Given a set S of integers, we say that S can be partitioned if it can be split into two sets U and V so that considering all u E U and all v E V, Σu =Σ v. Let PARTITION = { | S can be partitioned }.a. (5) Show that PARTITION E NP by writing either a verifier or an NDTM.b. (15) Show that PARTITION is NP-complete by reduction from SUBSET-SUM.

Answers

Answer 1

Therefore, the SUBSET-SUM problem can be reduced to the PARTITION problem in polynomial time. Since SUBSET-SUM is NP-complete, it follows that PARTITION is also NP-complete.

a. Verifier for PARTITION problem:

Given an input (S, U, V) where S is a set of integers and U, V are partitions of S, we can verify in polynomial time whether the sum of elements in U is equal to the sum of elements in V. Therefore, PARTITION is in NP.

b. Reduction from SUBSET-SUM to PARTITION:

To show that PARTITION is NP-complete, we need to show that it is both in NP and NP-hard. We have already shown that it is in NP. Now we will reduce the SUBSET-SUM problem to PARTITION.

Given an instance of the SUBSET-SUM problem, which is a set of integers S = {a1, a2, ..., an} and a target integer T, we can construct an instance of the PARTITION problem as follows:

Let S' = S U {2T} and let U and V be two partitions of S' such that the sum of elements in U is equal to the sum of elements in V. We can easily verify that such partitions exist if and only if there exists a subset of S whose sum is equal to T.

If there exists a subset of S whose sum is equal to T, then we can add 2T to that subset and obtain two partitions of S' with equal sums. Conversely, if we have two partitions of S' with equal sums, then we can remove 2T from the partition that contains it to obtain a subset of S with sum T.

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Related Questions

What is the difference between the profits Mr. Brown's store earned in the first quarter and the third quarter?

Answers

Answer:

Hi we need a picture or a chart.

Step-by-step explanation:

Answer:

2,411.44

Step-by-step explanation:

Carl is deriving the quadratic equation by completing the square. His work at one of the steps is shown. x + b/na = + or - b^2-4ac. Carl is not sure what the value of n is. What value should he use to continue deriving the quadratic equation correctly? A. 1 B. 2 C. 3 D. 4

Answers

Answer:

the correct option is B. 2

Step-by-step explanation:

As given,

x + [tex]\frac{b}{na}[/tex] = ± √b²-4ac

⇒x = -[tex]\frac{b}{na}[/tex] ± √b²-4ac

As e know that the quadratic formula is

x = [tex]\frac{-b + or - \sqrt{b^{2} - 4ac } }{2a}[/tex]

So , by comparing with the formula

we get

n = 2

So, the correct option is B. 2

P = 100 - 20 cos (8πt/3) That's (8 pi t /3) where t is the time (in seconds). What is the period of the model? Discuss what the period represents in the context of this model.

Answers

Answer:

The period of the model is [tex]\frac{3\pi}{4}[/tex] seconds. The period represents the time needed for the function to complete one cycle.

Step-by-step explanation:

Cosine is a trigonometric function and trigonometric functions are characterized by having a periodical behavior. The period is the time needed for the function to cover an angle of [tex]2\pi[/tex] radians. By this approach we find that:

[tex]\frac{8\pi\cdot t}{3} = \frac{2\pi\cdot t}{T}[/tex] (1)

Where:

[tex]t[/tex] - Time, measured in seconds.

[tex]T[/tex] - Period, measured in seconds.

Then, we solve (1) for [tex]T[/tex]:

[tex]\frac{8}{3} = \frac{2\pi}{T}[/tex]

[tex]T = \frac{6\pi}{8}\,s[/tex]

[tex]T = \frac{3\pi}{4}\,s[/tex]

The period of the model is [tex]\frac{3\pi}{4}[/tex] seconds. The period represents the time needed for the function to complete one cycle.

