Gemma makes a conjecture that the sum of an odd integer and itself is always an even integer. Which choice is the best proof of her conjecture?

A) Look at these different examples: 7 + 7 = 14, 13 + 13 = 26, 23 + 23 = 46. So the sum of an odd number and itself must be even
B) Let 2n + 1 be an odd number; (2n + 1) + (2n + 1) = 4n + 2. Because 4(n + 2) is divisible by 2, the sum of 2n + 1 and itself is even.
C) Let n represent an odd number, and let n + n be an even number. Therefore, n + n = n + n, which shows that the sum of an odd number and itself is even.
D) Every time you add an odd number and itself, the sum is an even number.Every time you add an odd number and itself, the sum is an even number.

Answers

Answer 1

Answer:

Let 2n + 1 be an odd number......  B/2nd option

Step-by-step explanation:

Answer 2

The best choice is

Let 2n + 1 be an odd number; (2n + 1) + (2n + 1) = 4n + 2.

Because 4(n + 2) is divisible by 2, the sum of 2n + 1 and itself is even.

What is Conjecture?

A hypothesis in mathematics is a conclusion or a proposition made tentatively without supporting evidence. Some conjectures, like the Fermat's Last Theorem or the Riemann hypothesis, have significantly influenced the development of new branches of mathematics.

First, Only three examples are given which is not appropriate at all.

Second, This is the best proof is

Let 2n + 1 be an odd number; (2n + 1) + (2n + 1) = 4n + 2. Because 4(n + 2) is divisible by 2, the sum of 2n + 1 and itself is even.

Fourth, State the meaning of Title without proof.

Learn more about Conjecture here:

https://brainly.com/question/29153415

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Related Questions

rounded to the nearest hundred thousandth the number 0.00005361 is ___​

Answers

Answer:

0.00005

Step-by-step explanation:

An airplane 30,000 feet above the ground begins descending at the rate of 2000 feet per minute. Assume the plane continues at the same rate of descent. whats the slope and y intercept ​

Answers

Answer:

The slope is -2000 and the y-intercept is 30,000

Step-by-step explanation:

slope-intercept form: y=-2000x+30,000

Explain how Main Sequence Stars
are different from Giant stars and
Dwarf stars?


Help me with thissss

Answers

A giant star is a star with substantially larger radius and luminosity than a main-sequence (or dwarf) star of the same surface temperature. They lie above the main sequence (luminosity class V in the Yerkes spectral classification) on the Hertzsprung–Russell diagram and correspond to luminosity classes II and III.

The stemplot shows the number of magazines sold by students in a band. One data value was inadvertently omitted from the stemplot. A stemplot titled magazines sold has values 8, 9, 12, 12, 13, 15, 16, 16, 16, 18, 21, 22, 23, 27, 28, 32, 34, 40. Which statement is true? If the missing data value was 55, the range of the data would change significantly. If the missing data value was 55, the interquartile range of the data would change significantly. If the missing data value was 22, the range of the data would change significantly. If the missing data value was 22, the interquartile range of the data would change significantly.

Answers

Answer:

If the missing data value was 55, the range of the data would change significantly

If the missing data value was 22, the interquartile range of the data would change significantly

Step-by-step explanation:

Given the data

8, 9, 12, 12, 13, 15, 16, 16, 16, 18, 21, 22, 23, 27, 28, 32, 34,40

The range of the data is the difference between the highest value and the lowest value of the data.

Highest value = 40

Lowest value = 8

Range = 40-8

Range = 32

If 55 was missing, we need yo find the range of the data if 55 was included.

Highest value will be 55

Lowest value = 8

Range in this case = 55-8

Range = 47

Difference in range = 47-32= 15

This means that if 55 was missing, it will significantly affect the value of the range.

- Interquartile range = Q3-Q1

Q3 is the median value of the other half of the data.

Q1 is the median value of the first half of the data.

