**Answer:**

So, the expected value of the time it takes to commute is **16 minutes.**

**Step-by-step explanation:**

Let X is time it takes you to commute. We calculate E(X)?

We know that the probability that you will have to wait for a train is 1/5, or .20. If you don’t have to wait, the com mute takes 15 minutes, but if you have to wait, it takes 20 minutes.

The probability that you will have to wait for a train is
:

The probability of not waiting for a train is:

So we get the following probability distribution:

We calculate E(X):

So, the expected value of the time it takes to commute is **16 minutes.**

Expected value is not always the actual travel time, because it can sometimes take anywhere from 15 to 20 minutes.

Answer:

x=35; y=55; z=55

Step-by-step explanation:

x+y=90; z+x=90

z+35=90

z=90-35= 55

x=90-55= 35

y= 90-35 =55

**Answer:**

(x+6)(x-2)

**Step-by-step explanation:**

you need to find 2 numbers with a sum of 4 and a product of -12, which is 6 and -2, then you factor it out.

The length would be 5 miles

**Answer:**

3.42857143

**Step-by-step explanation:**

You multiply 4/7 by 6 to isolate the variable