Math - Others Questions

1 You have decided to accept an offer from your parents of a loan to finance your new car The amount you have budgeted for is 15000 over 42 months Your parents decided to charge a reasonable SIMPLE INTEREST rate of 2 5 per year How many years is 42 months 4 2 4 3 5 2 You have decided to accept an offer from your parents of a loan to finance your new car The amount you have budgeted for is 15000 over 42 months Your parents decided to charge a reasonable SIMPLE INTEREST rate of 2 5 per year What is 2 5 as a decimal 0 025 0 25 I 131250 F 0 0025 3 You have decided to accept an offer from your parents of a loan to finance your new car The amount you have budgeted for is 15000 over 42 months Your parents decided to charge a reasonable SIMPLE INTEREST rate of 2 5 per year How much interest do you owe your parents at the end of the 42 months 1575

Write an estimate of the number in scientific notation 406793 40670

rate of 30 per year a Write an equation to represent the value of the car after n years b What is the value of the car after 3 years alue of the car depreciates at a C 13 T 13 c What is the value of the car after 6 years 9 A loaf a bread costs 2 but the rate of inflation is 3 per year C 13 T 13 a Write an expression to represent the cost of a loaf of bread after n years b How much would the loaf of bread cost in 2 years c How much would the loaf of bread cost in 10 years

Fill in the table Transformed Function Mapping Notation Amplitude Period Horizontal Axis Phase 2 COS 7 x 1 3 g x 2 cos cos

Determine the possible values of 0 ses 2n in each case if possible find exact valu a cos 1 2 b cot 1 7

A certain sector in a circle has an arc length of 10cm and an area of 20cm Determine the radius of the circle and the angle of the sector

Call centers typically have high turnover The director of human resources for a large bank has compiled data on about 70 former employees at one of the bank s call centers The accompanying table shows this data In writing an article about call center working conditions a reporter has claimed that the average tenure is no more than two years Formulate and test a hypothesis using these data to determine if this claim can be disputed Use a level of significance of 0 05 Click the icon to view the call center data Is there sufficient evidence at the 0 05 level of significance that the average tenure is no more than two years Determine the null hypothesis Ho and the alternative hypothesis H Ho H 2 H H 2 Type whole numbers Compute the test statistic Round to two decimal places as needed 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 A Gender 0 1 0 0 0 0 0 1 1 1 0 0 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 B Length of years 7 03 3 48 2 07 1 78 4 43 3 28 3 05 0 47 0 59 3 12 2 94 2 15 4 01 3 52 2 47 2 14 3 27 1 08 1 77 1 94 2 89 3 03 2 54 1 82 2 87 2 21 1 44 C D 1 1 1 0 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 0 1 0 1 1 1 E 2 53 1 41 1 08 0 98 0 64 1 31 2 13 2 28 2 06 2 14 2 11 2 16 2 04 1 71 2 11 1 73 2 13 2 13 0 36 1 95 1 02 1 27 1 04 1 64 1 76 1 71 1 27 F G 0 0 1 1 1 0 0 1 0 0 TOOOOO 1 0 0 0 0 0 H 1 47 1 29 1 46 1 88 1 15 1 16 1 04 0 95 1 25 0 79 0 87 0 99 0 74 0 31 0 34 0 56

5 Consider the function y sin x 30 3 a Sketch the graph for two cycles 50 100 b What is the amplitude C What is the period e 150 200 d What is the equation of the axis State the domain and range 250 300 350 400 450 500 550 3 marks 600 650 1 mark 1 mark 1 mark 2 marks

On the evening of the famous final the stadium was packed Fortunately the Soci t de transport de Montr al has provided free shuttles to avoid traffic congestion at the end of the game The fact remains however that a good number of people have found a place to park their car in one of the neighboring parking lots and will leave the premises at roughly the same time The diagram below illustrates the expected traffic flow around the stadium after the game The numbers and the xi variables indicate the average number of vehicles traveling per hour and the arrows indicate the direction of traffic The city hires you as a traffic management specialist to analyze the situation Des Pins 300 P 100 200 University Stade Percival Molson C 150 Aytmer 400 600 550 D Du Pare 750 1200 P a Give the system of linear equations associated with this graph and express it in the form of a matrix equation AX B b Use the Gauss Jordan method to invert if possible the matrix A found previously c Establish the circulation flow by solving the system of linear equations by the inverse matrix method

