Determine which of the following pairs of events are independent. a: a bird lands on your head. b: the bird lays an egg. a: a mosquito lands on your arm. b: you get a mosquito bite. a: a chicagoan visits new york on vacation. b: he visits central park. a: a green ball is drawn from a box with five balls and placed next to the box. b: a red ball is drawn next and placed next to the green one.

Independent events are those where event A is not dependent on event B. With changes is another event, the event does not change.

A: A bird lands on your head.

B: The bird lays an egg.

This is independent event as this does not have any correlation between them.

A: A mosquito lands on your arm.

B: You get a mosquito bite.

This is dependent as it is very much possible that a mosquito bites you when it sits on your arm.

A: A Chicagoan visits New York on vacation.

B: He visits Central Park.

This is also dependent event.

A: A green ball is drawn from a box with five balls and placed next to the box.

B: A red ball is drawn next and placed next to the green one.

Lets suppose both the times, balls are taken from the same box. So, this can also be dependent events. If these are from different boxes, then independent events.

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