Math - Others Questions

a Place the digits 4 6 7 8 and 9 in the circles to make the sums across and vertically equal 19 b Is there more than one answer to part a a Choose the correct answer below OA O C OD

a Place the digits 10 12 13 14 and 15 in the circles to make the sums across and vertically equal 37 b Is there more than one answer to part a a Choose the correct answer below A 10 OB 10 12 14 O C 12 D 12 15

7 Consider the following subspace W and find a basis for W W Span 2 3 3 0 8 6 2 3

Find the domain and range of f 4 2 0 2 4 6 O Domain 4 2 6 8 7 5 0 Range 4 2 0 2 4 6 8 O Domain 5 8 Range 4 8 O Domain 4 8 Range 5 8 O Domain 4 8 Range 5 8 O Domain 5 8 Range 4 8 O Domain 4 2 0 2 4 6 8 f x 4 2 6 7 5 0

Find the slope of the line graphed below 5 3 ma 1

What calculation does the sequence of sketches to the right illustrate Choose the correct answer below A 527 500 20 7 OB 527 1 263 2 OC 527 2 263 R1 OD 527 263 2 1 GEXEST

The following table shows the depth D in inches of snow on the ground h hours after the beginning of the nowfall h hours D depth 2 3 3 LO 5 n your response answer the following questions 1 What is the value of D 8 2 Calculate the average rate of change from 5 to 8 5 8 8 10

The graphs of y2r and y 4 z are shown below These two graphs split the plane into 4 regions which we will call Regions A B C and D 1001 92 VS 22 y S 2r 92 4 z 22 4 z 22 y s y s D Match each of the following systems of inequalities with the region shown above A C y 2r B y 4 x

What property of multiplication is shown in the diagram that follows 0 0 1 1 2 4 2 3 3 Choose the correct answer below 4 4 2 OE The closure property OF The multiplication by zero property 5 5 6 4 6 OA The distributive property of multiplication over addition B The associative property OC The multiplicative identity property of one D The commutative property 2 7 7 8 8 9

is symmetric therefore it is orthogonally diagonalizable 1 Find an orthogonal matrix P and a diagonal matrix D such that PDPT A 15 pts 11 The matrix A

Write the number as a Mayan numeral 116 Which of the following is the equivalent Mayan numeral OA OB OC

ab a b for any real number n but a b a b forn 1 Multiplying 3x5 Adding 3 5 Factors Terms 2 Explain why the computational result in each of the following two parts is wrong and the correct answers a 3 x 7 3x 7 b x h x h c 3x 3x

Suppose a runner claims that her mile run time is less than 9 minutes on average Several of her friends do not believe her so the runner decides to do a hypothesis test at a 10 significance level to persuade them She runs 12 time trials collects the proper data and works through the testing procedure Ha u 9 Ha R 9 a 0 1 significance level The test statistic is B 20 Select the correct answer below I po n 7 7 9 12 The critical value is 20 1 1 28 Conclude whether to reject or not reject Ho and interpret the results 4 5 Reject Ho At the 10 significance level the test results are not statistically significant and at best provide weak evidence against the null hypothesis Reject Ho At the 10 significance level the data provide sufficient evidence to conclude that the mean time is less than 9 minutes Do not reject Ho At the 10 significance level the test results are not statistically significant and at best provide weak evidence against the null hypothesis Do not reject Ho At the 10 significance level the data provide sufficient evidence to conclude that the mean time is less than 9 minutes

200 15 pts 10 Diagonalize the matrix A 1 2 10 matrix P and a diagonal matrix D such that PDP A Make sure to explicitly write down the matrices P and D and verify the equality PDP A 1 That is find an invertible

