Probabilities
In the following multiple choice questions, circle the correct answer.
1.
The counting rule that is used for counting the number of experimental outcomes
when n objects are selected from a set of N objects where order of selection is not
imp
OPTIMIZATION
1. A company begins a radio campaign to market a new product. The percentage of the
target market is presented by the function
, where
is percent (in
p (t )
p (t ) 1 e0.04t
decimal form) of people that would buy the product after t days of th
Deferred annuities
The first payment is made not at the beginning or end of the first period but at a later
date.
0
1
2
(k-1)
k
1
2
3
(n-1)
Payments are deferred by k periods. Number of payments n.
Formula to calculate the present value of deferred annuit
FORMULAS FOR THE FINAL EXAM CMS2 - 500
Finance
Simple interest:
A P 1 it
I Pit
Compound interest:
mt
r
A P 1
m
Present value annuities:
PR
Future value annuities:
1 1 i
A P 1 i
or
n
or
These annuities are for the end of the period, A or
n
i
(1 i )n 1
MATHEMATICS FOR MANAGEMENT
Promissory Notes
A promissory note is a written promise by one party to pay a certain sum of money to
another party on a specific date, or on demand.
The required elements and the general rules of law that apply to promissory no
NORMAL DISTRIBUTION
1. Given that x is a normally distributed random variable with a mean of
60 and a standard deviation of 10,find the following probabilities:
(a) P (x>60); (b) P (60<x<72); (c) P (57<x<83); (d) P (65<x<82)
2. For a particular age group
Counting
1.
(a)
(b)
(c)
How many four digit numbers can be formed with the 7 digits: 0, 2, 3, 4, 6, 7, 9, if
repetitions are allowed
repetitions are not allowed
the number must be less than 5000 and repetitions are not allowed
2. Four different mathematic
COMPOUND INTEREST
If the interest due at the end of a unit payment period is added to the principal, so that the
interest computed for the next unit payment period is based on this new principle amount
(old principal plus interest), then the interest is s
Counting
1. An exam consists of 10 true-false questions and 10 five-answer multiple-choice
questions. How many different answer sheets are possible?
2. A department store manager is asked to select and rate the top 3 clerks, the top 3
bookkeepers, and the
Annuities
1. John has paid $350 per month into an annuity for 10 years at 6% compounded monthly.
He has moved money into another plan that pays 8% compounded quarterly. He will
contribute $1000 at the end of every three months. What is the total amount th
Binomial probability distribution
1. A basketball player has a history of making 80% of the foul shots
taken during games. What is the probability that he will miss three of
the next five foul shots he takes?
2. A machine produces parts, of which 0.5% are
Prerequisites on Algebraic Functions
CMS2-500
Jan. 2016
Objectives
Review functions, including function notation, composition of functions,
and quadratic functions
Functions
A [ mathematical ] function consists of three things, namely, a set of inputs,
a
Week 1
Jan. 13, 2016
Mathematics for Management
Overview:
Our first class begins with a quick review of prerequisite algebra and functions
skills from Math CMSC-000. Then we learn how to work with exponential
functions and logarithmic functions. These two
Assignment 9
Solutions
page 1
Section 11.5:
8
y2 x3 4 0
dy
3x2 0
dx
dy 3 x 2
2y
dx
2y
12
dy 3 2
3
At 2,2 ,
dx
2 2
4
2
16
2 x3 y x3 5 0
dy
2 x dx y 6 x 3 x
3
2
2
0
2
dy 3 x 6 x 2 y 3 x 1 2 y 3 1 2 y
dx
2x3
2x3
2x
dy 3 1 2 3 3 5 15
At 1,3 ,
2
dx
2 1
2
Assignment 10
Solutions
page 1
Section 12.2:
20
f x x4 6 x
f x 4 x3 6 2 2 x3 3
f x 12 x 2
Critical value is
3
3 1.144714243
2
Possible point of inflection is x = 0.
f x
f x
f x
x < -1.1447
Dec
Conc Up
x = -1.1447
Loc Min
Conc Up
-1.1447< x < 0
Inc
Conc U
Assignment 7
Solutions
page 1
Section 10.1:
48
(A)
(B)
1
x3
x3
(except when x is 3)
2
x 3 x x x 3 x
x3
x3
1
1
1
lim
lim
lim 2
x 3 x 3 x
x 3 x x 3
x 3 x
3
3
x3
x3
1 1
lim
lim which doesnt exist: the limit at 0 does
lim 2
x 0 x 3 x
x 0 x x 3
x 0 x
0
Assignment 8
Solutions
page 1
Section 11.1:
18 A Pe
(A)
0.0528t
dollars
How much is $10 000 worth in three years?
0.0528 3
10000e
Solution: A Pe
Conclusion: It will be worth $11 716.35
0.0528 t
11716.34755
(B)
How long will it take to be worth $11 000?
Assignment 6
Solutions
page 1
Section 9.3:
12
x
102.8
8.5666.
12
s
70.3666.
2.5292
11
Conclusion The sample mean is 8.5667 minutes and the sample standard deviation is 2.5292
minutes.
14
From Problem 16, section 9.2, we have x 10 , so:
5 2 10 54 7 10 .
Assignment 4
Solutions
page 1
Section 7.1:
17
(A)
(B)
There are 6 + 3 = 9 possibilities
There are (6)(3) = 18 possibilities
35 There are (5)(3)(4)(2) = 120 different variations of this car model.
39
(A)
(B)
(C)
There are (10)(9)(8)(7)(6) = 30 240 combinat
Assignment 2
Solutions
page 1
Section 3.3:
A2
93
S 350 1 0.045
354.0130137
365
Maturity value is $354.01
A4
216
S 575 1 0.075
600.5205479
365
Maturity value is $600.52
A6
104
S 230 1 0.075
234.9150685
365
Maturity value is $234.92
A8
30
Assignment 1
Solutions
page 1
Section 2.1
120.
(a)
The revenue function is R x xp x 2000 x 60 x thousand dollars
2
Domain is 1 x 25 thousand computers
(b)
NB: the following are in 1000s.
x
1
5
10
15
20
25
R(x)
1,940
8,500
14,000
16,500
16,000
12,500
18,00