Answer:
To practice for a competition, Jasmine swam in those 4 weeks a total of
Step-by-step explanation:
Hi
First of all, we need to determine how many days did Jasmine went to the pool in total, so if we have , and if She has been going for 4 weeks, therefore
.
Then we use Jasmine's rate of practice .
So or
is the total distance swam by Jasmine in the four weeks.
You want to multiply two consecutive numbers, and see when you get a multiple of three.
Since two consecutive numbers share no divisors (except 1), either n or n+1 must be a multiple of 3.
So, your experiments succeeds if n is itself a muliple of three, or if lies immediately before one. So, 2 numbers out of 3 are ok.
Let me try to visualize the situation: I'll list some integers. Below, I'll write if they are multiple of three (M) or not (N). Above, I will write if they will cause the experiment to succeed (S), i.e. n(n+1) will be dibisible by 3, or to fail (F), i.e. n(n+1) will not be a multiple of three. We have
So, since there are exactly 99 numbers between 1 and 99, and 2/3 of the numbers work, the probability that you will choose a number n such that n(n+1) is divisible by 3 is 2/3.