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#### 1313T017

Course: MATH 1313, Fall 2008

School: U. Houston

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You 1. choose 4 cards at random from a wellshuffled deck of 52 playing cards. How many outcomes are possible? a. b. c. d. e. 52 6,497,400 208 270,725 None of the above 2. How many ways can 6 people be seated in a row of 6 chairs? a. b. c. d. e. 36 1 720 6 None of the above 3. A catering service offers 8 appetizers, 10 main courses, and 7 desserts. A banquet chairperson is to select 3 appetizers, 4 main courses,...

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You 1. choose 4 cards at random from a wellshuffled deck of 52 playing cards. How many outcomes are possible? a. b. c. d. e. 52 6,497,400 208 270,725 None of the above 2. How many ways can 6 people be seated in a row of 6 chairs? a. b. c. d. e. 36 1 720 6 None of the above 3. A catering service offers 8 appetizers, 10 main courses, and 7 desserts. A banquet chairperson is to select 3 appetizers, 4 main courses, and 2 desserts a for banquet. How many ways can this be done? a. b. c. d. e. 24 287 246,960 71,124,480 None of the above 4. A math department of a high school has 25 teachers. The department has to appoint a committee to formulate a homework policy. In how many ways can t...

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U. Houston - MATH - 1313
Section 7.1 Experiments, Sample Spaces, and Events An experiment is an activity with observable results (outcomes). A sample point is an outcome of an experiment. A sample space is a set consisting of all possible sample points of an experiment. A Fi
U. Houston - MATH - 1313
Section 6.4 Permutations and Combinations Definition: n-Factorial For any natural number n, n!= n(n 1)( n 2) 3 2 1 . 0! = 1 A permutation is an arrangement of a specific set where the order in which the objects are arranged is important. Formu
U. Houston - MATH - 1313
1. A coin is tossed 9 times. How many outcomes are possible? a. b. c. d. e. 27 12 512 81 NOA2. You toss a coin 15 times. In how many outcomes do at most 2 tails occur? a. b. c. d. e. 121 105 32,663 120 None of the above3. A basket contains 28 app
U. Houston - MATH - 1313
1. Let A and B be subsets of a universal set, U. c c Given that n(U ) = 100, n( A U B ) = 43, and c n( A ) = 20. Find n( A I B c ).a. b. c. d. e.15 Not enough info is given. 5 23 NOA2. A disc jockey can play 4 records in a 20-minute segment of
U. Houston - MATH - 1313
Section 6.2 The Number of Elements in a Finite Set Let A be a set, then n(A) is the number of elements in the set A.Given two sets A and B. 1. If A and B are disjoint then n( A U B ) = n( A) + n( B ). 2. If A and B are not disjoint then n( A U B )
U. Houston - MATH - 1313
1. Which region(s) is(are) in the set:( B I A)a. b. c. d. e.I, II, III I III II None of the aboveA III B III IVUA I II V IV VII C VI VIII B III2. Which region(s) is(are) in the set:a. b. c. d. e.I, II, III, V, VIII I, II, III, VIII
U. Houston - MATH - 1313
1. Given U = {1,2,3,4,5}, A = {3,5} and B = {1,3,4,5}. Find B . a. {1,2,4} b. {2} c. {3,5} d. NOAc2. Given U = {1,2,3,4,5}, A = {3,5} and B = {1,3,4,5}. Find (B U A ) a. {1,2,4} b. {2} c. {3,5} d. NOAc c c.U A I II B IIIIV3. Which region(
U. Houston - MATH - 1313
Section 6.1 Sets and Set Operations A collection of objects is called a set. An object of a set is called an element. Notation:= element of = not an element ofThe set C = {x | x 2 = 9 } is in set builder notation. The set C can also be written as
U. Houston - MATH - 1313
1. You invested a sum of money 4 years ago in a savings account that has since paid interest at the rate of 6.5% per year compounded monthly. Your investment is now worth \$19,440.31. How much did you originally invest? Identify the type of problem. a
U. Houston - MATH - 1313
Section 5.3 Amortization and Sinking FundsTo Amortize means to pay off a debt by installment payments. Amortization Formula The periodic payment R on a loan of P dollars to be amortized over n periods with interest charged at the rate of i per peri
U. Houston - MATH - 1313
1. Jackie wishes to purchase a new living room set in 2 years. She anticipates that the set will cost her \$2,000. How much must she deposit today in an account that pays 2.25% per year compounded quarterly, in order to have the funds available in 2 y
U. Houston - MATH - 1313
Section 5.2 Annuities A sequence of equal periodic payments made at the end of each payment period is called an ordinary annuity. Examples of annuities: 1. Regular deposits into a savings account. 2. Monthly home mortgage payments. 3. Payments into a
U. Houston - MATH - 1313
1. Which of the following matrices are in row-reduced form? 1 - 2 0 1 1 1 9 10 I. 0 0 0 0 , II. 0 1 - 1 2 and 0 0 0 0 0 0 0 0 a. I, II 1 0 0 0 2 b. I, III 0 1 - 7 0 - 13 III. c. II, III . 0 0 0 1 2 d. I, II, III 0 0 0 0 0 e.
