Basic Math Questions and Answers

Virtual Realities are one example of circumstances Select one O a an experiment O b a universe O c a simulation O d a bias which is used to create alternate realities to compare outcomes with given

10 SAVINGS MONTHLY MONEY HOUSING UTILITIES TRANSPORTATION Monthly Gross Wage Net Wage monthly Emergency Savings 5 Savings Account Investing Account Retirement Total Monthly Savings Monthly Amount for Budget Monthly Rent Mortgage Renter s Insurance Cable Satellite Intemet Mobile Phone Trash Gas Electricity Sewer Total Cost of Living Public Transportation Car Payment Car Insurance Car Maintenance Gas Fuel Total Cost of Transportation 0 0 0 0 DIV 0 DIV 0 DIV 0 DIV 0 DIV 0 DIV 0 DIV 0 0 DIV 0 DIV 0 DIV 0 DIV 0 DIV 0 DIV 0 0 DIV 0 Record saved Record Invested Record saved Record your address apartment complex city If you have a roommate and if you are renting or purchasing Record Cable Type of people Record Internet plan of people Phone Plan of people Home size of people Record which city s example you used here Record the price of your car year make model and loan term Record your cars MPG of miles you drive here

Maustry for your future career Click on your future career or closest option if not listed Under Job Outlook click on Local Salary Info and enter the zipcode of the city you want to live in after college If your preferred city isn t found choose the closest large city Be excel spreadsheet as this will also affect your commute time miles notate this on your Scroll down to full details and use the Annual QL 257 value in the given salary range for sure to that city Record that amount under Annual Gross Wage on your budget Click Back to Career Report and scroll down to education Record the required education

If an is an arithmetic sequence with a 8 such that S8 118 find ag and d ag d

1 Dylan would like to substitute a healthier option instead of buttered popcorn He should try O A cheesy O B buttered and salted O C unbuttered D caramel popcorn instead

et A a b f h i j Let B a c d h j Let C a d f g j Determine An C Choose the correct answer below and if necessary fill in the answer box in your choice OA ANC Use a comma to separate answers as needed OB An C is the empty set

nn diagrams to determine r the following statements are equal for all sets A B and C BNC UB N AUC we statements equal for all sets A B and C No Yes GT IV

MnN and M UN Are M n N and M UN equal statements No O Yes COLLD COD IV II

B and A B the statements equal for all sets A and B No Yes CARRO ITS

ill in the blank with an appropriate word phrase or symbol s the number of regions created when constructing a Venn diagram with three overlapping se he number of regions created when constructing a Venn diagram with three overlapping se

roster form is whole number Use a comma to separate answers as needed 0

U Store 1 Store 2 Store 3 Store 13 Store 14 A Store 2 Store 3 Store 4 Store 11 Store 13 B Store 3 Store 4 Store 8 Store 9 Store 14 C Store 3 Store 5 Store 7 Store 11 Store 12 Choose the correct Venn diagram below OA D U U 13 C 57 12 C 4 11 3 89 14 10 8 12 1 6 10 3 Q Q B OE U 11 3 13 11 16 10 57 12 2 STEE 7 12 14 10 OC OF U 13 2 13 C 3 57 12 57 12 8 14 311 Me 6 10 10

the correct choices that complete the sentences an constructing a Venn diagram with three oping sets region is generally completed first en constructing a Venn diagram with three oping sets after completing the region answered in 3 the next regions generally completed are II IV an constructing a Yenn diagram with three overlapping sets region IV V VII VI III VIII COLO is generally completed

3 A Describe the end behaviour of a polynomial with a negative leading coefficient and an even degree K 1 mark B Determine the equation of a cubic function that has zeros at 3 order 1 and 1 order 2 and f 2 12 K 1 mark

2 Identify the points of holes V A H A x intercepts and y intercepts then Sketch x x 6 the function f x C2 marks 4x 16x 12

Rationalize the denominator and simplify 3 2 3 3 a 5 2 5 2 3 2 2

1 Factor the expression y x x 7x x 6 K2 marks

Consider the two functions Function 1 Function 2 y x 91 4 What is the distance in units between the y intercepts of the two functions Answer type your answer

3 Although Oscar Bluemner s painting is titled Evening Tones it relies on geometric shapes and symbols to communicate its message This style is known as

The table represents the relationship between the number of days x and the number of patients in a hospital showing flu symptoms y Which statement is true X 1 4 6 7 9 y 106 63 48 29 13 A The number of patients showing flu symptoms decreases at a constant rate as the number of days increases B The number of patients showing flu symptoms decreases as the number of days increases but not at a constant rate C The number of patients showing flu symptoms increases at a constant rate as the number of days increases D The number of patients showing flu symptoms increases as the number of days increases but not at a constant rate

Consider the absolute value function Which statement is true y 13x 61 A The x intercept of the function is located at 0 2 and the y intercept of the function is located at 6 0 B The x intercept of the function is located at 0 2 and the y intercept of the function is located at 6 0 C The x intercept of the function is located at 2 0 and the y intercept of the function is located at 0 6 D The x intercept of the function is located at 2 0 and the y intercept of the function is located at 0 6

Consider the two functions For which interval is f x g x 000 x 4 a 0 0 x 4 f x x4 g x 4

Suppose we have two convergent series oan A and o bn B where A B R a Prove that o an bn A B b Prove that whenever k R we have kan kA c Is it the case that no anbn AB Why or why not 0

