Math - Others Questions

the IB SL formula booklet Round to 3 s f if not otherwise specified Viding all work You may use a graphing calculator and 5 In a school 200 students solved a problem in a mathematics competition Their times to solve the problem were recorded and the following cumulative frequency graph was produced a cumulative frequency a i a ii 225 200 175 b 150 125 100 75 50 25 0 0 10 Use the graph to find the median time 200 2 the lower quartile 200 100 38 9 a lii the upper quartile 50 32 20 a iv the interquartile range 50x3 150 43 30 time seconds Q3 Q1 43 32 11 Cedric took 14 seconds to solve the problem Q3 1 5x IQR Determine whether Cedric s time is an outlier SHOW ALL WORK Upper bound i 40 555 50 60 Lower bound S QI 5xIan

A group of 20 students travelled to a gymnastics tournament together Their ages in years are given in the following table Age years Frequency 13 14 15 14 15 1 2 a ii For the students in this group write down the median age 14 15 16 17 18 19 20 22 141 8 17 6 25 1XG The lower quartile of the ages is 16 and the upper quartile is 18 5 16 b Draw a pox and whisker diagram for these students ages on the following grid V 17 18 4 X 17 16 7 1 19 20 22 1 1 3 18 19 20 21 Age years 22 23 24

uations have 4 as a solution 6 y 2 y 9 13 3y 12 24 y 7 Select all the equations that have 4 as a solution A 3y 12 OB 6 y 2 DC 24 y 7 OD y 9 13

instruct the Lagrange s interpolation formula b Use the table below to evaluate the formula in a above and hence compute 1 x 1 f x 2 3 6 10 7 12

S 7 An airplane is heading due west at 400 km h when it encounters a wind from the northeast at 120 km h Using Cartesian Vectors components determine how far the airplane will travel in three hours Round to the nearest kilometre

9 Explain why it is not possible to determine a vector that is mutually perpendicular to vectors 2 1 and 6 2 2

O 6 A bolt is tightened by applying a force a 0 15 m wrench The angle between the wrench and the force vector is 40 and the magnitude of the torque about the centre of the bolt is 0 58 N m Determine the magnitude of the force applied to the wrench to the nearest unit 0 15 m 40

21 x y ez x y 2020 A 2020 min x y max x y B 60 C 20 D O E 2020

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40 a b e Z a 20 b min a b A 18 6 B 14 ASLAN HOC C 10 IN HOCA YO yo D 8 720156 E

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8 3 5 1 2 3 4 70 A 55 B 40 3 1 243 4 5 C 35 D 33 E 27 HOLA HOS 70 3

38 a bez ARGANTS 9 10 11 12 22 a b A 18 B 14 C 10 2 D 8

36 ASE 1 2 3 4 11 10 x x A 10 66 B 11 1 P C 12 D 11 212 ASLAN H E 12

E it uzunluktaki kenarlar ndan biri 1 birim olan renkleri d nda e ikizkenar 9 gen ekildeki gibi birle tirilerek dokuzgen olu turmu tur Buna g re genlerden birinin taban uzunlu u a a dakilerden hangisine e ittir A 2 cos 20 B 2 sin 20 D cosec 20 2 E C 2 sec 20 sec 20 2

P2 P1 D1 D2 Creative Commons The price P of designer jeans is affected by the supply S and the demand D Which of these represents an equilibrium price for designer jeans 5 points The line marked D1 The line marked Q1 Q2 O The arrow pointing to D2 The intersection of R1 and 01

ara bir yolun x km sini gitti inde geriye 2x 20 km daha yolu kal yor Kalan yol gitti i yoldan 60 km daha fazla oldu una g re yolun tamam ka km dir

Two dice are rolled Find the odds in favor of rolling the following a A sum of 5 b A sum of 7 or 12 c A sum less than 8 d Not a sum of 7

In a test a student gets an aggregate of 52 5 marks in for subjects Maths English Hindi and Science in the ratio of 4 3 2 5 If the passing marks are 50 and the maximum marks for each subject is same in which subject s did he fail in the examination

10 Find E Y for the joint pdf given by f x y 0 y x 1 0 elsewhere Hint Use a double integral with order of integration dydx

3 Are individuals likely to face increasing risks from wildfires in the future a No wildland fire suppression techniques are very sophisticated so wildfire poses little danger in modern times b No modern construction techniques and materials make buildings virtually fireproof c No zoning laws and regulations prevent development in areas where wildfires may occur d No modern scientific forest management practices have eliminated most of the risk from wildfire e Yes climate change resulting in higher atmospheric temperatures is a o occurring

4 The highest priority for wildfire management officials is to preserve a natural resources b infrastructure c buildings and structures d human life

14 Determine all the roots of the equation 2 cos x in the interval 2 x 2 Explain how x you did this 2

Find the altitude of a isosceles triangle Round your answer to twe decimal place 0 1 b M E Use Simples radical form Tood

