Basic Math Questions and Answers

4 3 2 3 8 1 3 4 2 3 4 q Which of the following is the equation for the graph shown above Or 3 cos 20 T 1 2 cos 0 r 3 sin 20 Or 3 cos 30 Or 1 2 sin 0 Submit uestio

E PI 5 O r 1 3 cos 30 r 0 sin 0 CT r Hr 5 sin 0 2 a b a a

7 There are many cylinders with volume 452 cm Let r represent the radius of these cylinders and h represent the height This means the formula of the volume V in cubic centimeters of these cylinders is V Tr h and the equation for the surface area in square centimeters is S 2 r 2 rh Write an equation for S as a function of r when the volume of the cylinder is 452 cm

5 Find all values of that make the equation true 2x 1 x 1 x 2

Write a polar equation for the graph below Enter theta for if needed 6 3 r 0 2 6 E 4 3 2 1 2 3 4 Question Help Video

Use the addition table to answer part a through d Click the icon to view the addition table Write a rule for finding such sums almost at a glance Choose the correct answer below A Sum upper right entry 4 B Sum 4x upper right entry OC Sum upper left entry x lower right entry OD Sum upper right entry 4 E Sum 2x upper right entry b Find the sum of the entries in these squares of entries from the table 0 1 1 2 2 3 3 4 Sum 18 10 11 12 11 12 13 12 13 14 OA Sum upper left entry x lower right entry OB Sum upper right entry 2 3 C Sum 9 x upper right entry D Sum 4x upper right entry OE Sum upper right entry 9 Sum 108 c Write a clear and simple rule for computing these sums Choose the correct answer below 13 14 15 Sun

Given the triangle 39 Area 25 Question Help Video Submit Question 29 find the area of the triangle Round your final answer to 4 decimal places units

1 The government decides to implement quotas on importing t shirts The supply will increase decrease Which determinant causes this change Which way will the supply curve shift Left or right Draw the new supply curve P

Letitia Brianne and Jake met at the mall on December 31 Letitia said that she intends to come to the mall every third day throughout the next year Brianne said that she intends to be there every fourth day and Jake said that he would be there every seventh day Letitia said that she knew she would be at the mall a total of 121 days since 365 3 is 121 with a remainder of 2 Brianne said that she d be at the mall 91 days since 365 4 is 91 with a remainder of 1 Moreover Brianne said that of those 91 days she would expect to see Letitia 30 times since they will both be coming every 12 days and 365 12 is 30 with a remainder of 5 Complete parts a through d below a How many days will all three friends meet at the mall in the next year There will be 4 day s when all three meet b Use reasoning similar to that of Letitia and Brianne to construct a three loop Venn diagram that shows the number of times the three friends go to the mall in all of the possible combinations O A B OC OD L 78 157 13 J 26 4 26 9 52 B 121 365 30 91 1760 J 52 13 B L B 3 12 4 39 84 21 28 7 206 82 365 12 21 28 30 56 B

2 Define T R2 R by T a Is T linear If so find the standard 2 43 matrix of T 2x1 3x2 4x1 5x2 X2

3 Find the limit lim A 6 B 30 C 1 D x 3 x 2x 9x 18 x 3

6 Simplify x 1 1 x 1 by multiplying the LCD

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 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

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

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

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

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

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

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

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

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

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

Gwen walks the same route home every day and she often finds coins lying on the ground There is a 42 chance that Gwen will find one dime on her way home Gwen walked home 30 times this past month Is it possible to use the normal approximation to the binomial distribution How do you know Assuming she never found more than one dime each day what is the probability she found more than 8 dimes this past month

3 a Consider a game in which you roll a regular eight sided die When you roll an odd number you win double the amount When you roll an even number you lose half the amount How many points would you expect to win or lose per roll

14 Does the following data show inverse variations 810 5 10 20 O C no yes y 13 26 52

11 Which of the following data sets best represents an inverse variation OF 82 80 78 77 I 1 10 1 4 C y 5 12 1 2 5 2 75 y 0 2 4 I 175 10 172 6 170 10 167 16 10 y Y 160

2 Match the type of discrete probability distribution with the correct definition You will not select all options uniform binomial hypergeometric Choices A B C OD each dependent trial can be either success or failure all outcomes are equally likely the waiting time before success occurs each independent trial can be either success or failure

13 Does the following data show inverse variations 2 18 8 7 04 O yes O no 19 15 2 12 16

4 a 2 5 b 15 of the people in a town have hazel eyes A group of 5 people are randomly chosen Create a probability distribution table and graph for the number of people with hazel eyes in the group Show your work for at least one calculation P x P x 0 6 0 5 0 4 0 3 0 2 0 1 0 0 1 Calculate the expected number of people with hazel eyes in the group 2 3 4 5 Xx