The figure shows a small plane flying at a speed of 182 miles per hour on a bearing of N47 E The wind is blowing from west to east at 42 miles per hour The figure indicates that v represents the velocity of the plane in still air and w represents the velocity of the wind The ground speed of the plane is miles per hour Simplify your answer Round to the nearest tenth as needed Plane s speed 182 miles per hour ON35 3 W 47 N54 7 W Wind s speed 42 miles per hour V W Simplify your answer Type an integer or decimal rounded to the nearest hundredth as needed Type your answer in the form bj c The magnitude of v w called the ground speed of the plane gives its speed relative to the ground Find the ground speed in miles per hour V W d The direction angle of v w gives the plane s true course relative to the ground Approximate the true course to the nearest tenth of a degree What is the plane s bearing Choose the correct answer below N54 7 E ON35 3 E

Write the following complex number in rectangular form 10 cos 225 i sin 225 The rectangular form of 10 cos 225 isin 225 is Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominators Type your answer in the

the stant as of the on b Follow the seven step strategy and use the slant asymptote to graph the rational function f x x x 6 X 3 a Select the correct choice below and if necessary fill in the answer box to complete the choice A The equation of the slant asymptote is Type an equation B There is no slant asymptote onal b To graph the function first determine the symmetry of the graph of f Choose the correct answer below neither y axis symmetry nor origin symmetry v axis symmetry

A daredevil wants to jump over a canyon on his motorcycle He travels approximately 88 ft sec at an angle of 30 when the motorcycle leaves the ramp at the edge of the canyon Choose a coordinate system with the origin at the end of the take off ramp and assume he lands at the same height a Write parametric equations to define the path of the motorcycle as a function of the time t in sec after leaving the ramp b If a bird is at a position 99 27 at a time 1 3 sec after the motorcycle leaves the ramp will the motorcycle hit the bird Assume a 1 ft margin of error

f For the functions f x 2 x and g x x 2x8 find f g f g fg and Determine the domain for each function g f g x Simplify your answer What is the domain off g Select the correct choice below and if necessary fill in the answer box to complete your choice A The domain off g is Use a comma to separate answers as needed The domain of f g is OC The domain off g is B fog x Simplify your answer What is the domain of fg Select the correct choice below and if necessary fill in the answer box to complete your choice OA The domain of fg is Type your answer in interval notation Use a comma to separate answers as needed The domain of fa is

To save for retirement Karla Harby put 625 each month into an ordinary annuity for 11 years Interest was compounded monthly At the end of the 11 years the annuity was worth 110 344 What annual interest rate did she receive The interest rate she received was approximately Round to two decimal places as needed

1 Ethan throws a toy soldier with a parachute into the air from a balcony The path of the soldier can be modelled by h t 5 7t 18 where the height h t is in metres and the time t is in seconds a When will the soldier hit the ground 2 marks b How long will the soldier be above 15 m 2 marks

4 5000 is invested for 2 years at 10 per annum Determine the amount that this investment would grow in two years for different compounding frequencies a Semi annually b Quarterly c Monthly 2 marks 2 marks 2 marks