1 Determine whether each of the following sentences is an atomic statement a compound statement or not a statement at all i I am in the mood for sushi ii This sentence is false iii If I go swimming today then I will not go running 2 Assume that the given compound statement is true Determine the truth value of each propositional variable i p q ii p q p 3 Let A a b c and B c d Compute each of the following i A B ii P A B

4 Determine whether each of the following is true or false i 5 EN ii 0 0 iii If A B then AUB nA B ii Compute c b a b C a a a a b a b C 5 The multiplication table above is defined on the set S a b c Is a binary operation on S Explain why or why not i C a C b iii Does S have an identity with respect to If so what is it If not explain why not iv Which elements are invertible For each such element state its inverse v Is commutative in S Why or why not vi Let T be the set of invertible elements in S Determine if T is a group a mc that is not a group a semigroup that is not a monoid or not a semigroup Explain

A government agency reported that in 2020 5 4 of people with a bachelor s degree and 8 8 of people with a high school diploma but no college were unemployed Suppose that the reported percentages were based on independently selected representative samples of 500 people with a bachelor s degree and 500 people with a high school degree but no college Construct a 95 confidence interval for the difference in the proportion who were unemployed for these two groups Use Bachelor s Degree High School Diploma Only Enter your answer using interval notation Round your numerical values to four decimal places 0 054 0 088 USE SALT Submit Answer Interpret the interval We are 95 confident 0 that the true difference in the proportion of people with a bachelor s degree who are unemployed and the same proportion for people with a high school diploma but no college falls within this interval The bounds of the interval suggest the proportion was higher for those with a high school diploma but no college 2 6 6 Points X DETAILS PREVIOUS ANSWERS PECKSTAT3 11 R 041 S MY NOTES d too much time on their cell phones Of the 750 teens 02

Find the present value for the account in which the desired future value is 30000 at 9 68 interest compounded quarterly for 2 years Round to the nearest cent

For the proprablility distribution table below 8 0 1 f 2 3 4 P x 0 15 0 15 0 16 0 13 Find the mean Round to two decimal places 0 41 Find the standard deviation Round to three decimal places xP x x P x

Determine whether this table represents a probability distribution P x X 0 1 3 4 0 23 0 09 0 15 0 83 Yes because P x is 100 No because x 0 No because P x has negative No because x has negative No because P x is not 100

Building an Emergency Fund You are working two part time jobs Working at the local library pays 15 per hour and working as a personal trainer pays 20 per hour Last week you made 800 and worked 45 total hours

Cumpany needed a new building It found a suitable location with an existing old building on the land The company reached a agreement to buy the land and the old building for 929 000 cash The old building was demolished to make way for the needec new building Following is information regarding the demolition of the old building and construction of the new one Construction cost of new building Cost for parking lot Demolition of old building Prepare a single journal entry to record the above costs assuming all transactions are paid in cash View transaction list View journal entry worksheet No A Transaction 1 Building Land Land improvements Cash 8 906 000 336 000 236 000 General Journal Debit 8 906 000 Credit

1 46 Spencer Company has a 220 petty cash fund At the end of the first month the accumulated receipts represent 45 for delivery expenses 135 for merchandise inventory and 14 for miscellaneous expenses The fund has a balance of 26 The journal entry to record the reimbursement of the account includes a Multiple Choice Debit to Petty Cash for 220 Credit to Cash Over and Short for 26 Debit to Cash Over and Short for 26 Credit to Cash for 194 to Inventory for 135

33 How many O s are there at the end of 401 681 19

EX 4 vehicles and t is measured in minutes 0 t 30 A Find V t for t 18 V t 92 15 sin 6 96 19 100 75 60 25 B Make a sketch of the graph of time vs number of vehicles Be sure your graph has a scale C What is the average rate of change of the vehicles at the departing flights over the time interval 15 t 20 Indicate units of measure V t 92 15 sin where V t is measured in AROC 92 Time Interval 18 18 1 18 18 01 18 18 001 15 20 20 15 4 D Estimate the instantaneous rate of change of vehicles at t 18 by finding the average rates from t 18 to t 18 1 t 18 to t 18 01 and t 18 to t 18 001 34567 Average Velocity 4 8252 4 8032 4 8010 SEN 8 9 10 92 15sin E Why can t the instantaneous rate of change of traffic in the departure lane with respect to time he calculated using the method in part 2

The total daily cost in dollars of producing x park benches is given by C x 2250 15x 0 1x A Sketch the graphs of the average cost function and the marginal cost function on the same set of coordinate axes B Find the minimum average cost A Choose the correct graph below OB OA 200 100 0 0 100 200 B The minimum average cost is 200 100 0 100 200 O C 200 100 of 0 100 200 D 200 100 04 0 100 200 5

make sure the function is in canonical form and convert it first in minterm notation d X Z XZ XY Z e XZ W XY WXY W YZ WY Z 8 37 PM

