Jamal has a bag of marbles. He gives exactly
1/3 of his marbles to Isaac, and has 2/3 of his
original number of marbles remaining. If
Jamal is able to repeat this action at least 3
more times without breaking any marbles
into pieces, how many marbles could he have
started with?

James wants to promote his band on the internet. site a offers website hosting for $4.95 per month with a $49.95 startup fee. site b offers website hosting for $9.95 per month with no startup fee. for how many months would james need to keep the website for site a to be a better choice than site b? define a variable for the situation. write an inequality that represents the situation. solve the inequality to find out how many months he needs to keep the website for site a to be less expensive than site b. using words, describe how many months he needs to keep the website for site a to be less expensive than site b.

Let f (x) = x e8x. find a formula for the nth derivative of f, where n is any positive integer. use x and n in your answer if needed. f (n)(x) =

Arefrigeration system at your company uses temperature sensors fixed to read celsius (°c) values, but the system operators in your control room understand only the fahrenheit scale. you have been asked to make a fahrenheit (°f) label for the high temperature alarm, which is set to ring whenever the system temperature rises above –10°c. what fahrenheit value should you write on the label