Basic Math Questions and Answers

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

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

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

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

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

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 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

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

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

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

When adding or subtracting fractions with different denominators each fraction s denominator must be converted to an equal value Which of the following terms describes that equal value

ferentiatle woth respect to x y x 7x 4 2 3

3 a Solve x 2 b Solve 1 xy xy 1 xy ydx 0 UNIT II OR 7M 8M

5 There are 200 ants in a nest the ant population double every month a Write an expression to represent the number of ants after n months b What will the population of the ants be after 6 months Round to 1 decimal place c What will the population of the ants be after 1 year Round to 1 decimal place 6 A new car is purchased at a cost of 25000 The value of the car depreciates at a rate of 30 per year a Write an equation to represent the value of the car after years b What is the value of the car after 3 years c What is the value of the car after 6 years 7 A loaf a bread costs 2 but the rate of inflation is 3 per year a Write an expression to represent the cost of a loaf of bread after 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

A long year end status report for work is 465 pages long You need to print 203 copies for a meeting next week How much is the paper going to cost for those reports Paper is sold in reams 500 pages for 14 each Answer Give your answer to the nearest cent only for the paper you use partial reams are OK

1 Evaluate the following expressions Leave your answers in fraction form where applicable a 3 b 9 d 2 2 Solve for x in the following exponential equations a 3 36 c 8 32 20 7 49 2 32 5 11 e 5 125 978 2 32x 8 b d c 3 3 Complete the chart by first by first writing the powers with the same base Then solve the equation Equation Rewrite with Common Base 62x 5 1 6 f 343 9 3 2 Solve for x

se the number line model to illustrate the following operation 2 1 3 2 1 2

Subtract Illustrate using fraction strips 31 25 3

Multiply using the rectangular area model 3 4 1 7 1 1 20

4 Consider this image below Use ex 5 5 5 8 25 525 5 Consider this image below Use exponent laws to evaluate them 3 3 5 9 9 6 Consider this image below Use exponent laws to evaluate them 2 2 2 2 16 16 1 16 7 Write in radical form and then evaluate the following

1 Match the picture to the Exponent Law a amn Product Law Quotient Law Power of a Power Power of a Product Zero Exponenet Law Negative Exponent Law 2 Match the picture to the Exponent Law a d am n Product law Quotient law Power of a Power Power of a Product Zero Exponent Law Negative Exponent Law 3 Match the picture to the Exponent Law axa amen

1 Match the picture to the Exponent Law a Product Law Quotient Law Power of a Power Power of a Product Zero Exponent Law Negative Exponent Law 2 Match the picture to the Exponent Law a 1 Product Law Quotient Law Power of Power Power of a Product Zero Exponent Law Negative Exponent Law 3 Match the picture to the Exponent Law ab arb Product law Quotient Law Power of a Power Power of a Product

1 Simplify the following Express final answer with POSITIVE EXPONENTS ONLY 9x y 4x y 12x y 8 2 Simplify the following Express final answer with POSITIVE EXPONENTS ONLY 6x y 5 2x y 3ry 4 3 Solve for x in each of the following equations by obtaining a common base on both sides of the equation 4 64 Question 3 options 21 3 4 Solve for x in each of the following equations by obtaining a common base on both sides of the equation 1 32 Question 4 options 0 In The tab bre doe

1 Solve for x in each of the following equations by obtaining a common base on both sides of the equation 3x www Question 5 options 3 1 3 3 27 2 Solve for x in each of the following equations by obtaining a common base on both sides of the equation Upload your solutions 2 marks 625 3 Solve for x in each of the following equations by obtaining a common base on both sides of the equation Upload your solutions 2 marks C 21 8 4 Solve for x in each of the following equations by obtaining a common base on both sides of the equation Upload your solutions 2 marks 32 4 27 2 5 Consider this image for the following questions Joel has two investment options Option 1 Option 2 500 invested at 5 per year compounded annually The amount A after a years is given by the equation A 500 1 05 400 invested at 7 25 per year compounded annually The amount A after years is given by the equation U

7 Evaluate the following expression exactly no decimals Draw a diagram for full credit arccos csc arccos

OR a Find the real root of the equation tanx x using Bisection method

25 Kamini is constructing the kite shown below The kite includes 2 perpendicular supports one of length 40 inches and the other of length 28 inches The ends of the supports are connected with string to form a 4 sided figure that is symmetric with respect to the longer support A layer of paper will cover the interio of the 4 sided figure Which of the following is closes to the area in square inches that Kamini will cove with paper A 101 B 280 560 D 840 E 980 string 28 in 40 in

The sum of 2 and 200 of 1 has the same value as which of the following calculations 2 2004 100 of 2 B 150 of 2 300 of 2 C D 300 of 1 E 400 of 1

UNIT IV 7 a Fit a polynomial for the following data x0 1 2 3 4 5 y 10 12 19 25 30 42 b Find the y 4 for the following data X 1 2 V 7 8 5 9 12 30 8M 7M

A city would like to know how many vehicles it could move through its streets in an emergency The most likely situation is an evacuation starting at the school and ending at the park The connections between these two locations plus their capacity and direction is shown below Path A B C Capacity 30 10 20 DE F G 15 30 15 15

A bank found that in recent years the average monthly charge on its credit card was 1 350 With an improving economy they suspect that this amount has increased A sample of 40 customers resulted in an average monthly charge of 1 376 11 with a standard deviation of 182 57 Do these data provide statistical evidence that the average monthly charge has increased Formulate the appropriate hypothesis fest and draw a conclusion Use a level of significance of 0 05 Is there sufficient evidence at the 0 05 level of significance that the average monthly charge has increased Determine the null hypothesis Ho and the alternative hypothesis H Ho H 1350 H 14 1350 Type whole numbers Compute the test statistic 0 90 Round to two decimal places as needed Using a level of significance of 0 05 what is the critical value 1 68 Round to two decimal places as needed Find the p value for the test Round to three decimal places as needed

1 Given that sin 0 7818 use equivalent trigonometric expressions to evaluate the following 3 14 cos

Standard Product Cost Atlas Furniture Company manufactures designer home furniture Atlas uses a standard cost system The direc labor direct materials and factory overhead standards for an unfinished dining room table are as follows Direct labor 28 00 per hr 5 0 hrs 12 00 per bd ft 18 bd ft standard rate standard time per unit standard price standard Variable factory overhead standard rate Fixed factory overhead standard rate a Determine the standard cost ner dining room table X P Incorrect Direct materials oak quantity Feedback 2 00 per direct labor hr 3 80 per direct labor hr b A standard cost system provides Atlas Furniture Company s management a cost control tool using the principle of management by exception Using this principle major cost deviations from standards can be investigated and corrected Check My Work Remember the process discussed in chapter for calculating standard cost

Find y as a function of tif 5y 300 0 9 1 0 4 6 Note This particular webWork problem can t handle complex numbers so write your answer in terms of sines and cosines rather than using e to a complex pow

The sodium potassium pump is called an electrogenic pump because it decreases the voltage difference across the membrane is used to drive the transport of glucose against a concentration gradient pumps equal quantities of Na and K across the membrane in opposite directions generates voltage across the membrane

4 How can double angle and compound angle identities help us solve trigonometric equations and simplify trigonometric expressions

1 Given that sin cos 3 14 0 7818 use equivalent trigonometric expressions to evaluate the following