Basic Math Questions and Answers

1 Summer says there are 2 hundreds in 3 267 Isaiah says there are 32 hundred in 3 267 The teacher says they are both right How can that be so Explain 1 Fill in the blanks and complete the equations for each array 12 X 4 40 10 3 100 X 5

In a town whose population is 4300 a disease creates an epidemic The number of people N infected t days after the disease has begun is given by the function 4300 N t Complete parts a through c below 0 5t 1 19 6e a How many are initially infected with the disease t 0 Round to the nearest whole number as needed

The points 4 27 and 9 r lie on a line with slope 5 Find the missing coordinate r r 08

The first three terms of a sequence are given Round to the nearest thousandth if necessary 13 19 25 Find the 48th term

13 ou are given the graph of a function of the form y A sin B x C with A 0 y 2 R amplitude 8 phase shift 8 4 8 75 27 Identify the amplitude period and phase shift Give the phase shift from the interval 0 2 Give exact answers Use symbolic notation and fractions where needed X period T

Evaluate the expression P 7 2 P 7 2

A group of people took part in a quiz Table 1 shows the scores of everyone who played From the statements below shade FOUR that are DEFINITELY TRUE A Twelve people took part in the quiz B Nobody scored 23 marks C Everybody scored more than 19 D Twenty four people E The lowest score was 0 F The quiz was out of 25 G At least one person scored more than 24 marks H The most common score was 24 points Table 1 Score Freque 20 21 22 23 24 25 3

Q1 A manager surveys his employees to find out how they travel to work Number of people 25 20 15 10 S Walk Cycle Bus a What is the least popular method of transport b What is the most popular method of transport c Calculate the total number of employees Car

A group of parents were asked how far they live from their children s school The results are below Complete the grouped frequency table for this data 0 5 1 7 0 4 1 2 0 3 0 1 0 3 0 9 8 1 5 1 5 3 4 4 5 0 5 10 5 Distance in miles x Frequency f 0 x 1 1 x 2 2 x 5 5 x 10 10 x 20

The table shows how many students take part in after school clubs during the week Complete the pictogram key O 4 Monday Tuesday Wednesday Thursday 8 10 14 9 Monday Tuesday Wednesday Thursday

1 point What is the unit vector for the vector 17 53 10 76 6 34 000 Answer

1 point Find the length of OR R 2 9 7 OR

1 point Which of the following vectors is perpendicular to a 1 2 3 and b 1 1 2 A 7 1 3 OB 7 1 3 OC 7 1 3 OD 1 2 6 E 5 5 10 F at least two of the above G none of the above

v 10 9 6 w 2 9 10 Find the cocin

1 point Find a vector orthogonal to both 3 1 0 and to 0 1 2 of the form 00

assign7 Problem 1 1 point Several unit vectors 7 s t u and e in the xy plane not three dimensional space are shown in the figure Using the geometric definition of the dot product are the following dot products positive negative or zero You may assume that angles that look the same are the same 1 n e 2 7 S 3 e s 44 5 5 t u 6 n t 7 F u 8 e F it 3 Click on graph to enlarge TO Note You can earn 10 partial credit for 2 4 correct answers 60 partial credit for 5 6 correct answers and 80 partial credit for 7 correct answers

Find k such that the following matrix M is singular M 4 4 4 9 k 4 10 2 2 2 4

Question 3 of 6 possible This question 5 point s possible Submit quiz The division of student services at a school is selecting two men and two women to attend a leadership conference in Honolulu Hawaii If 10 men and nine women are qualified for the conference this problem is choosing 4 people from a group of 19 yet the answer is not C 19 4 Explain this How does the fundamental counting principle apply here OC There are unequal numbers of men and women OD The combination should be C 4 19 How does the fundamental counting principle apply here Why is the answer not C 19 4 OA Not all choices of four people were acceptable For example it is not possible to select all four women OB Because the answer should use permutations and is P 19 4 OA Multiply the number of women and their number of conference spaces with the number of men and their number of conference spaces OB We first add the number of ways to select the two women and the number of ways to select the two men 2 2 2

0 898 round to Sf

Evaluate the expression C 12 7 C 12 7

4 17 Billing Date Previous Balance 4 27 Payment 4 29 Charge 5 7 Payment The average daily balance is Multiple Choice 910 34 755 17 1 100 700 300 50

i g x 41 16 The function C i 2 54i converts a ii g x 16 measurement C centimetres a Write the function as an equation in 2 variables of i inches to a measurement of b Determine the value of C 12 What does this number represent c Determine the value of i when C i 100 What does this number represent

A 4 Which arrow diagrams represent functions a doubled isp Chant m 5 N abilite 6 8 4 10 mitrios poilu the ituloa b c 3 2 2 is 3 3 1 2 or at3 squared is 4 9

x2 x 12

If det a b c def ghi 1 a 4g 6b 24h c 4 4i

Assignment6 Problem 13 1 point If the determinant of a 4 x 4 matrix A is det A 10 and the matrix B is obtained from A by multiplying the first row by 2 then det B Preview My Answers Submit Anguore

Fill in the blanks to complete the table Number Number Row Symbol Z A of of Protons Electrons 1 2 3 4 5 Ca 1 Ga 1 42 40 90 16 1 1 1 1 71 1 H 1 1 48 36 1 1 46 Number of Neutrons 22 16 66 Charge 2 2 1 1

