The major axis of the eclipse is 12 units long
The given parameters can be represented as:
See attachment for illustration
To solve this question, we make use of the following theorem
The distance between a point and the foci sums up to the major axis
This translates to:
First, simplify
to
/ Your problem should look like:
Second, simplify
to
/ Your problem should look like:
Third, multiply both sides by 12 (the LCM of 3 and 4) / Your problem should look like:
Fourth, subtract 2 from both sides. / Your problem should look like:
Fifth, simplify -9x + 12 - 2 to -9x + 10. / Your problem should look like:
Sixth, add 9x to both sides. / Your problem should look like:
Seventh, add 8x + 9x to get 17x. / Your problem should look like:
Eighth, divide both sides by 17. / Your problem should look like:
Answer as fraction: x =
Answer as decimal: x = 0.5882
Let’s say, hypothetically speaking, you chose the second marble without replacing the first marble so, events are hypothetically dependent. Events are dependent if the occurrence of one hypothetical event hypothetically does affect the likelihood that the other events occur. The probably of two or more dependent events A and B is the probability of A times the probability of B after A hypothetically occurs
P(A and B) = P(A) x P(B after A)
Choose the first marble
The total number of hypothetical marbles are, hypothetically speaking, 4 on a hypothetical basis, and there is one red marble.
P(red)=1/4
Choose the second marble
Without hypothetically replacing the hypothetical first marble, you choose the hypothetical marble, hypothetically speaking. So, the total hypothetical number of marbles are, hypothetically, 3, and there is, hypothetically, one green marble.
P(green) = 1/3
The probability of choosing red and then, hypothetically, green is:
P(red and green) = P(red) x P(green)
=1/4 x 1/3
= 1/12
P(red and green) is hypothetically equal to 1/12 on a hypothetical account.
Final hypothetical answer: 1/12
