Your class is in groups, working on an induction worksheet. One of the questions asks to prove that if n is even, then 8n is also even. Your group proves it, but you're then asked if the converse is also true. Your classmate suggests that it is. What would you say to explain how this suggestion is flawed, and how would you help correct them

Answers

Answer 1

Answer:

The answer is "this statement is not true".

Step-by-step explanation:

It is true because it can be achieved by using the initiation method. (Or at even a look, as n is still n=2m for the whole m, and the same number is 8n=8* (2*m)=2*(8*m). So it's confirmed !! )

Now the opposite declaration says, "If 8n would be an even amount then n is an even number", that's why the statement is not true.

An easy way of demonstrating why an argument also isn't valid is to show an example it against. Take into consideration the 24. 24=8*3. i.e. the shape is 8n, where it is n=3. Of course, 24 is also an equivalent number, but n=3 is an odd number here. So, we at least this one event, wherein the opposite statement could be sustained. (q.e.d).  

Note:- "8n would be an even number per each integer n." is true since 8n=2*(4n), even for all integer n.


Related Questions

Which type of transformation is described by (x, y)
->
+ (x + 3, y — 2)?

Answers

Answer:

(x, y) → (x+3, y-2) means Translation 3 units left and 2 units down.

Step-by-step explanation:

Given the rule of transformation:

(x, y) → (x+3, y-2)

If we move horizontally 3 units to the right, 3 is added to the x-coordinate of any given point, and then 2 units down.

In other words,

(x, y) → (x+3, y-2) means Translation 3 units left and 2 units down.

For example,

Let say if we have the point A(4, 5)

Using the translation rule:

(x, y) → (x+3, y-2)

A(4, 5) → A'(4 + 3, 5 - 2) → A'(7, 3)

Therefore, the new position of A(4, 5) after translating 3 units left and 2 units down would be: A'(7, 3)

Find the perimeter of the following shape:

Answers

Answer:

itas niot hard. its 10+10+7+7. the 9 is meaning if it was a striaghjt line, and that is the length of the straight line.

Step-by-step explanation:

I really need help on this question.!

Answers

Answer:

[tex]60 + 55 + x + 20 = 180 \\ x + 135 = 180 \\ x = 180 - 135 \\ x = 45[/tex]

Please help! I'm writing a test and don't have much time. Step by step please! (20 point)

Answers

Answer:

-3+6x

x+3

Step-by-step explanation:

Answer:

23x^3+9x^2-5x+1/x^2

Step-by-step explanation:

I hope you don't mind me putting my explanation as a screenshot of this lol

There were 10 bunches of roses and tulips. Each bunch had 5 of the same flowers. There were 2 more bunches of tulips than roses. How many tulips were there?

Answers

Answer:

I think the answer is 12 (sorry if i misunderstood the question)

Step-by-step explanation:

Because if there are 10 things of roses and tulips and then 2 more tulips are added in the question in total thats 12.... 10+2=12

Please. help me guys. ​

Answers

Answer:

40

Step-by-step explanation:

there are 4 quarters so if one quarter is 10 then 4 quarters are 40

10 x 4 = 40

Complete the following statements.

A soda bottle contains 2 liters of liquid. Therefore:

The soda bottle contains  fluid ounces of liquid.

The soda bottle contains  gallons of liquid.

A milk jug contains 2 gallons of milk. Therefore:

The milk jug contains  quarts of milk.

The milk jug contains  liters of milk.

Answers

Answer:

A soda bottle contains 2 liters of liquid. Therefore:

The soda bottle contains  67.62 fluid ounces of liquid.

The soda bottle contains 0.525  gallons of liquid.

2) A milk jug contains 2 gallons of milk. Therefore:

The milk jug contains 8  quarts of milk.

The milk jug contains 7.6 liters of milk.

Step-by-step explanation:

We need to complete the statements.