U. Houston - MATH - 1313
Section 3.3 Linear Programming Consider the following figure which is associated with a system of linear inequalities:ySxThe set S is called a feasible set. Each point in S is a candidate for the solution of the problem and is called a feasible
U. Houston - MATH - 1313
Section 5.1 Simple Interest, Future Value, Present Value, and Effective Rate Interest that is computed on the original principal only is called simple interest. Formula: I = Pr t where P = principal r = rate t = time (in years)The sum of the princi
U. Houston - MATH - 1313
U. Houston - MATH - 1313
U. Houston - MATH - 1313
Section 3.2 Linear Programming A function subject to a system of constraints to be optimized (maximized or minimized) is called an objective function. A system of equalities or inequalities to which an objective function is subject to are called cons
U. Houston - MATH - 1313
Section 2.5 Multiplication of Matrices If A is a matrix of size mxn and B is a matrix of size nxp then the product AB is defined and is a matrix of size mxp. So, two matrices can be multiplied if and only if the number of columns in the first matrix
U. Houston - MATH - 1313
Section 2.6 The Inverse of a Square Matrix In this section we discuss a procedure for finding the inverse of a matrix and show how the inverse can be used to help us solve a system of linear equations. Let A be a square matrix of size n. A square mat
U. Houston - MATH - 1313
Section 2.4 Matrices A matrix is an ordered rectangular array of numbers. A matrix with m rows and n columns has size or dimension mxn. The entry in the ith row and jth column is denoted by a ij . The real numbers that make up the matrix are called e
U. Houston - MATH - 1313
The reduced form for the augmented matrix of a system with 3 equations and 3 unknowns is given. Give the solution to the system, if it exists. 1. 1 0 0 100 2. 1 0 - 3 4 0 0 1 - 9 1 0 1 0 - 7 0 0 0 0 1 0 0 0 a. No solution. b. x = 100,
U. Houston - MATH - 1313
Section 2.3 Solving Systems of Linear Equations II In the previous section we studied systems with unique solutions. In this section we will study systems of linear equations that have infinitely many solutions and those that have no solution. We als
U. Houston - MATH - 1313
Section 2.2 Solving Systems of Linear Equations I As you may recall from College Algebra, you can solve a system of linear equations in two variables easily by applying the substitution or addition method. Since these methods become tedious when solv
U. Houston - MATH - 1313
Section 1.4 Break Even Analysis When a company neither makes a profit nor sustains a loss this is called the break-even level of operation. Note: The break even level of operation is represented by the point of intersection of two lines. The break ev
U. Houston - MATH - 1313
Math 1313 Finite Mathematics with Applications Instructor: Beatrice Constante Email Address: beatrice@math.uh.edu Website: www.math.uh.edu/~beatrice Prerequisite: Math 1310, College Algebra. Beginning of the Semester To-Do List 1. Read the Syllabus a
U. Houston - MATH - 1310
Section 4.3 Roots of Polynomial Functions Note: a 2 + b 2 can be factored over the complex numbers:a 2 + b 2 = (a + bi)(a bi)The Factor Theorem Let f(x) be a polynomial. a. If c is a zero of f(x) (f(c) = 0), then x c is a factor of f(x). b. If x
U. Houston - MATH - 1310
Section 4.2 Dividing Polynomials Long Division of Polynomials Recall: Divided = Quotient*Divisor + Remainder Example 1: Divide. 12 x 3 - x 2 - x a. 3x - 1b.3x 4 - x 3 - 15 x2 + 5Section 4.2 Dividing Polynomials1Dividing Polynomials Using S
U. Houston - MATH - 1310
Let P ( x) = -( x - 3)(1 - x )31. What is the degree of this function? a. 4 b. 3 c. 2 d. 1 e. NOA 2. What are the zeros of the function? a. {-3, -1} b. {-1, 3} c. {1, 3} d. {-3, 1} e. NOA7 Let f ( x) = -2 x - 6 x - ( x + 1)11. 8 3. Find the
U. Houston - MATH - 1310
Section 4.1 Polynomial Functions and Their Graphs Definition of a Polynomial Function Let n be a nonnegative integer and let a n , a n -1 ,., a 2 , a1 , a 0 , be real numbers, with a n 0 . The function defined by f ( x) = a n x n + . + a 2 x 2 + a1
