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{[Math from BIM]}
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The randomized min-cut algorithm, such as the Karger's algorithm, is an iterative algorithm that repeatedly contracts edges in a graph until only two nodes (or a small number of nodes) remain. At that point, the remaining edges represent a cut in the graph.

In each iteration of the algorithm, an edge is chosen uniformly at random to be contracted. This contraction merges the two nodes connected by the chosen edge into a single super-node. The process continues until only two nodes remain, representing the cut in the graph.

To analyze the algorithm, let's consider a graph with n vertices. At each iteration, the number of vertices decreases by one since two vertices are merged into one. Therefore, after k iterations, there are n - k vertices remaining in the graph.

Now, let's consider the number of distinct cuts that can be formed by the remaining vertices. For n vertices, the total number of possible cuts is [tex]2^(n-1)[/tex]since each vertex can be on one side of the cut or the other. However, some of these cuts may be identical because the order in which the vertices are contracted can change the representation of the cut.

To see why, suppose we have a set of vertices A and a set of vertices B. The order in which the vertices are contracted can result in different representations of the cut. For example, if we contract vertex A before vertex B, the cut might be represented as (A, B). However, if we contract vertex B before vertex A, the cut might be represented as (B, A). Both cuts are essentially the same, but the order of the vertices determines the representation.

Since there are (n-1) edges that need to be contracted to reach the final cut of two vertices, there are (n-1)! possible orders in which the vertices can be contracted. However, each order produces the same cut, so we need to divide by (n-1)! to account for the different representations.

Therefore, the number of distinct cuts that can be formed by the remaining vertices is [tex]2^(n-1)[/tex]/ (n-1)!. Simplifying this expression, we get:

[tex]2^(n-1) / (n-1)! = n(n-1)(n-2)...(2)(1) / (n-1)(n-2)...(2)(1) = n[/tex]

So, there can be at most n distinct min-cut sets in the graph.

In summary, using the analysis of the randomized min-cut algorithm, we can argue that there can be at most n(n - 1)/2 distinct min-cut sets.

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Answer:

yes,yes,yes,no :) hope it helps

Step-by-step explanation:

Answer:

1. Yes

2. No

Definition of a Polygon: a plane figure with at least three straight sides and angles, and typically five or more.

1) Play

2)Dribble

3)Paint

4)Center

5)Assists

6)Perimeter

7)Benchwarmer

8)Aboard

9)Technical

10)Rebound

11)Penalty

12)screen

13)Overtime

14)guard

15)? Host

16)Quarter

17) Bounce

18)Swish

19)Halftime

20)Backcourt

Answer:

The Pythagorean Theorem is helpful for two-dimensional navigation.   You can use it along with two lengths to calculate the shortest path. The lengths north and west will be the triangle's two wings, and the diagonal will be the shortest line separating them.  The same principles can be used for air navigation. He is best known in the modern day for the Pythagorean Theorem, a mathematical formula which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.

- Hope this helps! :)

The sequence continues as follows:2, 5, 11, 21, 36, 67, ...

Given sequence2 5 11 21 36...

First differences 3 6 10 15...

Second differences 3 4 5...

Third differences 1 1...

The third differences are constant, which means that we can use a cubic polynomial for the fitting.

The formula for a cubic polynomial is

an³ + b

n² + c

n + d

Let us denote the nth term of the sequence by fn. Then, we have

f1 = 2, f2 = 5, f3 = 11, f4 = 21, f5 = 36...

We can write a system of equations using the first four terms of the sequence.

2 = a + b + c + d

5 = 8a + 4b + 2c + d

11 = 27a + 9b + 3c + d

21 = 64a + 16b + 4c + d

Solving this system, we get a = 1/3, b = 1, c = 11/3, and d = 0.

Thus, the closed-form expression for the nth term of the sequence isf(n) = (1/3)n³ + n² + (11/3)n

The next term in the sequence is f(6) = (1/3)(6)³ + (6)² + (11/3)(6) = 67.

