Answer:
Check the explanation
Step-by-step explanation:
Let 
be the indicator random variable that takes the value 1 if the ith coin is the first coin in a sequence of 19 consecutive heads.
For any sequence of length 19, the starting coin can be from toss i ,
such that i is between 1 and n - 19+1
Thus the number of such sequences is
Kindly check the attached image below for the step by step explanation to the question above.
2 equations: the first one is the sum of 2 unknown numbers x and y: x + y = 72. Now the difference is 25, so x - y = 25. Solve the first equation for y: y = 72 - x. Sub that into the second equation to solve for x: x - (72 - x) = 25. x - 72 + x = 25 and 2x - 72 = 25. Therefore, 2x = 97 and x = 48.5 That's the larger of the 2 numbers; since we subtracted y from x we defined x as the larger of the 2. Just for fun, plug x in to find that y = 23.5
If you flipped the graph y=x^2+2x-2 vertically, you would get the graph y=-(x^2+2x-2) this is True.
