A 5-gallon bucket is full of pure water. Suppose we begin dumping salt into the bucket at a rate of 1/4 pounds per minute. Also, we open the spigot so that 1/2 gallons per minute leaves the bucket, and we add pure water to keep the bucket full. If the salt water solution is always well mixed, what is the amount of salt in the bucket after: a. 1 minute?
b. 10 minutes?
c. 60 minutes?
d. 1000 minutes?
e. a very very long time?

If you shift the linear parent function, f(x)=x, up 13 units, what is the equation of the new function?

An observer(o) spots a plane(p) taking off from a local airport and flying at a 29 degree angle horizontal to her line of sight and located directly above a tower(t). the observer also notices a bird circling directly above her. if the distance from the plane(p) to the tower(t) is 6,000ft., how far is the bird(b) from the plane(p).

When booking personal travel by air, one is always interested in actually arriving at one’s final destination even if that arrival is a bit late. the key variables we can typically try to control are the number of flight connections we have to make in route, and the amount of layover time we allow in those airports whenever we must make a connection. the key variables we have less control over are whether any particular flight will arrive at its destination late and, if late, how many minutes late it will be. for this assignment, the following necessarily-simplified assumptions describe our system of interest: the number of connections in route is a random variable with a poisson distribution, with an expected value of 1. the number of minutes of layover time allowed for each connection is based on a random variable with a poisson distribution (expected value 2) such that the allowed layover time is 15*(x+1). the probability that any particular flight segment will arrive late is a binomial distribution, with the probability of being late of 50%. if a flight arrives late, the number of minutes it is late is based on a random variable with an exponential distribution (lamda = .45) such that the minutes late (always rounded up to 10-minute values) is 10*(x+1). what is the probability of arriving at one’s final destination without having missed a connection? use excel.