Basic Math Questions and Answers

Determine the values of r for which det A rI 0 r A 15 15 4 8 Simplify your answer Use a comma to coporto

dX Find for the given matrix function dt dX dt sin 2t cos 2t e 2t X t sin 2t 4 cos 2t 3e 2t 3 sin 2t cos 2t e 2t 11

dx Find for the given vector function dt dx dt x t e t 3e t e t

Find the matrix function X t whose value at t is the inverse of the given matrix X t et est 3 et 7e5t X t x t

A 3 4 6 8 and B 43 63 Verify that AB BA

31 Let A 0 2 and B 14 11 2 04 2 Find a AB and b BA

For the given simplex tableau a list the basic and the nonbasic variables b find the basic feasible solution determined by setting the nonbasic variables equal to 0 and c decide whether this is a maximum solution a What are the basic variables S S2 Z Use a comma to separate answers as needed What are the nonbasic variables X1 X2 X3 Use a comma to separate answers as needed b Find the basic feasible solution by setting the nonbasic variables equal to 0 x x x3 z COLL X X2 X3 S S2 425 2 2 3 1 3202 5010 Z 1 0 29 0 0 16 0 1 14

Blossom Clark opened Blossom s Cleaning Service on July 1 2022 During July the following transactions were completed July 1 1 3 5 12 18 20 21 25 31 Blossom invested 19 800 cash in the business Purchased used equipment for 9 000 paying 3 900 cash and the balance on account Purchased cleaning supplies for 1 900 on account Paid 1 680 cash on a 1 year insurance policy effective July 1 Billed customers 4 600 for cleaning services Paid 1 500 cash on amount owed on truck and 1 300 on amount owed on cleaning supplies Paid 2 500 cash for employee salaries Collected 3 500 cash from customers billed on July 12 Billed customers 6 100 for cleaning services Paid 350 for monthly utilitiy bill for the equipment Use Utilities Expense

For the given simplex table list the basic and nonbasic variables write the feasible solution and decide whether this is a maximum solution 16 X1 X2 X3 S1 S2 Z 1345 0 1 0 3200 1 2 0 16 0 1 0 24 0 3 1 40

20 How is zero represented in 2 s complement form

Use the indicated entry as the pivot and perform the first pivoting process 15 x1 x2 s1 2 3 z 2 1 0 1 1 1 2 1 0 0 10 0 0 1 0 4 0 0 0 1 0

7 Set up the linear programming problem Do not solve A baker has 60 units of flour 132 units of sugar and 102 units of raisins A loaf of raisin bread requires 1 unit of flour 1 unit of sugar and 2 units of raisins while a raisin cake needs 2 4 and 1 units respectively If raisin bread sells for 3 a loaf and a raisin cake for 4 how many of each should be baked so that the gross income is maximized What is the maximum gross income Let x represent the number of raisin bread loaves and x2 represent the number of raisin cakes

8 What is the highest decimal number that can be represented by each of the following numbers of binary digits bits a two b three

et up the linear programming problem Do not solve 12 Kim is told to take at least 2400 mg of iron 2100 mg of vitamin B 1 and 1500 mg of vitamin B 2 One Maxivite pill contains 40 mg of iron 10 mg of vitamin B 1 and 5 mg of vitamin B 2 and costs 6 cents One Healthovite pill provides 10 mg of iron 15 mg of vitamin B 1 and 15 mg of vitamin B 2 and costs 8 cents What combination of Maxivite and Healthovite pills will meet Kim s requirement at lowest

3 Operations on rational expressions 1 Review operations on polynomials Adding Subtracting polynomials Remove all parentheses change the sign when subtracting Combine like terms Multiplying polynomials Multiply each term of the first polynomial by each term of the second polynomial and then combine like terms Special products i Distributive property a b c ab ac ii FOIL method first terms outer terms inner terms last terms a b c d ac ad bc bd iii Squaring Binomials a b a 2ab b 2x 3 x 2x x 2x 3 x 3x Example 2x x 3 x 6 2x x 3x 6 2x 2x 9 c 2m 5 6m m 1 Examples Distributive 2 x 4 2x 8 FOIL t 3 t 7 t 7t 3t 21 t 4t 21 Squaring binomials m 3 a b a 2ab b iv Multiplying the sum and difference of two terms a b a b a b You may also use the tabular method to multiply polynomials Multiply 2x 3 x 3x 5 m 2 m 3 3 m 6m 9 x 6 x 2 x 6 6 x 12x 36 Product of sum and difference 2 x x x x 1 4 3x 2x 3x 6x 3 3x 9x Answer 2x 3 x 3x 5 2x 3x 19x 15 1 Simplify the following a 2 x 3 b r 2 7 r d x 3y 5 2x 5 10x 3 5 15

