Find the 52nd term of the arithmetic sequence -8 -12 -16
1 answer:
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Answer:
Step-by-step explanation:
The problem states that there are only two types of busses - M104 and M6 with probable occurence of 0.6 and 0.4 respectively.
If the average number of busses arriving per hour is λ, the average number of M6 busses per hour is 0.4λ
Now consider a set of 3 M6 busses as an event. The average number of such events per hour will be
μ = 0.4λ / 3
The expected number of hours for the event "THIRD M6 arrives", let's say X is
E[X] = 1 / μ ( exponential distribution) = 3 / 0.4λ
= 7.5 / λ
The variance of event X is =
Answer:
Step-by-step explanation:
Begin by squaring both sides to get rid of the radical. Doing that gives you:
Now use the Pythagorean identity that says
and make the replacement:
. Now move everything over to one side of the equals sign and set it equal to 0 so you can factor:
and then simplify to
Factor out the common cos(x) to get
and there you have your 2 trig equations:
cos(x) = 0 and 1 - cos(x) = 0
The first one is easy enough to solve. Look on the unit circle and see where, one time around, where the cos of an angle is equal to 0. That occurs at
The second equation simplifies to
cos(x) = 1
Again, look to the unit circle and find where the cos of an angle is equal to 1. That occurs at π only.
So, in the end, your 3 solutions are