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# Finite Math with Applications MATH 1313

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This 18 page Class Notes was uploaded by Alvena McDermott on Saturday September 19, 2015. The Class Notes belongs to MATH 1313 at University of Houston taught by Cornelia Schirber in Fall. Since its upload, it has received 5 views. For similar materials see /class/208390/math-1313-university-of-houston in Mathmatics at University of Houston.

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Date Created: 09/19/15

Math 1313 Course Objectives ChapterSection Objective and Examples Material Covered by End of Week 12 Given two points on a line determine the slope and 1 equation of the line in point slope form and slope intercept form Example Find the equation of the line in point slope form and slopeintercept form that passes through 3 5 and 01 ChapterSection Objective and Examples Material Covered by End of Week 13 Given a system of linear equations determine 1 whether is has a unique solution no solution or inf39mitely many solutions Example Determine whether the following system has a unique solution no solution or in nitely many solutions y 3X 6 y 5x 10 ChapterSection Objective and Examples Material Covered by End of Week 31 Given a linear system of inequalities determine the 1 solution set Example Determine the solution set for the following system of linear inequalities Math 1313 Course Objectives 1 2x4ygt16 x3y37 Given the graph of a system of linear inequalities determine the system of linear inequalities Example Write the system of linear inequalities that describes the shaded region 10 ChapterSecti0n Objective and Examples Material Covered by End of Week Given a linear depreciation problem nd the rate of depreciation the expression that expresses the book value at the end of t years and the value of the asset after a given amount of years Example A company purchased a car in 2000 for 13000 The car is depreciated linearly for 5 years The scrap value of the car is 4000 What is the rate of depreciation Write the expression that expresses the book value of the car aftert years of use What is the value of the car in 2003 Given the production cost selling price of a product and the xed costs of the company nd the cost function revenue function pro t function and compute the pro t or loss corresponding to certain production levels 2 Math 1313 Course Objectives Example A company has a fixed cost of 100000 The product sells for 20 per unit What is the cost function What is the revenue function What is the pro t function What is the breakeven point What is the profit or loss corresponding to a production level of 12000 and 20000 units and a production cost of 14 for each unit produced ChapterSecti0n Objective and Examples Material Covered by End of Week Given a word problem find break even quantity break even revenue and break even point for the company Example A company has a fixed cost of 100000 The product sells for 20 per unit What is the breakeven quantity What is the breakeven revenue What is the breakeven point and a production cost of 14 for each unit produced 2 ChapterSecti0n Objective and Examples Material Covered by End of Week Given a set of data or a word problem nd the equation for the least square line of the data and use this equation to predict a certain future value Example The size of the average farm in a certain town has been growing steadily over the years The accompanying data was collected and gives the size of the average farm y in acres from 1945 to 1995 Here x 0 corresponds to the beginning of the year 1945 2 Math 1313 Course Objectives Year x 0 10 20 30 40 Number of Acres y 57 63 76 88 92 Find the equation of the leastsquares line for these data Use the result in part a to estimate the size of the average farm in the year 1998 E Fquot ChapterSecti0n Objective and Examples Material Covered by End of Week 22 Given a linear system of equations give the 4 augmented matrix Example Write the augmented matrix corresponding to the given system of equations Given an augmented matrix give the corresponding system of equations Example Write the system of equations corresponding to the given augmented matrix 1 6 9 0 31 7 Given an augmented matrix determine whether its in row reduced form Example Indicate Whether the matrix is in row reduced form 109 01 7 Given a linear system of equations use the Gauss Jordan elimination method to solve Math 1313 Course Objectives Example Solve the system of linear equations using the GaussJordan elimination method 2x 7 3y 7 3x y 4 ChapterSecti0n Objective and Examples Material Covered by End of Week 23 Given an augmented matrix in row reduced form 4 determine the solution or solutions if they exist Example Given that the augmented matrix in row reduced form is equivalent to the augmented matrix of a system of linear equations Determine whether the system has a solution and nd the solutions to the system if they exist 1 0 3 0 l 9 0 0 0 Given a system of linear equations use the Gauss Jordan elimination method to solve Example Solve the system of linear equations using the GaussJordan elimination method 2x 7 y 3 x 2y 4 2x 3y 7 ChapterSecti0n Objective and Examples Material Covered by End of Week 24 Given a matrix find its size a certain element its 5 transpose etc Math 1313 Course Objectives 5 Example Refer to the following matrices 9 2 3 4 5 8 10 11 A 9 0 6 7 2 l 0 0 a What is the size of A b Find 6134 c Find the transpose of A Given matrices perform indicated operations Example Refer to the following matrices 6 5 8 5 6 9 2 4 A J B 3 3 2Cl 3 8 9 0 4 7 0 l 7 1 Perform the indicated operation if possible a AC b BiD Given a matrix equation