1)

A soda bottle contains 2 liters of liquid. Therefore:

The soda bottle contains -------  fluid ounces of liquid.

Converting Liters to fluid ounces

We know that 1 liter = 33.81 fluid ounces

So,  2 liter = 2 x 33.81 = 67.62 fluid ounces

The soda bottle contains 67.62  fluid ounces of liquid.

The soda bottle contains  gallons of liquid.

Converting liters to gallons

As, we are not given direct conversion from liters to gallons, first we convert liter to quarts and then convert quarts to gallons

We know that

1 liter = 1.05 quarts

2 liters = 2 x 1.05 = 2.1 quarts

4 quarts = 1 gallon

1 quarts = 1/4 gallon

2.1 quarts = 1/4 * 2.1 = 0.525 gallon

The soda bottle contains 0.525  gallons of liquid.

2)

A milk jug contains 2 gallons of milk. Therefore:

The milk jug contains -------- quarts of milk.

Converting gallons to quarts

We know:

1 gallon = 4 quarts

2 gallons = 2 x 4 = 8 quarts

The milk jug contains 8 quarts of milk.

The milk jug contains ------  liters of milk.

Converting gallons to liters

We know:

1 gallon = 4 quarts

2 gallon = 8 quarts

1.05 quarts = 1 liter

1 quarts = 1/1.05 liter

8 quarts = 1/1.05 * 8 = 7.6 liter

The milk jug contains 7.6 liters of milk.

Craig has 5/8 of a bottle of glue but the recipe calls for three quarters a bottle. Does he have enough

Answers

Answer:

No, he doesn't have enough

Step-by-step explanation:

In eights, three quarters of a bottle is equal to 6/8.

Since 5/8 is smaller than 6/8, Craig won't have enough glue.

So, the answer is no.

Answer:

NO

Step-by-step explanation:

3/4 converted to eighths is 6/8. and 6/8 is greater than 5/8

solve for x -2x + 2 = x -13

Answers

Answer:

x = 5

Step-by-step explanation:

Add 2x to both sides: 2 = 3x - 13

Add 13 to each side: 15 = 3x

Divide both sides by 3: 5 = x

Isolate with the variable by dividing each side by factors that don't contain the variable. So, x= 15

-4x-y=24 complete the missing value in the solution to the equation

Answers

Answer:

point

Step-by-step explanation:

This is another 2 step. Please be sure to answer the question fully and show all of your work! I don't like reporting people.

Answers

Answer:

JR = 29∠JLM = 25°

Step-by-step explanation:

Diagonals of the parallelogram bisect each other

Note. The first question is repeated as A and B

A) KR = 1/2KM

Substitute and solve for x:

x + 7 = 1/2(3x - 5)2x + 14 = 3x - 53x - 2x = 14 + 5x = 19

Find JR

JR = 1/2JL JR = 1/2(4x - 10) = 2x - 5 = 2*19 - 5 = 34 - 5  = 29

B)

∠LJM ≅ ∠JLK as alternate interior angles∠JKL ≅ ∠JML as opposite angles of parallelogram

Interior angles of the triangle sum to 180°:

m∠JLK + m∠LJK + m∠JKL = 180°m∠JLM = m∠JLK = 180° - (56° + 27° + 72°) = 25°

PLEASE HELP WITH THESE QUESTIONS I HAVE 5 MINUTES LEFT

What is 4 superscript 5 written in expanded form?
O 4 + 4 + 4 + 4 + 4
O 4 times 4 times 4 times 4 times 4
O 5 + 5 + 5 + 5
O 5 times 5 times 5 times 5

Answers

Answer:

4+4+4+4+5

Step-by-step explanation:

is 5 times the number only expanded

Answer:

4+4+4+4+5

Step-by-step explanation:

wei kiat is 4 times as old as hafiz. Find the ratio of Wei kiat's age to hafiz's age. pls help​

Answers

1:4
Example:
There are 4 squares and 1 triangle
There are 4 more times as many squares than triangles


2. Using the ruler below, construct a triangle that has side lengths of 3 cm, 4 cm, and 5 cm.
triangle does this appear to be? Verify by using your protractor to measure angles.
What type of

Answers

Step-by-step explanation:

if to apply the Piphagorean theoreme, then one of the angles is 90° (opposite to the side with the length 5):

3²+4²=5²; ⇔ 9+16=25.