Therefore, the sequence continues as follows:2, 5, 11, 21, 36, 67, ...

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Answer:

rectangular prisim

Step-by-step explanation:

Answer:

rectangular prism

Step-by-step explanation:

rectangle shaped box

Answer:

5/12

Step-by-step explanation:

add 3/12 and 2/12 to get 5/12 (decimal form is .416)

Answer:5/12 pounds

Step-by-step explanation: You take the 3 and add it with the 2 and you get 5/12

[tex]\frac{3}{12}[/tex] + [tex]\frac{3}{12}[/tex] = [tex]\frac{5}{12}[/tex]

Answer:

126+111+43+8=288

360-288=72

72÷12=6

x=6

Answer:  

x=6

Step-by-step explanation:

Step by step explaination attached below.

Inverse Laplace transform of f(s) = s³ / (s² + 6s + 13) is

[tex]f(t) = [(-3 + 2i)^{13} / (2i)] e^{(-3 + 2i)t} + [(-3 - 2i)^{13} / (-2i)] e^{(-3 - 2i)t[/tex]

The inverse Laplace transform of f(s) = s¹³ / (s² + 6s + 13) needs to be found.

To find the inverse Laplace transform, we first need to factor the denominator of f(s) using the quadratic formula:

s² + 6s + 13 = 0

s = [-6 ± √(6² - 4(1)(13))] / 2(1)

s = -3 ± 2i

Now we can rewrite f(s) as:

f(s) = s¹³ / [(s + 3 - 2i)(s + 3 + 2i)]

Using partial fraction decomposition, we can write:

f(s) = A / (s + 3 - 2i) + B / (s + 3 + 2i)

where A and B are constants to be determined. Multiplying both sides by the denominator, we get:

s¹³ = A(s + 3 + 2i) + B(s + 3 - 2i)

Substituting s = -3 + 2i, we get:

(-3 + 2i)¹³ = A(2i)

Solving for A, we get:

A = (-3 + 2i)¹³ / (2i)

Similarly, substituting s = -3 - 2i, we can solve for B:

B = (-3 - 2i)¹³ / (-2i)

Now we can write f(s) as:

f(s) = [(-3 + 2i)¹³ / (2i)] / (s + 3 - 2i) + [(-3 - 2i)¹³ / (-2i)] / (s + 3 + 2i)

Taking the inverse Laplace transform of each term separately using the table of Laplace transforms, we get the final answer:

[tex]f(t) = [(-3 + 2i)^{13} / (2i)] e^{(-3 + 2i)t} + [(-3 - 2i)^{13} / (-2i)] e^{(-3 - 2i)t[/tex]

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The given question is incomplete, the complete question is below

Find the inverse Laplace transform. f(s) = s¹³ / (s² + 6s + 13)

Answer:

exponential growth or exponential decay , and what ... The value of a car purchased for $20,000 decreases ... population, P, increases by 20%each year,

Sherri has 35 apps on her phone and Bill has 64 apps on his phone.

Let's represent Sherri’s apps with x.

Then, the number of Bill's apps will be x+29 (since he has 29 more apps than Sherri).

Their total number of apps is 99.Thus, the mathematical equation is:x + (x+29) = 99

Simplifying this equation gives:2x + 29 = 99

Subtracting 29 from both sides of the equation gives:2x = 70

Dividing both sides by 2 gives:x = 35

This means Sherri has 35 apps on her phone.

Substituting that into x+29 gives:35+29 = 64

Therefore, Bill has 64 apps on his phone.

Hence, each person has Sherri has 35 apps on her phone and Bill has 64 apps on his phone. The total number of apps between the two of them is 99 apps.

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Answer:

32x

Step-by-step explanation: 4(8x)=32x

Answer:

The measure of the inscribed angle is [tex]40^{\circ}[/tex]

Step-by-step explanation:

Recall that the measure of the inscribed angle is one-half the measure of the central angle subtended by the same arc.

