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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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Which ordered pair is generated from the equation shown below? y = 2x + 4 A. (1, 6) B. (1, 2) C. (3, 6) D. (8, 16)
USPshnik [31]

Answer:

The ordered pair generated from the equation is (1, 6).

Step-by-step explanation:

An ordered pair is a pair of numbers, representing two variables, in a specific order. For instance, (<em>x</em>, <em>y</em>) = (1, 2) here <em>x</em> = 1 and <em>y</em> = 2.

The equation provided is:

y=2x+4

Check for all the options:

  • A (1, 6): y=2x+4\Rightarrow\ 6=(2\times 1) +4\Rightarrow\ 6=6
  • B (1, 2): y=2x+4\Rightarrow\ 2=(2\times 1) +4\Rightarrow\ 2\neq 6
  • C (3, 6): y=2x+4\Rightarrow\ 6=(2\times 3) +4\Rightarrow\ 6\neq10
  • D (8, 16): y=2x+4\Rightarrow\ 16=(2\times 8) +4\Rightarrow\ 16\neq20

Thus, the ordered pair generated from the equation is (1, 6).

8 0
3 years ago
HELP QUICK 30 POINTS!!
vlada-n [284]

Answer:

B

Step-by-step explanation:

For answer A it is stretching the graph of function f by a factor of 15.

For answer C and D it is changing the function itself and that is not what the question is asking.

5 0
3 years ago
Read 2 more answers
F(x)=-3x+21,find x when f(x)=6
balu736 [363]

Answer:

x=5

Step-by-step explanation:

F(x)=-3x+21,

f(x)=6 = -3x+21

6 = -3x+21

Subtract 21 from each side

6-21 = -3x+21-21

-15 = -3x

Divide each side by -3

-15/-3 = -3x/-3

5 = x

6 0
3 years ago
What is the solution set for the inequality?
Sliva [168]

Answer:

the answer is the 2nd one from my point of view u will understand so the solution set for the quality is the 2nd answer either way or

3 0
3 years ago
HELPP!!!! 100 points. Which expression is equivalent
devlian [24]

Answer:

\Large \boxed{\sf A}

Step-by-step explanation:

\displaystyle 2x\sqrt{44x}-2\sqrt{11x^3}

Let<em> x</em>  = 2 because x > 0

\displaystyle 2(2)\sqrt{44(2)}-2\sqrt{11(2)^3}=4\sqrt{22}

See which expression is equal to 4√22 when <em>x</em> = 2

2(2)\sqrt{11(2)}=4\sqrt{22}

The expression is option A

8 0
2 years ago
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