plane. The formula for the rate of change is (y2 - y1)/, where y stands for the dependent variable and x for the independent variable (x2 - x1).

Given:

Carlos gives  353535 minutes to harvest a total of 151515 cassavas.

Find:

We have to find the total number of cassavas.

Solution:

Carlos harvests cassava at constant rate is 353535 minutes per 151515 cassavas

= 151515/353535

= 0.429

A formula for the quantity of cassava (C) that Carlos harvests each time (T).

This means that after 353535 minutes, 151515 cassavas have been harvested, after 700000 minutes, 300000 cassavas, and so on.

Hence, the required constant rate is 0.429T.

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It is found that y in terms of x is given by the expression: y = (3x - 2)^2

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

In mathematics, when we express “the product” we mean a multiplication. So the expression "the product of 3 and x "  is represented by:

3x

When we express "less than" we mean a subtraction. So the expression “If 2 less than the product of 3 and x” is represented by:

3x-2

When we express "square" we mean an exponent equal to two. So the expression “If 2 less than the product of 3 and x is squared, the result is y” is represented by:

(3x-2)^2 = y

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