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# intersections, primes

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(1) What is the greatest number of points of intersection that can occur when 2 different circles and 2 different straight lines are drawn on the same piece of paper?

(2) Let p be a prime number between 40 and 60. What is the probability that p+12 is also a prime number? Express your answer as a common fraction

tertre  Dec 3, 2017
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### 2+0 Answers

#1
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(1)  I believe the answer to this is 11

The circles can intersect  at 2 points

Each line can intersect each circle twice  = 8 points

And as long as the lines do not intersect at any of the other points, they can intersect at 1 additional point

(2) Primes between 40 and 60  are

41  , 43 ,  47,  53 , 59

And  adding 12 to these  =

53 , 55 , 59, 65 , 71

And  3 out of the 5 are prime  [ 53, 59, 71 ]

So....the probability that p + 12 is prime is   3 / 5

CPhill  Dec 3, 2017
#2
+1609
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thanks so much!

tertre  Dec 3, 2017

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