U. Houston - MATH - 1310
x 1. Find the domain of: f ( x) = 2 x + 4 x 12a. ( , 6) U (6,2) U (2, ) b. [0, ) c. ( , ) d. ( , 0 ) U ( 0 , ) e. None of the above2. Given x 3 + 1, x &lt; 2 f ( x) = 7, x = 2 2 x, 2 &lt; x Find f(-2). a. 9 b. -7 c. -2 d. 4 e. NOA3. Giv
U. Houston - MATH - 1310
Section 3.7 Inverse Functions Let f be a function with domain A. f is said to be one-to-one if no two elements in A have the same image. Example 1: Determine if the following function is one-to-one. a. Domain a b c b. Domain a b cfRange -1 2 5g
U. Houston - MATH - 1310
Print TestPage 1 of 15PRINTABLE VERSIONPractice Test 3Question 1 GivenCalculate f(8). a) n j k l mj k l m b) nj k l m c) nj k l m d) nj k l m e) n j k l m f) n None of the above.Question 2 GivenCalculate f(2).j k l m a) nj k l m
U. Houston - MATH - 1310
1. Let f(-5) = 9, f(10) = -5, and f(0) = 0. -1 Find f (-5). a. b. c. d. e. Not possible. 9 10 0 NOA7 2. Let f ( x) = . -x+6 Find its inverse.6 a. f ( x) = x+7-1x+6 b. f ( x) = 7 6x - 7 -1 c. f ( x) = x-1e. NOA3. Which of the following func
U. Houston - MATH - 1310
Section 3.5 Maximum and Minimum Values A quadratic equation is of the form f ( x) = ax 2 + bx + c , where a, b, and c are real numbers and a 0 . Graphs of Quadratic Functions The graph of any quadratic function is called a parabola. If a &gt; 0 then th
U. Houston - MATH - 1310
Section 3.6 Combining Functions Let f and g be two functions. The sum f + g, the difference f g, the product fg, and the f (g cant be equal to 0) are functions whose domains are the set of real quotient g numbers common to the domain of f and g (in
U. Houston - MATH - 1310
1. Write f ( x) = - x + 18 x - 1 in standard form.2a. b. c. d. e.f ( x) = -( x - 9) + 80 2 f ( x) = -( x + 9) + 802f ( x) = -( x - 9) - 822f ( x) = -( x + 9) 2 - 82NOA2. Write f ( x) = 9 x - 36 x + 10 in standard form.2a. b. c. d. e
U. Houston - MATH - 1310
g ( x) = x 2 3, 1. Given f ( x ) = x + 1 and find ( g o f )( x).a. x 2 x 2 2 b. x 2+ 2 x + 2 c. x 2 x 2 x2 2x + 2 d. e. None of the above2g ( x) = x 2 3, 2. Given f ( x ) = x + 1 and find ( f o g )(1).a. b. c. d. e. 3 5 -3 -1 None of
U. Houston - MATH - 1310
1. The transformations needed to sketch the graph off ( x) = ( x - 1) + 3,are: a. right 1 unit and up 3 units. b. left 1 unit and down 3 units. c. right 1 unit and down 3 units. d. left 1 units and up 3 units. e. None of the above.2. The transfo
U. Houston - MATH - 1310
Section 3.4 Transforming Functions Definition of Even and Odd Functions Even Function: A function f is an even function if f(-x) = f(x) for all x in the domain of f and the graph is symmetric with respect to the y-axis. This means that the left half
U. Houston - MATH - 1310
1. Given the following piece-wise defined function. x + 3, if x -3 f ( x) = - ( x + 3), if x &lt; - 3 Find f(0) a. 3 b. -3 c. 6 d. 0 e. None of the above2. Find the domain of the following graph. 54 3 2 1 x -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 76y
U. Houston - MATH - 1310
Section 3.3 Modeling Using Variation Direct Variation: If a situation is described by an equation in the form y = kx where k is a nonzero constant, we say that y varies directly as x or y is directly proportional to x. The number k is called the cons
U. Houston - MATH - 1310
1. Let f ( x ) Find f(-1) a. b. c. d. e.= x + x 2.3 2-4 -2 4 0 None of the above2. Given the following mapping Domain f Range a -10 b 0 c 3 d 10 Is f a function? a. Yes b. No3. Given the following mapping Domain f Range a b 3 c d 10 Is f a
U. Houston - MATH - 1310
Section 3.2 Functions and Graphs Definition: The graph of a function f consists of those points (x, y) such that x is in the domain of f and y = f(x). Vertical Line Test If you can draw a vertical line that crosses the graph more than once, it is NOT
U. Houston - MATH - 1310
Section 3.1 Basic Ideas Definition: A function, f, is a rule that assigns to each element x in a set A exactly one elements, called f(x), in a set B. Definition: The set A is called the domain and is the set of all valid inputs for the function. Defi