Sara was cliff jumping. She was on a cliff 25 feet above sea level. She jumped into the sea and descended a total of 37 feet. How many feet below sea level did she travel? Justify your reasoning.

Answers

Answer:

12 feets below sea level

Step-by-step explanation:

Initial height = 25 feets above sea levwl

Total descent = 37 feets

Distance traveled below sea level = 37 feets - 25 feets = 12 feets

Hence, Sarah traveled 12 feets below sea level

What is the radius of a circle with a circumference of 81.64 feet.

Answers

Answer:

Step-by-step explanation:

Your answer

Circumference = 2 * π* r = 81.64

r = 12.99 → 13

Mark it as Brainlist answer. Follow me.

What is the missing angle
120°
70°

Answers

Answer:

the measure of angle B is 50

Step-by-step explanation:

the measure on the other side of the 120 is 60

hope this helps!!

x2 + 3x + 2 by x + 1​

Answers

Answer:

x²+3x+3

Step-by-step explanation:

hope it helps you

please mark me as brainlist

5x+2 x x+1
5x+2x+1
7x + 1

SMART PEOPLE PLEASE TAKE THE TIME TO ANSWER THIS!!!!!!!!!

Answers

Answer:

40% ⋅ x = 35

x = 87.5

Step-by-step explanation:

To write an equation representing this situation, use the key words. 40% stays 40%. "Of" is the same as multiplication. "X" remains "x". "Is" is the same as equal to. 35 remains 35. So, the new equation you get is: 40% ⋅ x = 35.

To solve for "x", first turn the 40% into a decimal: 0.4. Now divide 0.4 from both sides to get: x = 87.5.

Note:

The dot "⋅", stands for the multiplication sign. I'm not using the "x" symbol for it because there is a variable x in the equation already.

Hope it helps!

Dxfcv gnhbjmftvgyhgbyhgtyuvgyuibgiuguyvfgtyuik

Answers

Answer:

25.12 inches

Step-by-step explanation:

What is the solution to the equation sqrt 2x+3 minus sqrt x+2=2? x =

Answers

Answer:

x= 1/4 or 0.25

Answer:

23

Step-by-step explanation:

on edg

In the figure above, PQRS is a circle. If PQT and SRT
are straight lines, find the value of x.

Answers

Given:

PQRS is a circle, PQT and SRT  are straight lines.

To find:

The value of x.

Solution:

Since PQRS is a circle, PQT and SRT  are straight lines, therefore, PQRS isa cyclic quadrilateral.

We know that, sum of opposite angles of a cyclic quadrilateral is 180 degrees.

[tex]m\angle SPQ+m\angle QRS=180^\circ[/tex]

[tex]81^\circ+m\angle QRS=180^\circ[/tex]

[tex]m\angle QRS=180^\circ-81^\circ[/tex]

[tex]m\angle QRS=99^\circ[/tex]

Now, SRT  is a straight line.

[tex]m\angle QRT+m\angle QRS=180^\circ[/tex]             (Linear pair)

[tex]m\angle QRT+99^\circ=180^\circ[/tex]

[tex]m\angle QRT=180^\circ-99^\circ[/tex]

[tex]m\angle QRT=81^\circ[/tex]               ...(i)

According to the Exterior angle theorem, in a triangle the measure of an exterior angle is equal the sum of the opposite interior angles.

Using exterior angle theorem in triangle QRT, we get

[tex]m\angle PQR=m\angle QRT+m\angle QTR[/tex]

[tex]x=81^\circ+22^\circ[/tex]

[tex]x=103^\circ[/tex]

Therefore, the value of x is 103 degrees.

Find the value of x.

Answers

Answer:

x=7

Step-by-step explanation:

Since the two lines, the transversal intersects are parallel we know that the angles are same-side interior. This means they are supplementary or add up to 180. Therefore, to solve add the two expressions and set them equal to 180, then solve with properties of equality.