A pharmaceutical manufacturer wants to investigate the bioactivity of a new drug A completely randomized single factor experiment was conducted with three dosage levels and the following results were obtained Dosage 20 gm 30 gm 40 gm 24 37 42 Observations 28 37 39 52 30 35 38 Is there evidence to indicate that dosage level affects bioactivity

a How would you show that for any whole number a a 0 a if you were starting from our definition of addition and the audience is your university class b How would you show that for any whole number a a 0 a if you were talking to your class of fourth graders a Choose the correct answer below OA O is the cardinal number of the empty set that is n 0 If the set A has a elements in it n A a then n A n n A U because A and are disjoint But A U A since there are no elements in to add to the set A Thus n A U n A a OB Start with two disjoint sets of the same cardinality A and B with n A n B a Then write the equation Since n A n B a n AUB a Since they are disjoint AnB Then a 0 n AU ANB which is equal to n AUB a OC Use manipulatives to show that the union of a collection with a collection with no elements has the same number of elements as the first collection OD O is the cardinal number of the empty set that is n 0 If the set A has a elements in it n A a then n A n n An because A and are disjoint But An A since there are no elements in to add to the set A Thus n AU n A a

2 Random samples of two first year students two second year studer year students and two fourth year students each from four dormitories were asked to rate on a scale from 1 poor to 10 excellent the quality of the dormitory environment for studying The results are shown in the table Your First Second Third Fourth Donitory A Dormitory B Dormitory C Dormitory D 75 86 98 99 68 55 78 76 68 659 54 74 67 75 89 78 67 Carry out the analysis of variance and prepare the ANOVA table Use a 0 05 6 What can you say concerning the H hypotheses

5 Simplify each expression if possible x 2 a x 2 x 2 2 x 1 x 1 x b x x 1 x 1

The FOIL method is a useful way to recall how to expand the product of two binomials a b x c d Multiply the First terms Outer terms Inner terms and the Last terms of the binomials and sum the four products to obtain the formula a b x c d ac ad bc bd Explain how the rectangular area diagram shown to the right justifies the FOIL method What is the area of F The area of Fis a b F 1 C 0 L d

Given the NYSE advancing declining Num and volume Vol Advancing Declining Day 1 2 3 4 5 Num Vol Num Vol 972 1240 1923 2000 2324 2665 607 578 1112 957 1830 2199 672 837 2277 3140 1973 1733 940 1111 What is the Arms Index or TRIN for day 5 O 1 5184 O 1 4672 O 1 3957 O 1 5674

3 Calculate the determinant of matrix A by using the cofactor expansion along its third row 2 1 1 3 4 2 0

In the first 3 years that Jill owns her sports car she drives 63 350 kms Jill maintains her vehicle according to the distance maintenance schedule below taking into consideration both kilometres driven and elapsed time The fuel consumption rating for her sports car is 8 3 L 100 km Each year Jill pays 1960 for insurance and 98 for her vehicle license plate registration During those 3 years Jill renews her driver s licence at a cost of 80 The average cost of fuel is 1 06 L Determine Jill s average monthly operating cost during the 3 years Use the table provided see attached to organize your answers Recommended Service Lube oil and filter Tire rotation and brake inspection Wheel alignment inspection Automatic transmission Frequency kms 5000 10000 Cooling system 50000 Tune up and emission 85000 control Insurance Registration License 25000 85000 Recommended Service Vehicle Maintenance Schedule Gas Lube oil and filter Tire rotation and brake inspection Wheel alignment inspection Cooling system Tune up and emission control Automatic transmission Frequency months 3 6 Vehicle Operating Maintenance Cost Price 15 Total Frequency 24 30 51 Approximate cost 36 95 63 99 79 95 84 95 165 00 175 Total

