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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

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A friend of yours, a senior, took the Graduate Record Exam in September and scored in the 99th percentile. InFebruary, your frie
Alecsey [184]

Answer:

"differential selection"

Step-by-step explanation:

If your friend took the test twice and passed both times with a score above 90% then the minor difference in price is most likely due to "differential selection". The first test had  questions that he had a little more experience in solving, while the second time he was most likely given a couple questions that he wasn't as prepared for as he was the first time. This is most likely the cause for the difference in percentiles.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

3 0
2 years ago
0.000007 in standform
Murljashka [212]

Answer:

7.0 x 10 to the 6th

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
You have 88 grams of a radioactive kind of actinium. How much will be left after 44 years if its half-life is 22 years?
mash [69]

Answer:

22 grams

Step-by-step explanation:

loses 50% of it's mass per 22 years

so after 22 years the mass would be 44 grams

22 years later would leave 50% of 44 grams = 22 grams

3 0
2 years ago
I'LL GIVE BRAINLIEST FOR FASTEST CORRECT ANSWER AND YOU NEED TO EXPLAIN!!
Kazeer [188]

Answer + Explanation:

5 Cupcakes = $7.5.
How: First you see that 1 cupcake is $1.50. Multiply 5 by 1.50 and you get 7.50

18 Dollars = 12 Cupcakes
How: First you see that 1 cupcake is $1.50. Multiply 1.50 by numbers until you see 18.

18 Cupcakes = $27
How: First you see that 1 cupcake is $1.50. Multiply 18 by 1.50 and you get 27.


I Hope This Helped :D

6 0
1 year ago
Read 2 more answers
A signalized intersection has a cycle length of 60 seconds and an effective red time of 25 seconds. The effective green time is
alexandr402 [8]

Answer:

effective green time = 35 seconds

Step-by-step explanation:

given data

cycle length = 60 seconds

effective red time = 25 seconds

solution

we get here  effective green time that is express as

effective green time = cycle length  - effective red time   ...........................1

put here value and we will get

effective green time = 60 seconds - 25 seconds

effective green time = 35 seconds

3 0
3 years ago
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