The sum of 3 consecutive odd #s is 51 what are the 3#s?
2 answers:
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Answer:
A) He should take the route with 4 crossings
B) The probability that he took the 4 crossing route is 0.2158
Step-by-step explanation:
Lets call X the number of crossings he encounters, A if he takes route 1 and B if he takes route 2.
Note that X given A is a binomial random variable with parameters n = 4 p = 0.1, and X given B has parameters n = 2, p = 0.1
The probability that the Professor is on time on route 1 is equal to
P(X|A = 0) + P(X|A = 1) = 0.9⁴ + 0.9³*0.1*4 = 0.9477
On the other hand, the probability that the professor is on time on route 2 is
P(X|B = 0) = 0.9² = 0.81
Hence, it is more likely for the professor to be late on route 2, thus he should take the route 1, the one with 4 crossings.
B) Lets call L the event 'The professor is late'. We know that
P(L|A) = 1-0.9477 = 0.0524
P(L|B) = 1-0.81 = 0.19
Also
P(A) = P(B) = 1/2 (this only depends on the result of the coin.
For the Bayes theorem we know, therefore that
Hence, the probability that he took the 4 crossing route is 0.2158.
Using the apothem, a, and the perimeter, p, the area, A, of a regular polygon is
You need to calculate the area of the octagon and subtract the area of the square.
The perimeter is 8 times the side.
You need to calculate the area of the octagon and subtract the area of the square.
The perimeter is 8 times the side.
Answer:
Step-by-step explanation:
300 degrees is in the fourth quadrant (it's between 270 and 360); sine is negative in the fourth quadrant.
Given we're in the fourth quadrant, the reference angle is 360 - 300 = 60 degrees
sin(60°) =
And since sine is negative, this value turns negative:
sin(300°) =