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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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Use the substitution method to find the solution for the system of equations. Write the answer as an ordered pair. 3x+2y=23 (1/2
mario62 [17]

Answer:

x = 7.75       y = -0.125

Step-by-step explanation:

3x + 2y = 23                         1/2x - y = 4

2(1/2x - y) = (4)2                   1x - 2y = 8

    3x + 2y = 23

+   1x - 2y = 8

4x = 31

x = 7.75

3(7.75) + 2y = 23

23.25 + 2y = 23

2y = -0.25

y = -0.125

8 0
3 years ago
Bev earns $2 a week for taking out her neighbor’s trash cans. Complete the table of values. Then state the domain and range.
Eduardwww [97]

Domain : \{1,2,3,4\}

Range: \{2,4,6,8\}

Explanation:

It is given that Bev earns $2 a week.

Thus, for n number of weeks, we shall multiply $2 with n.

Where n=1,2,3,4 is the number of weeks.

For 1 week, Bev earns 2n=2(1)=2 ⇒ $2

For 2 weeks, Bev earns 2n=2(2)=4 ⇒ $4

For 3 weeks, Bev earns 2n=2(3)=6 ⇒ $6

For 4 weeks, Bev earns 2n=2(4)=8 ⇒ $8

Thus, we can see that the domain is the number of weeks.

Hence, Domain : \{1,2,3,4\}

Also, the money earned is the range.

Hence, Range: \{2,4,6,8\}

6 0
3 years ago
5p + 3 = 15<br>please make this into a word problem​
Pani-rosa [81]

Answer:

p equals two and four tenths

Step-by-step explanation:

First let's write our equation

five p plus three equals fifteen

<h3>Subtract three from both sides</h3><h3 />

five p equals twelve

divide both sides by 5

p equals two and four tenths

_______________________________

Word Problem

You bought 5 pears that were worth x dollars, you have an extra 3 dollars, the total of the money you spent and you have is 15 dollars. How much does one pear cost?

4 0
3 years ago
I don't understand this question. can someone help?
ss7ja [257]
Sure I can help you.

First and foremost, your graph shows that the slope is 0 since the equation of this graph is y= 4. We can also say that whatever the input is, it will always give you the same output. Therefore the output is just the same all through out.

Hope this helps !

Photon
3 0
3 years ago
Find GCF of 40 and 120​
vagabundo [1.1K]

Answer:

Hi there!

<h2>Find the GCF of 40 and 120</h2>

  • The GCF of 40 and 120 is 40

40 ÷ 40 = 1

120 ÷ 40 = 3

<h3>Hope its help!</h3>
5 0
2 years ago
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