solve for an indicated variable Example Solve for ag and y 9 4 2 5 9 1 a b c 589l867 84dL4 0 3 6 8 10 y e f 9 ChapterSection Objective and Examples Material Covered by End of Week Math 1313 Course Objectives 6 25 Given matrices find an indicated product if possible 6 9 3 Example Let A and 0 0 7 9 2 3 4 B 5 6 l 9 Compute the product AB if 3 0 1 1 possible 9 6 7 2 2 1 Let A 8 7 and B l 2 Compute the 44 50 3 7 product AB ifpossible Given a word problem use matrix multiplication to solve Example The total output of loudspeaker systems of the Acrosonic Company in their three production facilities for May and June is given by the matrices A and B respectively where M odelA M 061613 M odelC M odelD A Location 120 321 200 130 Location 340 560 333 110 Location 630 230 34 0 M odelA M 061613 M odelC M odelD Location 143 340 230 100 2 Location 200 440 200 100 Location 22 400 3 200 The unit production costs and selling prices for these loudspeakers are given by matrices C and D respectively where Modell 130 Modell 230 M 061613 240 M 061613 340 and D M odelC 330 M odelC 440 M odelD 500 M odelD 670 Compute AC and wain the meaning of the entries Math 1313 Course Objectives ChapterSection Objective and Examples Material Covered by End of Week 26 Given two matrices show that they are inverses of each other Example Show that the given matrices are inverses of each other 1 3 2 3 and 1 2 1 1 Given a matrix find it s inverse if it exists Example Find the inverse of the given matrix if it exists Verify your answer 6 7 1 9 Given a system of equations use the inverse of the coefficient matrix to solve the problem 2x5y3 x3y2 Given a word problem write it s corresponding system of equations write the system as a matrix equation and use the inverse of the coefficient matrix to solve the problem Example A cruise ship charges 8 adult and 4 child for a roundtrip ticket On a certain weekend in July 1000 people took the cruise on Friday and 800 people took the cruise on Saturday The total receipts for Friday were 6400 and the total receipts for Saturday were 4800 a Write the each system of equations as a matrix equation b Determine how many adults and children took the cruise on Friday and Saturday 6 Math 1313 Course Objectives ChapterSection Objective and Examples Material Covered by End of Week 32 33 Set up and solve a linear programing problem 6 7 Example A company manufactures two products A and B on two machines I and II It has been determined that the company will realize a pro t of 3 on each unit of product A and a profit of 4 on each unit of product B To manufacture a unit of product A requires 6 min on machine I and 5 min on machine II To manufacture a unit of product B requires 9 min on machine I and 4 min on machine II The company has 5 hours of machine time on machine I and 3 hours of machine time on machine II in each work shift How many units of each product should be produced in each shift to maximize the company s pro t Set up the linear programming problem then solve it ChapterSection Objective and Examples Material Covered by End of Week 5 l 52 53 Given a certain math of nance problem recognize 7 8 8 what kind of problem it is and solve it The kind of problems given will be simple interest future value or present value with simple interest effective rate future value or present value with compound interest future value or present value of an annuity amortization or sinking fund Example A company would like to have 50000 in 2 years to replace machinery The account they wish to invest in earns 345 per year compounded quarterly How much should they deposit into this Math 1313 Course Objectives account each quarter to have the desired funds in 2 years a What kind of problem is this b Solve the problem Example Karen has decided to deposit 300 each month into an account that earns 234 per year compounded monthly How much will she have in this account after 3 years a What kind of problem is this b Solve the problem ChapterSecti0n Objective and Examples Material Covered by End of Week 61 Given sets list the subsets and proper subsets of a set 9 Find the union intersection and0r complement of ceItajn given sets Example Let U l234567abcdeA l2345abc B l356acd and C 247bde and D l2a a List the subsets of D b Find A U B 3 H C U A Use Venn diagram shading to nd the union intersection and0r complement of certain given sets Math 1313 Course Objectives 10 Example Given the following Venn diagram shade the given set C n B U A U ChapterSecti0n Objective and Examples Material Covered by End of Week 62 Find the number in sets by using formulas or Venn 10 diagram shading Example Of 30 elementary school children 15 read a book last summer 17 practiced math last summer and 7 read a book and practiced math last summer How many of the 30 children a did not read a book last summer b read a book but did not practice math last summer c did not read a book and did not practice math last summer ChapterSecti0n Objective and Examples Material Covered by End of Week 63 64 Solve word problems by using counting techniques 10 11 such as the multiplication principle combination or permutation Math 1313 Course Objectives 11 Example A coin is tossed 20 times how many outcomes are there Example In how many ways can you arrange 3 different pictures from 5 available on a wall from left to right Example In how many ways can you choose 3 mystery books from a collection of 15 mystery books and 5 romance books from a collection of 20 romance books ChapterSection Objective and Examples Material Covered by End of Week 7 l 72 Given a set of data or a certain experiment list the 11 11 simple events nd the probability of each of the simple events nd the probability distribution and nd the probability