Basic Math Questions and Answers

How long will it take to drive 825 km at 75 km per hour if you take a two hour break after every 5 hours 12 hours

0 Sal recorded the outdoor temperature as 4 F at 7 30 A M At noon it was 22 F Sal said the temperature changed by 18 F because 22 4 18 A Critique Reasoning Is Sal right or wrong Explain F 20 10 0 10 20

mL 4 The doctor orders Unipen 400 mg IM The medication is supplied as Unipen nafcillin sodium 1 gram in powder form Directions for reconstitution Add 3 4 mL of sodium chloride diluent for injection to yield 1 gram 4 mL How many mL will be given

Convert the following improper fraction into a mixed number Simplify your answers to their lowest terms a b 31 5 26 11 6 8 1 5 2

Perform the arithmetic operations a 2 4 2 10 b 5 10 6 2 X 62 2 1 6 1 3 2

In the number 147 069 identify the digits that occupy the following place values a Tens b Ten Thousands

Convert to Scientific Notation a 0 0658 X 10 Round to two decimal places b 44 430 000 000000 Round to three decimal places X 10

Evaluate the following expressions a 77 13244 5 b 16 x 18 6 12

0 09375 0 O 0 1 8 3 32 2 3 1 16

Fifty seven hundred thousandths 57 1000 O 0 0057 O 0 057 O 0 00057 O

Reduce the fractions to their lowest terms and write their reciprocals a 100 120 Reciprocal b 100 60 Reciprocal

An 18 wheeler cargo truck is used to transport steel rods from Toronto to Ottawa for a construction company The truck weighs 16 118 47 lb with no load However with a full load of steel rods the truck weighs 29 646 25 lb What is the weight of the steel rods Round the final answer to the nearest tenth O 000 OO Empty Truck 16 118 47 lb 0 00 ooooo 29 646 25 ck 29 646 25 lh lh Full Load Truck 4

Calculate the following a What amount is 50 less than 310 b What amount is 48 more than 270

Which of the following fractions is greater A 22 6 or B click to select 24 7

Calculate the following a 7 7 5 5 b 14 5 2 7 I

Convert to exponential notation a 3x3x3x3 x 3 b 10 x 10 x 10

Evaluate Give your answer in scientific notation 7 83 x 107 5 44 x 106 Round to two decimal places X 10

Evaluate the following Use Exponent Rules if possible a 810 8 b 53 x 53

Identify all the prime numbers within each range of numbers given below inclusive a From 21 to 37 b From 45 to 61

Round the following numbers to the indicated place values a 2 344 to the nearest ten b 6 339 to the nearest thousand c 82 827 to the nearest 1 000 d 476 to the nearest 10

Victoria bought 5 litres of milk and drank 1 litres litres of it How much milk was left

Assume no inter period compounding Interest is 5 5 annual compounded every 6 months What is the future value of a a 175 monthly deposit made for 30 yea 156 249 O 149 866 133 886 O 123 000

1 Given f x your answers a f g x b g f x 2 Let f x 3x 2 5x 1 and g x 5 6 find the following functions Simplify Find f 0 3 Given f x 2x 3 x 5 x 2 answer the following questions a List the zeros of the function b What is the degree of f x c As x o f x d As x f x LESEY

1 6 For what integer a is x 3 x 90 divisible by x x a as polynomials

find the present value of the following deposit 100 per week for 2 years interest is 6 per year compounded daily 365 days per year

Attempt Sheffield Industries had the following inventory transactions occur during 2020 Units 2 1 20 Purchase 54 3 14 20 Purchase 95 5 1 20 Purchase 65 O 3576 O 3739 5960 O 6194 Cost unit 43 40 40 The company sold 149 units at 80 each and has a tax rate of 40 Assuming that a periodic inventory system is used what is the company s after tax income using LIFO rounded to whole dollars

M DO 9 DE a 200 mi 500 mi Catholic Lutheran Protestant Methodist D KU right Camperations d Wennst P PAE semed Sas 2058 2017 ASSEE Avesco OME IN CHINA Casearch Center What religion is reflected by most densely populated area of the map More than 50 0 50 0 25 1 191 25 0 0 1 10 0 None Reported L 200 mi

7 3 in 8 in

5 5 ft 2 ft

The height h in meters above the ground of a football t seconds after its been thrown can be modelled by the function h t 4 9t 19 6t 2 a What is the height of the ball when it was thrown b How long was the ball in the air to the nearest tenth of a second

1 Consider the IVP y t f t y write down the Taylor expansion of two variables up to order 2 for f t h 2 y h 2f t y at t y TIF

3 Consider the following Heun s method wo a w 1 w hf t w 3hf t 2 h w hf t 3 w hf t w a Write Heun s method in the general form of Runge Kutta method using updates k k2 k3 i e the format we use for RK4 in lecture 5 b Write down the Butcher Tableau for Heun s method c Show Heun s method is consistent and stable

