please workout and thoroughly explain number 6-11 in the document attached?
This is only a study guide but a study guide doesn't do much good If I don't know how to approach or do numbers 6-11 , please help?
MAT 172 Final Exam Study Guide You may use you calculator on the final exam, but no notes or textbooks. The last page of the
exam contains formulas that will be helpful. The same list will appear on the last page of the
1. Consider the following lists of test scores:
Class A: 98, 70, 32, 48, 71, 80, 85, 50, 46, 71
100 to 90
89 to 80
79 to 70
69 to 60 Frequency
1 a. Find the mean and median of each class with the help of your calculator.
Mean of Class A = _______________ Median of Class A = _______________ Mean of Class B = _______________ Median of Class B = _______________ b. If the standard deviation of Class A is 20 and the standard deviation of Class B is 7,
which class seems to have done better? Refer to your answers in part a as well as the
standard deviation to help you support your answer and make sure you indicate the
criteria you use to define ?better?. MAT 172 Final Exam Study Guide 2. How many license plates are possible consisting of 3 letters followed by 3 digits, if the first
letter must be a G? 2.____________________
3. Suppose we wish to seat six people, three men and three women, in a row of six chairs.
a. In how many ways can we seat the people with no restrictions? a.____________________
b. In how many ways can we seat the people if men must occupy the first three seats and
women the other three seats? b.____________________
c. If the men and women were seated in the chairs randomly, what would be the
likelihood that the men would occupy the first three seats and the women would
occupy the other three seats? c.____________________ MAT 172 Final Exam Study Guide 4. A law firm has ten male and eight female lawyers. A committee of five, two male and three
female lawyers, is to be chosen to represent the firm at a conference. How many committees
are possible? 4.____________________
5. The table below describes the relationship between annual income and the amount of time
consumers spend shopping on the Internet per month (rounded to the nearest hour).
Annual Income 10+ Hours 3-9 Hours 0-2 Hours Totals Above $60,000 192 176 128 496 $40,000 up to $60,000 160 208 144 512 Below $40,000 128 192 272 592 Totals 480 576 544 1600 a. What is the probability that a consumer we select has an income of $40,000 or
greater? a.____________________ b. What is the probability that a consumer we select randomly either spends 0-2 hours
per month shopping on the Internet or has an annual income below $40,000? b.____________________ c. What is the probability that a consumer we select randomly spends at least 3 hours
per month shopping on the Internet? c.____________________ MAT 172 Final Exam Study Guide 6. In solving a standard maximization problem with the Simplex Method, a student obtains the
following matrix: x1 x2 1 23 1
3 s2 z
4 1 0 1
0 1 16 0 0 Since there is a negative in the indicator row, this matrix does not correspond to an optimal
solution. Starting from this matrix, continue carrying out the Simplex Method to find the
optimal solution. Show all row operations that you use to get your final matrix. Row Operation: ____________________
Resulting Matrix: Row Operation: ____________________
Resulting Matrix: Optimal Solution is
x1 = ____________________
x2 = _____________
z = _____________ MAT 172 Final Exam Study Guide 7. The Marshall County trash incinerator in Norton burns 10 tons of trash per hour and cogenerates 6 kilowatts of electricity, while the Wiseburg incinerator burns 5 tons per hour and
co-generates 4 kilowatts of electricity. The county needs to burn at least 70 tons of trash and
co-generate at least 48 kilowatts of electricity every day. If the Norton incinerator costs $80
per hour to operate and the Wiseburg incinerator costs $50 per hour.
a. Set up the linear programming problem (but do not solve) to determine how many
hours the incinerators should operate each day with the least cost. Objective Function: Constraints: b. Construct the dual problem to the linear programming problem in a. Make sure you
find both the objective function and all constraints. Objective Function: Constraints: MAT 172 Final Exam Study Guide 8. A soon to retire community college teacher wishes to have $15,000 for a motorcycle when he
retires. He has $10,000 now and plans to retire in 5 years. What interest rate, compounded
quarterly, will he need to earn (to the nearest tenth of a percent)? To earn full credit, you
need to show the equation (see last page), all pertinent quantities and the steps you followed
to solve the equation. 9. A political action committee (PAC) has surveyed 240 probable voters regarding the
relationship between political affiliation and their preference in the presidential front runners.
The results are in the table below. Prefer Clinton
240 If a voter is selected randomly from those surveyed, find the probability that the voter is
a. a Democrat b. prefers Trump c. a Republican that prefers Clinton d. a Democrat, given that the voter preferred Trump e. preferred Clinton, given that the voter is am Independent MAT 172 Final Exam Study Guide 10. The Central Yavapai Fire District wants to take advantage of a state program to save money
to purchase a new fire truck. The truck will cost $400,000. To save for the truck, the district
will make a monthly deposit into an ordinary annuity paying 10.8% annual interest. If they
wish to have the money for the purchase in 60 months, how much should each payment into
the annuity be? 10. ____________________
11. The cost of producing x t-shirts is C(x) dollars where C ( x) 6 x 15000 . A t-shirt sells for
$16 each. Complete the parts below by solving appropriate equations algebraically or
graphically and document the steps you follow.
a. Find the break-even quantity. a.____________________
b. What profit will the company receive if it sells 2000 t-shirts? b.____________________
c. How many shirts will produce a profit of $20,000? c.____________________ MAT 172 Final Exam Study Guide USEFUL FORMULAS I PV rt FV PV (1 rt ) (1 i ) n 1 FV PMT i PMT i PV
1 (1 i ) n FV PV (1 i ) n (1 i ) n 1 1 FV PMT PMT
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