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ELEN [110]
2 years ago
5

Find with proof the minimum possible k such that every subset of f1; 2; : : : ; 2022g of size k must contain at least two elemen

ts a; b such that a < b and b is a multiple of a.
Mathematics
1 answer:
Helga [31]2 years ago
6 0

Answer:

Minimum possible K = 307

Step-by-step explanation:

Attached below is the detailed solution

Given set { 1, 2 , .......... 2022 }

The largest subset will contain prime numbers because they are not multiples of any number but 1

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The ratio of boys to girls in a class is 5 to 6 which is an equivalent. Ratio
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3x - 7 = 3x + 9; x =<br><br> Please can someone help me and show me the answers step by steps
anyanavicka [17]

Answer:

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2 years ago
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Which of the following is the quotient of the rational expressions shown below?
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The answer is D

Step-by-step explanation:

8 0
3 years ago
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Caden states that n^2 +3n + 2n is an equivalent expression to 6n. Why is Caden's statement incorrect?
malfutka [58]
\begin{gathered} \text{The simplification of n}^2+3n+2n\text{ is:} \\ i)n^2+5n \\ By\text{ collecting common term, this can be written in form of:} \\ ii)\text{ n(n+5)} \end{gathered}

Thus, options A and D hold, from the simplifications above.

Let's consider the validity of the remaining options provided.

\begin{gathered} \text{For option B)} \\ \text{substitute for n=1 into the expression n}^2+3n+2n,\text{ we have} \\ 1^2+3(1)+2(1)=1+3+2=6 \\ \text{substitute for n=1 into the expression 6n, we have} \\ 6(1)=6 \\ \text{Thus, the expression n}^2+3n+2n\text{ is equivalent to 6n, for n=1} \end{gathered}\begin{gathered} \text{For option C)} \\ \text{The expression n}^2+3n+2n\text{ does not simplify to 7n} \end{gathered}\begin{gathered} \text{For option E)} \\ \text{substitute for n=4 into the expression n}^2+3n+2n,\text{ we have:} \\ 4^2+3(4)+2(4)=16+12+8=36 \\ \text{substitute for n=6 into the expression 6n, we have:} \\ 6(4)=24 \\ \text{Thus, the two(2) expressions are not equivalent to each other, for n=4} \end{gathered}\begin{gathered} \text{For option F)} \\ \text{substitute for n=3 into the expression n}^2+3n+2n,\text{ we have:} \\ 3^2+3(3)+2(3)=9+9+6=24 \\ \text{substitute for n=3 into the expression 6n, we have:} \\ 6(3)=18 \\ \text{Thus, the two(2) expressions are not equivalent to each other, for n=3} \end{gathered}

Hence, the correct options that apply are options A, D, E and F

7 0
10 months ago
A circle and a square can intersect at how many points
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If the radius of the circle is smaller than 1/2 the side length of the square and the center is as described above, there are no points of intersection.

If the circle is located outside the square it can have 1 tangent point or 2 intersection points depending on the location conditions of the circle in relation to the square.

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3 years ago
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