Find the cost of the Hershey bar in 2023 using the formula c ose osat

es Factor Company is planning to add a new product to its line To manufacture this product the company needs to buy a new machine at a 479 000 cost with an expected four year life and a 20 000 salvage value Additional annual information for this new product line follows PV of 1 FV of 1 PVA of 1 and FVA of 1 Note Use appropriate factor s from the tables provided Sales of new product Expenses Materials labor and overhead except depreciation Depreciation Machinery Selling general and administrative expenses Required 1 Determine income and net cash flow for each year of this machine s life 2 Compute this machine s payback period assuming that cash flows occur evenly throughout each year 3 Compute net present value for this machine using a discount rate of 7 Complete this question by entering your answers in the tabs below Required 1 1 910 000 1 482 000 114 750 178 000 Required 2 Required 3 Compute net present value for this machine using a discount rate of 7 Note Do not round intermediate calculations Negative amounts should be entered with a minus sign Round your present value factor to 4 decimals and final answers to the nearest whole dollar

1 Answer the following questions using the graph of the function f x below 6 pts M ESUS In sibeqal sims 10touren a lim g x b lim g x 17 C lim g x 2 MAXI d lim g x morsinoleu TOY TO1 qooxe bewolls abie e The equations of the vertical asymptotes nofoviups to 2AD stigan 7 3 6 TOT 08 11 TOSIDING THOSE OF O 996 w woy guido do bus amaldorq gaivloe ai voy bis 01 a G

17 65 Determine the vertical and horizontal components of reaction at the pin support A and the angular acceleration of the 12 kg rod at the instant shown when the rod has an angular velocity of 5 rad s A 0 6 m

6 What is the only x 0 for which the statement below could be true If eggs cost x a dozen less then it would cost 1 less for x 1 eggs than if eggs were x a dozen more EGG SALE Please do not include unit in your answer

Hot 2 Sketch the graph of the continuous function f that satisfies all of the stated conditions 9 pts trpioiture ion zi nolemixoqqs fariseb s joviam TAH al to bollen instw f 0 2 f 1 0 2 2 Toile worla taumuoy GANI Y 42 20s moldong cut 3 f 0 0 f 2 0 sonen Shuleni vorla 21swage TUOY sidizzon f x 0 on 0 and 2 0 f x 0 on 0 2 berolamos f 1 0 6 isqe doteros 100 f x 0 on 1 00 f x 0 on 0 1 awab siin iso oluoso may oti bogguig too 2 1 AP 23 2 3 197 LET 4 LOV 150 D 6 the moy JORABO TV N 15y of Insom JOVJER 61

5 B2B Company is considering the purchase of equipment that would allow the company to add a new product to its line The equipment costs 379 200 and has a 12 year life and no salvage value B2B Company requires at least an 9 return on this investment The expected annual income for each year from this equipment follows PV of 1 FV of 1 PVA of 1 and FVA of 1 Note Use appropriate factor s from the tables provided Sales of new product Expenses Materials labor and overhead except depreciation Depreciation Equipment Selling general and administrative expenses Income a Compute the net present value of this investment b Should the investment be accepted or rejected on the basis of net present value Complete this question by entering your answers in the tabs below Required A Required B Compute the net present value of this investment Note Round your present value factor to 4 decimals and other final answers to the nearest whole dollar Years 1 through 12 Annual Net Cash Flows X 130 300 x Present Value of Annuity at 9 237 000 83 000 31 600 23 700 98 700 7 5361 Present Value of Net Cash Flows 981 954 my work

Find the optimum strategies for player A and player B in the following game Find the value of the game Be sure to look for a saddle point first 71 24 Find the optimum strategy for player B Choose the correct answer below and fill in the answer box es to complete your choice OA The game is not strictly determined Player B should choose column 1 with probability with probability Type integers or simplified fractions B The game is strictly determined Player B should choose column Type a whole number The value of the game is and column 2

a A Particle is released during an experiment It s Speed minutes after release is given by uv t 0 5t lot where u t is in meters per second How far dues the Particle travel during the first 5 seconds

3 A total of 1500 is invested at 1 2 and 4 annual interest The interest after 1 year equals 46 The amount invested at 2 is double the amount invested at 1 Find the amount invested at each rate

Good Times Bakers works out a demand function for its cookies and finds it to be g D X 967 25x where g is the quanity of cookies sold when the price per Cookie is x cents Find the elasticity function Find the elasticity at a price of 0 10 Per Cookie X 10 and state whether the demand is elastic or inelastic at that price At this price will raising the price increase revenue Find the price where the Revenue is a maximum

Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit given the following revenue R X and cost C x functions R X 5X and CC X 0 001x2 1 2x 60

Find the size of the permanent endowment needed to generate an annual 21 000 forever at a continuous interest rate of 7