The following assumptions are made for each investigation The original mortgage is 300 000 amortized over 25 years at 3 99 compounded semi annually Unless otherwise indicated assume monthly payments are made Unless otherwise indicated assume the interest rate remains constant during the amortization period Your answers can be entered directly on this accianmont hut planen hand in all rough work no miestas 7 TONG Unchamp vs remung Is it better to own a home or to rent The answer to this question is no longer as one sided as it has been for years The attached article gives a financial breakdown comparing home ownership costs to rental costs The mortgage used in the home ownership case is the same as defined for the previous Investigations you just completed Read the article and answer the following 1 What conclusion was reached by Mr Tristani the man who completed the study regarding whether it s better to buy or rent these days 2 What factors other than financial do you think influence whether one buys a house or rents 3 The total mortgage payments for owning the home described here are 472 929 Look back to the results of Investigations 1 2 and 3 which you just completed Identify specifically how the homeowner could have decreased his her mortgage cost EU THAT 4 The maintenance cost of this house each year is set at 4 of the market value of the house According to Mr Tristani this cost goes up by about 3 each year as does the value of the house Calculate the maintenance costs for the first 5 years of the house The increase in the rate of maintenance has been done for you Year of home ownership 1 2 3 4 5 Market value of house 400 000 Rate of maintenance 4 0 4 12 4 24 4 37 4 50 Maintenance costs

1 point Including 8 sales tax an inn charges 140 40 per night Find the nightly cost at the inn before tax is added a Write an equation to model the problem Let x represent the nightly cost before tax Answer b Solve the equation to find nightly cost before tax Note Your answer should be in the form ddd cc

1 point The table below contains data for a linear function t 8 2 8 4 8 6 8 8 f t 789 2 803 4817 6831 8 Find a formula for the function f t

1 point Find the value of k so that the graph of x 5 k passes through the point 8 6 Y k help numbers

1 point 2 10 10 10 3 12 f x 12 g x Use the figures above which show the functions f x and g x to find the following values Note that you can find exact values 1 f g 7 2 g f 0 3 g g 1

Janet wants to buy her first car She knows the make and model she wants but has not decided whether it will be new or used The new car has an MSRP of 24 572 Janet negotiates a discount of 650 and needs to pay the following additional costs 685 freight charge 100 tire air tax 75 gas tax 85 administration fee 74 licence plate fee 20 gas fee 54 finance fee Janet has also found a used car of the same make and model that is 2 years old and has been driven 38 547 kilometers The price of the used vehicle is 14 950 Additional costs include 85 administration fee 74 licence plate fee 20 gas fee 54 finance fee The interest rate on the loan for the new car is 4 9 compounded monthly The interest rate on the loan for the used car is 9 9 compounded monthly In each case the car will be financed for 36 months MSRP or List Price Discount Purchase Price Freight Tire Air Tax Gas Tax Administration Fee Taxable Subtotal Trade in Allowance Deal Review Used car Gas Fee Lien Payout Delivery Price MFG Rebate Down Payment Finance Fee Amount Financed Interest Rate Loan Term

Jim has chosen the car he wants and must now decide whether to buy or lease it The car has an MSRP of 21 977 and a residual factor of 34 Jim negotiates a 500 discount and must pay the following additional costs 660 freight charge 100 tire air tax 75 gas tax 85 administration fee 74 licence plate fee 20 gas fee Regardless of whether Jim buys or leases the car the financing is 6 9 compounded monthly for 48 months If Jim buys the car the finance fee is 54 If he leases the car the finance fee is 36 MSRP or List Price Discount Purchase Price Freight Tire Air Tax Gas Tax Administration Fee Taxable Subtotal Trade in Allowance Taxable Total HST 13 Licence Plate Fee Deal Review New car Gas Fee Lien Payout Delivery Price MFG Rebate Down Payment Finance Fee Amount Financed Interest Rate Loan Term Monthly Payment Interest Due at Balance Due

Janet has also found a used car of the same make and model that is 2 years old and has been driven 38 547 kilometers The price of the used vehicle is 14 950 Additional costs include 85 administration fee 74 licence plate fee 20 gas fee 54 finance fee The interest rate on the loan for the new car is 4 9 compounded monthly The interest rate on the loan for the used car is 9 9 compounded monthly In each case the car will be financed for 36 months Janet wants to buy her first car She knows the make and model she wants but has not decided whether it will be new or used The new car has an MSRP of 24 572 Janet negotiates a discount of 650 and needs to pay the following additional costs 685 freight charge 100 tire air tax 75 gas tax 85 administration fee 74 licence plate fee 20 gas fee 54 finance fee MSRP or List Price Discount Purchase Price Freight Tire Air Tax Gas Tax Administration Fee Taxable Subtotal Trade in Allowance Taxable Total Deal Review New car Gas Fee Lien Payout Delivery Price MFG Rebate Down Payment Finance Fee Amount Financed Interest Rate Loan Term Monthly Payment

