Fall 2013 Math Determine whether the lines through the pairs of points A( 3, 2), B(5, 14) and C(3, 2), D( 12, 4) are perpendicular.
|
|
- Loren Lawson
- 6 years ago
- Views:
Transcription
1 Final Exam Answer key Fall 013 Math Determine whether the lines through the pairs of points A( 3, ), B(5, 14) and C(3, ), D( 1, 4) are perpendicular. m 1 = 14 5 ( 3) = 1 8 = 3, m = 4 ( ) 1 3 = 6 15 = 5 1 m 1. They are NOT perpendicular.. Break-Even Analysis A division of the Gibson Corporation manufactures bycycle pumps. Each pump sells for $6, and the variable cost of producing each unit is 60% of the selling price. The monthly fixed costs are $48, 000. What is the break-even point for the division? The cost is $6 (.6) = $3.6 C(x) = 3.6x + 48, 000, R(x) = 6x C(x) = R(x), 3.6x + 48, 000 = 6x, 48, 000 =.4x, x = 0, 000, R(0, 000) = $10, 000 The the break-even operation, the division should manufacture 0, 000 pumps, resulting in a break-even revenue of $10, 000 per month. 3. Using an augmented matrix and the Gauss-Jordan elimination method determine whether the system has a solution and find the solution or solutions, if they exist. (a) x + y + z = 0 x y + z = 9 x + y z = 18 The augmented matrix is R R R /( 3) R R 1 R /( 3) 1 0 / R 1 R 0 1 1/3 3 R 1 3 R R R Answer: x =, y = 1, z = /
2 (b) x y + z = 3 x + y z = 1 y z = The augmented matrix is R R R 3 R R / Answer: The system has no solutions For the system of linear equations x y = x + 3y = 15 (a) write a matrix equation that is equivalent to the system AX = B, where A = [ [ x, X = y [, B = 15 (b) solve the system using an inverse matrix A 1 = X = A 1 B = x = 3, y = 4. [ [ [ = [ = [ = 5. By constructing truth tables prove De Morgan s Law (p q) p q. Truth table: p q p q (p q) p q p q T T T F F F F T F T F F T F F T T F T F F F F F T T T T The fourth and seventh columns are equivalent. Hence, De Morgan s Law is true. Page
3 6. Determine whether the argument is valid. p q p q p q Truth table: p q p q p q p q p q T T F F T T F T F F T F T T F T T F F F F F F T T F T F The entries in the first row are both true, but the corresponding entry for the conclusion is false. Therefore, the argument is invalid.. How many days will it take for a sum of $500 to earn $30 interest if it is deposited in a bank paying ordinary simple interest at the rate of 6% per year? (Use a 365-day year.) 6% per year equals % = per day. Let the number of days be x. Then x = 30, x = = 3 days Loan Amortization A sum of $5, 000 is to be repaid over a 6-year period trough equal installments made at the end of each year. If an interest rate of 9% per year is charged on the unpaid balance and interest calculations are made at the end of each year, determine the size of each installment so that the loan (principal plus interest charges) is amortized at the end of 6 years. P = 5, 000, i = r =.09, n = 6 R = (5, 000)(.09), R = $ (1.09) 6 9. Find the sum of the first seventeen terms of the arithmetic progression whose fourth and eleventh terms are 14 and 35, respectively. a n = a + (n 1)d, a 4 = a + 3d = 14, a 1 1 = a + 10d = 35. Then a = 5, d = 3. S n = n (a + (n 1)d), S 1 = 1 ( 5 + (1 1) 3) = 493. Page 3
4 10. Let U = {, 4, 6, 8, 10, 1, 14, 16, 18}, A = {4, 6, 8, 10}, B = {, 6, 10, 14, 18}, C = {4, 6, 10, 1, 18}. List the elements of the sets (a) (A B C) c A B C = {, 4, 6, 8, 10, 1, 14, 18}, (A B C) c = {16} (b) (A B C) c A B C = {6, 10}, (A B C) c = {, 4, 8, 1, 14, 16, 18} (c) A c (B C) B C = {, 4, 6, 10, 1, 14, 18}, A c = {, 1, 14, 16, 18}, A c (B C) = {, 1, 14, 18} 11. A company car that has a seating capacity of seven is to be used by seven empoloyees who have formed a car pool. If only three of these employees can drive, how many possible seating arrangements are there for the group? P (3, 3) P (4, 4) = 3! 4! = 6 4 = Let S = {s 1, s, s 3, s 4, s 5 } be the sample space associated with an experiment and A = {s, s 3, s 4 }, B = {s, s 5 }. The probability distribution of the experiment is shown in the following table: Outcome s 1 s s 3 s 4 s 5 Probability Find (a) P (A) P (A) = P (s ) + P (s 3 ) + P (s 4 ) = =.6 (b) P (A B) A B = {s }, P (A B) = P (s ) =. Page 4