14x+7+10x+5=180

First, add like terms

24x+12=180

Then, subtract 12 from both sides

24x=168

Next, divide both sides by 24

x=7

select the correct choice and fill in the box to complete your choice. pls help!!!

Answers

Answer is Yes!! Hope this helps

Solve: -2x - 5 = -3
plz help me hurry

Answers

Answer:

x=-1

Step-by-step explanation:

-2x - 5 = -3

add 5 to both sides

-2x = 2

divide both sides by -2

x = -1

Answer:

x = -1

Step-by-step explanation:

-2x - 5 = -3

Same to both sides:

-2x = -3 + 5

Simplify:

-2x = 2

Divide by -2 on each side to isolate x:

x = -1

Let me know if you have any questions

Determine the slope of the line

Answers

Answer:

2 !!

Step-by-step explanation:

use RISE/RUN !! you would go up from the 1 point, on the y axis !! from there, ud go up 2, then to the right 1, so ur slope is 2/1 .... which is 2 !!

i hope this helped !

Find the missing length?

A. 18in
B. 6in
C. 2in
D. 36in

Answers

Answer:

B. 6in

Step-by-step explanation:

We can use the Pythagorean theorem [ a² + b² = c² ] to find the missing side.

8² + b² = 10²

64 + b² = 100

b² = 36

b = 6

Best of Luck!

I need help with B. Do you I think this will mean the end of life on earth?

Please answer ASAP

Answers

Answer:

yes

Step-by-step explanation:

funny corona-virus meme

Answers

Answer:

lol thats funny

Step-by-step explanation:

hahahahahahahahahahahahahahahahahahahahahahahaha!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! That is funny;)

8 students in Mr. Webb's class got an A on the exit ticket. There are 25
students in his class total. What percent of students got an A?*

Answers

Answer:

32%

Step-by-step explanation:

To find the percentage, we have to multiply 25 and 8 by 4.

25x4 = 100

8x4 = 32

So, 8 out of 25 is 32%.

how many odd integers are between -20 and 10?

Answers

9514 1404 393

Answer:

  15

Step-by-step explanation:

The given range of numbers is -20 to 10, so is 10-(-20)+1 = 31 numbers. Since the end points of the range are both even, there is one more even number than there are odd numbers in the range. The number of odd numbers is ...

  (31 -1)/2 = 15

There are 15 odd numbers between -20 and 10.

there are 15 odd integers between -20 and 10

Which of the following is a situation in which an equation cannot be solved
using the quadratic formula?
A. The coefficient of the x-term is zero.
B. One term of the polynomial has a degree of 3.
C. The right-hand side of the equation is zero.
D. The coefficient of the XP-term is 1.

Answers

Answer:

B One term of the polynomial has a degree of 3

the answer for this problem is B

1. In Mr. B's classroom, there are 20 students.
Twelve students got a B, one student got a C, and
the rest received an A. What percent of the class
received an'A?


Help please

Answers

Answer:

1.5%

Step-by-step explanation:

Cash loan $100 20.0% 3 years $6 (100 x .2 x .3) $106 ($100 + $6) Big-screen TV $500 9.0% 4 years $ (500x $ College loan $13,000 4.5% 15 years $ $

Answers

Answer:

Cash loan = $160

Big screen TV = $680

College loan = $$21775

Step-by-step explanation:

Cash loan :

Loan amount or principal = $100

Interest rate, r = 20.0%

Time, t = 3 years

Using the relation :

Simple interest = Principal * rate * time

$100 * 0.2 * 3 = $60

Final amount = loan amount + interest on loan

Final amount = $100 + $60 = $160

Big Screen TV:

Principal = $500

Rate, r = 9.0%

Time, t = 4 years

Interest amount = (500 * 0.09 * 4)

Interest amount = $180

Final amount = principal amount + interest on loan

Final amount = $500 + $180 = $680

College loan

Principal, = $13,000

Rate, r = 4.5%

Time, t = 15 years

Interest amount = (13000 * 0.045 * 15)

Interest amount = $8775

Final amount = principal amount + interest on loan

Final amount = $13000 + $8775 = $21775

Can you see the image I’m not sure if you can please let me know

Answers

Answer:

you can't sorry

Step-by-step explanation:

ycucycycufycycycyc

Answer:

no I can't see

Step-by-step explanation:

please mark me as brainlist

A particular country has 60 total states. If the areas of all 60 states are added and the sum is divided by 60​, the result is 187,626 square kilometers. Determine whether this result is a statistic or a parameter.