of an event that consists of more than one simple event Example A pair of dice is cast List the simple events Assign probabilities to each of the simple events Find the probability distribution of the experiment Find the probability that the sum of the numbers is even ChapterSection Objective and Examples Material Covered by End of Week 73 Given a word problem use formulas or Venn ll diagram shading to nd the probability of the union intersection andor complement of certain events Example Of 30 elementary school children 15 read a book last summer 17 practiced math last summer Math 1313 Course Objectives 12 and 7 read a book and practiced math last summer What is the probability that a child selected at random a did not read a book last summer b read a book but did not practice math last summer c did not read a book and did not practice math last summer ChapterSecti0n Objective and Examples Material Covered by End of Week 74 Use counting techniques to nd the probability 0f 12 celtajn events Example A box contains 25 batteries of which 5 are defective A random sample of 4 is chosen What is the probability that at least 2 are defective ChapterSecti0n Objective and Examples Material Covered by End of Week 75 Use the conditional probability formula or tree 12 diagrams to aid in f39mding celtain probabilities Example A group of senators is comprised of 48 Democrats and 52 Republicans Seventyone percent of the Democrats served in the military whereas 68 of the Republicans served in the military What is the probability that a senator chosen at random a is Republican b Is a Democrat and did not serve in the military c served in the military d did not serve in the military given that heshe is a Math 1313 Course Objectives 13 Democrat Given that certain events are independent nd the probability of the intersection of those independent events Example If A and B are independent events and PA04 and PB06 nd PAU B ChapterSection Objective and Examples Material Covered by End of Week 76 Use tree diagrams and Bayes formulas to nd certain 13 conditional probabilities Example A group of senators is comprised of 48 Democrats and 52 Republicans Seventyone percent of the Democrats served in the military whereas 68 of the Republicans served in the military What is the probability that a senator chosen at random is a Republican given that heshe served in the military ChapterSection Objective and Examples Material Covered by End of Week 81 Given a probability distribution nd ceItain l3 probabilities and draw a histogram associated With the given probability distribution Construct the probability distribution of a random variable Example The probability distribution of the random variable X is shown below x PXx 1 02 2 03 Math 1313 Course Objectives 14 a Find P1lt X5 3 b Draw the histogram corresponding to the given probability distribution Example Given the following frequency table construct the probability distribution associated with the random variable X ChapterSecti0n Objective and Examples Material Covered by End of Week 82 Find the expected value of a given probability 13 distribution 0r of a word problem Example The following probability distribution tables describes the number of cars x that a certain car dealer will sell in a given day along with its associated probability Find the expected number of cars the car dealer will Math 1313 Course Objectives 15 sell in a given day Given a word problem nd the odds in favor odds against or given the odds nd a certain probability Example The odds in favor of an event occurring are 4 t0 5 What is the probability of the event not occurring ChapterSection Objective and Examples Material Covered by End of Week 83 Given a probability distribution or a word problem find the variance and standard deviation Examp e Given Find the variance and standard deviation Use Chebychev s inequality to estimate a certain probability Example The expected lifetime of a certain machine is 24 m0 and the standard deviation is 3 m0 Use Chebychev s inequality to estimate the probability that one of these machines will last between 20 and 28 m0 l4 Math 1313 Course Objectives ChapterSection Objective and Examples Material Covered by End of Week 84 Given a binomial experiment nd certain probabilities the mean the variance and the standard deviation Example The probability that a certain CD player will be defective is 004 lfa sample of 15 CD players is chosen at random what is the probability that the sample contains E no defective CD players at most 3 defective CD players Find the mean variance and standard deviation of this experiment 09 14 ChapterSection Objective and Examples Material Covered by End of Week 85 Given a standard normal distribution find certain probabilities or given the probability find the value of z Example Let Z be a standard normal random variable Find a PZ lt 134 b PZgt 233 c P023 lt Z lt 122 Example Let Z be a standard normal random variable Find the value of 2 if a PZ gt z 08749 b Pz lt z lt z 04908 Given a normal distribution possibly a word problem standardize it to find certain probabilities Example Let X be a normal random variable The mean is 25 and the standard deviation is 4 Find 15 Math 1313 Course Objectives a PX lt 30 b PX gt 10 c P15 ltX lt 25 ChapterSection Objective and Examples Material Covered by End of Week 86 15 Use the normal distribution to approximate a binomial distribution Example Use the normal distribution to approximate the following binomial distribution A biased coin is tossed 100 times The probability of obtaining a head is 30 What is the probability that the coin will land heads at least 90 times Math 1313 Course Objectives 18

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