If 55 wasn't included, the first part of the data:

8, 9, 12, 12), 13, (15, 16, 16, 16

Q1 = 13 (median value of the extracted data)

The second part of the data if 55 wasn't included:

18, 21, 22, 23), 27, (28, 32, 34, 40

Q3 = 27 (median value of the second part of the data)

IQR = Q3-Q1

IQR = 27-13

IQR = 14

If 55 was included, the data will be;

8, 9, 12, 12, 13, 15, 16, 16, 16, 18, 21, 22, 23, 27, 28, 32, 34, 40,55

Q1 = N+1/4 the value

N is the sample size = 19

Q1 = 19+1/4

Q1 = 20/4

Q1 = 5th value

The 5th value in the data is 13, hence Q1 is 13

Q3 = 3(N+1)/4th value

Q3 = 3(19+1)/4

Q3 = 60/4

Q3 is the 15th value in the dataset. Since the 15th value is 28, Q3 is 28

IQR = 28-13

IQR = 15 (if 55 was included)

Difference in IQR = 15-14 = 1

This means that if 55 was the missing data, the IQR will not change significantly.

Note that the range of the data will not change if the missing value is 22 because, the 22 is a value lower than the highest value of the dataset, hence the range will remain the same (40-8 = 32) irrespective of 22 missing or not.

For the Interquartile range

If 22 was in

Q3 = 3(N+1)/4th value

Q3 = 3(19+1)/4

Q3 = 60/4

Q3 is the 15th value in the dataset. Since the 15th value is 28, Q3 is 28

IQR = 28-13

IQR = 15 (if 55 was included)

Difference in IQR = 15-14 = 1

This means that if 55 was the missing data, the IQR will not change significantly.

Based on the calculation, the correct options are:

- If the missing data value was 55, the range of the data would change significantly

- If the missing data value was 22, the interquartile range of the data would change significantly

Answer:

a

Step-by-step explanation:

edge 2021

Solve for r.
-13 = r/9 + 8

Answers

Answer:

Your answer is going to be r= -189

Step-by-step explanation:

(-13)-8=(r/9+8)-8

9(-21)=(r/9)9

r=-189

12) 12 ft. = ? yd. (1yd. = 3 ft)

13) 2 gal. = ? qt. (4qt.= 1 gal.)

14) 2 gal. = ? oz. (1qt. = 32 oz.)

Help!!

Answers

12. 4 yds.
13. 8 qts.
14. 118 oz

Open-Ended Which of these situations can be represented by the opposite of 53? Use pencil and

paper. Describe two more situations that can be represented by the opposite of 53.

A book was 53 pages shorter than you expected.

Andrew spent $53.

The temperature was 53°F.

Jennifer sold 53 apples.

Select each situation that can be represented by the opposite of 53.

O A. Andrew spent $53.

OB. Jennifer sold 53 apples.

OC. A book was 53 pages shorter than you expected.

D. The temperature was 53°F.

Answers

Answer:

A book was 53 pages shorter than you expected

Jennifer sold 53 apples.

Andrew spent $53.

Step-by-step explanation:

The question proposed that we should determine which situation can be said to be the opposite of 53. From the listed option, we will realize that the following:

A book was 53 pages shorter than you expected

Jennifer sold 53 apples.

Andrew spent $53.

The above options are the opposite of 53. This is because a book that was shorter than expected will need to be refilled.

Suppose Jennifer has x apples, and She sold 53 apples out of it. It means x = -53, which is the opposite of 53.

Andrew spent $53; let say Andrew had y+$53. After spending $53, he has y = - $53, which is the opposite of 53.

But the temperature, which was 53°F, will still be at that position on the thermometer provided it is not being affected by external conditions.

PLEASE PLEASE HELP AND FAST
Morrie completed the work to solve this problem. Is his work correct?

Negative StartFraction 5 over 6 EndFraction minus (negative three-fourths) = Negative StartFraction 5 over 6 EndFraction minus three-fourths = Negative StartFraction 8 over 10 EndFraction = Negative four-fifths

What were Morrie’s errors? Check all that apply.
He should have made all the signs positive.
He should have changed Negative StartFraction 5 over 6 EndFraction minus (negative three-fourths) to Negative StartFraction 5 over 6 EndFraction + three-fourths
He should have found the common denominator, 12.
He should have subtracted StartFraction 5 over 6 EndFraction and Three-fourths
The answer should be Negative StartFraction 1 over 12 EndFraction

Answers

Answer:

The correct answers are B, C, and E.

Step-by-step explanation:

Answer:

b c e

Step-by-step explanation:

Nine less than one fourth of a number 6. Find the number.

Answers

5.3057(600)578)542)(200)

-3 ( -4 - 5x) = -18 i'll help with your questions :)))

Answers

Answer:

-15

Step-by-step explanation:

-3(-4-5x)= -18

12+15x= -18-12

15x= -30

x= -30÷15

x= -15

Capella is the 6th brightest star in the sky and is 41 light-years from earth. How many miles will light from Capella travel on its way to earth?