5 (c) P (A B c ) B c = {s 1, s 3, s 4 }, A B c = {s 1, s, s 3, s 4 }, P (A B c ) = P (s 1 ) + P (s ) + P (s 3 ) + P (s 4 ) = =. 13. Urn A contains five green balls and five blue balls. Urn B contains three green balls and four blue balls. A ball is drawn from urn A and then trasferred to Urn B. A ball is then drawn from Urn B. What is the probability that the transferred ball was green given that the second ball drawn was blue. Let A denote the event that the transferred ball was green and B denote the event that a ball is then drawn from Urn B was blue. We need to find the conditional probability P (A B). By Bayes Theorem P (A B) = P (A) P (B A) P (A) P (B A) + P (A c ) P (B A c ) P (A) = 1, P (B A) = 1, P (Ac ) = 1, P (B Ac ) = 5 8 P (A B) = = 4 9 = An experiment consists of two independent trials. The outcomes of the first trial are A and B with probabilities of occuring equal to.3 and. respectively. The outcomes of the second trial are C and D with probabilities of occuring equal to.8 and. respectively. Draw a tree diagram representing this experiment and use it to find: (a) P (B C) P (B C) = P (B) P (C B) = (.)(.8) =.56 (b) P (D A) P (D A) =. (c) Are A and C independent events? Yes. 15. An exam consists of eight true-or-false questions. If a student guesses at every answer, what is the probability that he or she will answer exactly three questions correctly? Page 5
6 C(8, 3) 8 = = 5 = 3 = Driving Age Requirements The minimum age requirement for a regular driver s license differs from state to state. The frequency distribution for this age requirement in the 50 states given in the following table: Table 1: Driving Age Requirement Distribution Minimum Age Frequency of Occurence (a) Describe a random variable X that is associated with these data. X is a minimum driving age requirement in different states. (b) Find the probability distribution for the random variable X Table : Driving Age Requirement Probability Distribution x P (X = x) (c) Compute mean, variance, and standard deviation of X µ = 15(.04) + 16(.8) + 1(.06) + 18(.5) + 19(.06) + 1(.04) = 1.44, Var(X) = , σ = = If the probability that a certain tennis player will serve an ace is., what is the probability that she will serve exactly three aces out of seven serves? (Assume that the seven serves are independent). p = C(, 3)(.) 3 (.8) 4 = Let Z be the standard normal random variable. (a) Find the probability P (0.3 < Z < 1.64) Take data from the provided table. P (0.3 < Z < 1.64) = P (Z < 1.64) P (Z < 0.3) = = Page 6
7 (b) Find the value of z if z satisfies the condition P (Z < z) = z =.48 Page
8 The Standard Normal Distribution z Page 8
9 19. The tread lives of the Super Titan radial tires under normal driving conditions are normally distributed with a mean of 35, 000 mi and a standard deviation of 305 mi. What is the probability that a tire selected at random will have a tread life of less than 40, 000 mi? P (X < 40, 000) = P ( Z < ) 40, , 000 = P (Z < 1.56) = A charitable organization estimates that in a certain community 80% of the people who make a donation this year will make a donation next year. It also estimates that 30% of the people who do not make a donation this year will make a donation next year. (a) Find the transition matrix corresponding to this situation. T = [ (b) Suppose that this year 40% of the people made a donation. What is the initial distribution matrix? X 0 = [ (c) What percentage of the people is expected to donate next year? X 1 = T X 0 = [ [ = [ (d) What percentage of the people is expected to donate in the long run? T X = X, where X = [ x y.8x +.3y = x.x +.y = y x + y = 1 [ 60 X = 40.x +.3y = 0.x.3y = 0 x + y = 1 x 3y = 0 x + y = 1 y = 3 ( x x = 3 5 = 60% ) x = 1 y = 5 = 40% Page 9
Systems of Linear Equations in Two Variables. Break Even. Example. 240x x This is when total cost equals total revenue.
Systems of Linear Equations in Two Variables 1 Break Even This is when total cost equals total revenue C(x) = R(x) A company breaks even when the profit is zero P(x) = R(x) C(x) = 0 2 R x 565x C x 6000
More informationMath 101 Final Exam Review Solutions. Eric Schmutz
Math 101 Final Exam Review Solutions Eric Schmutz Problem 1. Write an equation of the line passing through (,7) and (-1,1). Let (x 1, y 1 ) = (, 7) and (x, y ) = ( 1, 1). The slope is m = y y 1 x x 1 =
More informationMath 1313 Course Objectives. Chapter.Section Objective and Examples Week Covered 1.2 Slopes, Equations of a line.
Math 1313 Course Objectives 1.2 Slopes, Equations of a line. Example: Find the equation of the line, in pointslope form and slope-intercept form, that passes through (3, 5) and (0,1). Parallel and Perpendicular
More informationRe: January 27, 2015 Math 080: Final Exam Review Page 1 of 6
Re: January 7, 015 Math 080: Final Exam Review Page 1 of 6 Note: If you have difficulty with any of these problems, get help, then go back to the appropriate sections and work more problems! 1. Solve for
More informationMath 101: Final Exam Review Sheet
Math 101: Final Exam Review Sheet (Answers are at the end.) Exam Coverage: Everything we learned in the course. Exam Date: Friday, December 11, 2015 Exam Time: 10:30 am 12:30 pm (Arrive at least 10 minutes
More informationPattern & Algebra Practice Problems
Pattern & Algebra Practice Problems Solve Linear Inequalities 1. Solve for x. A. x > -3 B. x > 0 C. x < 0 D. x < -3 4x < -6 + 2x Symbolize Problem Situations 2. Scott is draining his swimming pool. The
More informationUNIVERSITY OF KWA-ZULU NATAL
UNIVERSITY OF KWA-ZULU NATAL EXAMINATIONS: June 006 Solutions Subject, course and code: Mathematics 34 MATH34P Multiple Choice Answers. B. B 3. E 4. E 5. C 6. A 7. A 8. C 9. A 0. D. C. A 3. D 4. E 5. B
More informationMAT 121: Mathematics for Business and Information Science Final Exam Review Packet
MAT 121: Mathematics for Business and Information Science Final Exam Review Packet A. Calculate the exact distance (i.e., simplified radicals where appropriate, not decimal approximations using a calculator)
More informationMATH6 - Introduction to Finite Mathematics
MATH6 - Introduction to Finite Mathematics Final Exam ANSWES June, 007. (6 points) Find the solution set for the following system: 3x y 8z+ 7t = x+ y z t = 3 x y 3z+ 3t =. 3 8 7 3 3 3 3 3 8 7 3 3 3 0 5
More informationNotes for Math 324, Part 17
126 Notes for Math 324, Part 17 Chapter 17 Common discrete distributions 17.1 Binomial Consider an experiment consisting by a series of trials. The only possible outcomes of the trials are success and
More information1.4 CONCEPT QUESTIONS, page 49
.4 CONCEPT QUESTIONS, page 49. The intersection must lie in the first quadrant because only the parts of the demand and supply curves in the first quadrant are of interest.. a. The breakeven point P0(
More informationIntroduction to Probability, Fall 2009
Introduction to Probability, Fall 2009 Math 30530 Review questions for exam 1 solutions 1. Let A, B and C be events. Some of the following statements are always true, and some are not. For those that are
More informationMTH 201 Applied Mathematics Sample Final Exam Questions. 1. The augmented matrix of a system of equations (in two variables) is:
MTH 201 Applied Mathematics Sample Final Exam Questions 1. The augmented matrix of a system of equations (in two variables) is: 2 1 6 4 2 12 Which of the following is true about the system of equations?
More informationMATH 1710 College Algebra Final Exam Review
MATH 1710 College Algebra Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) There were 480 people at a play.
More informationName: Section Registered In:
Name: Section Registered In: Math 125 Exam 1 Version 1 February 21, 2006 60 points possible 1. (a) (3pts) Define what it means for a linear system to be inconsistent. Solution: A linear system is inconsistent
More informationSection 2.3 Objectives
Section 2.3 Objectives Use the inequality symbols to compare two numbers. Determine if a given value is a solution of an inequality. Solve simple inequalities. Graph the solutions to inequalities on the
More informationRecord your answers and work on the separate answer sheet provided.
MATH 106 FINAL EXAMINATION This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually.
