On the planet Zog, the lottery has a different set of rules to the ones us mortals are accustomed toon Earth. Each alien can choose 8 distinct numbers from a choice of 60, and each week 12 numbersare drawn without replacement live on ZogTV to give an unordered set of winning numbers. Alienswho have chosen all of their 8 numbers correctly get a tier 1 prize, aliens who have chosen 7 numberscorrectly get a tier 2 prize and so on, until aliens who have chosen only one number correctly receivea tier 8 prize. LetPkbe the probability of winning a tierkprize once you have chosen your numbers. Find a general formula forPkin terms ofk

Chanelle deposits $7,500 into the bank. she does not withdraw or deposit money for 6 years. she earns 6% interest during that time. what will the balance be when she is finally able to withdraw her money?

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?

Which expression is equivalent to 64 - 9x^2?