U. Houston - MATH - 1310
U. Houston - MATH - 1310
Section 2.8 Absolute Value Definition: The absolute value of x, denoted |x|, is the distance x s from 0.Solving Absolute Value Equations If C is positive, then |x| = C if and only if x = C.Special Cases for |x| = C: Case 1: If C is negative then
U. Houston - MATH - 1310
1. Solve. |5 x| + 2 = 17 a. b. c. d. e. x = 10 or x = -20 x = -5 x = -10 or x = 20 x = -3 None of the above2. Solve. 2 + 3|x + 1| &gt; 11 a. [-4, 2] b. (-4, 2) , c. ( 4) U(2, ) , d. ( 4]U[2, ) e. None of the above3. Solve. 2 - 3|x + 1| &gt; -1 a. (-2,
U. Houston - MATH - 1310
1. Solve. -3 &lt; 4 x &lt; -1a. b. c. d. e.(5, 7) [5, 7] (-7, -5) [-7, -5] None of the above.2. Solve. -(3 - x) &lt; -x + 3a. (3, ) b. [3, ) c. (- , 3] d. (- , 3) e. None of the above.3. Solve.1 x+2 1 5 10 2a. (0, 3) b. [0, 3] c. (- 0) U(
U. Houston - MATH - 1310
Print TestPage 1 of 15PRINTABLE VERSIONPractice Test 2Question 1 Find the solutions of the equation | -5x | = 8a) n {x = 0,x = 8/5} j k l m b) n {x = -8/5} j k l m c) n {x = 8/5} j k l m d) n {x = -3,x = -3} j k l m e) n {x = -8/5,x = 8/5} j
U. Houston - MATH - 1310
Section 2.6 Linear Inequalities An inequality in the variable x is linear if each term is a constant or a multiple of x. The inequality will contain an inequality symbol: &lt; &gt; is less than is less than or equal to is greater than is greater than or
U. Houston - MATH - 1310
1. Solve by completing the square.x - 10 x + 10 = 02a. - 5 15 b. 5 15 c. 20 d. 5 15 e. NOA2. Find all solutions of100 x 2 + 49 = 0a. No solution7 b. i 10c.7 107 d. 0, 10 ie. NOA3. Find all solutions ofx + 49 x = 03a. No
U. Houston - MATH - 1310
Section 2.4 An Introduction to Complex Numbers Definition: A complex number is a number that can be written in the form a + bi, where a is called the real part and bi is called the imaginary part. The a and b are real numbers. Complex numbers cannot
U. Houston - MATH - 1310
1. Add. (4 i) + ( -5 + 2i).a. 1 i b. -1 i c. 1 + i d. -1 + i None of the above2. Divide.2+i 1+ i1 3 a. + i 2 2b. c. d. e.2 + 2i -3 + i -2 + i 3 1 - i 2 23. Simplify.i87a. b. c. d. e.1 i -i -1 NOA
U. Houston - MATH - 1310
1. Solve.4 x + 11x + 6 = 02a. b. c. d. e.x = -2, x = 1 x = 3/4, x = -2 x = 6, x = -1 x = -3/4, x = -2 None of the above.2. Solve.x + 5 x - 50 = 02a. b. c. d. e.x = 10 , x = 5 x = -10 , x = -5 x = -10, x = 5 x = -5, x = 10 None of the
U. Houston - MATH - 1310
Section 2.3 Quadratic EquationsSolving by Factoring A quadratic equation is an equation that can be written in the form ax 2 + bx + c = 0 where a, b, and c are real numbers with a 0. To solve a quadratic equation by factoring, rewrite the equation
U. Houston - MATH - 1310
1. Solve the following system.2x y = 5 x + 2y = 5a. b. c. d. e. x=3 (1, 4) (3, 1) No solution. Infinitely many solutions.2. A rectangles length is twice its width. If the perimeter is 132 inches, find the length? a. b. c. d. e. 12 inches 24 inc
U. Houston - MATH - 1310
Section 6.1 2X2 Linear Systems Solving 2X2 Linear Systems To solve a system of two linear equations ax + by = c dx + ey = f means to find values for x and y that satisfy both equations. The system will have exactly one solution, no solution or i
U. Houston - MATH - 1310
Section 2.2 Applications Using Modeling to Solve Problems Step 1: Step 2: Step 3: Step 4: Step 5: Define variables. Express each unknown quantity in terms of one variable. Write the equation in one variable which models the situation given. Solve the
U. Houston - MATH - 1310
Section 2.1 Linear Equations Definition: To solve an equation in the variable x using the algebraic method is to use the rules of algebra to isolate the unknown x on one side of the equation. Definition: To solve an equation in the variable x using t
U. Houston - MATH - 1310
Section 1.2 Lines Definition: The slope of a line measures the steepness of a line. The Slope Formula The slope of a line that passes through two points ( x1 , y1 ) and ( x 2 , y 2 ) on the line is given by y y1 m= 2 x 2 x1 Example 1: Find the slop