(THIS IS 30 POINTS!!) In Ms. Hollbrook's class, 62% of the class enjoys watching anime. If there are 32 students in Ms. Hollbrooks class, about how many students enjoy watching anime?

A) 12 students

B) 14 students

C) 16 students

D) 20 students​

Answers

Answer:

D)

Step-by-step explanation:

32*0.62=19.84≈20.

What is the slope-intercept form of this equation?
3x + 9 y = 18

Answers

y = -1/3x + 2

Explain: subtract 3x from 18, which will get you -3x + 18.
Next, get 9y and divide it by everything so it’ll look like 9y = -3x + 18
-——-————
9y
and you’ll get y = -1/3x + 2
Hope this helped

Write the equation of a line that passes through the point (4, -2) and is perpendicular to y = 3.

Answers

Answer:

x = 4

Step-by-step explanation:

When something is perpendicular, it must form a 90° or right angle [it will make a square]. Also keep in mind that perpendicular lines have reciprocal [numerator and denominator switch] slopes [steepness]

If you are given a line with a slope of zero like y = 3, any given line of x will be perpendicular. This is because when y = n; x is undefined. When x = n ; y is undefined. Since you want a line that will go through point (4, -2) and will be perpendicular to y = 3, just set x to the value of x in the coordinate. And in this case x is 4 so x = 4 will be the equation.

identify the independent variable for this function

Answers

Answer: Time

Explanation:

Time progresses without any control over it, so it's something that does not depend on any other factor such as distance. On the other hand, as the time value changes, the distance changes. So the distance is dependent on the time.

The horizontal axis is the x axis, and the x value is always the independent variable. The vertical y axis is the distance. The y value is always the dependent variable.

Someone help me on question 10 please!

Answers

Answer:

Step-by-step explanation:

500÷9=55.56miles/h (correct to 3 decimal places)

The table shows values for functions f(x) and g(x) .

What is the solution to f(x)=g(x) ?
Select each correct answer.

A. −3

B. −2

C. −1

D. 0

E. 1

F. 2

G. 3

Answers

G. 3 but I’m not sure you should double check

Simplify using Synthetic Division

Answers

Step 1
Write down the first coefficient without changes:
−3223−10−3
−3
2
3 −10 −3
2

Step 2
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
−3223(−3)⋅2=−63+(−6)=−3−10−3

3
2
3
−10 −3
(

3
)

2
=

6
2
3
+
(

6
)
=

3

Step 3
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
−3223−6−3−10(−3)⋅(−3)=9(−10)+9=−1−3

3
2 3

10
−3 −6
(

3
)

(

3
)
=
9
2

3
(

10
)
+
9
=

1

Step 4
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
−3223−6−3−109−1−3(−3)⋅(−1)=3(−3)+3=0

3
2 3 −10

3
−6 9
(

3
)

(

1
)
=
3
2 −3

1
(

3
)
+
3
=
0

We have completed the table and have obtained the following resulting coefficients: 2,−3,−1,0
2
,

3
,

1
,
0
.
All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.
Thus, the quotient is 2x2−3x−1
2
x
2

3
x

1
, and the remainder is 0
0
.
Therefore, 2x3+3x2−10x−3x+3=2x2−3x−1+0x+3=2x2−3x−1
2
x
3
+
3
x
2

10
x

3
x
+
3
=
2
x
2

3
x

1
+
0
x
+
3
=
2
x
2

3
x

1
Answer: 2x3+3x2−10x−3x+3=2x2−3x−1+0x+3=2x2−3x−1

Given that P=x+y. Find P when: x=−5 and y=−3

Answers

Answer:

P = - 8

Step-by-step explanation:

Given

P = x + y ← substitute x = - 5 and y = - 3

P = - 5 + (- 3) = - 5 - 3 = - 8

A man spend 10% of his salary on rent, 25% on food, 18% on transportation and the balance he saves. If his salary is $1500 per month, how much does he save each month?

