Suppose you toss a coin about which you know that, on average, in one third of all cases it shows "tails" and in two thirds of all cases "heads". consider the following situation: each time you observe "heads" you roll a fair die and note the number of dots x. if the coin shows "tails" you do not roll the die but, instead, note x = 0 for the observed number of dots. find the moment generating function of x = "number of dots".

Enter the number of complex zeros for the polynomial function f(x) = x 4+ 5x² +6

Convert 50 kilogram to pounds. (the conversion factor from kilogram to pound is 2.2046.) a. 52.2 lb. b. 110.2 lb. c. 22.6 lb. d. 47.8 lb.

Finally, the arena decides to offer advertising space on the jerseys of the arena’s own amateur volley ball team. the arena wants the probability of being shortlisted to be 0.14. what is this as a percentage and a fraction? what is the probability of not being shortlisted? give your answer as a decimal. those shortlisted are entered into a final game of chance. there are six balls in a bag (2 blue balls, 2 green balls and 2 golden balls). to win, a company needs to take out two golden balls. the first ball is not replaced. what is the probability of any company winning advertising space on their volley ball team jerseys?