Find a vector g so that if F i that if F F co C C2 g 0 00 co C C2 C3 then F F g 0 30 20 cz

Let 3 f x 2 1 1 1 x Y f x y g x y 3 2 T 2 w X and g x y fog x 2 X T X In the Figure above match the colors of the graphs in this Figure with the functions given Enter y for yellow r for red and g for green as appropriate 3 1

Find numbers C1 C2 C3 such that C1 C C3 1 1 0 1 C1 number 2 significant figures number 2 significant figures number 2 significant figures 0 0 0 1 C2 1 0 1 1 C3 1 2 0

Mitchell made payments of 157 37 at the end of every month into a retirement fund which accumulated to 46 000 over 20 years a At what interest rate compounded monthly was the fund growing Assume that the interest rate remained constant throughout the term Round to two decimal places b At what interest rate would he have been able to accumulate the same 46 000 in only 11 years

4 The discussion of electricity costs in section 8 6 stated that coal costs of 1 00 1 50 per million BTU are equivalent to about 24 36 per ton and that natural gas costs of 2 00 5 00 per million BTU correspond on an equivalent energy basis to 12 30 per barrel of oil Use the data on fuel properties in table 8 1 to confirm these equivalencies

2 Evaluate a root using Muller s method from the function f x 3 704x 16 3x 21 97x 9 34 Terminate if Es 0 00255

Determine f where the periodic function is described by its graph Af t 2 f s a 2a Triangular wave 3a 4a Q

If the line slopes upward toward the right the slope is positive If the line slopes downward toward the right the slope is negative The slope of a horizontal horizontal line is 0 because Ay 0 The slope of a vertical vertical line is undefined because Ax 0 Step 2 Determine the slope of the graph below y 10 5 10 5 10 The slope of the line Select 3 negative 10 X positive negative

A certain colery of bacteria grows exponentally If the celory doubles in size every 13 days How long does it take to triple in size

Determine f where f t is periodic with the given period Also graph f t f t t 0 t 3 and f t has period 3 Determine f f s

70 60 50 40 30 20 10 50 t y 100 150 290 t b From the equation identify the maximum point on the graph of y p t Round your answers to two decimal place X c In what year is the percent of women workers at its maximum according to this model x

Assume that revenue is R x 500x 2x and cost is C x 3700 100x 2x a Find the profit function P x b Find P 50

Let s X ANB C and Y A B n A C 1 Draw a Venn diagram for sets X and Y 2 Determine which relationship C 2 between sets X and Y is true Show your work in a blue book

For the function f Z Z f n 31 complete the questions below 1 Graph the function use the graphing paper provided 2 Determine if the function f is a one to one function injective Justify your answer 3 Determine if the function f is an onto function surjective Justify your answer 4 Is f a bijection Explain why or why not Show

Some integers are divisible by 3 or by 7 1 3 pts Express the statement given above in logical form 2 3 pts Form the negation using the logical form found in 1 and then simplify it so no 3 3 pts Express the negation of the given statement in words 4 1 pt Determine the truth value of the negation

Use Mathematical induction to prove that 2 divides n 3n whenever n is a positive integer

How many permutations of the letters A B C D E F starts with A a Show your work in a blue book

How many bit strings of length six have at least five 0 bits a Show your work in a blue book

QUESTION 9 For the given sequence select a closed formula and recurrence relation with the initial condition that generale 9 4 1 6 11 16 Da a 5 a Da a1 9 a 1 a 9n 5 n20 a 5n 9 n20 a 5n 9 n21 R 5 a 4 O a a 5 a 9

force needed to lift the machine that has a weight of 10 kN 3 m 2 m 10 kN A 20 Prob 3 61 cables 1 25 m 1 25 m