Points 0 of 5 SIGHTS WILI CHTULEM Save Using the accompanying MBA Motivation and Salary Expectations data determine how well a linear function models the relationship between pre and post MBA salaries Compare it to a third order polynomial Would the polynomial model have a logical explanation Click the icon to view the MBA Motivation and Salary Expectations data O Click here to view chart a Compare the two models Would the polynomial model have a logical explanation OA Both the linear and polynomial models have similar R2 values Neither model is strictly better than the other because they pass through roughly the same number of data points One might explain it by suggesting that post MBA salary is not dependent on pre MBA salary OB The polynomial model has a much higher R2 value than the linear model The polynomial will always be better because polynomial models always have high R2 values One might explain it by suggesting that an MBA will most affect a person s salary if their pre MBA salary is either very low or very high OC The linear model has a much higher R2 value than the polynomial model The linear model will always be better One might explain it by suggesting that the higher the pre MBA salary is the higher the post MBA salary will be OD Both the linear and polynomial models have similar R2 values The polynomial will always be better because it has additional terms One might explain it by suggesting that the higher the pre MBA salary is the post MBA salary will grow at an increasing rate as a percentage of the pre MBA salary However when the pre MBA salary is high the effect starts to level off 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 A Age B Gender 31 M 32 M 31 M 35 M 25 M 25 F 40 M 28 F 32 F 26 M 24 M 31 F 30 M 24 F 25 M 32 F 39 M 38 M 24 M 27 F 32 M 27 M 25 F 28 F 34 F C Years Work Experience More than 6 More than 6 4 to 6 More than 6 1 to 3 4 to 6 More than 6 4 to 6 More than 6 1 to 3 1 to 3 4 to 6 4 to 6 4 to 6 4 to 6 More than 6 More than 6 More than 6 1 to 3 4 to 6 More than 6 4 to 6 None 4 to 6 More than 6 D Motivation Career Change Career Advancement Higher Financial Earnings Career Change Higher Financial Earnings Career Advancement Genuine Interest Higher Financial Earnings Genuine Interest Career Change Higher Financial Earnings Career Change Career Change Career Advancement Career Change Genuine Interest Higher Financial Earnings Genuine Interest Career Advancement Higher Financial Earnings Higher Financial Earnings Genuine Interest Genuine Interest Career Advancement Career Change F E Pre MBA Salary Post MBA Salary 105000 84500 87000 100000 69500 100500 95500 126500 52500 60500 47000 70500 70000 130000 55000 74500 75500 109500 50000 43000 70000 55000 60000 65000 90000 86500 109500 37000 59500 73000 57500 45000 65000 85500 80500 85500 90000 69500 89500 79500 110500 105500 126000 70000 74500 94000 75000 80500 89000 99500

The accompanying data shows the data on 70 former employees at one of the bank s call centers For each of the following assume equal variances of the two populations a Is there evidence at the 0 05 level of significance that the average length of service for males is the same as for females a Test the null hypothesis that the average length of service for males is the same as for females b Test the null hypothesis that the average length of service for individuals without prior call center experience is the same as those with experience c Test the null hypothesis that the average length of service for individuals with a college degree is the same as for individuals without a college degree 13 d Now conduct tests of hypotheses for equality of variances Were your assumptions of equal variances valid If not 14 repeat the test s for means using the unequal variance test 15 Click the icon to view the call center data Determine the null hypothesis Ho and the alternative hypothesis H Let males be population 1 and females be population 2 Ho H Type integers or decimals Do not round 1 5 6 7 22 8 19 9 10 11 16 17 2 18 19 20 20 21 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 A Gender 1 0 1 F 1 0 0 1 1 0 0 0 1 0 19 1 4 ST 1 7 0 1 2 10 19 0 19 1 1 0 1 1 B C D Prior Call Center Experience College Degree Length of Service years 0 53 0 57 0 63 0 59 0 76 0 76 0 76 0 1 1 1 1 1 7 0 1 7 0 4 1 1 7 0 0 0 0 0 0 0 2 1 7 0 n 0 0 0 0 0 0 0 0 2 0 0 3 0 0 4 1 9 0 7 10 0 29 1 1 0 0 1 7 0 1 0 1 1 1 1 0 88 0 66 0 97 UST 0 94 0 97 0 98 1 04 1 04 1 2 1 06 1 14 1 14 1 16 1 17 1 25 243 1 3 2 1 3 Exp 1 32 LDA 229 13 1 43 141 E F 1 7 1 7 1 20 1 0 1 T 0 7 1 0 9 0 1 10 A 0 al 0 1 1 0 1 0 0 0 1 1 1 0 G 7 1 1 7 0 0 0 0 0 of 0 1 0 0 0 1 0 0 1 1 0 1 7 1 7 0 1 0 0 H 0 1 0 1 0 0 1 0 0 0 0 1 0 7 1 0 1 1 1 0 0 1 1 0 ol 1 1 5 1 67 1 76 1 78 1 82 7 1 79 1 86 1 84 1 91 201 1 97 Sear 2 01 2 09 2 12 2014 2 16 2 17 2 1 2 17 2 1 2 17 2 15 2 19 2 2 2 25 2 3 J K 1 0 0 9 0 0 1 1 3 GI 1 4 0 0 1 1 O 0 0 L 1 1 1 a 0 1 P 1 0 0 O 0 S 1 0 0 0 M

