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
Express as a single fraction a/b+b/b - b/a-a/a​
Harrizon [31]

Answer:

a exponent 2-b exponent 2

ab

5 0
3 years ago
How many 1-centimeter squares fit along the length of the rectangle
Damm [24]
It would depend on how large the rectangle is
4 0
2 years ago
Is my answer A or d??
alexira [117]

Answer:

d

Step-by-step explanation:

The answer must have a negative slope because the graph is decreasing.

The y-intercept is 10. The equation must have +10 at the end.

y = -3x + 10

8 0
3 years ago
Please answer the question. ​
GalinKa [24]
Answer: x = 11

Explanation: if u want more math questions just ask me ok
5 0
2 years ago
Read 2 more answers
Find the length of an arc made by a 180-degree central angle in a circle with a 10ft radius
mixas84 [53]

Answer:

the length of an arc = 10π ft.

Step-by-step explanation:

The length of an arc with angle Θ and radius r will be equal r * Θ

note the angle must be in radian

Given: Θ = 180° = π  and radius = r = 10 ft.

<u>So, the length of the arc = π * 10 = 10π ft.</u>

8 0
3 years ago
Other questions:
  • If you horizontally compress exponential function f(x)=2^x by a factor by a of 5, which of these is the equation of the new func
    11·2 answers
  • Activity
    11·1 answer
  • Which is greater 5/6 or 83%
    11·1 answer
  • The mean sustained wind velocity, v, can be determined by the equation , where p is the air pressure, in millibars, at the cente
    15·2 answers
  • If all the dimensions of a triangle are doubled,the area of the triangle will be doubled,too
    12·2 answers
  • What is the area of the figure in square feet
    11·1 answer
  • What is the value of “y” in y = -3x if the value of ‘x’ is 2?
    5·1 answer
  • PLEASE HURRY! i’ll give brainliest
    5·1 answer
  • Solve the system of linear equations 3x-2y=1 9x-6y=1​
    9·1 answer
  • Which expression is equivalent to this polynomial? 4x^2 + 27
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!