Answer:
Let's start with one. This is a sin graph because at x = 0, the sinusoid isn't at a peak or trough(the tops and bottoms of the wave).
The equation becomes 0.5 sin(x) + 1.
The 0.5 comes from fact that the wave goes 0.5 above the middle and 0.5 below. the + 1 comes from the fact that the middle is at y = 1.
Second one now. A little harder to explain, but you can look up some stuff on probability and combinations to understand this better. This kind of question can be answered with a simple formula though:
[tex]\frac{n!}{k!}[/tex]
Where k is number of times any letter that repeats. For example, E repeats 3 times, so you'd have 3!. You have to do this for each letter. n is the number of letters. Thus with no restrictions:
[tex]\frac{15!}{2!3!}[/tex] = 108972864000 ways!
Might have miscounted, but I don't see any repeating letters other than E and N.
For part b of 2, try to divide up the problem into cases, so you can see where all the vowels are together.
I'll let someone else take over as I'm goona sleep now lol.
