Prove: if n is a positiveinteger and n2 is
divisible by 3, then n is divisible by3.

If is divisible by 3, the n is also divisible by 3.

Step-by-step explanation:

We will prove this with the help of contrapositive that is we prove that if n is not divisible by 3, then, is not divisible by 3.

Let n not be divisible by 3. Then can be written in the form of fraction , where x and y are co-prime to each other or in other words the fraction is in lowest form.

Now, squaring

Thus,

It can be clearly seen that the fraction is in lowest form.

Hence, is not divisible by 3.

Thus, by contrapositivity if is divisible by 3, the n is also divisible by 3.

1 and 2

step-by-step explanation:

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation: