Can you please assist me with answering exercise five.

 

 

Q1. A retired couple has $190,000 to invest to obtain annual income. They want some of it
invested in safe Certificates of Deposit yielding 7%. The rest they want to invest in AA
bonds yielding 10% per year. How much should they invest in each to realize exactly
$17,200 per year?
a. $120,000 at 7% and $70,000 at 10%
b. $130,000 at 7% and $60,000 at 10%
c. $130,000 at 10% and $60,000 at 7%
d. $140,000 at 10% and $50,000 at 7%
Q2. Solve the system using the inverse method. a. x = 1, y = -2
b. x = -2, y = 1
c. x = -1, y = 2
d. x = 2, y = -1
Q3. Verify that the values of the variables listed are solutions of the system of equations. x = 5, y = 5
a. not a solution
b. solution
Q4. A movie theater charges $8.00 for adults and $5.00 for children. If there were 40
people altogether and the theater collected $272.00 at the end of the day, how many of
them were adults?
a. 16 adults
b. 10 adults
c. 29 adults
d. 24 adults
Q5. Solve the system of equations. a. x = 0, y = 1, z = 0
b. x = 1, y =1, z = 1
c. x = 0, y = 1, z = -1 d. x = 0, y = 0, z = 1
Q6. Solve the system. a. inconsistent (no solution)
b. (-9, 0)
c. (0, 0)
d. y = - - 9, where x is any real number Q7. Use the elimination method to solve the system. a. x = 11, y = -11
b. x = -2, y = 9
c. x = 9, y = -9
d. x = -9, y = 9
Q8. Find the inverse of the matrix. A= a. b. c. d.
Q9. A flat rectangular piece of aluminum has a perimeter of 62 inches. The length is 15
inches longer than the width. Find the width.
a. 31 inches
b. 38 inches
c. 8 inches d. 23 inches
Q10. Jenny receives $1270 per year from three different investments totaling $20,000. One
of the investments pays 6% , the second one pays 8%, and the third one pays 5%. If the
money invested at 8% is $1500 less than the amount invested at 5%, how much money has
Jenny invested in the investment that pays 6%?
a. $8500
b. $4500
c. $10,000
d. $1500
Q11. Perform the indicated operations and simplify. Let A = ,B= , and C = . Find AB + BC. a.
b.
c.
d.
Q12. Perform the indicated operation, whenever possible. + a. b. c. d.
Q13. Use the properties of determinants to find the value of the second determinant, given
the value of the first. Given > = 3, find the value of >. a. -24
b. -3
c. 24
d. 3
Q14. A tour group split into two groups when waiting in line for food at a fast food counter.
The first group bought 8 slices of pizza and 4 soft drinks for $29.40. The second group
bought 7 slices of pizza and 6 soft drinks for $30.30. How much does one slice of pizza
cost?
a. $2.26 per slice of pizza
b. $2.76 per slice of pizza
c. $2.33 per slice of pizza
d. $1.83 per slice of pizza
Q15. Rob bought 2 pairs of shorts, 3 shirts and a pair of shoes for $146.64. Jessie bought 3
pairs of shorts, 5 shirts and 2 pairs of shoes for $256.35. Allen bought a pair of shorts and 4
shirts for $104.07. What is the price of a pair of shorts? Express answer rounded to two
decimal places.
a. $14.55
b. $50.40
c. $22.38
d. $10.30
Q16. Solve the system using the inverse method. a. x = -36, y = -38, z = -14
b. x = -14, y = 88, z = -32
c. x = -60, y = 82, z = -34
d. x = 8, y = 24, z = 10
Q17. Write the partial fraction decomposition of the rational expression. a. + b. + c. + d. + + Q18. An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per
gallon in highway driving. A 300-mile trip required 15.5 gallons of gasoline. How many
whole miles were driven in the city?
a. 153 miles
b. 168 miles
c. 147 miles
d. 132 miles
Q19. Write the partial fraction decomposition of the rational expression. a. + b. + c. + d. + Q20. The Family Fine Arts Center charges $21 per adult and $12 per senior citizen for its
performances. On a recent weekend evening when 486 people paid admission, the total
receipts were $6894. How many who paid were senior citizens?
a. 208 senior citizens
b. 368 senior citizens
c. 118 senior citizens
d. 278 senior citizens

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