More informationMATHEMATICS: PAPER I
NATIONAL SENIOR CERTIFICATE EXAMINATION NOVEMBER 017 MATHEMATICS: PAPER I Time: 3 hours 150 marks PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This question paper consists of 11 pages and an Information
More informationGRADE 12 SEPTEMBER 2012 MATHEMATICS P1
Province of the EASTERN CAPE EDUCATION NATIONAL SENIOR CERTIFICATE GRADE 12 SEPTEMBER 2012 MATHEMATICS P1 MARKS: 150 TIME: 3 hours *MATHE1* This question paper consists of 8 pages, 3 diagram sheets and
More informationNotes for Math 324, Part 19
48 Notes for Math 324, Part 9 Chapter 9 Multivariate distributions, covariance Often, we need to consider several random variables at the same time. We have a sample space S and r.v. s X, Y,..., which
More informationCreated by T. Madas ARITHMETIC SERIES. Created by T. Madas
ARITHMETIC SERIES Question 1 (**) non calculator The first few terms of an arithmetic sequence are given below 5, 9, 13, 17, 21,... a) Find the fortieth term of the sequence. b) Determine the sum of the
More information(MATH 1203, 1204, 1204R)
College Algebra (MATH 1203, 1204, 1204R) Departmental Review Problems For all questions that ask for an approximate answer, round to two decimal places (unless otherwise specified). The most closely related
More informationFall IM I Exam B
Fall 2011-2012 IM I Exam B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following equations is linear? a. y = 2x - 3 c. 2. What is the
More informationALGEBRA I SEMESTER EXAMS PRACTICE MATERIALS SEMESTER (1.1) Examine the dotplots below from three sets of data Set A
1. (1.1) Examine the dotplots below from three sets of data. 0 2 4 6 8 10 Set A 0 2 4 6 8 10 Set 0 2 4 6 8 10 Set C The mean of each set is 5. The standard deviations of the sets are 1.3, 2.0, and 2.9.
More informationMATH 081. Diagnostic Review Materials PART 2. Chapters 5 to 7 YOU WILL NOT BE GIVEN A DIAGNOSTIC TEST UNTIL THIS MATERIAL IS RETURNED.
MATH 08 Diagnostic Review Materials PART Chapters 5 to 7 YOU WILL NOT BE GIVEN A DIAGNOSTIC TEST UNTIL THIS MATERIAL IS RETURNED DO NOT WRITE IN THIS MATERIAL Revised Winter 0 PRACTICE TEST: Complete as
More informationGeometry Pre-Test. Name: Class: Date: ID: A. Multiple Choice Identify the choice that best completes the statement or answers the question.
Class: Date: Geometry Pre-Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. An equilateral triangle has three sides of equal length. What is the equation
More information7.1 Solving Systems of Equations
Date: Precalculus Notes: Unit 7 Systems of Equations and Matrices 7.1 Solving Systems of Equations Syllabus Objectives: 8.1 The student will solve a given system of equations or system of inequalities.
More informationCHAPTER 7: Systems and Inequalities
(Exercises for Chapter 7: Systems and Inequalities) E.7.1 CHAPTER 7: Systems and Inequalities (A) means refer to Part A, (B) means refer to Part B, etc. (Calculator) means use a calculator. Otherwise,
More informationMath 3 Proportion & Probability Part 2 Sequences, Patterns, Frequency Tables & Venn Diagrams
Math 3 Proportion & Probability Part 2 Sequences, Patterns, Frequency Tables & Venn Diagrams 1 MATH 2 REVIEW ARITHMETIC SEQUENCES In an Arithmetic Sequence the difference between one term and the next
More informationALGEBRA 1 END OF COURSE PRACTICE TEST
1) (A1.FLQE.5) A satellite television company charges a one-time installation fee and a monthly service charge. The total cost is modeled by the function y = 40 + 90x. Which statement represents the meaning
More informationMAT College Algebra - Gateway 2: Linear Equations and. Name: Date: B
Mathematics Department MAT 10 - College Algebra - Gateway : Linear Equations and Name: Date: 9919 B This exam covers material from Sections 1.1, 1.7,.1,.3, 3.1-3.3,.1, and.. The topics covered are function
More informationPractice Final Exam Answers
Practice Final Exam Answers 1. AutoTime, a manufacturer of electronic digital timers, has a monthly fixed cost of $48,000 and a production cost $8 per timer. The timers sell for $14 apiece. (a) (3 pts)
More informationMAT 135. In Class Assignments
MAT 15 In Class Assignments 1 Chapter 1 1. Simplify each expression: a) 5 b) (5 ) c) 4 d )0 6 4. a)factor 4,56 into the product of prime factors b) Reduce 4,56 5,148 to lowest terms.. Translate each statement
More information3. If 4x = 0, the roots of the equation are (1) 25 and 25 (2) 25, only (3) 5 and 5 (4) 5, only 3
ALGEBRA 1 Part I Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each statement or question, choose the word or expression that,
More informationPage Points Score Total: 100
Math 1130 Spring 2019 Sample Midterm 3c 4/11/19 Name (Print): Username.#: Lecturer: Rec. Instructor: Rec. Time: This exam contains 10 pages (including this cover page) and 10 problems. Check to see if
More informationMath Fall 2012 Exam 1 UMKC. Name. Student ID. Instructions: (a) The use of laptop or computer is prohibited.
