A fair, 12-sided die has numbers on each of its faces. There are three faces with a 1, three faces with a 2, one face with a 3, four faces with a 4, and one face with a 5.

What is the expected value when rolling this die?

2.75

Step-by-step explanation:

Let's start by making a frequency table. If there is one face, you have a 1/12 chance of getting the value--that's what the "frequency" column means.

Face                    Frequency

1                           3/12

2                          3/12

3                           1/12

4                           4/12

5                           1/12

Now to get E(X) we need to multiply each face by the frequency of it occuring and add all these together:

E(X) = 1(3/12) + 2(3/12) + 3(1/12) + 4(4/12) + 5(1/12)

      = 2.75

d

step-by-step explanation:

given

y + 3 = - 4(x - 2) ← distribute the parenthesis

y + 3 = - 4x + 8 ( subtract 3 from both sides )

y = - 4x + 5 → d