Project #161555 - math4

Mathematics Tutors

Subject Mathematics
Due By (Pacific Time) 12/24/2016 12:00 am

Q1. 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

Q2. Solve the system using the inverse method.


    a. x = -19, y = -61, z = -35
    b. x = -1, y = -3, z = -2
    c. x = 15, y = -49, z = 27
    d. x = -2, y = -28, z = 20

Q3. Perform the indicated operation, whenever possible.

 + 
    a. 
    b. 
    c. 
    d. 

Q4. 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

Q5. Write the partial fraction decomposition of the rational expression.


    a.  + 
    b.  + 
    c.  + 
    d.  + 

Q6. Find the inverse of the matrix.

A = 
    a. 
    b. 
    c. 
    d. 

Q7. Perform the indicated operation, whenever possible.

 - 
    a.   [-2]
    b. 
    c. 
    d. 

Q8. 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

Q9. Solve the system.


    a. inconsistent (no solution)
    b. (-9, 0)
    c. (0, 0)
    d. y = -  - 9, where x is any real number

Q10. 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

Q11. 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

Q12. 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

Q13. Find the inverse of the matrix.


    a. 
    b. 
    c. 
    d. 

Q14. Write the partial fraction decomposition of the rational expression.


    a.  + 
    b.  + 
    c.  + 
    d.  +  + 

Q15. 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%

Q16. Perform the indicated operations and simplify.

Let A =  , B =  , and C = . Find AB + BC.
    a. 
    b. 
    c. 
    d. 

Q17. Find the inverse of the matrix.


    a. No inverse
    b. 
    c. 
    d. 

Q18. 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

Q19. 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

Q20. Verify that the values of the variables listed are solutions of the system of equations.


x = 0, y = -5, z =-4
    a. solution
    b. not a solution




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