Maths Multiple Choice Questions and Other Problems

MULTIPLE CHOICE
1. Carol purchases a car for $36,000, makes a down payment of 10%, and finances the rest with a 6-year car loan at an annual interest rate of 5.7% compounded monthly. What is the amount of her monthly loan payment?
A. $671.00
B. $603.90
C. $591.54
D. $532.39
2. Find the result of performing the row operation (5)R1 + R2

R2

3. Find the values of x and y that maximize the objective function 4x + 7y for the feasible region shown below.
A. (x, y) = (5, 15)
B. (x, y) = (8, 10)
C. (x, y) = (0, 20)
D. (x, y) = (10, 0)

4. The weights of Acme beef hot dogs are normally distributed with a mean of 60 grams and a standard deviation of 1.5 grams. What is the probability that a randomly chosen hot dog weighs between 58.5 grams and 61.5 grams?
A. 0.9544
B. 0.7580
C. 0.5000
D. 0.6826
5. Determine which shaded region corresponds to the solution region of the system of linear inequalities

For #6 and #7:
A merchant makes two raisin nut mixtures.
Each box of mixture A contains 12 ounces of peanuts and 4 ounces of raisins, and sells for $3.50.
Each box of mixture B contains 8 ounces of peanuts and 3 ounces of raisins, and sells for $2.70.
The company has available 2,100 ounces of peanuts and 900 ounces of raisins. The merchant will try to sell the amount of each mixture that maximizes income.
Let x be the number of boxes of mixture A and let y be the number of boxes of mixture B.
6. Since the merchant has 900 ounces of raisins available, one inequality that must be satisfied is:
A. 2,100x + 900y Ñ 3.50
B. 3.50x + 2.70y £ 900
C. 20x + 7y Ñ 900
D. 4x + 3y £ 900
7. State the objective function.
A. 3.50x + 2.70y
B. 12x + 4y
C. 2.70x + 3.50y
D. 2,100x + 900y
8. A jar contains 12 red jelly beans, 18 yellow jelly beans, and 20 orange jelly beans. Suppose that each jelly bean has an equal chance of being picked from the jar.
If a jelly bean is selected at random from the jar, what is the probability that it is not orange?

9. When solving a system of linear equations with the unknowns x1 and x2 the following reduced augmented matrix was obtained. 9. _______

What can be concluded about the solution of the system?
A. There is no solution.
B. The unique solution to the system is x1 = −3 and x2 = − 1.
C. There are infinitely many solutions. The solution is x1 = − 3t − 1 and x2 = t, for any real number t.
D. There are infinitely many solutions. The solution is x1 = 3t − 1 and x2 = t, for any real number t.

10. Which of the following is NOT true?
A. The variance is a measure of the dispersion or spread of a distribution about its mean.
B. The variance must be a nonnegative number.
C. The variance is the square root of the standard deviation.
D. If all of the data values in a data set are identical, then the standard deviation is 0.

11. In a certain manufacturing process, the probability of a type I defect is 0.05, the probability of a type II defect is 0.08, and the probability of having both types of defects is 0.03. Find the probability that neither defect occurs.
A. 0.97
B. 0.90
C. 0.87
D. 0.84

12. Which of the following statements is NOT true? 12. ______
A. If only two outcomes are possible for an experiment, then the sum of the probabilities of the outcomes is equal to 1.
B. If an event cannot possibly occur, then the probability of the event is a negative number.
C. A probability must be less than or equal to 1.
D. If events E and F are mutually exclusive events, then P(E Ç F) = 0.

SHORT ANSWER:

13. Let the universal set U = {1, 2, 3, 4, 5, 6, 7, 8}. Let A = {2, 3, 4, 5, 6} and B = {1, 2,3, 8}.

14. Consider the following graph of a line.

(a) State the x-intercept. Answer: ______________
(b) State the y-intercept. Answer: ______________
(c) Determine the slope. Answer: ______________
(d) Find the slope-intercept form of the equation of the line. Answer:
____________________
(e) Write the equation of the line in the form Ax + By = C where A, B, and C are integers. Answer: ____________________

15. 400 employees at a particular company were asked their status (full-time or parttime) and their primary means of transportation to and from work. The following table was obtained.

(Report your answers as fractions or as decimal values rounded to the nearest hundredth.)

Find the probability that a randomly selected employee:
(a) travels by subway and is part-time. Answer: ______________
(b) travels by subway or is part-time. Answer: ______________
(c) travels by subway, given that the employee is part-time. Answer: ______________

SHOW YOUR WORK
16. For an eight-year period, Joanna deposited $600 each quarter into an account paying 4.4% annual interest compounded quarterly. (Round your answers to the nearest cent.)
(a) How much money was in the account at the end of 8 years? Show work.
(b) How much interest was earned during the 8 year period? Show work.
Joanna then made no more deposits or withdrawals, and the money in the account continued to earn 4.4% annual interest compounded quarterly, for 5 more years.
(c) How much money was in the account after the 5 year period? Show work.
(d) How much interest was earned during the 5 year period? Show work.

17. A contest has 24 finalists. One finalist is awarded first prize, another finalist is awarded second prize, and another is awarded third prize. How many different ways could the prizes be awarded? Show work.

18. A student club has 16 members. 6 of the club members are full-time students and 10 are part time students.
(a) In how many ways can the club choose 5 members to form a committee? Show work.
(b) In how many ways can the club choose 5 members to form the committee, if 2 committee members must be full-time students and 3 committee members must be parttime? Show work.
(c) If a 5-person committee is selected at random from the 16 club members, what is the  probability the committee consists of 2 full-time students and 3 part-time students? Show work.

19. In 1968, there were 3.1 trillion cigarettes purchased worldwide, and in 1976, there were 3.7 trillion cigarettes purchased worldwide. Let y be the number of cigarettes purchased worldwide (in trillions) in the year x, where x = 0 represents the year 1968.
(a) Which of the following linear equations could be used to predict the number of trillions of cigarettes y purchased worldwide in a given year x, where x = 0 represents the year 1968? Explain/show work.
A. y = 0.60x − 1.1
B. y = 0.60x + 3.1
C. y = 0.075x − 144.5
D. y = 0.075x + 3.1
(b) Use the equation from part (a) to estimate the number of cigarettes purchased worldwide in the year 2000. Show work.
(c) Fill in the blanks to interpret the slope of the equation: The rate of change of cigarettes purchased worldwide with respect to time is ______________________ per ______________.
(Include units of measurement.)

20. Solve the system of equations using elimination by addition or by augmented matrix methods (your choice). Show work.

2x − 3y = 1
8x − 9y = 7
21. The feasible region shown below is bounded by lines 2x − y = 4, x + y = 3, and y = 0. Find the coordinates of corner point A. Show work.

22. A survey of 120 households found the following:
65 households have a cell phone. 72 households have a landline phone.
112 households have a cell phone or landline phone (or both).
(a) How many households have both a cell phone and a landline phone? Show work.
(b) Let circle C = {households having a cell phone} and circle L = {households having a landline phone}

Determine the number of survey respondents belonging to each of the regions I, II, III, IV.

23. Consider the sample data 22, 78, 45, 60, 33, 33, 58.

(a) State the mode.
(b) Find the median. Show work/explanation.
(c) State the mean.
(d) The sample standard deviation is 19.5. What percentage of the data fall within one standard deviation of the mean? Show work/explanation.
A. 50%
B. 57%
C. 68%
D. 71%

24. If the probability distribution for the random variable X is given in the table, what is the expected value of X? Show work.

25. According to a recent report, 0.39 is the probability that a 25-34 year old American has a college degree. Six 25-34 year old Americans are randomly selected. Find the probability that exactly 3 of the 6 individuals has a college degree. Show work.