Which function has the smallest local minimum in the interval 3 x 3 f x 6 cos 2x A B a g x C a quadratic function opening upward wi a vertex at 6 4 g x is a polynomial function of degree with the given points x 5 3 1 4 g x 8 222 12 5

Young s inequality Let x y E R a Show that 2xy x y Hint Consider 0 x y b Show that 2xy x y Hint Consider 0 x y c Conclude that Young s inequality ry r y holds

Consider the functions Which statement is true A When x 12 the value of g x is always greater than the value of f x When x 12 the value of g x is always less than the value of f x When x 13 the value of g x is always greater than the value of f x When x 13 the value of g x is always less than the value of f x B C D C f x x 3x x 3 g x e 5 8 b

Consider the rational function What is the function f x f x f x 1 3 1 T 1 2 3 4 5

Consider the graph of the function Which statement is true The function is increasing for all values of x and the y intercept of the function is at 5 0 The function is increasing for all values of x and the y intercept of the function is at 0 5 The function is decreasing for all values of x and the y intercept of the function is at 5 0 The function is decreasing for all values of x and the y intercept of the function is at 0 5 A B C D C f x a

What is the y intercept of the graph of f x sin x 0 1 ND 1 0 1 0

Consider the three functions Which lists the functions in the correct order from smallest to largest rate of change as x increases without bound 0000 f x 2x g x 2x h x x f x h x g x f x g x h x h x g x f x g x f x h x

b To verify the solution and the interval convert xy5 xy5 sin x 1 to explicit function s y 1 x xsin x C Use a comma to separate answers as needed T

Consider the function 10 9 8 7 Which equation represents g x g x x 2 3 g x x 21 3 a g x x 2 3 g x x 2 3 W N gx 123 9 10

11 1101 1000100 At least one of the answers above is NOT correct 2 11111112 1012 1000100 1 point Compute the following sums using binary addition Do not use spaces in your answers 12 102 11 10002 1012 1101 2 11 N 1101 1000100 correct correct incorrect

100 1100001 11100100100 At least one of the answers above is NOT correct 2 100 2 1100001 1 point Compute the following products using binary multiplication Do not use spaces in your answers 12 1002 100 111112 x 11100 2 1100001 11100100100 correct incorrect incorrect

1 point Determine whether each of the following statements is true or false For all real numbers x if x 5 then x 5 A True B False For all x ER if x 5 then x 5 A True B False VI ER 5 x 7 x 5 OA True B False VI ER z 6 x 5 A True B False

1101100 at least one of the answers above is NOT correct 1 point Compute the following sums using binary addition Do not use spaces in your answers 1102 112 121 10111a 101a 1101100 10212 correct

Determine whether the Existence and Uniqueness of Solution Theorem implies that the given initial value problem has a unique solution y x y 0 7 dy dx Select the correct choice below and fill in the answer box es to complete your choice OA OB The theorem implies the existence of a unique solution because y4 8 x and Type an ordered pair COLLE a y x dy are both continuous in a rectangle containing the point 8 The theorem does not imply the existence of a unique solution because y x is continuous but a y x dy is not continuous in any rectangle containing the point Type an ordered pair OC The theorem does not imply the existence of a unique solution because y x is not continuous in any rectangle containing the point Type an ordered pair

Determine for which values of m the function x x is a solution to the given equation m a 4x2 d y b x20 dx dy 13x 4y 0 dx dy 3xdx 44y 0 a m Type an exact answer using radicals as needed Use a comma to separate answers as needed

dy a Show that y x 5 0 is an implicit solution to dx 1 3 4y b Show that xy5 xy5 sin x 1 is an implicit solution to the differential equation on the interval 0 5 dy x cos x sinx 1 y 5 x xsin x dx a To verify the solution and the interval convert y x 5 0 to explicit function s y Use a comma to separate answers as needed on the interval 0 0

1 Given the exponential function y 3 5 a State the starting value b State the growth decay factor c Is the function growing or decaying d Describe in words what this function is doing Refer to the language in the intro activity he result if x 3

Find the 30 term of the geometric sequence when a1 8000 and r

ou are selling cookies for a bake sale During the first hour you sell 27 cookies Each Our after you sell 6 more than the hour before How many cookies did you sell if orked for 8 hours 27 CONES 1kr 5 50 1 6

7 Find the specified term of the arithmetic sequence a ay 14 6 as 47 S 5 00 S SP S ED STIKK E m91 2 tenit sit bai 5 S 16 3yd visvienusan banitab al consup

the 30 term of the geometric sequence when as

dy Find when y dt O O O O O 1 2e t 2t 1 e2t 01 1 2t e4t O 1 2t e2t O 1 2t p2t O 2t t e2t

Find y when y x 1 x 6 3 O x 3x 12 x 6 O x 3x 12 x 6 O x x 3x 12 x 6 x 3x 12 x 6 x x 3x 12 12 O

7 Which one of the following is the correct sign diagram for the second derivative y of the 4xx 7 function y O O O O O I y 13 y 0 I 0 0 y 0 y Hot 0 213

2 Which one of the following is the correct sign diagram for the function y x 4x O O O O O 3 1 y 0 0 Y Y Y 3 1 0 0 13 0 0 1 3 0 0 3 1 3

6 Which one of the following is the correct sign diagram for the derivative y of the function y 4x x O O O O I I I y 0 0 0 3 0 0 3 0 0 0

3 Which one of the following is the correct sign diagram for the 4x x function y O O O O O I 2 02 y 0 0 0 2 Y 0 2 0 2 0 0 0 2 0 0 0 2 0 2 0 0 0 I 2 0 2