Suppose that you arrive at a bus stop randomly, so all arrival times are equally likely. the bus arrives regularly every 30 minutes without delay (say, on the hour and on the half hour). what is the expected value of your waiting time? explain how you got your answer.

E(x) = 15 minutes

Step-by-step explanation:

The random variable X (waiting time)  has a uniform distribution between the interval [0,30], because it is just as likely that you arrive in any time and then your waiting time is minimum 0 minutes and maximum 30 minutes

The expected value  of a random variable uniform is:

E(x) =

      Where a and b are the interval's extremes

Thus

E(x) =

E(x) = 15 minutes

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500