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<h3>Answer: Angle 1 is 80 degrees</h3>
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Explanation:
See the diagram below. I've extended one of the rays to form a full line. This is shown in red. The alternate interior angles 60 and x are congruent due to the parallel lines, so x = 60.
We can then find angle y
x+y+20 = 180 ... angles of a triangle add to 180
60+y+20 = 180
y+80 = 180
y = 180-80
y = 100
Use this to find z
y+z = 180
100+z = 180
z = 180-100
z = 80
Or you could use the remote interior angle theorem
x+20 = z
60+20 = z
80 = z
z = 80
Answer:
He wont foul out with probability 0.9093
Step-by-step explanation:
The total number of fools he picked is a Binomial ditribution noted by X with parameters p = 0.05 and N = 48. The mean of this random variable is μ = np = 48*0.05 = 2.4 and the variance is σ² = np(1-p) = 2.4*0.95 = 2.28, hence its standard deviation is σ = √2.28 = 1.51.
Note that, if approximate probability is asked, we could just approximate X with a Normal random variable with mean 2.4 and standard deviation 1.51 (this can be done because of the central limit theorem). We will calculate the probability manually. He wont foul out if he picks 0,1,2,3 or 4 fouls, thus
As a consecuence, he wont foul out with probability 0.9093.