Mathematics College

About Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2k+1 , where k is an integer. An even integer is an integer that can be expressed as 2k , where k is an integer. Prove each of the following statements using a direct proof.

a. The sum of an odd and an even integer is odd.
b. The sum of two odd integers is an even integer.
c. The square of an odd integer is an odd integer.
d. The product of two odd integers is an odd integer.

Answers

Answer 1

Answer:

a. The sum of an odd and an even integer is odd: 3 + 2 = 5

b. The sum of two odd integers is an even integer: 3 + 5 = 8

c. The square of an odd integer is an odd integer: 3² = 9

d. . The product of two odd integers is an odd integer.: 3 x 5 = 15

Step-by-step explanation:

Proving the following statements using a direct proof;

a. The sum of an odd and an even integer is odd:

let the odd integer = 3

let the even integer = 2

3 + 2 = 5

5 is an odd integer, proved

b. The sum of two odd integers is an even integer.

let the first odd integer = 3

let the second odd integer = 5

3 + 5 = 8

8 is an even integer, proved

c. The square of an odd integer is an odd integer. .

let the odd integer = 3

3² = 9

9 is an odd integer, proved

d. The product of two odd integers is an odd integer.

let the first odd integer = 3

let the second odd integer = 5

3 x 5 = 15

15 is an odd integer, proved

Answer 2

Answer:

a. The sum of an odd and an even integer is odd: 3 + 2 = 5

b. The sum of two odd integers is an even integer: 3 + 5 = 8

c. The square of an odd integer is an odd integer: 3² = 9

d. . The product of two odd integers is an odd integer.: 3 x 5 = 15

Step-by-step explanation:

Proving the following statements using a direct proof;

a. The sum of an odd and an even integer is odd:

let the odd integer = 3

let the even integer = 2

3 + 2 = 5

5 is an odd integer, proved

b. The sum of two odd integers is an even integer.

let the first odd integer = 3

let the second odd integer = 5

3 + 5 = 8

8 is an even integer, proved

c. The square of an odd integer is an odd integer. .

let the odd integer = 3

3² = 9

9 is an odd integer, proved

d. The product of two odd integers is an odd integer.

let the first odd integer = 3

let the second odd integer = 5

3 x 5 = 15

15 is an odd integer, proved

Related Questions

Compute the mean, median, and mode for the following three sets of scores saved.

Score 1 Score 2 Score 3

3 34 154
7 54 167
5 17 132
4 26 145
5 34 154
6 25 145
7 14 113
8 24 156
6 25 154
5 23 123

Answers

Answer/Step-by-step explanation:

Score 1:

3, 7, 5, 4, 5, 6, 7, 8, 6, 5

Mean = [tex] \frac{3 + 7 + 5 + 4 + 5 + 6 + 7 + 8 + 6 + 5}{10} = \frac{56}{10} = 5.6 [/tex]

Median: order the data from least to the greatest.

3, 4, 5, 5, 5, 6, 6, 7, 7, 8

The median is average of the fifth and sixth data value in the data set

Median = (5 + 6)/2 = 11/2 = 5.5

Mode = value with the highest frequency = 5

Score 2:

34, 54, 17, 26, 34, 25, 14, 24, 25, 23

Mean = sum of all values/10

Mean = 276/10 = 27.6

Median: order the data set from min to max.

14, 17, 23, 24, 25, 25, 26, 34, 34, 54

The median is average of the fifth and sixth data value in the data set

Median = (25 + 25)/2 = 50/2 = 25

Mode = 25 and 34 (both have frequencies of 2)

Score 3:

154, 167, 132, 145, 154, 145, 113, 156, 154, 123

Mean = sum of all values/10

Mean = 1443/10 = 144.3

Median: order the data set from min to max.

113, 123, 132, 145, 145, 154, 154, 154, 156, 167

The median is average of the fifth and sixth data value in the data set

Median = (145 + 154)/2 = 299/2 = 149.5

Mode = 154

I think of two numbers.
When I add the numbers, the answer is 8.
When I subtract the numbers, the answer
Is less than 6.
What can the numbers be?
The two numbers can be _ and _ .

Answers

Answer:

There are a variety of possible answers, including the following:

4 and 4 (4 + 4 = 8........4 - 4 = 0.......... 6 > 0)

6 and 2 (6 + 2 = 8........6 - 2 = 4.......... 6 > 4)

5 and 3 (5 + 3 = 8.........5 - 3 = 2.......... 6 > 2)

And for the subtraction, each can be reversed (2 - 6 ...... 3 -5 ...... etc.)