0 1 3 5 NAKE 7 9 11 13 15 17 ms

14 Convert each decimal fraction to binary using repeated multiplication by 2 a 0 98 b 0 347 c 0 9028

44 Convert each decimal number to octal by repeated division by 8 a 15

20 A pulse waveform with a frequency of 10 kHz is applied to the input of counter During 100 ms how many pulses are counted

Complete the following table showing equivalent numbers in each number system using four place values Decimal Binary 0000 0 1 2 3 45 4 5 6 7 8 9 10 11 12 Octal 0000 Hexadecimal 0000

6 List the sequence of levels HIGH and LOW that represent each of the following bit sequences a 1011101 b 11101001

The cost in dollars of producing x units of a certain commodity is C x 7 000 8x 0 05x a Find the average rate of change in per unit of C with respect to x when the production level is changed from x 100 to the given value Round your answers to the nearest cent 1 x 102 ii x 101 per unit per unit b Find the instantaneous rate of change in per unit of C with respect to x when x 100 This is called the marginal cost Its significance will be explained in a future chapter per unit

Frequency 10 8 6 A 2 1 7 9 11 13 a Based on the histogram above what is the bin width bin width 3 eri Sample size 5 data Enter an integer or decimal number more What is the sample size

11 Suppose a manufacturer has determined that the total cost C C 0 7x 19x 112 000 operating a factory is where x is the number of units produced At what level of production will the average cost per C unit be minimized The average cost per unit is

Solve the equation by factoring 49 36x 0 Step 1 Factor the left side of the equation Step 2 7 6x Solve each factor for x 7 6x 0 X 7 6x 0 X 7 6x 49 36x 0 7 6r 0

6 Homeworks Summer 2023 TTU Introductory Mathematical I total costs are C X 1600 1500X and total revenues are R X 1600X X find the break even points Step 1 Break even points occur where R x C x Equate revenue and cost set the left side equal to 0 and then factor the equation R X C X 1600x x 1600 1500x X 0 x 100 X 0 x 80 x 20 Step 2 Determine the values of x that satisfy the equation first factor x 80 0 second factor x 20 0 X 100 x 1600 20 ebassign net Finally give the break even points Enter your answers as a comma separated list C Homework 03 MATH 1

Consider the following power X 1 2 3 10 4 2426 5 1962 3 4 5 6 7082 6 7 3485 Find the equation of the function of the specified type that is the best fit for the given data Round your numerical values to two decimal places y x Y 6 Plot the data and the equation y 10 5 10 X 10 y 10 5 5 X 10 10 5 y 10 5

Tutorial Exercise If total costs are C x 1600 1500x and total revenues are R x 1600x x find the break even points Step 1 Break even points occur where R x C x Equate revenue and cost set the left side equal to 0 and then factor the equation R x C x 1600xx 1600 1500x 0 x 80 x 0 x 1 any points for the skipped part and you will not be able to come back to x 1600

If total costs are C x 2100 2000x and total revenues are R x 2100x x find the break even points Enter your answers as a comma separated list X

Consider the quadratic equation 4t2 4t 1 0 Factor the left side of the equation 0 Solve the equation Enter your answers as a comma separated list t

Tutorial Exercise Solve the equation by factoring 49 36x 0 Step 1 Factor the left side of the equation 7 6x 49 36x 0 0

Write the equation in general form 6x2 5x 6x 6

Next Problem 1 point The equation of the line that goes through the point 1 3 and is parallel to the line 2x 5y 5 can be written in the form y mx b where m is 2 5 and where b is 2 2

Next Problem 1 point Put the function y a x 3 3 a xh k and vertex form f x determine the values of a h and k h k help numbers help numbers help numbers 6 in