So, if the measure of the central angle is [tex]80^{\circ}[/tex], so the measure of the corresponding inscribed angle is:

[tex]\frac{1}{2}\times 80^{\circ}=40^{\circ}[/tex]

The confidence interval using a 90% confidence level is (1.601, 1.819)

Confidence Interval = Sample Mean ± Margin of Error

Given the parameters:

Sample Mean (x) = 1.71

Population Standard Deviation (σ) = 0.86

Sample Size (n) = 170

Confidence Level = 90%

The standard Error(SE) is given by:

SE = σ / √n

SE = 0.86 / √170 ≈ 0.0663

The margin of Error is related to standard error by the relation:

ME = Z × SE

ME = 1.645 × 0.0663 ≈ 0.109

Confidence Interval = Sample Mean ± Margin of Error

Confidence Interval = 1.71 ± 0.109

Confidence Interval= (1.601, 1.819)

A decrease in sample size from 170 to 120 would lead to increase in error margin , since decrease in sample size will increase the standard error.

If confidence interval were raised from 90% to 95% , the error margin would be larger since increase in confidence interval would increase the critical value

Based on the confidence interval , it is very likely that the mean number of personal computers is greater than 1.

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Answer:

i guess you multiply 3and 30good lu8ck

Step-by-step explanation:

Answer:

3x+30=90 complementary

3x=90-30

x=60/3=20

x=20° is your answer

Answer:

I think the volume of the figure is 60 but I'm not 100 % sure

Step-by-step explanation:

I belive the formula for this figure was (a+b)xh/(2)

So 40x 3 = 120

120/2 = 60

I think the answer would be B. The range is then total price of the tickets purchased and includes all whole numbers from 1 to 4.

The transitions are labeled with the input symbol, the symbol to be pushed onto the stack (ε indicates no symbol is pushed), and the symbol to be popped from the stack (ε indicates no symbol is popped).This PDA accepts strings in L where the number of 'a's is twice the number of 'b's.

To draw the state diagram of a PDA that accepts the language L = {w ∈ {a, b}^∗ | w has twice as many a's as b's}, we can design a simple PDA with two states.

State 1: Initial state

Transition: (a, ε, a) -> State 1

Transition: (b, a, ε) -> State 2

Transition: (ε, ε, ε) -> Accepting state

State 2: Secondary state

Transition: (b, a, ε) -> State 2

Transition: (ε, ε, ε) -> Accepting state

Accepting state: Final state to indicate that the input string is accepted.

Here is the state diagram representation of the PDA:

Note: Find the attached image for the state diagram representation of the PDA.

In this PDA, State 1 is the initial state, and State 2 is the secondary state. The transitions are labeled with the input symbol, the symbol to be pushed onto the stack (ε indicates no symbol is pushed), and the symbol to be popped from the stack (ε indicates no symbol is popped).

The PDA works as follows:

This PDA accepts strings in L where the number of 'a's is twice the number of 'b's.

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An object located at the point (4, 55) on a distance time graph is later located at the point (9, 45). If distance is in metres and time is in seconds, the average speed is -2 m/s.

To calculate the average speed of an object, we need to find the total distance traveled divided by the total time taken.

Given that the object is located at the point (4, 55) initially and later located at the point (9, 45), we can determine the total distance traveled and the total time taken.

Total distance traveled = Difference in distance = 45 - 55 = -10 meters (negative because the object moved from a higher distance to a lower distance)

Total time taken = Difference in time = 9 - 4 = 5 seconds

Average speed = Total distance traveled / Total time taken = -10 meters / 5 seconds = -2 meters/second

Therefore, the average speed of the object is -2 m/s.

Option (a) -2 m/s is the correct answer.

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Answer:

Choice B - (1.02)

Step-by-step explanation:

With the teachers starting salary being $40,000, we can rightfully assume that it their salary would not increase with Choice A, $40,000 * 0.2 = $800.

2% otherwise known as 0.02, would make the teachers yearly salary $40,000 * 1 + 0.02, or $40,000 * 1.02. Making the correct answer, Choice B - (1.02). (This would also give the teacher an additional $800 per year!)

