There are 7 people taking part in a raffle. Ann, Bob, Elsa, Hans, Jim, Kira, and Omar.
Suppose that prize winners are randomly selected from the 7 people.
Compute the probability of each of the following events.

Event A: Hans is the first prize winner, Elsa is second, Ann is third, and Jim is fourth.

Event B: The first four prize winners are Elsa, Omar, Bob, and Ann, regardless of order.

Write your answers as fractions in simplest form.

1/4 or 2/4

Step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

- both graphs increase on their domain.

- the graphs of both functions have the same x-intercept.

- neither graph has a y-intercept.