Math - Fall Exam UMKC Name Student ID Instructions: (a) The use of laptop or computer is prohibited. (b) Total time allowed for the exam: 75 min. (c) Calculators may not be shared. (d) For Part (Problems
More informationEstadística I Exercises Chapter 4 Academic year 2015/16
Estadística I Exercises Chapter 4 Academic year 2015/16 1. An urn contains 15 balls numbered from 2 to 16. One ball is drawn at random and its number is reported. (a) Define the following events by listing
More informationChapter 1: Whole Numbers
Chapter 1: Whole Numbers Prep Test 1. 8. 1 3 6 7 8 9 1 3. a and D; b and E; c and A; d and B; e and F; f and C.. Fifty Go Figure On the first trip, the two children row over. The second trip, one child
More informationPage: Total Points: Score:
Math 1130 Spring 2019 Sample Final B 4/29/19 Name (Print): Username.#: Lecturer: Rec. Instructor: Rec. Time: This exam contains 14 pages (including this cover page) and 12 problems. Check to see if any
More informationMath P (A 1 ) =.5, P (A 2 ) =.6, P (A 1 A 2 ) =.9r
Math 3070 1. Treibergs σιι First Midterm Exam Name: SAMPLE January 31, 2000 (1. Compute the sample mean x and sample standard deviation s for the January mean temperatures (in F for Seattle from 1900 to
More informationLesson 8: Representing Proportional Relationships with Equations
Lesson 8: Representing Proportional Relationships with Equations Student Outcomes Students use the constant of proportionality to represent proportional relationships by equations in real world contexts
More informationFinite Math - Fall Section Present Value of an Annuity; Amortization
Finite Math - Fall 016 Lecture Notes - 9/1/016 Section 3. - Present Value of an Annuity; Amortization Amortization Schedules. Suppose you are amortizing a debt by making equal payments, but then decided
More informationSystem of Linear Equations. Slide for MA1203 Business Mathematics II Week 1 & 2
System of Linear Equations Slide for MA1203 Business Mathematics II Week 1 & 2 Function A manufacturer would like to know how his company s profit is related to its production level. How does one quantity
More informationSolutions to Exercises (Sections )
s to Exercises (Sections 1.1-1.10) Section 1.1 Exercise 1.1.1: Identifying propositions (a) Have a nice day. : Command, not a proposition. (b) The soup is cold. : Proposition. Negation: The soup is not
More informationChapter 8 Sequences, Series, and Probability
Chapter 8 Sequences, Series, and Probability Overview 8.1 Sequences and Series 8.2 Arithmetic Sequences and Partial Sums 8.3 Geometric Sequences and Partial Sums 8.5 The Binomial Theorem 8.6 Counting Principles
More informationMath st Homework. First part of Chapter 2. Due Friday, September 17, 1999.
Math 447. 1st Homework. First part of Chapter 2. Due Friday, September 17, 1999. 1. How many different seven place license plates are possible if the first 3 places are to be occupied by letters and the
More informationMath 10 - Compilation of Sample Exam Questions + Answers
Math 10 - Compilation of Sample Exam Questions + Sample Exam Question 1 We have a population of size N. Let p be the independent probability of a person in the population developing a disease. Answer the
More informationMathematics Level D: Lesson 2 Representations of a Line
Mathematics Level D: Lesson 2 Representations of a Line Targeted Student Outcomes Students graph a line specified by a linear function. Students graph a line specified by an initial value and rate of change
More informationreview for finals 10. If f (x) = x 2 A If f (x) = x 0 + x x 1, find f (4). 13. If f (x) = (x 0 + x 1 2 ) 2, find f (9).