What is the direction of the vector defined by 5 12 Give your answer in degrees rounded to the nearest tenth

16 State sin B cosB and tan B as ratios fractions for the following triangle 3 marks A 17 15 B 8 C

to the nearest cent 1 a If you invest 2900 at the end of every six months in an account that pays 5 a compounded semi annually how much will you have earned after 7 years TVM solver https www fncalculator com financialcalculator type tvmAdvanced Calculator

Match the sign chart for the derivative with the correct graph of the function O N O 4 er 5 2 4 f f f f A B A C

At the start of your post secondary education your parents invest 12000 in an account that pays 6 5 a compounded weekly How much can you withdraw from the account at the end of every we ek while you are in school over the next 4 years

Find the derivative f x 5x 2x 7 5x4 4x 3x 1 af x 15x 4x 5x4 4x 3x 1 5x3 2x 7 20x 12x 6x b f x 15x 4x 5x4 4x 3x 1 5x 2x 7 20x 12x 6x c f x 15x 4x 5x 2x 7

Suppose the marginal revenue is MR x 16x Find the interval where the revenue is increasing a 4 U 0 4 b 3 U 0 3 OC 3 0 U 3 Od 4 0 U 4 00

Suppose x 3 is the only critical point for f x If the derivative of the function f x is negative on infinity 3 and positive on 3 infinity what must be true about f a Has a minimum at 3 b Has a maximum at 3 c Has an inflection point at 3 d None of the above

Find the derivative f x a f x Ob f x C 4x 2x 5 5x4 4x 3x 1 12x 4x 4x 2x 5 5x4 4x 3x 1 f x 12x 4x 5x4 4x 3x 1 4x 2x 5 20x 12x 6x 5x4 4x3 3x 1 12x 4x 4x 2x 5

Find the equation of the line tangent to f x x 3x 5x 7 with f x 3x 6x 5 at x 1 a y 29x 35 b y 2x 8 c y 14x 12 d y 5x 3

Find the derivative y x 4 x5 ay 6x 7 5x 6 b y 4x 5 5y 6 C y 7x 8 9x 10 Ody 2x 3 4x 5 ey 3x 4 6x 7

Find the derivative p x e In 7x 1 7x a p x e Ob p x e C 7 7x P x xe 1 Od p x xe 1 7x 7 7x

Find the derivative 8 x x x 5 a Ob g x d e 1 g x X 8 x x g x x 2 g x 2 1 2 3 12 x 1 2 2x 1 4 4 2 1 2 1 2 1 2 2 3 x 5 X 4x1 3 3 2 1 3 X 3 2 5 3 5

According to the Iceberg Model Hall 1976 some aspects of culture are overt or visible but most aspects of culture are covert or invisible Which of the following is an example of a covert aspect of culture Marketing Campaign Group Norms Organizational Logo

Which is true of a traditional organization but not true of an inclusive organization Decisions are made according to a hierarchy The organization creates and encourages change Risk and errors are accepted Loaders care deepby about customers stockholders and employees

