Shankar has decided to train to be a Carbucks Barrista. Being young and inexperienced, for every order he makes a mistake in making that order with probability 1/3 and makes the order correctly with probability 2/3, with the probabilities of making an error independent across different orders.

a. Shankar comes into work Monday morning. What is the probability that he makes no mistakes on his first 10 orders but the 11th order is a mistake?
b. Another Employee (Fran) and Shankar decide to have a competition: Every customer that comes in, both Fran and Shankar would make the order for that person (so each person would get 2 of the same item!). The first amongst either Fran or Shankar that makes a mistake quits Carbucks and goes to grad school to learn probability.
If Fran is more experienced and makes mistakes on an order with probability 1/6 independent across orders and independent of what Shankar is doing on an order, what is the probability that Shankar quits and goes to grad school?

The table shows population statistics for the ages of best actor and best supporting actor winners at an awards ceremony. the distributions of the ages are approximately bell-shaped. compare the z-scores for the actors in the following situation. best actor best supporting actor muequals42.0 muequals49.0 sigmaequals7.3 sigmaequals15 in a particular year, the best actor was 59 years old and the best supporting actor was 45 years old. determine the z-scores for each. best actor: z equals best supporting actor: z equals (round to two decimal places as needed.) interpret the z-scores. the best actor was (more than 2 standard deviations above more than 1 standard deviation above less than 1 standard deviation above less than 2 standard deviations below) the mean, which (is not, is) unusual. the best supporting actor was (less than 1 standard deviation below more than 1 standard deviation above more than 2 standard deviations below more than 1 standard deviation below) the mean, which (is is not) unusual.

How do i multiply two digit numbers

"which statement is necessarily true if bd is an altitude to the hypotenuse of right ? abc? a.) ? adb? ? bdc b.) ? adb~? bdc c.) abbc=acbd d.) ? bac? ? bdc"