Mathematics College

If n+1 integers are chosen from the set

1,2,3,…,2n
,where n is a positive integer, must at least one of them be even? Why?

Answers

Answer 1

Answer:

Pigeonhole Principle

Step-by-step explanation:

From series {1,2......2n} ; we need to select 'n + 1' integers.

Even integers series from above series = {2,4,6..........2(n-1), 2n}

Odd integers series from above series = {1,3,5........2(n-2), 2n-1}

So, we can choose only n odd integers from the series. Hence, if we choose n+1 integers, atleast one of them have to be even integer.

Eg : n = 5, Series = (1,2,3,4,5,6,7,8,9,10}, Odd series = {1,3,5,7,9}, Even series = {2,4,6,8,10}. If we choose 5 +1 ie 6 integers, there must be one even integer, as there are only 5 total odd integers in series.

Related Questions

Please help me with this question

Answers

Answer:

10 i think

Step-by-step explanation:

theres 10 x's

Answer:

10?

Step-by-step explanation:

i just counted the x's

PLS HELP!!!!!!!!!!!!!!!!!!!! Which number is divisible by both 5 and 6? A. 123,465 B. 132,640 C. 164,780 D. 184,290

Answers

A,B helps it help if you doubt used calculator

Alexis earns $50 a day for five days this week. Her weekly expenses are $280. How can she balance her budget?

a
increase her income $5 each day
b
increase her income $20 this week
c
decrease her expenses by $30
d
decrease her expenses by $20

Answers

Answer:

i think the answer is B

Step-by-step explanation:

Which of these expressions is equivalent to log
(12/5)
?
O A. log (12) - log (5)
O B. 12. log (5)
O C. log (12) + log (5)
O D. log (12) log (5)

Answers

The expressions that is equivalent to log (12/5) would be A. log (12) - log (5).

What is logarithm and some of its useful properties?

When you raise a number with an exponent, there comes a result.

Lets say you get

a^b = c

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

b = \log_a(c)

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

We have given an expression as ;

log (12/5)

We know that

[tex]log_a(b) - \log_a(c) = \log_a(\frac{b}{c})[/tex]

So,

log (12/5) = log (12) - log (5)

Thus, the correct option is A. log (12) - log (5)

The expressions that is equivalent to log (12/5) would be A. log (12) - log (5).

Learn more about logarithm here:

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-2(x + y)2 for for x =-3, y = 2 with steps

Answers

Step-by-step explanation:

-2(-3+2)2

(-2×-3)+(-2×2)2

(6-4)2

2(6-4)

(2×6)+(2×-4)

12-8=4

Fernando can run 600 meters
in 5 minutes. At this rate,
how many minutes would it
take him to run 1,500
meters?

Answers

Answer:

12.5 minutes

Step-by-step explanation:

Given that,

Fernando can run 600 meters  in 5 minutes.

We need to find how many minutes would it take him to run 1500 meters.

ATQ,

600 m = 5 min

1 m = (5/600) min

For 1500 m,

[tex]t=\dfrac{5}{600}\times 1500\\\\t=12.5\ min[/tex]

So, it will take 12.5 minutes to run 1500 m.

9.
A. 7
B. 15
C. 12
D

Answers

Answer: d=20?

Step-by-step explanation:

Please help :) I'm confused on this question.

Answers

This may be wrong since I don’t know exactly what lesson you’re learning, but I believe it would be:

0+3

3

3-4

-1

Hope this helped!

How many times larger is 9 x 10^4 than 3 x 10^2?

Answers

Answer: [tex]300[/tex] [tex]times[/tex]

Step-by-step explanation:

If f(x) = 7, then x = ______ .

Answers

Answer:

-10

Step-by-step explanation:

On a graph, f(x) means the same thing as y.  So if y=7, then x=-10

I WILL GIVE BRAINLIEST IF YOU EXPLAIN YOUR ANSWER!!
Kaylee and Rory have a circular swimming pool. The pool has a cover that fits snuggly over the top of it. If the radius of the pool is 11 ft, what is the surface area of the cover?

Answers

Answer:

380.13

Step-by-step explanation:

pi r^2

pi*11^2

pi*121

3.1415926*121

Answer:

379.94 sq. ft.

Step-by-step explanation:

HOPE THIS HELPS

-4=2/3 b

What would be the best first step to solving the
equation in one step

Answers

2728283939392928277282929292929282828292839393939

create a story problem about a fish tank for the tape diagram below. Your story must include a fraction.​

Answers

Answer:

Step-by-step explanation:

A large aquarium has a length of 84 inches. It is located in a large basement that is properly heated and ventilated. The width should be close to 1/2 the length and the height ought to be 1/6 the length. If the fish tank requires that an aerator be placed every 28 inches along the back edge, how many aerators are needed. Note: an aerator is not placed in either corner.

Width =_________________

Height= ________________

Aerators = ______________

Find the number of cubic inches of the fish tank. If an aerator will provide enough oxygen to aerate  5 cubic feet,, do you have enough aerators for the fish to live comfortably? If the answer is no, then how many aerators do you need?

Need answer ASAP please help!

Answers

9514 1404 393

Answer:

  31 square inches

Step-by-step explanation:

You can divide the shape into pieces several ways. The total area will be the sum of the areas of the pieces.

If we draw a horizontal line across the figure 2 inches up from the bottom, the figure is divided into a triangle and two rectangles.

The triangle has a base of 8 -3-2 = 3 inches, and a height of 4 -2 = 2 inches. Its area is ...

  A = (1/2)(3 in)(2 in) = 3 in²

The rectangle below the line has a base of 8 inches and a height of 2 inches. Its area is ...

  A = bh = (8 in)(2 in) = 16 in²

The rectangle above the line has a base of 3 inches and a height of 4 inches. Its area is ...

  A = bh = (3 in)(4 in) = 12 in²

Then the total area of the figure is ...

  (3 + 16 + 12) in² = 31 in² . . . . the area of the figure

ther are 9 thirds in 3 ones a multiply and divide equashon

Answers

Answer:

That is a division equation.

Step-by-step explanation:

Which scatterplot shows the correct division for using the Area Method to draw the trend line?

Answers

Answer:

A

Step-by-step explanation:

Got it right

The correct division for using the Area Method to draw the trend line is shown by Option A.

What is a Scatter Plot ?

A scatter plot is the plot that consists of data that is randomly spread and doesn't have a fixed pattern , A trend has to be determined from the data to understand the pattern.

The given scatter plot shows an upstream and a downstream , The correct division will be from the point where it start following a fixed pattern , Which is in the Option A attached.

Therefore The correct division for using the Area Method to draw the trend line is shown by Option A.

The missing Options are attached with the answer

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Muriel says she has written a system of two linear
equations that has an infinite number of solutions. One
of the equations of the system is 3y = 2x - 9. Which
could be the other equation?

Answers

Answer:

The other equation could be: 6y = 4x - 18

Step-by-step explanation:

System with infinite number of solutions:

A linear system has an infinite number of solutions when one equation is a multiple of another.

One of the equations of the system is 3y = 2x - 9. Which could be the other equation?

A multiple of 3y = 2x - 9

Multiplying by 2, the other equation could be: 6y = 4x - 18

Answer:

B: y=2/3 x -3

Step-by-step explanation:

I got it right on Edge

How do you solve an inequality when there is a negative number such as -8x is greater than 72

Answers

Answer:

When you divide both sides of an inequality, you need to flip the inequality sign.

Step-by-step example:

-8x > 72

Divide both sides by -8

x < -9

What is 5/8 divided by 1/4
001
001
00
100
001
00
001
IN
A
0 1

Answers

Answer:

Exact form: 5/2

Decimal form: 2.5

Mixed number form: 2 and 1/2

Step-by-step explanation:

when you divide a fraction you keep, change, flip

Equation: 5/8 ÷ 1/4

keep 5/8 the same

change the divide symbol into a multipulcation symbol

flip 1/4 the other way, so it's 4/1 (it's a whole number now)

then just multiply across

Equation now: 5/8 × 4/1

<7 is a complement of <8 and m<7 = 18 degrees. Find m<8.