Answers

A particular country has 60 total states. if the areas of all 60 states are added and the sum is divided by 60​, the result is 212 comma 469 square kilometers. determine whether this result is a statistic or a parameter.
Answer: Before solving the given question, let us understand what the parameter and statistic is:
Parameter: Parameter is a number that summarizes data for an entire population. Like Population mean Population standard deviation
Statistic: Statistic is a number that summarizes data for a sample. Like sample mean sample standard deviation .
From the given information, we can clearly see that given characteristic describes the population.
Therefore, the option d is correct
d. the result is a parameter because it describes some characteristic of a population. is correct.

Explanation: https://brainly.com/question/10888941

ABC is similar to XYZ. The length of AB is 3 inches. The length of BC is 5 inches. The length of YZ is 13 inches. What is the length, in inches of XY

Answers

Answer:

7.8

Step-by-step explanation:

When is the graph of f (x) = 2x2 – 5x – 3 negative?​

Answers

9514 1404 393

Answer:

  -1/2 < x < 3

Step-by-step explanation:

First you need to find the x-intercepts. Since the leading coefficient is positive, you know the graph is decreasing through the left x-intercept, so will be negative between the x-intercept values.

  f(x) = 2x^2 -5x -3

  f(x) = 2x^2 -6x +x -3

  f(x) = 2x(x -3) +1(x -3)

  f(x) = (2x +1)(x -3)

The x-intercepts are the values of x that make these factors zero:

  2x +1 = 0   ⇒   x = -1/2

  x -3 = 0   ⇒   x = 3

The graph of f(x) is negative on the interval ...

  -1/2 < x < 3

What is the value of x in the equation 6x + 3 + 4x =
(9 + 10x)?
Enter your answer in the box.
2
TIL
CON
4
6
7
8
CO

Answers

9514 1404 393

Answer:

  x = 3/10

Step-by-step explanation:

Given

  6x +3 +4x = 1/2(9 +10x)

We can collect term, then multiply by 2.

  10x + 3 = (1/2)(9 +10x)

  20x + 6 = 10x + 9 . . . . . . . multiply by 2

  10x = 3 . . . . . . . . . . . . . . . . subtract (6+10x)

  x = 3/10 . . . . . . . . . . . . . . . divide by 10

_____

Check

  6(3/10) +3 +4(3/10) = (1/2)(9 + 10(3/10))

  1.8 + 3 + 1.2 = 1/2(9 +3)

  6 = 6 . . . . . solution checks OK

me Digão qual e a resposta​

Answers

Answer:

As somas estão abaixo

Step-by-step explanation:

a) 158

b) 2095

c) 2819

d) 9082

Eu espero que isso ajude :)

PLEASE HELP,, A home decorator is adding new flooring to a living room using the blueprint shown.



image



What are the actual length and width of the living room? Show your work.

A.
7ft, 6ft

B.
14 ft, 10ft

C.
10ft, 8ft

D.
20ft, 16ft

Answers

The answer is 10 and 8 feet I hope you do good on this

Answer: 20ft, 16ft

Step-by-step explanation:

Because 0.5in=2ft, you would divide the length (5in) and the width (4) both by 0.5. Which give you 10 for the length and 8 for the width. Then you multiply both of those products by 2 and that gives you your answer. 20ft and 16ft. Hope this helps. :)

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