Which of the following pairs of events are mutually exclusive? Rolling a die; A={Rolling an even number}, B={Rolling a number greater than 4} Picking a card; A= {Selecting a 7}, B={Selecting a Heart} Tossing a coin twice; A ={no Heads}, B={at least 1 Head} Rolling two 6-sided dice; A={rolling a sum of 4}, B={rolling a 3 on one die}

Tossing a coin twice; A ={no Heads}, B={at least 1 Head}

Step-by-step explanation:

Mutually exclusive:

If two events are mutually exclusive, if one events happen, the other cannot happen, and vice-versa.

Rolling a die; A={Rolling an even number}, B={Rolling a number greater than 4}

A die has the following outcomes: 1,2,3,4,5,6

Even numbers: 2,4,6

Greater than 4: 5, 6

6 is an outcome of both events A and B, so they are not mutually exclusive.

Picking a card; A= {Selecting a 7}, B={Selecting a Heart}

Cards numbered from 1 to 13, each number with 4 types. So we can have a card of hearts numbered 7, which means that these events are not mutually exclusive.

Tossing a coin twice; A ={no Heads}, B={at least 1 Head}

If you get no heads, the probability of at least 1 head is 0.

If you get at least 1 head, the probability of no heads is 0.

This means that this is the answer, that is, these events are mutually exclusive.

Rolling two 6-sided dice; A={rolling a sum of 4}, B={rolling a 3 on one die}

(3,1) or (1,3) has a sum of 4 and a 3 on one die, which means that these events are not mutually exclusive.

no one knows lol

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