Answer:

2 and 3 is the answer we know it right

Four college friends (one is named Cathy) were all accepted to a graduate school.

Answers

Answer:

Wow that is great

Step-by-step explanation:

is there a question? uhhhmmmmm

Which relationships have the same constant of proportionality between Y and as the equation Y=5/2 X

Answers

Answer:

I'm pretty sure it's 10/4 but I'm not totally sure

Answer:

on Khan the answer is B,C,E

Make 3 1/2 cakes in 20 minutes how many cakes can you make in two hours

Answers

Answer:

Step-by-step explanation:

3 1/2+3 1/2=5 which is 40 min

5=40mins

5+3 1/2=81/2

1 hour=8 1/12

8 1/2+8 1/2= 17

17 in two hours

Please help ASAP.
Will mark brainliste

Answers

Answer:

i think its c but it could also be d sorry if im wrong T-T

Step-by-step explanation:

What value of p makes this equation true?
3/4 p- 1/4p + 3 = -2

Answers

Answer:

-10

Step-by-step explanation:

p/2=-5

p=-10

Answer:

-10

Step-by-step explanation:

3/4p-1/4p+3=-2

1/2p+3=-2

1/2p=-5

-10

When is it appropriate to model data with a liner function? Give an example of real world data that can be modeled with a linear function. Include the linear function and a sample of the data

Answers

Answer:

The linear function would be:

C = 10t + 2

where C is the cost and t is time in months

Step-by-step explanation:

Is 8.25 greater, equal or less than 8.250

Answers

Answer:

If this is basic mathematics its =

Step-by-step explanation:

You won't have to worry about sig figs until chemistry.

GET AN EASY BRAINLIEST FIRST RIGHT GETS BRAINLIEST

Answers

Answer:

Step-by-step explanation:

5-9=(-4)

hope this helps :3

Answer:

Can i get a brainliest please? :·3

Step-by-step explanation:

I wasn't here on time

PD: anyone play clash of clans?

PPD: join my clan if you do

PPPD: Link: https://link.clashofclans.com/en?action=OpenClanProfile&tag=2L9YRJYQC

PPPPD: We speak spanish and english

Identify the coefficients: -3h - 2h + 6h +9

Answers

Answer:

-23h

Step-by-step explanation:

It’s -3, 2, 6 is the answer

Brandon enters bike race. He bikes 9 1/2 miles every 1/2 hour

Answers

Since there is no table given I will assume that what you want me to do is to show that Unit rate of Brandon’s biking. SO here are the data that we need: => 8 and ½ miles = 8.5 miles => ½ hour = .5 hours or 30 minutes Now, let’s solve for the unit rate => SO in every 30 minutes he bikes around 8.5 miles => Since 1 hour is equals to 30 minutes, simply multiply 8.5 by 2 => 8.5 * 2 = 17miles => 17 miles / hour
Hope this helps:)

Name the points which satisfy the conditions. The ordinate is zero.

Answers

9514 1404 393

Answer:

Step-by-step explanation:

The one point with a y-value of 0 is the one on the x-axis: G.

The students can make 6 tickets from each sheet of paper. How many sheets of paper. How many sheets of paper are needed for 125 tickets?

Answers

Answer:

20.8333333

Step-by-step explanation:

6 x 20.8333333 = 125

The Law of Large Numbers states that as an experiment is repeated, the relative frequency of an event tends toward the real probability.
a. if the probability of a specific observed event is very small, it is unlikely that the assumption about the probability is correct.
b. the probability of obtaining a favorable outcome increases as the number of trials increases.
c. the sampling distribution of the sample mean will be approximately normally distributed as long as the sample size is sufficiently large.
d. the probability that an event will occur is derived from one's increasing knowledge of relevant circumstances.

Answers

Answer:

c. the sampling distribution of the sample mean will be approximately normally distributed as long as the sample size is sufficiently large

Step-by-step explanation:

The law of large numbers is a statistical law, that states : As sample size grows, the sample mean tends to go closer to whole population mean.

So, the sampling distribution of the sample mean will be approximately normally distributed as long as the sample size is sufficiently large

Please find the area and circumference of
the circle below

Answers

Answer:

area: 153.86

Circumference: 43.96 :D

Step-by-step explanation:

Please help I would appreciate

Answers

Answer:

the 1st 2nd and 5th since if there is even one negative in the fraction it makes the whole fraction negative

20 points & Brainliest

Why are rotations a rigid motion?

Answers

Answer:

RC,\α is a rigid motion.

