An ant starts at a point P on the top edge of a cylinder with radius R and height H. If the ant makes n complete circuits around the cylinder and finishes at a point Q directly below the starting point on the bottom edge, what is the shortest possible path for PQ? Steps:
a. Draw a cylinder and its net with points P and Q marked.
b. Label all the lengths you can.
c. Solve the problem when R = 4", H = 8', n = 3
d. Write a rule for PQ using R, H, n

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. (a) what is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips, inclusive? (b) what is the probability that a randomly selected bag contains fewer than 1125 chocolate chips? (c) what proportion of bags contains more than 1225 chocolate chips? (d) what is the percentile rank of a bag that contains 1425 chocolate chips?

Mickey needs to cut pieces of ribbon that are each 1 meter long tie onto balloons. if he has 8 pieces of ribbon that are each 1 dekameter long. how many 1 meter pieces of ribbon can he cut

Aparticular telephone number is used to receive both voice calls and fax messages. suppose that 25% of the incoming calls involve fax messages, and consider a sample of 25 incoming calls. (a) what is the expected number of calls among the 25 that involve a fax message?