5 Andrea and her sister get 5 for each A they make on a final exam and 2 for each B they make Together they racked up seven A s and B s Their parents had to pay them 29 How many A s did they make on their final exam The variable The variable Equation 1 Work Area represents the represents the Equation 2

What are your feelings about the executive compensation controversy

1 Simplify Answers should be in Scientific Notation Type the coefficient in the blue box Type the exponent in the purple box If your answer is correct it will turn green if your answer is incorrect it will turn red 610 910 9 10 3 6 10 5 10 8 10 12 710 4 4 3 10 4 7 2 105 5 9x105 6 2 108 5 9 108 1 6 107 3 4 105 110 2 1 10 8 6 10 7 3 10 1 10 910 X A 5 6 10 7 10 2 3 10 8 6 10 10 10 10 x 10 10 X x X x 10 x 10 x 10 x 10 10 x 10 x 10

A university is trying to determine what price to charge for tickets to football games At a price of 20 per ticket attendance averages 40 000 people per game Eve decrease of 2 adds 10 000 people to the average number Every person at the game spends an average of 3 00 on concessions What price per ticket should be charged in order to maximize revenue How many people will attend at that price

Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit Assume that revenue R x and cost C x of producing x units are in dollars R x 3x C x 0 01x 0 2x 9 What is the production level for the maximum profit units C

7 Evaluate f S x dA over the region enclosed by 2x y 0 2x y 4 x y 0 and x y 3 Use the change of variables u 2x y v x y 8 points

2 Calculate the iterated integral 7 points SS JS v x da Where D is the triangular region with vertices 2 0 0 2 and 2 5 5 4 3 2 1

6 Find the image of S the square bounded by the lines u 0 u 1 v 0 v 1 under the x v y u 1 2v2 HINT The end result is drawing a picture 7 points transformation 0 5

handspring Do you know how to do a back handspring True you haven t been to Turner Hall in years but every once in a while in your physical education class you horse around the mats enough to knock the rust off Tumbling is the one activity that allows you to harness your body s potential and power From Angelina Mirabella The Sweetheart Copyright 2014 by Angelina Mirabella first person second person inthia I was wondering You still know how to do a back third person limited

1 Calculate the iterated integral 7 points 22 1 1 x y xy dx dy

Entered det B 4 1 0 5 1 0 25 At least one of the answers above is NOT correct 256 If A and B are 3 x 3 matrices det A 1 det B 4 then det AB 4 det 24 0 5 det AT Answer Preview 4 0 5 1 1 4 256

276 Least multiple that is the same Add using renamed fractions or

Problem 2 Use the right angle triangle approach to find the exact values of the other five trigonometric functio of t by using the given information a cos t www b tan t c csc t 7 25 4 5 2 such that the terminal side of t lies in Quadrant II such that sec t 0 such that cot t 0

Which of the following propositions imply p V q Select all that apply A P B pe q C p q D p q E q Fp V q

Consider the proposition over Z given by q x y x y x y That is the variables x and y take integer values Put a checkmark next to those propositions which are true A Vx Ey q x y B q 1 1 C y q 1 y D 3x 3y q x y E V Vy q x y OF 3x Vy q x y

Problem 1 Assume that is an angle in standard position whose terminal side contains the point P Find the exact values of the six trigonometric functions of by answering the following questions a P 15 8 b P 3 4 c P 5 1

Problem 3 Use the fundamental identities approach quotient identities Pythagorean identities and reciprocal identities to find the values of the remaining trigonometric functions from the given information 3 1 sin 0 and cos 0 0 5 1 2 cot 8 csc 0 5 2 2 3 tan 0 15 8 and sin 8 0

Consider the following propositions p and q over the set S 1 2 8 p x x is even q x x 6 Compute the following sets a Tp 2 4 6 8 b T 2 4 c Tpq d Tpvq e Tap f T U Tg g T Tq B

Use the following information for problems 6 9 You are ready to buy a house and have 80 000 for a down payment and closing costs Closing costs are estimated to be 2 5 of the loan value You have an annual salary of 155 000 The bank is willing to allow your monthly mortgage payment to be equal to 28 of your monthly income The APR on the loan is 6 25 per year with monthly compounding for a 30 year fixed rate loan 6 How much money will the bank loan you 7 How much can you offer for the house 8 How does your answer change if rates fall to 5 5 9 Construct a loan amortization table in Excel for the original mortgage 6 25

5 Optimization Problem Exercise Given P x y z X Y 10 102 100 and 4x y 100 X Z 10 3 where P x y z are 1 What is the objective function 2 What are the constraints non negative numbers 3 Find X Y Z which produce P max 4 What is P max 5 Find x y z which produce P min 6 What is P min

1 a Ange l sningen till det ekvationssystem vars grafiska l sning visas i koordinatsystemet Endast svar 3 2 X 1 0 4 3 2 1 0 1 2 3 2

2 Three step Adams Bashforth method Consider the interpolation nodes ti 2 ti 1 ti where t t j jh a Write down the Lagrange interpolation polynomial P t for the function f t y t at the nodes above b Consider the IVP y t f t y t integrate the Lagrange polynomial P t from a exactly to determine bi b and by such that Yi 1 yih b f t y b f t 1 1 b3f t 2 Y 2 As usual y denotes the value of y t at t tk Your answers b should be given as fractions Hint you may note for b we have f L t dt 2h evaluate the integral and do the same for b2 b hb t ti 1 t ti 2 dt

2 points Jayson can invest his money in an account that pays 3 9 per year compounded monthly Determine the amount he must deposit at the end of each month to have 12000 in two years