Here C, is the rotacenter which is the fixed point and around C all other points move in a fixed distance by the definition of rotation.

the motion follows in a circularmanner with C as the center.

consider a point Q which changes to Q1 after rotation by an angle\alpha

Step-by-step explanation:

When considering rotational motion and subsequently rotational mechanics every point on the body must have same angular velocity and angular acceleration. If the body is not rigid different points on the body will have different angular velocity and angular acceleration.

Is f^-1(x) = x/9 - 5/9 a function?

Answers

⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀_____________

⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀;; ∥ • Given:

⠀[tex]f-¹(x)=\frac{x}{9}-\frac{5}{9}[/tex].

⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀_____________

⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀;; ∥ • To find out:

⠀Is a function [tex]f-¹(x)=\frac{x}{9}-\frac{5}{9}[/tex] or not.

⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀_____________

⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀;; ∥ • Hello, ZoFlo2020!

⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀_____________

⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀;; ∥ • Answer (Response Explanation):

⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀_____________

⠀No, it is not. Such an example is not even possible to solve, to be honest. It doesn’t have a single solution to find at least an approximate part of its solution and answer.

⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀_____________

⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀;; ∥ • Sincerely, Your ElskerNorge! :)

⠀ ⠀ ⠀ ⠀ ⠀ ⠀ ⠀_____________

what kind of line is this? 2y=19

Answers

straight line pretty sure

QUESTION:
An airplane flies with a constant speed of 660 miles per hour. How long will it
take to travel a distance of 2475 miles?

Answers

Answer:

5643

Step-by-step explanation:

you add them together then you divide

HELP WITH NUMBER 6 ASAP PLEASE!!!!!!!

Answers

move point (-5,0) to (-4.0) and move point (7,1) to (8,1) so that the points pass the vertical line test. note that this points can be moved to others places too, these are just a few examples

a stone which is dropped into a dry well hits the bottom in 2.2s how deep is the well. take g=10m/s

Answers

Answer:

23.7m

Step-by-step explanation:

Given parameters:

Time taken = 2.2s

Acceleration due to gravity = 10m/s

Unknown:

Depth of the well = ?

Solution:

To solve this problem, we simply apply one of the motion equations;

S = ut + [tex]\frac{1}{2}[/tex] gt²

where S = depth of the well

u = initial velocity

t = time taken

g = acceleration due to gravity

Input the parameters and solve for S;

Note initial velocity = 0;

S = [tex]\frac{1}{2}[/tex] x 9.8 x 2.2²

S = 23.7m

a bottle of hand lotion is on sale for $2.25. if this price represents a 50% discount from the original price, what is the original price to the nearest cent?

Answers

Answer:

4.50

Step-by-step explanation:

2.25 plus 2.25 aka half

Add parentheses to make 6-9-2+3x6 equal to 17

Answers

Answer:

6-(9-2)+3x6

Step-by-step explanation:

hope it helps

What is the other solution to the equation?
A: x=-6
B: x=-4
C: x=2
D: x=4

Answers

Answer:

to what

Step-by-step explanation:

i can't see the question

I believe it’s B which is x=-4

Plz help 30 points to whoever answers correctly. Write an equation of the parábola in intercept form. X-intercepts of 3 and 6 passes through (9,-9)

Answers

Answer:

k lemmee checkkkkkkkk

Which measure is equivalent to 126 in.?

1 ft = 12 in.

1 yd = 3 ft

Answers

Answer:

3.5 yd is your answer

Step-by-step explanation:

First, change in. to ft. Note that the measurement given to you is that 1 ft = 12 in.

Divide the amount of inches you have with 12.

126/12 = 10.5

Next, solve for yards. It is given to you that 1 yard = 3 feet.

Divide the amount of feet you have with 3.

10.5/3 = 3.5

3.5 yd is your answer

The following relation is a function: {(-8, – 9), (-4, 5), (1, 5), (4, 7)}

Answers

Answer:

Yes

Step-by-step explanation:

The following relation is a function. When graphed, it passes the vertical line test, and you don't go across any two points at the same time. So therefore, it is a function. Another easy way to determine if the relation is a function is by taking a look at the x-coordinates. If any x-coordinates are the same, then it's not a function. If all x-coordinates are the same, then it's a function.

Hope this helps. Please mark brainliest.

4cm
2cm
6cm
Find the area please

Answers

Step-by-step explanation:

ummm where is the pic? like bruh

Answer:

48 cm

Step-by-step explanation:

Multiply 4x2x6 and get the answer of 48 cm.

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