Suppose we play a game in which I give you a die to roll and offer to pay you in dollars the number that you roll (if you roll a 3, I'll pay you $3). I also stipulate that if you're dissatisfied with the number that you roll on your first try, I'll let you roll the die again with the same offer. I will allow a maximum of 3 "do-overs", though you can elect to stop after any roll. How much would you pay me to play this game?

Abaker makes 186 cookies. some are chocolate chip and some are oatmeal raisin, and both kinds are made with and without nuts, as shown in the table above. because they are more popular, the baker made 2/3 of the cookies chocolate chip. if a chocolate chip cookie is chosen at random, what is the probability that it will have nuts? a) 21/93 b) 21/62 c) 41/93 d) 21/41

During your cycling trip, you and your friends often stayed in hostels. the prices of these are listed below. hostel standard room (price per night) with breakfast (price per night) super sleep hostels £22.45 £28.65 normandy nights £18.55 £25 zzzola hostels £24.50 £30.99 belgian beds £11.20 £18.55 night-time rest days ? £33 what is the range in cost for a single night, including both standard room prices and with breakfast prices?

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?