Suppose a CD you just purchased has 15 tracks. After listening to th.pdf

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Solve triangle ABC. (Round the length to three declmal places and the angles to one decimal place.) 13 21 120 Need Help?W Need Help? WacTalk tos Tutor Save Progress Another Version 28. O-1.65 points STrig2 3.6.012 Solve triangle ABC. (Round your answers to one decimal place.) 4B 12 40 41 Solution 1) let b = 13, a= 21 length AB = c = ? angle C = 120 degree from law of cosine: c2 = b2 + a2 -2 *b*a* cos C c2 = ( 13)2 + ( 21)2 - 2*13*21*cos ( 120) c = 29.715 units from law of sine: sin A / a = sin B/b = sin C/c from sin A/ a = sin C/c sin A = ( a/c)* sin C sin A = ( 21 / 29.715) * sin ( 120) sin A = 0.6120 A = sin-1 ( 0.6120) = 37.7 degree B = 180 - A - C B = 180 - 37.7 - 120 = 22.3 degree ------------------------------------------------------ 2) let b = 12 a = 40 c = 41 from law of cosine: cos C = a2 + b2 - c2 / 2*a*b = 402 + 122 - 412 / ( 2*40*12) cos C = 0.0656 C = 86.2 degree cos A = b2 + c2 - a2 / 2*b*c = 122 + 412 - 402 / ( 2*12*41) cos A = 0.2286 A = 76.8 degree B = 180 - 86.2 - 76.8 = 17.0 degree.

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Suppose a CD you just purchased has 15 tracks. After listening to the CD you decide that you
like 2 of the songs. With the Random Feature on your CD player, each of the 15 songs is played
once in Random Order. Find the probability that among the first two songs played:
A. You like both of them.
Would this be unusual?
B. You like neither of them.
C. You like exactly one of them.
D. Redo A-C if a song can be replayed before all 15 songs are played.
ROUND TO THREE DECIMALS AS NEEDED
Solution
a) there are 15 songs and you like 2 of them. The probability the first is a song you like is 2/15.
Assuming that happens, there are now 14 songs, 1 of which you like. The probability the next is
a song you like is 1/14. . The probability both are songs you like is
(2/15)*(1/14) =0.0095
Yes it is unusual.
b) p = (13/15)*(12/14) = 0.743
c) p= (1/15)*(13/14) + (13/15)*(2/14) = 0.062 + 0.124 = 0.0186
d) both:
(2/15)*(2/15) =0.0178
Neither:
p = (13/15)*(13/15) = 0.751
Exactly one :
p= (2/15)*(13/15) + (13/15)*(2/15) = = 0.2311

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