Answers

Answer:

He saved $705 pls mark brainliest

Step-by-step explanation:

So 10% is $150 and 25% is 375 and 18% is 270 so you would add all those togeather to get 795 and 1500-795 is 705 so he saved $705!

So far this month you have achieved $100.90 in sales which is 50% of your monthly goal l. With 5 more workdays this month, how much do you need to sell each day to reach your goal?

Answers

20.18 per day for 5 days

dog's food bowl holds 3 cups of dog food. Tim uses a scoop that holds 1/4 of a cup of dog food. how many scoops will it take for Timothy to fill the dog bowl?

Answers

Answer:

12 scoops

Step-by-step explanation:

4 scoops = 1 cup

8 scoops = 2 cups

12 scoops = 3 cups

Evaluate the expression when b=9 .

24/9 + 8 =

Answer:

Answers

Answer:

Exact Form:

32 /3

Decimal Form:

10. 6

Mixed Number Form:

10

2 /3

Step-by-step explanation:

The number of boys at CMS is 56% of the total number of students. If there are 1050 students, how many are boys?

Answers

Answer:

558

Step-by-step explanation:

geometric mean of 384 and 6

Answers

Answer:

48 is the geometric mean of 384 and 6

48 is the meaning of geometric

A maintenance firm has gathered the following information regarding the failure mechanisms for air conditioningsystems:

Yes No
Evidence of electrical failure Yes 55 17
Electrical failure No 32 3


The units without evidence of gas leaks or electrical failure showed other types of failure. If this is a representative sample of AC failure, find the probability.

a. That failure involves a gas leak
b. That there is evidence of electrical failure given that there was a gas leak
c. That there is evidence of a gas leak given that there is evidence of electrical failure

Answers

Answer:

A) 0.8131 ≈ 0.81

B) 0.6322 ≈ 0.63

C)  0.7639 ≈ 0.77

Step-by-step explanation:

A)

Total number of  units

= 55 + 32 + 17 + 3

 = 107

hence the probability that the failure involves a gas leak

= ( 55 + 32 ) / 107

= 0.8131

B) probability that there is evidence of electrical failure given tat there is a gas leak

P ( A / B ) = [tex]\frac{P(A n B)}{P(B)}[/tex]

P( A∩B ) = 55/107 = 0.5140

P ( B ) = ( 55 + 32 ) / 107 = 0.8131

hence P ( A / B ) = 0.5140 / 0.8131 = 0.6322

A = failure due to electrical

B = failure due to gas leak

C)  Probability of a gas leak given that there is evidence of electrical failure

P ( B / A ) =  [tex]\frac{P(BnA)}{P(A)}[/tex]

P ( B ∩ A ) = 0.5140

P( A ) = ( 55 + 17 ) / 107  = 0.6729

hence P ( B / A ) = 0.5140 / 0.6729 = 0.7639

What is the ratio of the calories Robyn

burned on Wednesday le the celories she

burned on Monday?

Answers

Question isn't complete but we make assumptions in order to complete the question and explain

Answer and explanation:

If we are given a table on calories burned by Robyn on weekdays from Monday to Friday and on this table Robyn burnt 500 calories on Monday and burnt 400 calories on Wednesday, then we are required to determine the ratio of calories burnt on Wednesday to calories burnt on Monday:

Calories burnt on Wednesday = 400

Calories burnt on Monday =500

Ratio of calories burnt on Wednesday to calories burnt on Monday =400/500=4/5

Ratio =4:5

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