Name: ate: 1. If g(x) = (ax 1 x) 2, express g(10) in simplest form. 2. The value of the x-intercept for the graph of x 5y = 0 is 10. 5. 5. What is the inverse of the function y = 2x +? x = 1 2 y 2. y =
More information2014 SM4 Revision Questions Distributions
2014 SM4 Revision Questions Distributions Normal Q1. Professor Halen has 184 students in his college mathematics class. The scores on the semester exam are normally distributed with a mean of 72.3 and
More informationExam III Review Math-132 (Sections 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 8.1, 8.2, 8.3)
1 Exam III Review Math-132 (Sections 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 8.1, 8.2, 8.3) On this exam, questions may come from any of the following topic areas: - Union and intersection of sets - Complement of
More informationCoordinate Algebra A Final Exam Review
Class: Date: Coordinate Algebra A Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. Do NOT write on the test. You may use your calculator.
More informationChapter (4) Discrete Probability Distributions Examples
Chapter (4) Discrete Probability Distributions Examples Example () Two balanced dice are rolled. Let X be the sum of the two dice. Obtain the probability distribution of X. Solution When the two balanced
More informationChapter 1: Whole Numbers
1 Chapter 1: Whole Numbers Prep Test 1. 8 2. 1 2 3 5 6 7 8 9 1 3. a and D; b and E; c and A; d and B; e and F; f and C. 5. fifty Go Figure Section 1.1 On the first trip, the two children row over. The
More informationRecord your answers and work on the separate answer sheet provided.
MATH 106 FINAL EXAMINATION This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually.
More informationWeBWorK demonstration assignment
WeBWorK demonstration assignment The main purpose of this WeBWorK set is to familiarize yourself with WeBWorK. Here are some hints on how to use WeBWorK effectively: After first logging into WeBWorK change
More informationHow to handle and solve a linear equation (what s a linear equation?) How to draw the solution set for a linear inequality
Study guide for final exam, Math 1090 - College Algebra for Business and Social Sciences This guide is meant to be a help on studying what I think is most important important that you learn form this exam,
More informationSystems of Equations and Inequalities
1 Systems of Equations and Inequalities 2015 03 24 2 Table of Contents Solving Systems by Graphing Solving Systems by Substitution Solve Systems by Elimination Choosing your Strategy Solving Systems of
More informationSkills Practice Skills Practice for Lesson 1.1
Skills Practice Skills Practice for Lesson. Name Date Tanks a Lot Introduction to Linear Functions Vocabulary Define each term in your own words.. function 2. linear function 3. independent variable 4.
More informationSection 11.3 Rates of Change:
Section 11.3 Rates of Change: 1. Consider the following table, which describes a driver making a 168-mile trip from Cleveland to Columbus, Ohio in 3 hours. t Time (in hours) 0 0.5 1 1.5 2 2.5 3 f(t) Distance
More informationPre-Algebra Semester 1 Practice Exam B DRAFT
. Evaluate x y 5 6 80 when x = 0 and y =.. Which expression is equivalent to? + + + +. In Pre-Algebra class, we follow the order of operations in evaluating expressions. Which operation should a student
More informationDiscussion 03 Solutions
STAT Discussion Solutions Spring 8. A new flavor of toothpaste has been developed. It was tested by a group of people. Nine of the group said they liked the new flavor, and the remaining indicated they
More informationCHAPTER 8: Polar 1. Convert to polar.
