A coin, having probability p of landing heads, is continually flipped until at least one head and one tail have been flipped. (a) What is the probability that stop at the fifth flip? (b)Find the expected number of flips needed.

Sara needs to take a taxi to get to the movies the taxi charges $4.00 for the first mile and then $2.75 for each mile after that if the total charge is $20.50 then how far was sara’s taxi ride to the movie

Give the equations of two different lines that are perpendicular to the line 3x + 4y = 7.

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- 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. 3- 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 part b?