PLEASE EXPLAIN YOUR ANSWER THROUGHLY (i need to learn for a test)

Answers

9514 1404 393

Answer:

  2.41×10^14 miles

Step-by-step explanation:

The distance usually associated with a light-year is about 6 trillion miles. More precisely, it is about 5.879×10^12 miles. Then 41 light-years is 41 times that distance, or ...

  41 light-years = 41(5.879×10^12 miles) ≈ 2.41×10^14 miles

_____

You can figure the length of a light-year from the speed of light and the length of a year. The speed of light is about 186,282.4 miles per second. The number of seconds in a day is 86,400, and the number of days in a year averages 365.2425. Multiplying these values gets you to 5.878664e12 miles per year. The number used above is reasonable for most purposes. At astronomical distances, it is difficult to measure precisely.

Shelly runs 2.5 miles in 18 minutes. What is her mile time in minutes?​

Answers

Answer:

7.2 minutes

Step-by-step explanation:

You can just divide 18 minutes by 2.5, and you will get 7.2 minutes per mile. Hope it helps!

Write the sentence as an equation.
m divided by 341 equals 315

Answers

Answer:

m/341=315

Step-by-step explanation:

Answer:

m/341=315 because the divided symbol is / and the equals symbol is = so replace the words with the symbol.

help please i dont wanna fail

Answers

Answer:

it'd be 3,752

Step-by-step explanation:

since the perimeter is 268 X 14 = your answer

What is the coefficient in the simplified expression?

Answers

Answer:

poins lang talaga to

Step-by-step explanation:

hahahahahahahahahahahahahaha

Solve for x.
z=(x-5)k

Answers

Answer:

x=z/k+5

Step-by-step explanation:

the answer is z/k + 5 = x

there are 678 freshmen ,and 552 sophomore students. how many more freshmen than sophomore students are there?​

Answers

Answer: There is 126 more freshmen than sophomores.

Step-by-step explanation:

Subtract the number of freshmen by the number of sophomores.

678 - 552 = 126

Just subtract 678-552
Which equals 126
There are 126 more freshmen than sophomore students

what expression can be used to 80% of 120

Answers

Answer:

59%

Step-by-step explanation:

Answer:

96=80% of 120

Step-by-step explanation:

C Evaluate 7 . 2.7. 5 using the properties of numbers by matching each step with the property used. = 7.7.2.5 Choose... = (7-7) (2 - 5) Choose... = 49 - 10 Distributive Property Fir Commutative Property Please answer all parts of Closure Property Transitive Property Simplify. Associative Property 7.2 7.5= Substitution Property​

Answers

Answer:um this is hard i will give you the answer give me a sec

Step-by-step explanation:

You are making some chili and need some onions and peppers. One pound of onions costs $0.97 and one pound of peppers cost $1.30. What is the total cost of 0.76 pounds of onions and 1.5 pounds of peppers? The total cost of 0.76 pounds of onions and 1.5 pounds of peppers is $

Answers

Answer:

The cost of  0.76 pounds of onion is  [tex]x = \$ 0.988  [/tex]

The  cost of  1.5 pounds  of  peppers is [tex] y = \$ 1.455[/tex]

The  total cost is [tex]z =  \$ 2.443  [/tex]

Step-by-step explanation:

From the question we are told that

  The  cost of one pound of pepper is  C = $0.97

   The cost of one pound of onion is  [tex]C_o = \$ 1.30[/tex]

   Generally the cost of 0.76 pound of  onion is mathematically represented as

      [tex]x =  \frac{0.76 * 1.30}{1}[/tex]

=>      [tex]x = \$ 0.988  [/tex]

   Generally the cost of 1.5pound of  peppers  is mathematically represented as

            [tex] y  =  \frac{1.5 * 0.97}{1}[/tex]

=>          [tex] y = \$ 1.455[/tex]

The total cost of 0.76 pounds of onions and 1.5 pounds of peppers is

      [tex]z =  x+ y[/tex]

=>    [tex]z =  0.988 + 1.455 [/tex]

=>    [tex]z =  \$ 2.443  [/tex]

A kayak is originally priced at $100. The online retailer gives a discount and the kayak is now priced at $75. Enter the percentage discount for the cost of the kayak.