Next Problem 1 point Suppose y 2x 16x 34 In each part below if there is more than one correct answer enter your answers as a comma separated list If there are no correct answers enter NONE a Find the y intercept s y b Find the x intercept s X help numbers

Previous Problem Next Problem Problem List 1 point The function f x x 11x 28 has a enter maximum or minimum value

Next Problem 1 point An equation of a line through 3 6 which is parallel to the line y 3x 2 has slope 3 and y intercept at 12

Next Problem 1 point Write an equation for the line through the point 5 4 with slope 7 in point slope form y yo m x xo y formulas help

14 Use the table below to answer the following questions t h t 0 1 2 3 4 5 6 6 0 1 7 2 3 5 a Find h 6 b Solve h t c Find h 5 d alua h 1 0 7 89 8 49

Consider the graphs below Determine if the function in the graph is one to one A The function is one to one B The function is not one to one Determine if the function in the graph is one to one A The function is one to one B The function is not one to one

1 point Let f x g x f and and their respective domains 9 1 f g sqrt 1 x sqrt 4 x 4 x 2 What is the domain of f g Answer in interval notation 4 1 7 1 x and 16 x Find f g 9 9 3 f g 4 What is the domain of f g Answer in interval notation 4 1 f 9 5 f g 6 What is the domain of f g Answer in interval notation 4 1 1 11 f 8 What is the domain of 9 Answer in interval notation

1 point Suppose you are given a rectangular piece of cardboard having length 6x 2 inches and width 2x 4 inches Then you cut out a square from this piece of cardboard having side length x inches Find the area of the remaining piece of cardboard expressed in terms of x Answer

1 point Use the table of values for the functions p x and g x below to complete the tables for the composite functions defined in parts a and b a Complete the table of values for the composite function r x p q x at x 0 1 2 3 4 5 X r x O X 0 s x X 012345 p x 150342 q x 524310 0 1 10 b Complete the table of values for the composite function s x q p x at x 0 1 2 3 4 5 2 1 3 2 4 3 4 LO 5 5

REQUIRED RATE OF RETURN Pe 12 0 8 0 4 0 0 0 5 CAPM Elements Risk free rate TRF Market risk premium RPM Happy Corp stock s beta I 1 0 RISK Beta Return on HC s Stock 1 5 Value 2 0

im has chosen the car he wants and must now decide whether to buy or lease it The car has an MSRP of 21 977 and a residual factor of 34 Jim negotiates a 500 discount and must pay the ollowing additional costs 660 freight charge 100 tire air tax 75 gas tax 85 administration fee 74 licence plate fee 20 gas fee Regardless of whether Jim buys or leases the car the financing is 6 9 compounded monthly fo 8 months If Jim buys the car the finance fee is 54 If he leases the car the finance fee is 36 Term of Lease MSRP Gross Capital Cost Trade in Allowance Down Payment Total Capital Reduction Net Capital Cost Residual Factor Residual Value Depreciation Base Monthly Payment Monthly HST 13 Lease Quote Monthly Payment Interest Rate 1st Payment HST on Down Payment 13 1st Year Fees Other Fees HST on Upfront 13 Security Deposit Total Initial Payment

Write a polar equation for the graph below Enter theta for 0 if needed 3 2 1 5 4 3 2 1 r 0 1 2 3 Question Help 1 2 3 4 5 Video

Convert the Cartesian coordinate 2 6 to polar coordinates 0 0 2 r Enter exact value 0 in radian round to at least one decimal place Question Help Video 1 Video 2 Submit Question

In the following matrix how many columns are linear combinations of the columns preceding it 3 3 1 1 3 2 That is for how many i is column i a linear combination of columns 1 through i 1 0 01 O 2 0 3 4 A 0 2 1 0 2 2 0 2 1 3

Convert the Cartesian coordinate 6 2 to polar coordinates 0 0 2 r Enter exact value in radian round to at least one decimal place Question Help Video 1 Video 2 Submit Question

The hourly wages of a sample of 35 employees of a textile company are summarized in the table below Number of employees Hourly wage in dollars 3 A 13 10 6 00 8 00 9 75 11 00 Find the mean hourly wage of these 35 employees Round your answer to at least two decimal places