Answer:

h = 6.5 feet

Step-by-step explanation:

The height of the frog as a function of time is given by :

[tex]h= -0.5t^2 +3t+2[/tex] .....(1)

We need to find the maximum height reached by the frog. We can find it as follows :

Put [tex]\dfrac{dh}{dt}=0[/tex]

So,

[tex]\dfrac{d}{dt}(-0.5t^2 +3t+2)=0\\\\-t+3=0\\\\t=3[/tex]

Put t = 3 in equation (1).

[tex]h= -0.5(3)^2 +3(3)+2\\\\h=6.5\ feet[/tex]

So, the maximum height is 6.5 feet.

Answer:

I think the most upright answer would be D

Step-by-step explanation:

Answer:

5-8

Step-by-step explanation:

you just had to move the 8 over

The response to your graduate student's objection of taking multiple samples from each animal cannot increase statistical power is:

You should respond by saying that taking multiple samples from each animal is a well-known strategy for increasing statistical power.

In addition, increasing the number of observations per group improves the statistical test's accuracy and reliability.

The statistical test that one would use in this instance is the One-way ANOVA, or one-factor ANOVA.

A statistical test that can be used in this instance is the One-way ANOVA, or one-factor ANOVA.

This statistical test is a method used to determine if the average or mean of a numerical variable varies significantly between two or more groups of interest.

For this statistical test, it is best to use multiple samples to increase statistical power.

In addition, ANOVA is used to compare three or more sets of data for statistical significance by testing for variances.

ANOVA's null hypothesis is that all populations are equal, while the alternative hypothesis is that at least one population is different from the others.

The response to your graduate student's objection of taking multiple samples from each animal cannot increase statistical power is:

You should respond by saying that taking multiple samples from each animal is a well-known strategy for increasing statistical power.

In addition, increasing the number of observations per group improves the statistical test's accuracy and reliability.

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Answer: 11 units

Step-by-step explanation:

-3 and 3 are 6 units apart, so that would be 6 units, and when you add the -5 into the problem, the 6 units become 11 units. Hope this helped :)

Answer:

Exact Form:

√ 61

Decimal Form:

7.81024967 …

Answer:

Circumference ~ 233.7

Step-by-step explanation:

Use the distance formula to find the radius of the circle with the two coordinates given. The radius of this circle is about 37.2. Plug 37.2 into the formula 2(pi)r to find the Circumference. The answer is 233.7 rounded to the nearest tenth.

A differential equation is an equation involving a differentiable function, which is a critical tool in modeling physical phenomena like population growth, radioactive decay, and fluid flow.

A differential equation is an equation that involves a differentiable function. It is an equation in which the variables' derivatives appear. Differential equations are used to model physical phenomena like population growth, radioactive decay, and fluid flow. The order of a differential equation is the highest order of the derivative of the function. A first-order differential equation has the highest order of 1, and a second-order differential equation has the highest order of 2.A differential equation can be classified into three types: Ordinary Differential Equations (ODEs), Partial Differential Equations (PDEs), and Differential Algebraic Equations (DAEs). Ordinary differential equations have a single independent variable and one or more dependent variables that depend on it. Partial differential equations have more than one independent variable and multiple dependent variables that depend on each other. Differential algebraic equations have both derivatives and algebraic equations in them.A differential equation is essential in physics, engineering, and mathematics. It is used to model many natural phenomena and helps in predicting the future. Most differential equations can not be solved analytically, so numerical methods are used to find approximate solutions. In conclusion, A differential equation is an equation involving a differentiable function, which is a critical tool in modeling physical phenomena like population growth, radioactive decay, and fluid flow.

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Answer: 220 miles

Step-by-step explanation:

Car goes 55 miles in 1 hour.  

Constant speed.  

Formula is 55t = d.  

55 x 4 = 220 miles

Answer:

the guy above is right

Step-by-step explanation: