use a proof by contraposition to show that for integers m and n if m n is even then m is even or n is even

Answers

Answer 1

The contrapositive is true

Proving a contraposition involves proving that the contrapositive of a statement is true. The opposite of "if m n is even then m is even or n is even" is "if m is not even and n is not even then m n is not even".

To prove this statement by a proof by contrast, first assume that m is not even and neither is n. This means that both m and n are odd.

Since m and n are odd, m n is also odd. This can be expressed as:

If m and n are odd, we can write m as;

2k + 1 and n as 2l + 1 for integers k and l.

Then mn = (2k + 1)(2l + 1) = 4kl + 2k + 2l + 1 = 2(2kl + k + l) + 1,

which is odd. Therefore, m n is not even if m is not even and n is not even.

It turns out that the opposite of the original statement is true, so the original statement must also be true. Therefore, if m n is even, then we can say that   that m is even or n is even using a proof by contrast.

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Related Questions

Use the drop-down menu to complete the statement. What is 3 divided by 2/5?

Answers

Answer:

0.3

Step-by-step explanation:

Tell me if it's wrong I have another answer

Answer:

2/5 is the correct answer.

Step-by-step explanation:

What is the volume of the figure below?9 feet14 feet5 feet30ft60ft90ft120ft

What is the volume of the figure below?9 feet14 feet5 feet30ft60ft90ft120ft

Answers

The length of rectangular pyramid is l = 5 feet.

The width of rectangular pyramid is w = 4 feet.

The height of rectangular pyramid is h = 9 feet.

The formula for the volume of rectangular pyramid is,

\(V=\frac{l\cdot w\cdot h}{3}\)

Since there are two rectangular pyramid so net volume of figure is,

\(V^{\prime}=\frac{2}{3}\cdot l\cdot w\cdot h\)

Substitute the values in the formula to obtain the volume of figure.

\(\begin{gathered} V^{\prime}=\frac{2}{3}\cdot5\cdot4\cdot9 \\ =10\cdot4\cdot3 \\ =120 \end{gathered}\)

So volume of figure is 120 feet cube.

What is the quotient of the fractions below? 2/3÷5/4

Answers

answer:

2/3÷5/4 is equal to 8/15

the answer here is 8/15

si ABCD son los vertices de un cuadrado y A(2,2) y C (10,8) 2 vertices opuestos. Hallar los otros dos vertices, dar como respuesta la mayor de las ordenadas

Answers

The area of the square is given as 100 square unit

How to determine the area of square?

You should be aware that the square has all its sides equal

The perpendicular from opposite vertices represent distance

The given vertices are

(2,2) and (10,8)

Using the formula for distance between two points

d=√(10-2)²+(8-2)²

d=√8²+6²

d = √64+36

d=√100

This implies that d=10

The area of a square is given as s²

Area = 10²

Atrea = 100 square units

In conclusion, the area of the square is 100 square units

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Translated question:

The vertices of a square ABCD are A(2,2) and B(10,8), Find the area of the square

si ABCD son los vertices de un cuadrado y A(2,2) y C (10,8) 2 vertices opuestos. Hallar los otros dos

Solve the system of equations using the substitution or elimination method.
y = 4x - 7
4x + 2y = -2
.
Show your work
Correct x and y

Answers

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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wall has an
area
tim
9 123m2
of faint will couet 14 m²
Hattie needs to work out how
of paints will need to
many
use
A
A
المعلن
tin's
buy.
estimation to work out how many ting
needs.

Answers

Shehdhdhdhrhehhwuwud


What is the range of the exponential function shown below?
f(x)=11•(1/3)^x
A. y<0
B. y>0
C. All real numbers except 11
D. All real numbers

Answers

The range of the exponential function is B. y > 0.

The range of the exponential function f(x) = 11 × (1/3)ˣ can be determined by analyzing the behavior of the function as x approaches positive and negative infinity.

As x approaches positive infinity, (1/3) becomes smaller and smaller, tending towards zero.

f(x) approaches 11 × 0, which is equal to 0.

As a result, the function approaches 0 as x goes to infinity.

On the other hand, as x approaches negative infinity, (1/3)ˣ becomes larger and larger.

Since 1/3 is between 0 and 1, raising it to a negative power causes it to grow exponentially.

f(x) approaches infinity as x goes to negative infinity.

Combining these two behaviors, we can conclude that the range of the function f(x) = 11 × (1/3)ˣ is all positive real numbers, excluding zero.

In other words, the range is y > 0.

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What is the volume, in cubic in, of a cylinder with a height of 20in and a base radius of 2in, to the nearest tenths place?

Answers

Answer:

251.2

Step-by-step explanation:

The formula for the volume of a cylinder is \(\pi r^2h\). Plugging in your measurements...

Height = 20 inches.

Radius = 2 inches.

The volume is \(\pi2^2h\).

Simplification...

\(\pi2^220 = \pi4(20)= 4\pi 20\).

\(\pi\) ≈ \(3.14\)

3.14 * 4 = 12.56

12.56*20 = 251.2

A cyclist bikes at a constant speed for 24 miles. He then returns home at the same speed but takes a different route. His return trip takes two hours longer and is 30 miles. Find his speed.

Answers

Answer: they are ripped

Step-by-step explanation:

i guessed

Answer:

3 mi / hr

Step-by-step explanation:

It takes the cyclist 2 hours to go 6 miles further ( 30 -24 mi)

  6 mi / 2 hr = 3 m/hr    

It took Amari 2 hours to paint the first 14 feet of a 70 foot long fence. What percentage of the fence have they painted so far

Answers

Answer:

20%

Step-by-step explanation:

Divide

14/70 = 0.20

Convert from a decimal to a percent. You can multiply by 100 or move the decimal two places right.

0.20 x 100 = 20%

Solve for x. I attached the question. Pls help me :(

Solve for x. I attached the question. Pls help me :(

Answers

Answer:

x = 16°

Step-by-step explanation:

What we know:

∠JML = 47°

∠JKL = (7x + 21)°

∠JML is an inscribed angle

∠JKL is an inscribed angle

Inscribed angles are half of the value of their intercepted arc

So if m∠JML = 47° then mArc JL is double that or 94°

And ∠JKL is intercepted by Arc JML which is the rest of the circle not intercepted by ∠JML so

mArc JL + Arc JML = 360°

94 + Arc JML = 360

Subtract 94 from both sides to isolate Arc JML

Arc JML = 266°

So if Arc JML = 266° then it's intercepted inscribed angle is half of that.

Arc JML ÷ 2 = ∠JKL

266 ÷ 2 = ∠JKL

133 °= ∠JKL

Now we can use this value and set it equal to the expression to find the value of x

(7x + 21) = 133

Subtract 21 from both sides to isolate the x

7x = 112

Divide both sides by 7

x = 16

i give Brainliest please help!I​

i give Brainliest please help!I

Answers

Answer:

answer is A

Step-by-step explanation:

because I know it

Answer:

Point A because -1 go back to the left go up to positive 1 and 1/4


In a class, 40% of the students study math and science. 60% of the students
study math. What is the probability of a student studying science given he/she is
already studying math?

Answers

The probability of a student studying science given he/she is already studying math exists 2​​/3.

What is a Probability Distribution?

Probability distribution exists a part of a discrete variable whose integral over any interval exists the probability that the random variable determined by it will lie within that interval.

A probability distribution exists as a statistical function that defines all the possible values and likelihoods that a random variable can assume within a provided range.

Probability of Math's and Science students = 40​/100

= 2​/5

Probability of Math's students = 60/100 ​= 3​/5

P(Science/Math's) = P(S∩M)​/P(M)

= (2/5)​​ / (3/5) = 2​​/3

The probability of a student studying science given he/she is already studying math exists 2​​/3.

Therefore the correct answer is 2​​/3.

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Complete the square for y=x^2 - 6x-5?

Answers

Answer: y=(x-3)^2 -14

Step-by-step explanation:

use the formula (b/2)^2 to create a new term to complete the square

367 Times 10 -3
Express the following numbers in scientific notation

Answers

Answer:

To express a number in scientific notation, you need to write it as a number between 1 and 10, multiplied by a power of 10.

In this case, 367 can be written as 3.67 x 100, and 10-3 can be written as 0.001.

Therefore, 367 x 10-3 can be expressed in scientific notation as:

3.67 x 0.001 = 0.00367

This can also be written as 3.67 x 10^-3. The ^ symbol indicates an exponent, and in this case, it means that the base number (3.67) is multiplied by 10 to the power of -3.

Step-by-step explanation:

Translate 2 3 y − 9 < y + 1 into a sentence. Nine than two-thirds of number is less than the number .

Answers

The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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A square has an area of 56 units, find the length of the side in simplest form. Has to be an Improper fraction.

Answers

The length of the side of the square in simplest form is 2sqrt(14).

The area of a square is given by the formula \(A = s^2\), where A is the area and s is the length of a side.

We are given that the area of the square is 56 units, so we can set up the equation:

\(56 = s^2\)

To solve for s, we can take the square root of both sides of the equation:

sqrt(56) = \(sqrt(s^2)\)

We can simplify the square root of 56 by factoring it:

sqrt(56) = sqrt(222*7) = 2sqrt(14)

So, we have:

2sqrt(14) = s

This is an improper fraction because the numerator is larger than the denominator. Therefore, the length of the side of the square in simplest form is 2sqrt(14).

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which expression is equivalent to 25s^3+12s/5s

which expression is equivalent to 25s^3+12s/5s

Answers

Answer:

A

Step-by-step explanation:

1 Factor out the common term ss.

\frac{s(25{s}^{2}+12)}{5s}

5s

s(25s

2

+12)

2 Cancel s.

\frac{25{s}^{2}+12}{5}

5

25s

2

+12

hola feliz noche solo hago está pregunta para probar la aplicación cuántos es 7+1​

Answers

Answer:

es 8

Step-by-step explanation:

The plant grew 35 inches in a week. Find the unit rate in inches
per day.

