Math - Others Questions

You plan to take out a 30 year fixed rate mortgage for 275 000 Let P r be your monthly payment if the interest rate is r per year compounded monthly Interpret the equations as P 1648 75 and b P 6 176 80 a Interpret P 6 1648 76 Select the correct answer below A If the interest rate on the mortgage is 7 the monthly payment will be 176 80 B If the interest rate on the mortgage is 6 the monthly payment will be 1648 76 C If the interest rate on the mortgage is 7 the monthly payment will be 1648 76 D If the interest rate on the mortgage is 6 the monthly payment will be 176 80 b Interpret P 6 176 80 Select the correct answer below OA If interest rate decreases from 7 to 6 the monthly payment will be approximately 1648 76 B If the interest rate increases from 6 to 7 the monthly payment will decrease by approximately 176 80 OC If the interest rate decreases from 7 to 6 the monthly payment will increase by approximately 1648 76 OD If the interest rate increases from 6 to 7 the monthly payment will increase by approximately 176 80

4t 6et and B t 4 5et Let A t a Find SA tydt 1 9 cost 8 sin t 3 sint 6 cost b Find B t dt d c Find A t B t dt

A rectangle is loom long and occm brond and the range of 20 cm if the perimeter of the rectangle is not greater than boom and not less than 2eme

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

Evaluate the given determinant 13 9 52

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

28 22 0 04 C 13 72 B and C 87 Let A a Find AB b Find AB C c Find A B C

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

Graph the feasible region for the system of inequalities x 3y26 3x y 6 Use the graphing tool on the right to graph the feasible region for the system of inequalities Click to enlarge graph 10 B 40 8 6 12 77 de

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

Dimensions and masses of rectangular blocks and or cylinders made of the same material Dimension 1 cm Cylinder a Cylinder b C d e 1 89 2 19 0 00 0 00 0 00 Dimension 2 cm 2 59 3 10 0 00 0 00 0 00 Dimension 3 cm N A N A Mass g 8 198 0 000 0 000 0 000 0 000 Volume cm Density g cm 3 pts Based on the data you entered and the shape of your object your volume calculation is incorrect Make sure to use the correct formula for your object

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

Find the corner points of the feasible region of the linear programming problem 10 Maximize z 3x 4y subject to x y 6 2x y 8 x 0 y 0 The feasible region is given below ofy 4 2 2

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

Graph the feasible region for the system of inequalities 9 2x 3y 6 4x y 6 x 0 V20

Let U be the set of natural numbers 1 through 20 let A be the set of even numbers in U and let B be the set of numbers in U that are divisible by 3 a Find An B AUB AUB ANB b What two pairs of the four sets of part a are equal a List all the elements of each set below ANB 1 2 3 4 5 7 8 9 10 11 13 14 15 16 17 19 20 Use a comma to separate answers as needed AUB 1 2 3 4 5 7 8 9 10 11 13 14 15 16 17 19 20 Use a comma to separate answers as needed AUB 1 5 7 11 13 17 19 Use a comma to separate answers as needed AnB 1 5 7 11 13 17 19 Use a comma to separate answers as needed b Select all the choices below that show two pairs of sets that are equal A ANB AUB C AUB AUB DE ANB AnB B AUB AnB D ANB AUB OF AUB ANB Points 0 2c

Determine if each of the following sets is closed under addition a P 0 c N 7 10 12 b S 0 7 14 21 28 d xlx E integers x 10 a P 0 is closed under addition False True

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

Consider the following zero coupon bonds Bond Yrs to Mat Yield to Maturity 0 0433 0 046 0 0495 0 0511 0 0531 0 0555 a b CE4 d e 123456 f 6 What is the one year forward rate starting at the end of year5 0 0636 O 0 0611 O 0 0654 O 0 0676

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

b What is the profit on 343 items In the equation for P x the profit in dollars is represented by P and the number of items produced and sold is represented by x Therefore to find the profit when 343 items are sold we substitute 343 for in the equation P x 300x 3 300 Find P 343 P x 300x 3 300 Step 4 P 343 300 343 99600 343 99 600 3 300 That is if 343 items are produced and sold the total profit is 99600 99 600 c How many items must be sold to avoid losing money The manufacturer makes money if the profit is Select and loses money if the profit is Select When the manufacturer breaks even the profit is 0 So to avoid losing money the manufacturer must produce and sell the break even quantity which is the number of items that results in a profit equal to 0 We can find the break even quantity by solving the equation P x

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

y x x The vertex is a maximum point The vertex is a minimum point Find the coordinates of this point Find the zeros if any exist Enter your answers as a comma separated list If an answer does not exist enter DNE Find the y intercept y Sketch the graph of the function No Solution 10 7 6 5 4 3 2 1 10 8 7 6 5 4 3 2 4 2 9 10 Fill Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its properties

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 Find the inverse for each of the following functions f x 14x 13 x x 14 13 14 g x 15x 5 g x 14 x 5 h x h x 14 x 5 3 j x x 15 i x

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 LIST 1 point Use the quadratic formula to solve the quadratic equation 2x 3x6 0 Solutions separate by commas x