"jimi has 5000 songs on his ipod shuffle, which picks songs uniformly at" random. jimi plans to listen to 100 songs today. what is the chance he will hear at least one song more than once?

  about 63.1%

Step-by-step explanation:

For the first song, it is certain it isn't a duplicate. For the second song, the probability that it is not a duplicate is 4999/5000. The probability the third song is not a duplicate is 4998/5000.

Hence the probability that none of the 100 songs is a duplicate is ...

  5000!/4900!/5000^100 ≈ 0.369120

Then the probability that one or more is a duplicate is ...

  1 - 0.369120 ≈ 0.630880

341

step-by-step explanation:

all you have to do is 9x31 (which equals 279) and then 20x31 (which equals 620). then you have to subtract. 620-279=341.

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b