Write <em>z</em> in polar form:
<em>z</em> = 1 + √3 <em>i</em> = 2 exp(<em>i</em> <em>π</em>/3)
Taking the square root gives two possible complex numbers,
√<em>z</em> = √2 exp(<em>i</em> (<em>π</em>/3 + 2<em>kπ</em>)/2)
with <em>k</em> = 0 and <em>k</em> = 1, so that
√<em>z</em> = √2 exp(<em>i</em> <em>π</em>/6) = √(3/2) + √(1/2) <em>i</em>
and
√<em>z</em> = √2 exp(<em>i</em> 7<em>π</em>/6) = -√(3/2) - √(1/2) <em>i</em>
Answer:
The spinner has 6 equal-sized slices, so each slice has a 1/6 probability of showing up.
I guess that we want to find the expected value in one spin:
number 1: wins $1
number 2: wins $3
number 3: wins $5
number 4: wins $7
number 5: losses $8
number 6: loses $8
The expected value can be calculated as:
Ev = ∑xₙpₙ
where xₙ is the event and pₙ is the probability.
We know that the probability for all the events is 1/6, so we have:
Ev = ($1 + $3 + $5 + $7 - $8 - $8)*(1/6) = $0
So the expected value of this game is $0, wich implies that is a fair game.
Answer:
1/6 is your answer :))
Step-by-step explanation:
There is 1 four out of 6 possible numbers = 1/6
Cos(angle) = adjacent/hypotenuse
Cos(angle) = 1.5/10
Angle = arccos(1.5/10)
Angle = 81.37 degrees
Although the angle is close, it is over the 80 degrees, so the inspector should be concerned.