Answers

Complement is
72
Supplement is
162

A table of values of a linear function is shown below. Find the output when the input is n . Type your answer in the space provided.
input: 1 2 3 4 n
output: -10 -13 -16 -19 (Blank)

Answers

Answer:

5; -22

Step-by-step explanation:

A linear function has a positive relationship and as such an increase in one variable (input variable) causes an increase in the other variable (output variable) i.e the variables are directly proportional.

Given the following data;

Input: 1 2 3 4 n

Output: -10 -13 -16 -19

For an input variable of 1, 2, 3, 4; the output variable is -10, -13, -16, -19 respectively.

To find the value of n;

We can deduce that the input is increasing by a value of 1.

Thus, n = 4 + 1 = 5

For the output;

We can deduce that the output is increasing by a value of -3.

Thus, the next output = -19 + (-3) = -22

Answer:

5; -22

Step-by-step explanation:

Hope this will help

Can someone please solve this for me?

416 ÷ 652

Show your work and I'll give brianliest

Answers

Answer:  0.63803681

Step-by-step explanation:

652/416 simplified= 163/10

then just divide bc its easier.

hope it helped :))

Answer:

0.63803680981

Step-by-step explanation:

First, you can see there is no way to divide 652 into 416. So, you need to add a decimal to 416. Then, you would multiply 652 by 6 and get 3912. You subtract 3912 by 4160 and get 248. Then, you add a 0 to that number. And then, you would keep repeating the steps. Decimal, multiply, subtract.

What is 28% of 307
Enter your answer as a decimal in the box

Answers

Answer:

the answer is 85.96

Step-by-step explanation:

Hope this helps, =)

Samuel is offering a pair of boots with an original price of $80.Store A is offering a 25% discount off the original price of all boots. StoreB is offering a $10 discount off the original price of all boots.

Answers

B. Samuel will pay will 10 dollars less if he buys the boots from store A.

what is the answer and how​

Answers

the temperature at 9pm was -4° because the hottest temperature was 12° and then at 9pm the temperature dropped 16° which means the temperature was -4°

Answer:

-4°

Step-by-step explanation:

4 + 8 = 12

12 - 16 = -4

The temperature was -4 at 9pm

Find the area of the circle. Round your answer to the nearest hundredth.

Answers

Answer:

176.71^2 in

Step-by-step explanation:

yeh

The cost of DVDs will grow at a rate of $1.40 each year. In 2013, a new DVD cost $17.99. Let z be the number of years since 2013.
Which function models the price of a new DVD 2 years after 2013?
O f (z) - 17.99 + 1.0147
O f (2) - 17.99 +1.42
f (x) – 17.99(1.4)
O f(z) – 17.99(1.014)

Answers

Answer:

A, because A is the answer(I have my reasons) so A.

Find the area for the following figure.
O 124. 86 cm2
62.93 cm2
26.5 cm2
137.45 cm2

Answers

the answer is 62.93

What two numbers are exactly four units away from 6

Answers

Answer:

2 and 10

Step-by-step explanation:

6+4=10, and 6-4=2.

The number four units away from 6 are 2 and 10 and are represented below the number line.

What is a number line?

The number line is a straight line containing numbers arranged at equal segments or periods throughout its duration.

A horizontal number line is the most common representation and can be extended infinitely in any direction.

Given that,

Four units away from 6

Four units higher →

6 + 4 = 10

Four units lower →

6 - 4 = 2

In the below number line, it is shown diagrammatically.

Hence "The number four units away from 6 are 2 and 10 and are represented below the number line".

To learn more about the number line,

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find m<A to the nearest tenth degree​

Answers

I think it’s a hope this helps
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