Basic Math Questions and Answers

Find the value of the expression See Examples 3 5 Objective 2 32 2 1 4 2

Tutorial Exercise Find the value of the expression See Examples 3 5 Objective 2 2 3 Step 1 In the expression 32 3 is the base and 2 is the exponent The exponent of 2 indicates that the base of 3 is to be used as a factor expression as factors of 3 and simplifying we have 2 3 2 3 2 times Therefore rewriting the expon

Write the expression without using exponents See Example 2 Objective 1 4t3

Combine the Multiplication Principle and combinations to answer the question In a shipment of 30 portable stereos 8 are known to be defective In how many ways can a sample of 10 be chosen so that 2 ar defective and 8 are not defective ways

Find the value of the expression See Examples 3 5 Objective 2 G 7 3

Find the value of the expression See Examples 3 5 Objective 2 3 5 2 2 8 5

Tutorial Exercise Find the value of the expression See Examples 3 5 Objective 2 9 3 2 82 2

Write the expression without using exponents See Example 2 Objective 1 5z 4

Find the value of the expression See Examples 3 5 Objective 2 2 5 3

Use an inverse matrix to solve each system of linear equations a x 2x2 x3 0 X1 2x2x3 2 X1 2x2 x3 4 X1 X2 X3 b x 2x x3 1 X1 X 2x2x3 3 X1 2x2 x3 3 X1 X2 X3

A child goes to a concession stand at a basketball game and has two choices to make for a drink Choice 1 Size small medium or large Choice 2 Type of drink soda or lemonade Draw a tree diagram to represent all possible answers to the questions Tree Diagram Select Medium Large Select Description Lemonade Select Lemonade Soda Select C Determine how many ways a respondent could answer all of the questions

Find x such that the matrix is singular X A x 2 7 4

Evaluate the expression 0 4 7 3 2 74 33 9 6 1 9 8

5 Complete the other half of the graph of s t below if s is odd t 3 2 1 3 21 2 1 2 2 3 4 5 3 3

Find if possible AB and BA If not possible enter IMPOSSIBLE in any single cell 12 5 23 2 1 3 2 1 2 0 4 1 1 3 4 2 A a AB b BA 7 B 53

Find if possible AB and BA If not possible enter IMPOSSIBLE in any single cell 0 B 3 A 3 1 2 a AB b BA 32

Express the column matrix b as a linear combination of the columns of A Use A A2 and A3 respectively for the columns of A 11 b A 1 1 2 3 3 b

x y 19 4 9 4 3 13 11 12 02 4 0 1 19 3 0 4 13 2x 1 4 11 3x 2 3y 14 0

Solve for x y and z in the matrix equation 4 STEP 1 Simplify the right side of the equation 4 3 4x STEP 2 Set corresponding entries equal to each other to obtain four equations 4y 4z 4 X 41 z 1 STEP 3 Solve for x y and z x y z

Let A be a matrix with the following size A 4 x 3 If defined determine the size of the matrix 3A If an answer is undefined enter UNDEFINED X If not defined explain why O 3A is defined O 3A is not defined because the number of columns of A does not equal the number of rows of A O 3A is not defined because the number of columns of A equals 3 O 3A is not defined because the number of rows of A does not equal 3 O 3A is not defined because 3 is not a matrix

3 Let 4 A 3 0 3 0 3 a 3 points Determine a21 for matrix B b 3 points Find BT w and B c 6 points Determine the product AB if possible 9 3 6 4

Use the Venn diagram to write the elements of B Enter your answer as a set using the listing method 5 A ak 1 n h a f d B C i bo g b m U

Use the Venn diagram to write the elements of A n B Enter your answer as a set using the listing method 408 1 n A m h f g ro B a i j k C U

Which of the following statements are true More than one answer may be possible Select all that app 6 7 8 c 7 8 6 7 8 7 8 6 7 8 7 8 6 7 8 2 7 8

7 State all the asymptotes vertical horizontal or oblique of the following functions a y b y 4x 7x 6 3x 27 4x 2x 6 x 4 C 3 C 3

6 A piece of wire 10 m long is cut into two pieces One piece is bent into a square and the other is bent into an equilateral triangle How should the wire be cut so that the total area enclosed is a a maximum b a minimum Hint 1 Use the first derivative test to figure out if your answer is a min or max Hint 2 Think about whether you even need to cut the wire A 2 T 3

10 Differentiate the following functions You do not have to simplify a y 5x x4 b y tan ex KU 2 KU 3

1 Determine the following limits If the limit does not exist write DNE x 8x 12 x 4 a limx 27 b lim xo 2 x 2 x 2x 3x 2x 3 d Limx x 3x 1 x c limx 1 57 KU 2 KU 2 T 3 T 4

16 Find the vector parametric and symmetric equations of the line which contains the point 5 3 8 and is perpendicular to the plane 3x 6y 7z 3 0 A 3 T 2

5 A box with a square base and open top must have a volume of 32 000 cm Find the dimensions of the box that minimizes the amount of material ucod 102T 21

