# Principles of Math Test

1. Refer to Figure T3-1 on the “Information and Facts-Concepts Sheet”.   The graph shows the amount of money spent in the United states on video games played on mobile devices in 2013 and the projected amount for the years 2014-2018.  Assuming this trend continues, use the graph to predict the amount spent in the United States on video games played on mobile devices in 2021.
2. Donna is a long-distance runner whose average time per mile in marathons is 9 minutes 5 seconds. Estimate the time it will take her to complete a 26.2-mile marathon.
3. A faucet is leaking at the rate of two drops of water per second.  Assume that the volume of one drop of water is 0.1 cubic centimeters (0.1 cm3).  Determine the volume of water in cubic centimeters lost in one 30-day month.
4. Mary and Jane ran a 100-meter race, Mary won by 6 meters, which means that Jane had run only 94 meters when Mary crossed the finish line.  They decided to race again, with Mary starting 6 yards behind the starting line. Assuming both runners run the second race at the same speed of as the first race, who will win.  Must show work.
5. The last 30 boat rentals at Greens Rentals were 15 sail boats, 9 kayaks, and 6 rowboats. Use this information to determine the probability that the next boat is
1. A Kayak
2. A Kayak or a Sailboat

6.  Each individual letter of the word MISSISSIPPI is placed on a piece of paper and all 11 pieces of paper are placed in a hat.  If one letter is selected at random for the hat, determine the probability that

a.   The letter is an “S”

b.   The letter is a vowel

7.    In her wallet, Anne has 13 bills.  Six are \$1 bills, three are \$5 bills, two are \$10 bills, two are \$20 bills.  She passes a charitable

“kettle” and randomly selects one bill from her wallet.  Determine

a.   The odds in favor of her selecting a \$5 bill

b.   The odds against her selecting a \$20 bill

8.    The odds of an Opera selling out are 3:20.  Determine the probability that the Opera

1. Sells out
2. Does not sell out

9.     In a proposed business venture, Stephanie estimates that there is a 60% chance she will make \$75,000

and a 40% chance she will loose \$25,000.  Determine Stephanie’s expected value

10.    1,800 raffle tickets are sold for \$2 each. Two prizes will be awarded:  one for    \$1,200 and two

for \$800. Assume the probability that any given ticket selected for the \$1,200 prize is   and

the probability that any given ticket selected for the \$800 prize is .  Jose purchases one

ticket.  Determine the expected value for Jose to win a prize AND determine the fair price for

the raffle.

11.  A person randomly selects one of four envelopes from a hat. Each envelope contains cash that

the person can keep. Determine the person’s expectation if three envelopes contain \$50 and

one envelope contains \$100.

12.     At a town council meeting, a member can vote yes on a motion, no on a motion, or abstain on a

motion.  There are two motions that the board member must vote on.  Determine the number of

sample points AND draw the tree diagram of the sample space.

13.  Four coins (fair coins) are tossed.

a.   Determine the probability that no heads are tossed.

b.   Determine the probability that at least one head is tossed

14.  Shelby Gardens sells bonsai trees.  Customers can choose a juniper, maple or fir bonsai tree.

Customers can also choose a circular, oval, triangular or square base in which to plant the tree.

The Changs re going to select one of the bonsai tress and one of the bases at random

1.  Determine the number of sample points in the sample space.
2.  Determine the probability that they select the maple tree with a triangular base.