Answer: d
Step-by-step explanation:
The probability of not being purple is the probability of the three other colors. Suppose the number of purple marbles is x. Then we have 20+30+40+x = 90 + x marbles. Then the probability of not being purple is 90/(90+x). If this fraction can have a lowest term for some value of x, then the numerator of this lowest term must be a factor of 90.
Checking through the options, only option D has a non-factor of 90 as its numerator.
For this case we have that the commutative property establishes that the order of the factors does not alter the product. Example:

Then we have the following options illustrate the property:

It is necessary to emphasize that option b illustrates the associative property and in option c equality is not fulfilled
Answer:
Option A, D, E, F
That it has the highest y-intercept of all of the three linear functions.
(and that the question could be worded better, but don't put that in your answer)
Answer:
sin(π/8) = (1/2)√(2-√2)
Step-by-step explanation:
Using the half-angle formula ...

We can let θ = π/4 and simplify the result as follows:

About 8:00 is when they will all have met up ram will have ran 4 laps raju will have ran 3 laps and ravi will have ran 2 laps