In a poll the pollsters found that only 35 of 5th through 12th graders strongly agreed that they could find many ways ard problems that arise in their lives The survey had a margin of error of 0 092 percentage point a Write the results of the poll using plus minus notation Enter your answers in decimal form b Rewrite using interval notation Enter your answers in decimal form Simplify your answer completely c Let p be a percentage and write the interval as a compound inequality

A Translate the following verbal expressions to algebraic expressions 1 a number plus 4 2 7 decreased by a number 3 product of 8 and a number 4 half of a number B Translate the following algebraic expressions to verbal expressions X 4 9 x 5x n 9 C Evaluate the following algebraic expressions let x 5 y 10 z 2 1 2x 5 2 X Z 3 2x 3z 4 2 x y 5 2 x y 6 2 y 5

A Solve the following linear equation 2 x 5 x8 9 7 2x 1 X 3 5 2 2 x 4 6 B Solve the following literal equation 1 solve for x mx b 2 solve for h p h m 3 solve for a b c 4 solve for p p 2m r 5 solve for y 2y 3k b

S Simplify each expression 1 7p 21 9 p 3 a 5 a 4 4a 8 a 6a 8 2 w 6w 8 6w 54 4 1 x 24 4 X X w w

Review Course Packet on factoring quadratic polynomials using the AC gro Factor the following expression by applying the AC grouping method 15x 16x 15

Solve the equation by factoring the left hand side and then setting each factor equal to zero Enter your answers as a comma separated list 2x x 3 0 X 3 12 171 17 3 3 X

Solve the equation by factoring the left hand side and then setting each factor equal to zero Enter your answers as a comma separated list 4x 29x 24 0 X

Precalculus Review Course Packet on factoring techniques Simplify the expression by first factoring the numerator and the denominator x3 6x 7x 6x x 7

Find an equation of the line that passes through the point and has the indicated slope m Let x be the independent variable and y be the dependent variable 9 2 9 8 m

Find an equation of the line that passes through the point and has the indicated slope m Let x be the independent variable and y be the dependent varia 1 0 m 1 Submit Answer

Rewrite the following expression as a product by pulling out the greatest common factor 3x8 3 5x1 3 X

1 A company reports sales of 1 010 000 sales discounts of 2 400 sales returns and allowances of 11 400 cost of goods sold of 505 000 general and administrative expenses of 19 000 and selling expenses of 28 000 Compute gross profit ints 01 27 39 Gross profit

The voltage across a capacitor with the value C 3 F is given by the waveform in Fig P6 10 Find the waveform for the current in the capacitor for the time interval Os t t2 given that t2 13s v c t V 12 12 O t1 t2 Figure P6 10 t3 t4 t5 Notes on entering solution Enter your solution in Amps Pay attention to the interval given Enter your solution to 2 decimal points Do not include units in your answer ex 5W is entered as 5 00 t s

Savannah took out a 5 year loan for 6500 at a furniture store to be paid back with monthly payments at a 17 3 APR If the loan offers no payments for the first 21 months how many payments will Savannah be required to make OA 39 OB 21 OC 81 O D 60

The current in the inductor changed from 0 mA to a current of 1 129 mA in I a time of t 7 ms and induces a voltage of V 66 mV What is the value of the inductor Notes on entering solution Enter your solution in mH Enter your solution to 2 decimal points Do not include units in your answer ex 5 mW is entered as 5 00

Given a capacitor of C 2 F calculate the current going through the capacitor during the interval t1 st st2 when the capacitor voltage is as described in Fig 6 12 Assume V1 9V V2 9V and t1 7 S and t2 14 S Note values might be different than the above problem v t V A V1 V2 0 Figure P6 12 t1 t2 Notes on entering solution Enter your solution in Amps Enter your solution to 2 decimal points Pay attention to interval t3 Pay attention to signs Do not include units in your answer ex 5W is entered as 5 00 t s

If MR 0001 0000 1000 0100 O a Asymmetric O b Reflexive O C None d Symmetric then R is

Maria Anguiano s current salary is 62 000 per year and she is planning to retire 25 years from now She anticipates that her annual salary will increase by 2 900 each year That is in the first year she will earn 62 000 in the second year 64 900 in the third year 67 800 and so forth She plans to deposit 6 of her yearly salary into a retirement fu that earns 8 interest compounded daily What will be the amount accumulated at the time of her retirement Assume 365 days in a year The effective annual interest rate is Round to four decimal places

1 Assuming that xy x y 1 and xy xy x y are two binary operations defined for all x y ER i prove that oth and are commutative ii prove that both and are associative iii prove that is distributive with respect to iv verify if and have neutral elements v decide which numbers x ER have their inverse elements with respect to and and which do not

Consider the following inequality x 6 a Write the inequality in interval notation for a real number x Simplify your answer completely b List the values from x 0 1 2 3 4 5 6 7 8 9 10 11 that satisfy the given inequality Enter your answers as a comi separated list If there is no answer enter NONE