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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 school has 300 students.If the ratio of boys to girls is 31 to 44, how many more girls are there in the school?
garri49 [273]

Answer:

there would be 52 more girls I think

Step-by-step explanation:

let x = multiplier then

31x =number of boys

44x = number of girls

Boys + girls = 300

44x + 31x =300

75x = 300

x = 300/75

x = 4 is the multiplier

therefore:

44*4 = 176 girls

31*4 = 124 boys

dif = 52 more girls than boys

hope this helped :)

5 0
2 years ago
Fractions : $1,000 <br><br> 1/4. <br><br> Someone plz help
olga2289 [7]

Not 100% sure exactly what you’re asking, but if you are asking what is 1/4 of $1,000, all we need to do to find the answer is <u>divide</u> $1,000 by the <u>denominator</u> of the fraction which is <u>4</u>

$1,000 ÷ 4 = $250

Therefore, 1/4 of $1,000 is $250


Hope this helps you

-AaronWiseIsBae

8 0
3 years ago
Which are correct representations of inequality 6x&gt;3+4(2x-1)
abruzzese [7]

The correct representations of inequality 6x>3+4(2x-1) will be 6x ≥ 3 + 8x – 4.Option B is correct

<h3>What is the definition of inequality?</h3>

Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.

The complete question is;

"Which are correct representations of the inequality 6x ≥ 3 + 4(2x – 1)? Check all that apply.

A)1 ≥ 2x

B)6x ≥ 3 + 8x – 4"

6x ≥ 3 + 4(2x – 1)

6x≥3+8x-4

The correct representations of inequality 6x>3+4(2x-1) will be 6x ≥ 3 + 8x – 4.

Hence, option B is correct

To learn more about inequity, refer to brainly.com/question/20383699

#SPJ1

4 0
2 years ago
Eva is 29 years old and has 2 children, ages 3 and 5.  She makes $48,500 a year.  Eva decides to buy a $400,000 10-year term pol
nirvana33 [79]
I believe it's A. <span>Eva would have been better off selecting the 20-year term policy.
Unde current circumtances, 10-year term policy wouldn't guarantee thesafety of the kids because even after the policy ends, Eva's kids still haven't entered the age where they could find their own income (they would be 12, 13, and 15).
If Eva decided to add another 10 year despite the extra charge, The kids will be covered until they enter the productive age.</span>
8 0
3 years ago
Read 2 more answers
Simplify.<br> 12<br> 24<br> A) 3<br> 2<br> B) 6<br> 2<br> C) <br> 1<br> 2<br> D) <br> 2<br> 2
AleksandrR [38]
12/24 simplifies to 1/2, seeing as 12 is half of 24. :) Your answer is C.
5 0
3 years ago
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