Which of the following is not a characteristic of an Inclusive leader Culturally Intelligent Authoritative Collaborative Supportive

one sided handwritten mind map that summarizes all of the course information in advanced functions MHF4U Unit 1 polynomial functions Unit 2 Factor theorem and Inequalities Unit 3 Logarithmic and Exponential Function Unit 4 Trigonometry in Radians Unit 5 Trigonometric Identities Unit 6 Rates of Change Unit 7 Rational Functions Heres an example of a mind map for rational expressions from grade 11 function You need to do that for 7 units on one page Add small images if relate to content 34 12x3 2x 2x 4x2 8x3 X 0 Multiplyinal Divising factor State restrictions cancel common factors multiply top bottom statement restrictions Rule Cross multiplication I of fractions only happens when we have an equal Sign y 2 Rule we can Cancell out ONLY when 1 multiplying fractions ALWAYS STATE RESTRICTIONS ys b b apply when dividing flip 2nd after restrictions Unit 2 Rational Expressions xarb must find Common denominator bottom index get common denominator Expand numerators add or subract Simplify restrictions Adding Subtracting ab 2 ab Zab distribute Rule we can NOT Cancel out when or fractions xaxb top Power of a Power product Rational Exponents negative L xajb xa b Exponent Rules x a xa b Ex Quotient WI zero Sany power xb no 1 expect zero

What single cash payment is equivalent to payments of 3500 every six months at 7 compounded quarterly if the payments are made at the end of every six months for fifteen years

oes either the domain and or range of f x x need to be restricted in order to find an inverse function Explain why or why not

3 Use the determinate of the coefficient matrix to determine whether the system of linear equation has a unique solution 2x 5y 2 3x 7y 1

2 Given A FESS BIBLIVRE THER Y C 1 0 0 2 1 2 a Find the determinate of ATA

2 The following graph represents the escape of a rodent that was frightened by a hawk flying by Describe the motion of the rodent as shown on the graph TI a What is the average speed of the rodent over the intervals in the graph 0 4 4 12 4 20 4 8 12 10 20 10 b Estimate how fast the rodent was moving at the 2 second mark Specifically at that instant Use an average of 2 secant lines

1 Find the determinant for A 15 0 3 3 9 6 12 3 6

Jax Co uses a job costing system and has provided the following data for 2021 Direct materials purchased on account 87 000 Direct materials used in manufacturing Direct labor costs incurred Actual manufacturing overhead costs incurred 83 000 100 000 128 000 Jax allocates manufacturing overhead at 120 of direct manufacturing labor costs Calculate the amount of manufacturing overhead allocated for 2021

7 Describe the relationship between tangent lines secant lines instantaneous rate of change and average rate of change TI

1 Consider the data below for a car tire with a leak K Minutes after the leak began 0 5 10 Pressure of air in the tire in kilopascals kPa 400 335 295 15 255 20 225 25 195 30 b Estimate the instantaneous rate of change at 5 minutes using a surrounding interval 170 a Calculate the average rate of change over the 30 minute interval Explain the meaning of this rate using proper units

5 Use the graph to find the following limits K a lim f x x 00 b lim f x c lim f x x 0 d lim f x x 0 e limf x x 0 34 16 12 8 4 0 18 f x 12 16 X 2x 8x 4

6 Evaluate each limit if it exists App x 8x a limx 3 2x 1 b lim 2 3x 5x 2 x 2x 8

4 Find the equation of the derivative for the following function Also find the instantaneous rate of change for the function when x 2 and x 3 K a f x 4x 1

x ay 5 2x 6y b In the system of equations above a and b are constants If the system has one solution which of the following could be the values of a and b A a 3 b 10 B a 3 b 12 C a 3 b 4 D a 10 b 3

An online office supply store sells pens at p dollars per box and offers free shipping on orders of 75 or more If John decides to order new pens from this store which of the following inequalities expresses the number of boxes n that he must purchase for the order to qualify for free shipping A n 75 B 11 7 5 n C n D n 75 P 75