1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
madreJ [45]
3 years ago
7

Suppose you pick 6 different numbers in [10]. Prove that 2 of the numbers are next to each other. (Hint: use the pigeonhole prin

ciple. What are the pigeons and what are the holes?)
Mathematics
1 answer:
Masja [62]3 years ago
4 0

Step-by-step explanation:

We are picking 6 numbers from the numbers 1,2,3,4,5,6,7,8,9,10. Since we care about numbers being next to each other, we might think of the 10 numbers as being distributed in 5 boxes (which you can think of as the holes):

|   1 2   |   3 4   |   5 6   |   7 8   |   9 10  |

So on the first box we have the numbers 1 and 2, on the second box we have the numbers 3 and 4, and so on. Since we are picking 6 numbers from those 10 numbers, that means we'll have to pick 6 boxes (and inside each box we pick a number), but we only have 5 available boxes, so by the pigeonhole principle, we'll have to pick 1 same box at least two times. Since on each picked box we'll need to pick a number, on this box which was picked two times, we will have to pick both of its numbers. And so those 2 numbers inside that box will be next to each other (meaning they're consecutive numbers).

You might be interested in
Complete the table using the rule y=x-1/4
IgorLugansk [536]
If y=X-1/4 then this is what your chart will look like:

Y = X
1 = 0.75
2 = 1.75
3 = 2.75
4 = 3.75
5 = 4.75

Plz mark brainliest
3 0
2 years ago
Match the factored form
Brut [27]
(3x - 8)(3x + 8) is 3.) 9x^2 - 64
(x + 6)^2 is 4.) x^2 + 12x + 36
(3x - 2)(x + 5) is 1.) 3x^2 + 13x - 10
5x(x - 1)(x + 7) is 2.) 5x^3 + 30x^2 - 35x
(x - 8)(x + 7) is 5.) x^2 - 10x + 16

I hope this helps!
7 0
3 years ago
When ringing up a customers cashier needs 25 seconds to process payment as well as 1 second to scan each item being purchased. H
Sergio [31]

Multiply the amount of seconds to ring up items by the amount of items.

1 × 17 = 17

Now add the amount of seconds to process a payment to the product.

17 + 25 = 42

<h2>Answer:</h2>

<u>It takes </u><u>42 seconds</u><u> to ring up a customer with 17 items.</u>

5 0
3 years ago
Can someone help me with both of these? What do I do with the 68 and 79?
Nutka1998 [239]
What he said just click on that
3 0
2 years ago
Can someone please help? ^^ &lt;3<br><br> y=-1/2x+7/2<br> in standard form! &lt;3
Marina CMI [18]

Answer:

2y = -x + 7

Step-by-step explanation:

y = -1/2x + 7/2 (Multiply by 2)

2y = -x + 7

6 0
2 years ago
Other questions:
  • I'm not sure what they're asking for here.
    7·1 answer
  • The length of a rectangle is 4 meters less than three times its width. Its area is 615 square meters. What are the dimensions of
    13·1 answer
  • $(60) = 21–42 + 10.7<br> V<br> ON<br> f(x)<br> O
    13·1 answer
  • Can you help me solve for z<br><br><br> Please shower work so I can understand
    14·1 answer
  • The pair of variables x=–3, y=8 is the solution to the equation 5x+by=17. Find the coefficient b.
    11·1 answer
  • Please help with 7!!!!!!
    15·1 answer
  • Solve for x 18=r/2 as a fraction​
    13·1 answer
  • An online clothing store had 450,082 visitors in May, 450,566 visitors in June, and 405,987 visitors in July. What is the order
    12·1 answer
  • Select all the factors that can be divided out to simplify the multiplication problem: 8/15x5/16
    8·1 answer
  • What is 30/72 in simplest form?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!