Answer:
0 ≤ c ≤ 12
Step-by-step explanation:
The function can be rearranged to ...
p = 200c(12 -c) -4700
suggesting that revenue will be zero for a charge of 0 or for a charge of 12, and that fixed expenses are 4700. Charges less than 0 are uninteresting, and charges high enough to cause the number of customers to be negative also don't make any sense in this context.
Though out of the range of likely consideration, charges low or high enough to cause profit to be negative (more than 9.54, for example) seemingly can be reasonably modeled by this function.
Find the Greatest Common Factor of both numbers which is 5. Then divide the numerator by 5 and the denominator by 5 and you will get 5/16 as the simplest form

is a complex number that satisfies
![\begin{cases}r\cos x=-3\\[1ex]r\sin x=4\\[1ex]r=\sqrt{(-3)^2+4^2}\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dr%5Ccos%20x%3D-3%5C%5C%5B1ex%5Dr%5Csin%20x%3D4%5C%5C%5B1ex%5Dr%3D%5Csqrt%7B%28-3%29%5E2%2B4%5E2%7D%5Cend%7Bcases%7D)
The last equation immediately tells you that

.
So you have
![\begin{cases}\cos x=-\dfrac35\\[1ex]\sin x=\dfrac45\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%5Ccos%20x%3D-%5Cdfrac35%5C%5C%5B1ex%5D%5Csin%20x%3D%5Cdfrac45%5Cend%7Bcases%7D)
Dividing the second equation by the first, you end up with

Because the argument's cosine is negative and its sine is positive, you know that

. This is important to know because it's only the case that

whenever

. The inverse doesn't exist otherwise.
However, you can restrict the domain of the tangent function so that an inverse can be defined. By shifting the argument of tangent by

, we have

All this to say

So,

.
Answer:
66.6%
Step-by-step explanation:
The probability that it is blue or odd, would be the quotient between the marbles of these characteristics and the total number of marbles.
Now, we know that there are four blue marbles altogether. The odd ones, in the case of the red ones since there are eight, are the marbles 1,3,5,7 and in the blue ones the odd ones are not counted because they are already included as blue; therefore there are a total of four odd marbles. In total, between odd and blue there are eight marbles.
Which means that the probability is as follows, knowing that there are a total of 12 marbles:
8/12 = 0.666, that is, there is 66.6% chance that the marble that is drawn is blue or an odd number.