I got 15 problems i had to do for homework and i have been able to do about seven of them but i need some pointers on the others
1) What is the probablity that a 10 inch stick which has been broken at two random places falls into three pieces, none of which is more than 5 inches long. It had an example, if the breaks are at 4.3 inches and 8 inches the pieces have lengths 4.3 3.7 and 2.0? If it can break into decimal places there could be an infinate amount of possiblities couldn't there?
2) Find all integers n> 3 that n-3 divides evenly into n^2 -n. Now is there any easy way to solve this because it seems to me that there could be a massive amount of possiblities?
3) How many numbers from 1 to 100 inclusive can be written as the sum of two or more consecutive integers. Now so far i have gotten 3,5,6,7,9,10,11,12,13,14,15, and i can't really find a pattern, is there any way to do this besides just going number by number?
4) Find the pime factors of 2^22 +1. I have only found one and i'm not 100% sure it is prime, 838861.
5) One solution of a(b-c)x^2 + b(c-a)x + c(b-a) = 0 is x=1 for some fixed real numbers a,b,and c. What is the other solution for x. I'm not sure about this one if someone could just point me in the right direction.
6)A team of six students are traveling by bicycle. On leaving they drstractedly picked up their six helmets at random. What is the probabilty thast exactly three of the students picked up the correct helmet.
7) In each of the 999 fractions 1/1997, 2/1996, 3/1995..., 999/999 the sum of the numerator and the denominator is 1998. How many of these fractions are irreducible. Now i have tried this one for the first 20 fractions and i can't find a pattern how would you do this without going through them all.
8) Find all the ordered pairs of integers (a,b) such that a+b =ab. Now this one the only answer i can come up with is (2.2). Are there any others?
1) What is the probablity that a 10 inch stick which has been broken at two random places falls into three pieces, none of which is more than 5 inches long. It had an example, if the breaks are at 4.3 inches and 8 inches the pieces have lengths 4.3 3.7 and 2.0? If it can break into decimal places there could be an infinate amount of possiblities couldn't there?
2) Find all integers n> 3 that n-3 divides evenly into n^2 -n. Now is there any easy way to solve this because it seems to me that there could be a massive amount of possiblities?
3) How many numbers from 1 to 100 inclusive can be written as the sum of two or more consecutive integers. Now so far i have gotten 3,5,6,7,9,10,11,12,13,14,15, and i can't really find a pattern, is there any way to do this besides just going number by number?
4) Find the pime factors of 2^22 +1. I have only found one and i'm not 100% sure it is prime, 838861.
5) One solution of a(b-c)x^2 + b(c-a)x + c(b-a) = 0 is x=1 for some fixed real numbers a,b,and c. What is the other solution for x. I'm not sure about this one if someone could just point me in the right direction.
6)A team of six students are traveling by bicycle. On leaving they drstractedly picked up their six helmets at random. What is the probabilty thast exactly three of the students picked up the correct helmet.
7) In each of the 999 fractions 1/1997, 2/1996, 3/1995..., 999/999 the sum of the numerator and the denominator is 1998. How many of these fractions are irreducible. Now i have tried this one for the first 20 fractions and i can't find a pattern how would you do this without going through them all.
8) Find all the ordered pairs of integers (a,b) such that a+b =ab. Now this one the only answer i can come up with is (2.2). Are there any others?
