Algebra

5. Find x in the series 1, 1/3, 0.2, x.
6. Find the 10th term of the progression 6/5, 4/3, 3/2 . . .
7. Find the sum of the first 10 terms of the Geometric Progression 2, 4, 8, 16 . . .
8. The fourth term of a geometric progression is 189 and the sixth term is 1701. Find the 8th term.
9. Find the sum of the infinite geometric progression 6, -2, 2/3 . . .
10. Find the fourth term of ½, 0.2, 0.125 . . .

Suppose 3 items are inspected and if at least one defective is found, the lot will be 100% inspected. Otherwise, the lot will be passed on. How likely it is that a lot containing 5 defectives will be passed on?

A Metra commuter train leaves
Union Station in Chicago at 12 noon. Two hours later, an
Amtrak train leaves on the same track, traveling at an
average speed that is 50 miles per hour faster than the
Metra train. At 3 PM the Amtrak train is 10 miles behind the
commuter train. How fast is each going?

A life raft, set adrift from a sinking ship
150 miles offshore, travels directly toward a Coast Guard
station at the rate of 5 miles per hour. At the time that the
raft is set adrift, a rescue helicopter is dispatched from
the Coast Guard station. If the helicopter’s average speed is
90 miles per hour, how long will it take the helicopter to
reach the life raft?

An 8-horsepower (hp) pump can fill a
tank in 8 hours. A smaller, 3-hp pump fills the same tank in
12 hours. The pumps are used together to begin filling this
tank. After four hours, the 8-hp pump breaks down. How
long will it take the smaller pump to fill the tank?

Two pumps of different sizes, working
together, can empty a fuel tank in 5 hours.The larger pump
can empty this tank in 4 hours less than the smaller one. If the
larger pump is out of order, how long will it take the smaller
one to do the job alone?

On a recent flight from Phoenix to Kansas
City, a distance of 919 nautical miles, the plane arrived
20 minutes early.On leaving the aircraft, I asked the captain,
“What was our tail wind?”He replied, “I don’t know, but our
ground speed was 550 knots.” How can you determine if
enough information is provided to find the tail wind? If possible,
find the tail wind. (1 knot = 1 nautical mile per hour)