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
Firlakuza [10]
3 years ago
14

You randomly select k integers between 1 and 100, inclusive. What is the smallest k that guarantees that at least one pair of th

e selected integers will sum to 101? Prove your answer.
Mathematics
1 answer:
vredina [299]3 years ago
6 0

Answer:

51

Step-by-step explanation:

The possible components to sum up to 101 can only be divided into 2 groups, 1 is larger than 50 and the other is less than or equals to 50

For example

50 + 51 = 101

52 + 49 = 101

60 + 41 = 101

...

99 + 2 = 101

100 + 1 = 101

Therefore, the worst case scenario is to pick all numbers from only 1 group, either all number less than or equal to 50, which there are 50 of them from 1 to 50, or greater than 50, which there are 50 of them from 51 to 100.

So k has to be at least 51 to guarantee that at least one pair of the selected integers will sum to 101

You might be interested in
Khalid and Jesse took different overnight trains
qwelly [4]
You didnt give enough information but 40
3 0
3 years ago
What is 47%as a fraction
ivolga24 [154]

Answer:

47/100

Step-by-step explanation:

47 -> 0.47      47/100 = 0.47

6 0
3 years ago
Read 2 more answers
A taxi cab charges a $3.50 flat fee plus a $1.20 fee mile. Write an equation for the total cost, y, after riding for x miles
oksian1 [2.3K]

y = $3.50 + ($1.20/mile)x

8 0
3 years ago
Read 2 more answers
Draw the multiplication table on the P=(3,5,7,9) in module 12​
Lisa [10]

Answer:

Find the attached file for the solution

Step-by-step explanation: To draw the multiplication table on the P=(3,5,7,9) in module 12, create the table where all the given parameters will be at the top of horizontal axis and vertical axis,

When multiply by each other, any value that is below 12 will be written down while the value greater than 12 will be divided by 12 and the remainder will be written down.

Find the attached file for the solution and table.

8 0
3 years ago
on a certain map, 3/4 inch represents a distance of 150 miles. what distance d, in terms of x, is represented by x inches on the
exis [7]

Answer:

x=80

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • How many solutions does this system of equations have?
    10·1 answer
  • What strategy would be the best to solve this problem?A theater charges $8 for an adult ticket, and $6 for a children's ticket.
    8·2 answers
  • What is the greatest common factor for 12&15
    10·1 answer
  • What is the reason for each step in the solution of the equation? -6= -2(x+12). Drag and drop the reasons into the boxes to corr
    6·1 answer
  • In a city school of 900 students, 35% of the students are on the honor roll, 63% have a part-time job, and 26% are on the honor
    8·1 answer
  • How do I solve 0.6÷3.89
    15·1 answer
  • Solve for N<br><br><br><br><br><br><br><br> Thanks!!!!!!!!!!!!!!!!
    14·1 answer
  • Simultaneous equations<br>x+y=5<br>x squared-y squared=15​
    9·2 answers
  • Write the phrase as a numerical expression; the product of 5 and 7
    14·1 answer
  • Dave's father is paying him to paint the storage
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!