CHAPTER 8: Polar 1. Convert to polar. a. 3,. Convert to rectangular. a. 4, 3 b. 4 4i b. 5cis10 3. Use DeMoivre s Theorem to find a. i 8 4. Graph a. r 4cos3 b. the cube roots of 4 4 3i b. r 3sin 5. Convert
More informationAlgebraic Expressions
6-1 Algebraic Expressions Algebraic expressions can be written from verbal descriptions. Likewise, verbal descriptions can be written from algebraic expressions. In both cases, it is important to look
More informationAlgebra I Midterm Exam Review
Chapter 1: Expressions, Equations, and Functions Lesson 1.1 Variables and Expressions Write a verbal expression for each algebraic expression. 23f 5m 2 + 2c 3 4n 1 7 Write an algebraic expression for each
More informationMATH 1310 (College Mathematics for Liberal Arts) - Final Exam Review (Revised: Fall 2016)
MATH 30 (College Mathematics for Liberal Arts) - Final Exam Review (Revised: Fall 206) This Review is comprehensive but should not be the only material used to study for the Final Exam. It should not be
More informationEngage Education Foundation
A Free Exam for 2006-15 VCE study design Engage Education Foundation Units 3 and 4 Further Maths: Exam 2 Practice Exam Solutions Stop! Don t look at these solutions until you have attempted the exam. Any
More informationCourse 1 Solutions November 2001 Exams
Course Solutions November Exams . A For i =,, let R = event that a red ball is drawn form urn i i B = event that a blue ball is drawn from urn i. i Then if x is the number of blue balls in urn, ( R R)
More informationSection 6.2 Larger Systems of Linear Equations
Section 6.2 Larger Systems of Linear Equations Gaussian Elimination In general, to solve a system of linear equations using its augmented matrix, we use elementary row operations to arrive at a matrix
More informationARITHMETIC PROGRESSIONS
ARITHMETIC PROGRESSIONS 93 ARITHMETIC PROGRESSIONS 5 5.1 Introduction You must have observed that in nature, many things follow a certain pattern, such as the petals of a sunflower, the holes of a honeycomb,
More informationGauss-Jordan Row Reduction and Reduced Row Echelon Form
Gauss-Jordan Row Reduction and Reduced Row Echelon Form If we put the augmented matrix of a linear system in reduced row-echelon form, then we don t need to back-substitute to solve the system. To put
More informationUnit 3 and 4 Further Mathematics: Exam 2
A non-profit organisation supporting students to achieve their best. Unit 3 and 4 Further Mathematics: Exam 2 Practice Exam Solutions Stop! Don t look at these solutions until you have attempted the exam.
More informationCh 13 & 14 - Regression Analysis
Ch 3 & 4 - Regression Analysis Simple Regression Model I. Multiple Choice:. A simple regression is a regression model that contains a. only one independent variable b. only one dependent variable c. more
More informationAlgebra 2 Level 2. Final Exam June 2003
Algebra 2 Level 2 Final Exam June 2003 Teachers: Chris Doucette, Frances Tee, Jim Williams Name Directions: Formulas are provided in each section of the exam and there is also a formula sheet on the last
More informationMath Final Exam December 14, 2009 Page 1 of 5
Math 201-803-Final Exam December 14, 2009 Page 1 of 5 (3) 1. Evaluate the expressions: (a) 10 C 4 (b) 10 P 4 (c) 15!4! 3!11! (4) 2. (a) In how many ways can a president, a vice president and a treasurer
More informationSection 2.2 Objectives
Section 2.2 Objectives Solve multi-step equations using algebra properties of equality. Solve equations that have no solution and equations that have infinitely many solutions. Solve equations with rational
More informationGrade 6 Math Circles. Gauss Contest Preparation - Solutions
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 6 Math Circles March 25/26, 2014 Gauss Contest Preparation - Solutions General Information The Gauss
More informationAlgebra 1 Unit 6: Linear Inequalities and Absolute Value Guided Notes
Section 6.1: Solving Inequalities by Addition and Subtraction How do we solve the equation: x 12 = 65? How do we solve the equation: x 12 < 65? Graph the solution: Example 1: 12 y 9 Example 2: q + 23
More informationPractice Questions for Math 131 Exam # 1
Practice Questions for Math 131 Exam # 1 1) A company produces a product for which the variable cost per unit is $3.50 and fixed cost 1) is $20,000 per year. Next year, the company wants the total cost
More informationWeek 04 Discussion. a) What is the probability that of those selected for the in-depth interview 4 liked the new flavor and 1 did not?
STAT Wee Discussion Fall 7. A new flavor of toothpaste has been developed. It was tested by a group of people. Nine of the group said they lied the new flavor, and the remaining 6 indicated they did not.
More informationMAT 111 Final Exam Fall 2013 Name: If solving graphically, sketch a graph and label the solution.
MAT 111 Final Exam Fall 2013 Name: Show all work on test to receive credit. Draw a box around your answer. If solving algebraically, show all steps. If solving graphically, sketch a graph and label the
More informationDiscussion 01. b) What is the probability that the letter selected is a vowel?
STAT 400 Discussion 01 Spring 2018 1. Consider the following experiment: A letter is chosen at random from the word STATISTICS. a) List all possible outcomes and their probabilities. b) What is the probability
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA. Tuesday, June 12, :15 to 4:15 p.m., only
ALGEBRA I The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION ALGEBRA I Tuesday, June 12, 2018 1:15 to 4:15 p.m., only Student Name School Name The possession or use of any communications
More informationFunction: State whether the following examples are functions. Then state the domain and range. Use interval notation.
