Answer:
We have been given a unit circle which is cut at k different points to produce k different arcs. Now we can see firstly that the sum of lengths of all k arks is equal to the circumference:

Now consider the largest arc to have length \small l . And we represent all the other arcs to be some constant times this length.
we get :

where C(i) is a constant coefficient obviously between 0 and 1.

All that I want to say by using this step is that after we choose the largest length (or any length for that matter) the other fractions appear according to the above summation constraint. [This step may even be avoided depending on how much precaution you wanna take when deriving a relation.]
So since there is no bias, and \small l may come out to be any value from [0 , 2π] with equal probability, the expected value is then defined as just the average value of all the samples.
We already know the sum so it is easy to compute the average :

Answer:
B. (see attached)
Step-by-step explanation:
All the answers agree that the function is x² for x < 1. Where they disagree is in the slope and y-intercept of the linear portion for x > 1.
The line has a slope that is less than 1 unit of rise for 1 unit of run, so will not be selections A or C, which have slopes of 3.
The y-intercept is clearly positive if we extend the line to the left until it reaches the y-axis. This eliminates selection D from consideration, leaving only selection B.
Answer:
B: 6.0
Step-by-step explanation:
-3t^2+9t+54 = 0
This is the equation that needs to be solved
Divide both sides by -3
t^2 - 3t - 18 = 0
The factors of 18 are: (1 18) (2 9) (3 6)
3 - 6 = -3 and 3 x -6 = -18
So: (t + 3) (t - 6) = 0
t = -3, 6
It can't be negative so the answer is 6
Answer:
a-2/3b
Step-by-step explanation:
If we draw in OX, OY, OZ we have two congruent right triangles, right angles at the tangent points.
We know XOZ is 132 degrees, which is the meaning of the arc measure
So YOX is half that, 66 degrees.
That leaves 180 - 90 - 66 = 24 degrees for OYX
Angle Y aka XYZ is double that, 48 degrees.
Answer: C