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Unformatted text preview: Final MATH110: section 0203
8811 2003 J.Harlim Show all work. Give some reason or justiﬁcation for each answer. Circle the
ﬁnal answer. 1. Solve the following: (a) Calculate the slope of a line through (1,2) and (2,2). (2pts) (b) Find an equation of the line passes through (2,3) and (—2,0) (6pts) (c) Find the linear equation through (2,3) and parallel to —a:+4y = 7.
(6ptS) (01) Find the linear equation through (1,3) and perpendicular to y = 6.
(6ptS) 2. The General Manager of Washington Wizard manages the number of
tickets sold on every game. There are two different class of ticket seats
offered: $96 per ticket for the lower bowl seat and $48 per ticket for
the upper bowl seat. Given the capacity of the MCI center is 18,800
seats. How many lower bowl tickets should the team sell per game in
order to earn $1,267,200, assuming the tickets are sold out ? (15pts)
(Deﬁne Variables, Setup equations and Solve.) 3. A group of students taking pre—calculus ﬁnal exam were surveyed to
determine the relationship between hours spent studying for the ﬁnal
exam and the grade obtained on the exam. The results of this survey
are given in the following table. mun“
mammals! (a) Find the mean of the hour of study. (3pts) (b) Find the mean, median, and mode of the grade of the ﬁnal exam.
(713128) (c) Using Least square linear regression to ﬁnd the bestﬁt line (Let
X=hours of study, Y=grade on exam). Give the equation of this
line. (4pts) (d) According to the model found in part (c), for every additional
hour spent studying, how many more (or fewer) points can the
student expect to obtain on the exam ? (4pts) (e) According to the model found in part (0), what grade can a stu
dent expect to obtain who does not study for the exam ? (2pts) 4. Model the following situation but DO NOT SOLVE. Clearly identify
the variables, objective and constraints. A local bakery makes two different types of bread: Purpleshaq and
Brownclown. Each loaf of Purpleshaq requires 5 eggs, 1/2 liter of
milk, and 12 gram of sugar. Each loaf of Brownclown needs 3 eggs,
3/4 liter of milk and 23 gram of sugar. The store has 200 eggs, 56 liter
of milk, and 600 gram of sugar. If the bakery makes $3 proﬁt on each
Purpleshaq and $2 proﬁt on each Brownclown. How many loaf of each
type should the bakery make to maximize proﬁt ? (15pts) 5. Graph the feasible region: :8 Z 0, y _>_ x — 2, a: + y _<_ 5. Label every
line, shade the feasible region and indicate it with letter S. (10pts) 6. i. Let S = {0,1,2,3,4,5,6,7,8,9} be the universal set and let A =
{4, 6, 9} and B = {9,1,0}. List the element of the following sets: (a) A U B. (2pts) (b) A’ D B. (2pts) (c) A U B’. (2pts) (01) A’ U <15 (2pm) ii. Let S=all student in this school be the universal set and let
B={all student taking biology}, M={all student taking math}, and P={all student taking physics} Write each of the following
sets in terms of B, M, and P (as an intersection, union, etc) (a) All students not taking math. (3pts) (b) All students taking math and physics (3pts) (0) All student not taking biology but taking math (3pts) (d All student who are not taking either math or biology (3pts) )
7. Let P(A) = 52—,P(B) = —2%,P(A D B) = 126' Find the following: (C) P (AIB) (4ptS) 8. Anne surveyed 50 peoples on what they had for the breakfast. 20
said they had donuts, 10 said they had pancakes, and 18 said they
had cereals. 5 said they had donuts and pancakes, 6 said they had
pancakes and cereals. 8 said they had cereals and donuts. Only 2 said
they had all donuts, pancakes and cereals. (a) Draw the diagram Venn. (15pts)
(b) How many students do not eat any of the three foods ? (5pts) 9. The probability that Samuel Adams failed MATHl 10 is 70%, the prob
ability that he becomes poor is 40%. The chance that he be poor and
failed MATHllO is 20%. What is the probability that he be either
poor or failed the MATHllO ? (5pts) What is the probability that he passes the math class and stay wealthy ? (5pts) ,._i__._,___________‘_______..~___F__ 10. Let X be the difference between the number facing up when you rolled
two dice. (a) State X. (4pts) (b) Find the probability distribution of X. (8pts)
(0) Calculate the expected value of X. (4pts) (01) Draw the histogram of X. (4pts) For number 11, 12 and 13 state the formula needed to solve the problems,
identify the values of the variables and solve. All interest rates are annual
unless otherwise stated. Useful Formula: INT 2 PVrt, FV = PV(1 + rt), FV = PV(1 + —)mt FV = PV(1+ £3)“ + PMT ,.
m __ 1 L —mt PV = FV(1+ ﬁrm + PMTiig—m—l— 11. Bill invests $20,000 on a bill with interest rate 5%. (a) How much money he own after 3 years if the bill counts simple
interests ? (6pts) (b) If the interest is compounded quarterly (every 3 months), how
much money he has after 3 years ? (9pts) 12. Bill is planning his retirements in 10 years and has decided to start an
annuity. How much money should he deposit monthly into this annuity
if it pays 12%, compounded monthly, and he wants the annuity to be
worth $300,000 when he retires ? (10pts) 13. Keith wants to buy a car of price $25,000. He finance the car for 5
years with interest rate 6%, compounded monthly. Given $2000 down
payment, how much monthly installment should he pay ? (15pts) The following is the bonus question, worth 15 points. 14. A bag contains ﬁve blue marbles, two red marbles, and four yellow
marbles. Jim is going to take four marbles in random. Find the
probability he has one blue, one yellow and two red ? Find also the
probability he gets another three yellow given he has one yellow ? END ...
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