Name Period Date MIDTERM REVIEW Algebra 31 1. What is the definition of a function? Functions 2. How can you determine whether a GRAPH is a function? State whether the following examples are functions.
More informationDepartment of Statistics & Operations Research College of Science King Saud University. STAT 324 Supplementary Examination Second Semester
بسم االله الرحمن الرحيم Department of Statistics & Operations Research College of Science King Saud University STT 324 Supplementary Examination Second Semester 1424-1425 Student Name: Student Number:
More informationUNLV University of Nevada, Las Vegas
UNLV University of Nevada, Las Vegas The Department of Mathematical Sciences Information Regarding Math 14 Final Exam Revised.8.018 While all material covered in the syllabus is essential for success in
More informationMath 1314 Test 2 Review Lessons 2 8
Math 1314 Test Review Lessons 8 CASA reservation required. GGB will be provided on the CASA computers. 50 minute exam. 15 multiple choice questions. Do Practice Test for extra practice and extra credit.
More informationMath Analysis Notes Mrs. Atkinson 1
Name: Math Analysis Chapter 7 Notes Day 6: Section 7-1 Solving Systems of Equations with Two Variables; Sections 7-1: Solving Systems of Equations with Two Variables Solving Systems of equations with two
More informationChapter 3 Test, Form 1
Chapter 3 Test, Form 1 Write the letter for the correct answer in the blank at the right of each question. 1. Where does the graph of y = 3x 18 intersect the x-axis? A (0, 6) B (0, 6) C (6, 0) D ( 6, 0)
More information1 Functions, Graphs and Limits
1 Functions, Graphs and Limits 1.1 The Cartesian Plane In this course we will be dealing a lot with the Cartesian plane (also called the xy-plane), so this section should serve as a review of it and its
More informationLinear Equations in One Variable *
OpenStax-CNX module: m64441 1 Linear Equations in One Variable * Ramon Emilio Fernandez Based on Linear Equations in One Variable by OpenStax This work is produced by OpenStax-CNX and licensed under the
More informationSenior Math Circles November 19, 2008 Probability II
University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Senior Math Circles November 9, 2008 Probability II Probability Counting There are many situations where
More informationNATIONAL SENIOR CERTIFICATE GRADE 11
NATIONAL SENIOR CERTIFICATE GRADE 11 MATHEMATICS P1 NOVEMBER 01 MARKS: 150 TIME: hours This question paper consists of 8 pages. Copyright reserved Mathematics/P1 DBE/November 01 INSTRUCTIONS AND INFORMATION
More informationSeven is less than 11. Four more than seventeen. Four is not equal to three.
Prealgebra.1: Translations, Simplifying and Evaluating Expressions Words such as,, and indicate addition. Words such as,, and indicate subtraction. Translate each of the following into mathematical symbols.
More informationtheir contents. If the sample mean is 15.2 oz. and the sample standard deviation is 0.50 oz., find the 95% confidence interval of the true mean.
Math 1342 Exam 3-Review Chapters 7-9 HCCS **************************************************************************************** Name Date **********************************************************************************************
More informationHere are the exams I wrote when teaching Math 115 in Fall 2018 at Ferris State University. Each exam is followed by its solutions.
Here are the exams I wrote when teaching Math 5 in Fall 208 at Ferris State University. Each exam is followed by its solutions. Fall 208 Exam. (a) Find the slope of the line passing through the points
More informationRATES AND UNIT RATES
RATES AND UNIT RATES 7.. 7.. Rate of change is a ratio that describes how one quantity is changing with respect to another. Unit rate is a rate that compares the change in one quantity to a one-unit change
More informationMath 1101 Chapter 2 Review Solve the equation. 1) (y - 7) - (y + 2) = 4y A) B) D) C) ) 2 5 x x = 5
Math 1101 Chapter 2 Review Solve the equation. 1) (y - 7) - (y + 2) = 4y A) - 1 2 B) - 9 C) - 9 7 D) - 9 4 2) 2 x - 1 3 x = A) -10 B) 7 C) -7 D) 10 Find the zero of f(x). 3) f(x) = 6x + 12 A) -12 B) -2
More informationReview for Final Review
Topics Review for Final Review 1. Functions and equations and graphing: linear, absolute value, quadratic, polynomials, rational (first 1/3 of semester) 2. Simple Interest, compounded interest, and continuously
More informationPart 1 1 st 6weeks material
Name Date Period Part 1 1 st 6weeks material 1. Write an expression that can be used to determine the number of blocks in the n th figure. 2. Write an expression to represent the sequence below: 5, 8,
More information