#4.4 Matrices and Determinants

Aim 1: to find the inverse of a 2x2 matrix
Aim 2: to solve a matrix equation
Aim 3: skip
Aim 4: to convert a message into row matrices
Aim 5: to encode a message
Aim 6: to decode a message

• (13-35) odd
• (40, 44)
  
  
  FunCAT Quiz NAME _________________
  
  Due at the beginning of class on Friday, March 7, 2008!!! Put All Work and Answers on Your Own Paper --- Work must be Shown to Earn Credit!!!!!!
  
  1. The “lightweighting” process makes it possible for manufacturers to use less material to produce glass bottles. In 1972 it took 75.7 pounds of glass to produce 100 16-ounce glass bottles. In 1992 it took 48 pounds of glass to make the same number and size of bottles. What is the percent decrease in the number of pounds of glass used in 1972 compared with 1992 to produce 100 16-ounce bottles?
  
  2. Tanisha and some friends from her bicycle club went on a training ride from West Palm Beach to Miami. They planned to ride 45 miles from West Palm Beach to Ft. Lauderdale, another 10 miles to Hollywood, and finally 15 miles to Miami. Tanisha’s bicycle got a flat tire north of Miami, and she was unable to complete the training ride. Her odometer showed she had traveled 60 miles. Approximately what percent of the training ride did Tanisha complete?
  
  3. A bicycle store owner sells all merchandise at 25% above original cost. A customer bought a bicycle for $140.00. How many dollars did the store owner originally pay for the bicycle?
  
  4. At the close of the stock market on Monday, the value of a certain stock was $12.00 per share. By the close on Tuesday, the value of the stock went up 50% per share. At close on Wednesday, the value of the stock was down 5% per share from Tuesday’s closing value.
  
  A: determine the value of the stock at closing on Tuesday.
  B: determine the value of the stock at closing on Wednesday.
  C: determine the percent change in the value of the stock from Monday to
  Wednesday.
  
  5. The Regal High Debate Club qualified for the state meet. How many possible two-member debate teams can be formed from a pool of six students in the Regal High Debate Club?
  
  6. The four members of an a cappella singing group, two men and two women, always stand in a row when they sing. If they line up in random order, what is the probability that a woman will be at each end of the row?
  
  7. A geneticist studying twins read that fraternal twins occur in 1 out of every 80 births. In a sample of 560 mothers-to-be, how many would be expected to give birth to fraternal twins?
  
  8. Ed bowled six games at Jordan’s Bowlerama. For the first 5 games that Ed bowled, his mean score was 120. He bowled a score of 180 for his 6th game. What was his mean bowling score for all 6 games?
  
  9. A wholesaler is offering two different package deals of roses and carnations to florists. One package contains 20 dozen roses and 34 dozen carnations for $504.00. The other package contains 15 dozen roses and 17 dozen carnations for $327.00. This information can be represented by the system of equations below, where r represents the cost of one dozen roses and c represents the cost of one dozen carnations.
  20r + 34c = 504
  15r + 17c = 327 Solve the system of equations to find the cost of a
  dozen roses.
  
  10. Chris stopped for gas twice on along car trip. The price of gas at the first station was $1.45 per gallon, and the price of gas at the second station was $1.55 per gallon. On the trip, Chris bought a total of 20 gallons of gas and spent $29.80. This information can be represented by the following equations, where x is the number of gallons of gas Chris bought at the first station and y is the number of gallons of gas Chris bought at the second station.
  
  x + y = 20
  1.45x + 1.55y = 29.80
  
  Solve the system of equations to find the number of gallons of gas Chris bought at the first station.
  
  11. At the end of 1980, the population of Jacksonville, Florida, was approximately 541,000. By the end of 1990, the population had increased by about 20%. If the population continues to increase at this rate, what will be the population of Jacksonville at the end of 2020?
  
  12. Krista has decided to enter a local marathon. As part of her training, she is going to increase the number of miles she runs every week by 3 miles. If Krista runs 12 miles in the first week, how many miles will she run during the ninth week?
  
  13. The drama club plans to sell cans of orange soda and lemon-lime soda at its annual theater event. The club has enough money to buy a total of 288 cans of soda and has decided to buy twice as many cans of lemon-lime soda as orange soda. Determine the number of cans of each flavor of soda the drama club will buy for the event.
  
  14. A science lab needs a right circular cylindrical container that holds exactly 15 gallons of liquid and is 24 inches tall. A reference manual states that 231 cubic inches is equivalent to one gallon. What is the approximate radius in inches, of the container?
  
  15. A rectangular piece of window screen has a width of 1.75 feet. The packaging label says the screen is 42 square feet. What is the length of the screen?
  
  16. On December 17, 1903, Wilbur and Orville Wright flew their first powered airplane near Kitty Hawk, North Carolina. They flew the plane a distance of 852 feet in 59 seconds. If the Wrights’ plane had continued at the same rate of speed, about how many minutes would it have taken them to fly 1 mile?