Answers

Answer:

25%

Step-by-step explanation:

Discount:

  $100 * .25 = $25

New Price:

  $100 - $25 = $75

Adam wants to create an outdoor rectangular kennel. The length will be three feet more than twice the width. Write and use an equation to find the length and width of the kennel if Adam has 54 feet of fencing. Write and solve an equation to solve this problem.

Answers

Step-by-step explanation:

l = 3 + 2w

P= 2w t 2l

= 2w+2(3+2w)

=2w+6+4w

=6w+6 = 54

6w=48

w=8

divide 6 both side

l=3+2(8)=3+16=19

answer

width 8feet and length 19 feet

PLEASE HELP MEE ASAP!

Answers

Answer:

Step-by-step explanation:

1/6

Can someone help me with this math question? First to answer will get Brainliest! :)

Answers

Answer:

A

Step-by-step explanation:

yiu have to rotate it in order to make that

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Use the distributive property to factor the expression.

2
k

+

10

Answers

Answer:

Step-by-step explanation:

2k+10   | Both terms share the common factor two, so you can take it out (divide both terms by 2)

2(k+5)  | Now if you use the Distributive Property to double check, you get 2k+ 10 again

the distance between Two Cities on a map is 4.125. find the actual distance if the scale on the map was 2 inches = 40 miles

Answers

Answer:

85 miles.

Step-by-step explanation:

Lets begin by figuring out the number of miles in 4 inches. Since every 2 inches make 40 miles, we can figure out that there are 80 miles in 4 inches. To figure out that .125 part, we multiply 40 by .125, to get 5. We can add 80 plus 5 to get our grand total of 85 miles.

Can someone explain how to find the slop and y-intercept?

Answers

Answer:

slope: 4/5

y-intercept: (0,4)

slope intercept form: y = 4/5 x + 4

Step-by-step explanation:

to find the slope, you have to find the difference of the x coordinants and the difference of the y coordinants. since the two coordinants we have are 0,4 and 5,0 and we know that 0 - 5 is -5 and 0 - 4 is -4 we then have to divide the two. so now we get -4/-5. since a negative divided by a negative is a positive, the negative signs cancel out. since the fraction is in simplest form, that is our answer. also, since its rise over run, it means that everytime you go up or down 4 and over 5, you will reach a whole number on the graph.

okay, now the y-intercept is when the line crosses the y-axis/when x=0. the y-intercept for this example would be 4 or (0,4). i hope that makes sense. like i said ill get back to you on the slope thing in a minute just a second...

Which property is shown: 3t + 2r = 2r + 3t?​

Answers

Answer:

Commutative Property

Step-by-step explanation:

The commutative property shows two values or equations that are similar, but in a different order.

Examples:

3 + 4 = 4 + 3

5x + 2h = 2h + 5x

IF YOU KNKW WHAT THE ANSWER IS PLEASE HELP ME

Answers

Answer:

exponential

Step-by-step explanation:

This function can be expressed as 125*3^x, where x is the number of hours passed.

Since linear equations are expressed as mx+b, quadratics are expressed as ax^2+bx+c, and exponential functions are expressed as ab^x, only the exponential function would be a valid answer.

Tom walks 3.2 km every morning. How many feet are in 3.2 km, given that 1 mile = 1.609 km and 1 mile = 5,280 feet? 2,654.85 feet 8,500.67 feet 10,500.93 feet 16,901.15 feetTom walks 3.2 km every morning. How many feet are in 3.2 km, given that 1 mile = 1.609 km and 1 mile = 5,280 feet? 2,654.85 feet 8,500.67 feet 10,500.93 feet 16,901.15 feet

Answers

Answer:

10,500.93 feet

Step-by-step explanation:

From the question, we are told that Tom walks 3.2km every morning.

1 mile = 1.609km

1 mile = 5280 feet

Step 1

1.609km = 1 mile

3.2km = x mile

Cross Multiply

x mile × 1.609km = 3.2km × 1 mile

x mile = 3.2km × 1 mile/1.609.

= 1.9888129273 miles

1 mile = 5280 feet

1.9888129273miles = y

Cross Multiply

y = 1.9888129273 × 5280 feet/1 mile

= 10500.932256 feet

Approximately = 10,500.93 feet

Therefore, Tom walks for 10,500.93 feet

10560

Answer:

10,500.93 feet

Step-by-step explanation:

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