2 Consider the midpoint method for IVP and assume that f is Lipschitz continuous in a b x R Show that a the midpoint method is stable b the local truncation error of midpoint method is O h

The table lists numbers N of employees in millions of a supermarket x years after 1980 a Find a power function f that models the data in the table b Use f to predict the number of employees in the year 2013 Did your answer involve interpolation or extrapolation c When did the number of employees first reach 1 million Points 0 of 1 12 17 22 X 7 27 N 0 19 0 36 0 67 1 4 2 1

Use the fundamental counting principle A password for a computer consists of five different digits from 0 to 9 followed by three different letters of the alphabet How many different passwords are possible How many distinct passwords are possible OA 78 624 000 OB 655 200 OC 471 744 000 OD 3 931 200

Suppose that the surface area S of a bird s wings in square feet can be modeled by S w 1 24w wings having a surface area of 4 square feet W 3 1 where w is the weight of the bird in pounds with 1 ws 10 Estimate the weight of a bird with

You are taking a multiple choice test that has 7 questions Each of the questions has 4 answer choices with one correct answer per question If you select one of these choices for each question a leave nothing blank in how many ways can you answer the questions You can answer the questions in ways C

Find the equation of the perpendicular bisector of each of the following line segments a the line segment joining A 2 2 and B 4 6 b CD if the equation of the line passing through C and D is x y 3 and the midpoint of CD is 2 1

Find the gradient of a line which is parallel 10 cach line with the given equation a y x 6 b x 7 Find the gradient of a line which is perpendicular to each of the following lines a y 3x 11 b b 2y 0

2 The distance between two towns P and Q is 2 km On a coordinate system town P has coordinates x 7 and Q has coordinates 3 5 The values of the coordinates are given in kilometres Find the value of x

3 A tracking station lies at the origin of a coordinate system with the x axis due east the y axis due north and the z axis vertically upwards Two aircraft have coordinates 20 25 11 and 26 31 12 relative to the tracking station All coordinates are given in km a Find the distance between the two aircraft at this time

Kerri Jungemann owner of Flowers 4 You operates a local chain of floral shops Each shop has its own delivery van Instead of charging a flat delivery fee Jungemann wants to se the delivery fee based on the distance driven to deliver the flowers Jungemann wants to separate the fixed and variable portions of her van operating costs so that she has a better idea how delivery distance affects these costs She has the following data from the past seven months Click the icon to view the data Read the requirements Requirement 1 Determine the company s cost equation use the output from the Excel regression Round the amounts to two decimal places y X Data table Month January February 17 400 March 15 400 April 16 300 May 16 500 June 15 200 July 14 400 Miles Driven Van Operating Costs 15 500 5 390 5 280 4 960 5 340 5 450 5 230 4 680 I X

4 2 point In class we showed Vf x is the direction in which a differentiable f increases the most a What is the direction that f decreases the most Use similar analysis we did in class to justify your answer b Suppose you are walking on a surface with elevation modeled by 2 2 Find a direction a unit vector in R2 from the point 2 2 in which the rate of increase is half that of the maximum direction x y 20

5 2 points Let C be the set of all points on the unit sphere x y 1 where the tangent plane contains the point 1 1 1 C is a circle Find its center and radius

Question 1 If the formula y z is changed by adding six shown in bold below what effect would that change have on the function s values f x x 6 Select an answer What effect would it have on the graph Select an answer

Please give complete well written solutions to the following exercises and submit via Grade scope 1 2 points Let f x y t represents the temperature at a position x miles east and y miles north of New York City and time t hours after noon Suppose that temperature increases by 02 for every mile south and decreases by 03 for every mile east But temperature everywhere also depends on time of day and thus contains a term of the form 12 cos 2 Suppose you drive southwest at 10 27 mph at 2pm Estimate d Is it getting hotter or cooler

Which situation demonstrates the law of large numbers If it snowed four days last month it will snow four days this month If you roll a six sided number cube 36 times you will roll a 4 six times If 800 people are randomly surveyed about the TV shows they watch about 400 of them will be women If you flip a coin 44 times you will get heads about 22 times

Exercise 8 5 1 For each matrix below compute the determinant using all three methods 2 3 1 4 4 4 5 6 7 1 2 3 b A 3 3 1 2 3 2 1 1 1 0 0 1 1 1 a A c A 1 0

Exercise 8 5 3 Check that the well known formula for the determinant of a 2 x 2 matrix det satisfies the three properties of Definition 8 2 1 and thus is a correct formula for the determinant

Exercise 7 3 3 Why is it true that if B is a basis for W and L VW is a linear map whose image includes B then L is urjective What can you further say about the rank of L if you knew about the length of the basis B