Answer:
The casino should charge for this game at least $1 to break even.
Step-by-step explanation:
We can define the prize function as
where M is the prize money and n is the number of tails in continous flips.
The probability of n consecutive tails can be calculated as 
. The probaility of getting a head after the n consecutive tails is 
, so the probability of having n consecutive tails and a head is 
Then we can calculate the expected value of M as
The expected money prize for this game is $1, so the casino should charge to play at least $1 to break even.
Answer:
7, -3/4, -3
Step-by-step explanation:
Note that all three of the given functions are linear. We can read the slopes directly from these functions: 7, -3/4, -3. Between any two values of x, the slope is exactly the same in each of these three functions.
Thus,
1) the average rate of change of f(x) = 7x - 4 over the interval [2,4] is 7.
2) the average rate of change of g(x) over the given interval is -3/4.
3) the average rate of change of h(x) over the given interval is -3.
Parts a and b are straight-forward. You add them in part a: 4x + 9 + 3x - 5 and you get 7x + 4. For part b, you are multiplying them (4x + 9)(3x - 5) by FOILing them:
which simplifies to
The last one is a composite; you are told to find a of b of x. The way you do that is to take your inside function and put that whole function into the other function every place you see an x, like this:
a(b(x))= 4(3x-5) + 9. Now distribute the 4 into the parenthesis to get 12x - 20 + 9, which simplifies to 12x - 11. And that's it!
6.4 *10^-1
6.4 times ten to the negative one, or divided by 10