Answers

ANSWER: 5 The plant grows 5 inches per day because 7 days are in a week, so you divide 35 by 7 which is 5

Ten years ago the average age at a company was 36. A manager believes that employees are younger now. He is going to perform a hypothesis test. Which hypothesis below represents the correct alternative hypothesis?
1. Ha.u=36
2. Ha.uis not equal to 36
3. Ha.u>36
4. Ha.u<36

Answers

Answer:

(4)\(H_a: \mu <36\)

Step-by-step explanation:

The alternate hypothesis is that which establishes the claim in the research.

Ten years ago the average age at a company was 36.A manager believes that employees are younger now.

The claim of the hypothesis test is that the average age of employees is less than 36 now.

Therefore, the alternate hypothesis is:

\(H_a: \mu <36\)

Select the correct choice and fill in the blank if necessary

Select the correct choice and fill in the blank if necessary

Answers

C)

Answer: the correct option is D

Explanation:

From the information given,

f^-1(x) = (x - 3)/7

The domain is the set of all values of x that satisfies the function. For the given function, it the set of all real numbers.

The range is the set of all values of y that satisfies the function. For the given function, it the set of all real numbers.

Thus, the correct option is D

What is -5+2(8-12) ?

Answers

Answer: -13

Step-by-step explanation: Here to help! So first, you do 8-12, then you get -4, right? So then, you multiply 2 times -4, then you get -8. After that, you add -5 to -8, so it's -5 + -8, and you get -13.

Answer:

-13

Step-by-step explanation:

-5+2(8-12)

distribute the 2

-5+16-24

add

11-24

subtract

-13

slope intercept form for (3,3) and (2,4)with work please I'm trying understand how to do it on my own

Answers

P1 = (3,3)

P2 = (2, 4)

x1 = 3 y1 = 3 x2 = 2 y2 = 4

1.- Find the slope

2.- Find the equation of the line

y - y1 = m(x - x1)

Substitution

y - 3 = -1(x - 3)

Simplification

y - 3 = -x + 3

y = -x + 3 + 3

Result

y = -x + 6

The equatin of the line is y = -x + 6

slope intercept form for (3,3) and (2,4)with work please I'm trying understand how to do it on my own

Match the statement with the equation: (Choices are below) (MAFS.912.A-SSE.1.1)

A. Her salary is one dollar more than twice John’s salary.

B. John’s salary is twice hers plus $1.

C. Twice John’s salary is the same as her salary plus one.

D. Twice her salary is the same as John’s salary plus $1.


Choices : 1. 2H = J + 1 3. 2J = H + 1

2. H = 2J + 1 4. J = 2H + 1

Answers

Answer:

A. Her salary is one dollar more than twice John’s salary. Answer: 3) 2J = H + 1

B. John’s salary is twice hers plus $1. Answer: 4) J = 2H + 1

C. Twice John’s salary is the same as her salary plus one. Answer: 2) H = 2J + 1

D. Twice her salary is the same as John’s salary plus $1. Answer: 1) 2H = J + 1

Step-by-step explanation: hope this help

KAJSKSKSKWKWKSKSKSKSKSKSKSKSKR

Answers

Answer:

ok

Step-by-step explanation:

There are eight members of a jazz club who are listed below. A concert director can choose some or all of them to be part of a large show. She must choose at least one of them.

Anh, Bryan, Carol, Dan, Elise, Felix, Harry, Joy

In how many different ways can the director choose the members for the show? (The order the members are chosen doesn't matter.)

Answers

Answer:

40320 ways

Step-by-step explanation:

Given

Members = 8

Required

Number of ways they can be selected

Since, the order does not matter;

They can be selected in 8! ways

\(8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1\)

\(8! = 40320\ ways\)

Hence, there are 40320 ways which the director can select them for the concert

John drove from here to San Antonio which is 180 miles away in 3 hours. Which rate is equivalent to
the rate at which John drove to San Antonio?

Answers

The rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

Which rate is equivalent to the rate at which John drove to San Antonio?

From the question, we have the following parameters that can be used in our computation:

John drove from here to San Antonio which is 180 miles away in 3 hours.

This means that

Distance = 180 miles

Time = 3 hours

Using the above as a guide, we have the following:

Speed = Distance/Time

Substitute the known values in the above equation, so, we have the following representation

Speed = 180/3

Evaluate

Speed = 60

Hence. the rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

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Graph the function. Decsribe how it was translated from fig=%.f(x)=x2-8

Answers

The original function is given by the expression:

\(g(x)=x^2\)

It is subtracted by 8, on such cases the function is translated eight units down. Therefore the graph will be a parabola with the concavity up, but with the vertex on -8. The graph of the translated figure is shown below.

Graph the function. Decsribe how it was translated from fig=%.f(x)=x2-8

You get hired for a job through ACME Employment Agency. You signed a contract that requires you to pay 20% of your first 6 weeks pay. The job pays you $42,700 per year. How much must you pay ACME for their services?

Answers

Assuming you get paid every week.
Total num of weeks in a year = 52
Therefore weekly salary = 42,700/52 = 821.15
Salary of first 6 weeks = 821.15 * 6 = 4926.92
20% of first 6 weeks salary = 0.2 * 4926.92 =985.38

You must pay the ACME $985.38
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