Train A departs from Point A with a velocity of 100 km/h, Train B departs from Point B with a velocity of 200 km/h, and the dist
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Answer:
In the long run, ou expect to lose $4 per game
Step-by-step explanation:
Suppose we play the following game based on tosses of a fair coin. You pay me $10, and I agree to pay you $n^2 if heads comes up first on the nth toss.
Assuming X be the toss on which the first head appears.
then the geometric distribution of X is:
X geom(p = 1/2)
the probability function P can be computed as:
where
n = 1,2,3 ...
If I agree to pay you $n^2 if heads comes up first on the nth toss.
this implies that , you need to be paid
∵ X
geom(p = 1/2)
Given that during the game play, You pay me $10 , the calculated expected loss = $10 - $6
= $4
∴
In the long run, you expect to lose $4 per game
Answer:
B. m∠B = 118°, a = 17, c = 18
Step-by-step explanation:
The answer choices all agree on the values of ∠B and c, so we only need to compute the value of side a.
We can verify angle B is ...
∠B = 180° -30° -32° = 118°
By the law of sines, ...
a/sin(A) = b/sin(B)
Multiplying by sin(A), we get ...
a = b·sin(A)/sin(B) = 30·sin(30°)/sin(118°) ≈ 16.98855
a ≈ 17.0 . . . units . . . . . matches choice B
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If you like, you can also verify side c:
c = b·sin(C)/sin(B) = 30·sin(32°)/sin(118°) ≈ 18.00512
c ≈ 18.0 . . . units
For this case we have that by definition, the slope of a line is given by:
Two points are needed through which the line passes:
Substituting:
Rounding:
Answer: