Here are 5 red marbles, 8 blue marbles, and 12 green marbles in a bag.

what is the theoretical probability of randomly drawing a red marble?

Probability of randomly drawing a red marble is

Step-by-step explanation:

Given 5 red marbles, 8 blue marbles, and 12 green marbles in a bag. we have to find the 5 red marbles, 8 blue marbles, and 12 green marbles in a bag.

As Probability of an event  is the chances of an event to occur. It is defined as the favourable outcomes by total number of outcomes.

As no. of red marbles are 5 and

Total number of marbles are 5+8+12=25 marbles.

Hence, probability of randomly drawing a red marble is

the correct answer is 5 6 and 7

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