Triplets adam, bruce, and charlie enter a triathlon. if there are 9 competitors in the triathlon and medals are awarded for first, second, and third place, what is the probability that at least two of the triplets will win a medal?

Probability that at least two of the triplets will win a medal is19/24

Step-by-step explanation:

Total number of cmpetitors=9

Total number of selecting 3 winners out of 9 competitors=9C3=84

Number of ways of selecting 2 out of 3 triplets=3C2

Number of selecting 1 out of 6 others =6C1

Number of selecting 2 out of 3 triplet and o1 out of 6 others= 3C2 ×6C1=18

Number of selecting 3 out of 3 triplets=3C3=1

Total ways of selecting less than 2 or 2 triplets= 18+1=19

Probability that at least 2 of the triplets will win is 19/84

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

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step-by-step explanation:

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