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3 years ago

Is the answer a, b, c, or d

Mathematics

2 answers:

Sveta_85 [38]3 years ago

3 0

Answer: 30

Step-by-step explanation:

Yuliya22 [10]3 years ago

3 0

Answer:

30°

Step-by-step explanation:

360° : 12 = 30°

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3 years ago

Five point six times four point eight

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Answer:

26.88

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3 years ago

Problem number 26 of the Rhind Papyrus says:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

Pigeon Hole Principle :

yaroslaw [1]

Answer:

A proof can be as follows:

Step-by-step explanation:

Let $S=\{a_{1},a_{2},...,a_{n},a_{n+1}\}$ be a set of $n+1$ integers. By the division algorithm the possible remainders when we divide by $n$ are $0,1,2,....,n-1$ . Then, each integer $a_{i}\in S$ can be written as:

$a_{i}=np_{i}+r_{i},\,\,0\leq r_{i}$

Observe that the set of remainders $\{r_{1},r_{2},...,r_{n+1}\}$ has $n+1$ elements and each element has $n$ possible values. By the Pigenhole principle at least two remainders have the same value. Suppose that this two elements are $a_{i}, a_{j}$ . Then,

$\begin{array}{c}a_{i}=np_{i}+r\\a_{j}=np_{j}+r\end{array}$

Where $r_{i}=r_{j}=r$ . Then, $a_{i}-a_{j}=np_{i}-np_{i}=n(p_{i}-p_{j})$ . Then we have that $n$ divides $a_{i}-a_{j}$ .

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3 years ago