Vectors Questions and Answers

LEM and b have a 0 68 angle between them The magnitude length of a is 142 and the magnitude of bis 207 We can write this as la 142 and 6 207 See Diagrams gmtobuz a Find la bl This means what is the magnitude of the sum of the two vectors Hint Law of Cosines 3 marks 68 b doing two tony 30 igen auli no id TB b a b b What angle does a b make with a Shown as on the diagram 3 marks Note this angle is NOT half of 68 To find this you will need to use the Law of Cosines or Law of Sines

You may need to use the appropriate appendix table or technology to answer this question A simple random sample with n 58 provided a sample mean of 24 5 and a sample standard deviation of 4 4 Round your answers to one decimal place a Develop a 90 confidence interval for the population mean to b Develop a 95 confidence interval for the population mean to c Develop a 99 confidence interval for the population mean to d What happens to the margin of error and the confidence interval as the confidence level is increased As the confidence level increases there is a smaller margin of error and a wider confidence interval As the confidence level increases there is a larger margin of error and a wider confidence interval As the confidence level increases there is a smaller margin of error and a more narrow confidence interval As the confidence level increases there is a larger margin of error and a more narrow confidence interval

Macmillan Learning During a routine check of the fluoride content of Gotham City s water supply the given results were obtained from replicate analyses of a single sample 0 709 mg L 0 691 mg L 0 713 mg L 0 687 mg L and 0 717 mg L Determine the mean and 90 confidence interval for the average fluoride concentration in this sample mean 90 confidence interval mg L mg L

Let T R4 R3 be the linear transformation represented by T x Ax where 1 210 A 0 1 2 4 0 001 a Find the dimension of the domain 3 b Find the dimension of the range c Find the dimension of the kernel d Is 7 one to one Explain OT is one to one since the ker 7 0 OT is one to one since the ker 7 0 OT is not one to one since the rank 7 0 OT is not one to one since the ker 7 0 OT is not one to one since the ker 7 0 e Is T onto Explain OT is onto since the rank 7 is equal to the dimension of the domain OT is not onto since the rank 7 is not equal to the dimension of the domain OT is not onto since the rank 7 is equal to the dimension of the co domain OT is not onto since the rank 7 is not equal to the dimension of the co domain OT is onto since the rank 7 is equal to the dimension of the co domain f Is 7 an isomorphism Explain Select all that apply OT is not an isomorphism since it is not onto OT is not an isomorphism since it is not one to one

2 i Simplify each expression to a single term tn r in Pascal s triangle C 2 ii Find the numerical value of this term K U 2 a t32 20 32 21 b t40 12 139 12

Multiply Write your answer in simplest form 92 9 4935 1

Divide Write your answer in simplest form 3j 4 3j 2 9j 18j 8

9 a For the equation below 2x 12x 18 0 Part A Find the discriminant of the quadratic equation Part B How many real solutions does the quadratic equation have A Two Real Solutions B One Real Solution C No Real Solutions

Which of the following equations would form a parabola when graphed there may be more than one A 2x 7 10 By 3x x 5 1 Cy 2x3 5x 2 y 3x 4x 19 Dy

Consider the equation given below and solve for x by using quadratic formula 5x2 4x 2 0 H

Multiply the complex numbers 7 i 3 i A 20 4i B 22 4i C22 10i D 20 10i

Select the solutions to this quadratic equatio x 6x 8 0 Ax 2 BX 4 CX 0 DX 2 EX 1

Grays Company has the following purchases and sales during the month of August Using the FIFO perpetual inventory method what amount will reported as cost of goods sold for the 12 units that were sold Date August 1 Activities Units Acquired at Cost Units Sold at Retail August 3 August 6 Beginning inventory Purchase Sales 18 units 46 460 28 units 48 968 12 units sold Multiple Choice 572 526 556

graph one full cucle of y csc 3x 3 3

Use the figure at the right to complete the proportion BC CD HJ B E F G H K

Select all functions below that would have the end behavior that falls to the left and rises to the right Multiple answer f x 2x 3x 5 f x 2x 3x 5 f x 3x5 2x 5 f x 3x 2x 5

Which of the following expressions are examples of either the sum or the difference of cubes Mark all that are an example of the sum of cubes OR the difference of cubes A b 5 b 56 25 B u 3 u 3u 9 d 6 d 12d 36 D h 4 h 2 4h 16 E a 10 a 10a 100 F x 11 x 11x 121

Which of the following is an example of discrete data OA The distance between two cities OB The number of siblings each student in a class has O C Weights of sumo wrestlers O D The length of a movie

Which of these pieces of data about a football team is considered numerical data O A Mascot representation OB Points scored O C Stadium type OD Jersey color

In a survey conducted at a pet store 150 customers were asked if they ownec birds or fish The survey data are shown in the relative frequency table Own fish Do not own fish Total Own a bird OA 6 OB 0 1 O C 10 OD 4 0 04 0 02 Do not own a bird 0 06 0 88 What percentage of the people surveyed own fish Total

Which of these frequency counts would be represented by the largest number of dots in a dot plot O A 25 OB 23 OC 26 OD 24

A teacher asks her students to fill out a survey about themselves Which piece of data would be considered categorical data O A Age O OC Eye color B Height D Number of siblings

A company conducted a survey to see whether its new toothpaste was more popular with children or adults Of the adults surveyed about 11 use the toothpaste Compare this with the percentage of children who use the toothpaste Children Adults Total Select the true statement Use toothpaste 0 07 0 08 0 15 Do not use toothpaste 0 18 0 67 0 85 Total 0 25 0 75 1 0 O A A greater percentage of children 28 use the toothpaste OB A smaller percentage of children 7 use the toothpaste OC A greater percentage of children 46 use the toothpaste O D A smaller percentage of children 8 use the toothpaste

If the data below were represented with a stem and leaf plot a stem of 2 would have how many leaves 17 22 53 74 42 26 93 15 67 29 50 OA 2 OB 3 OC 5 OD 4

The table below shows data for stuffed animals sold at a zoo gift shop If the data were represented with a comparative dot plot which animal would have more dots for month 2 than month 1 Giraffe Elephant Tiger Rhino Lion A Rhino B Lion C Tiger D Elephant Month 1 18 21 20 15 12 Month 2 15 16 19 18 11

Use a calculator to evaluate each expression to the nearest tenth of a degree 39 sin 0 1702 40 sin 0 1702 41 cos 0 8425

Bessel s Correction N 1 Friedrich Bessel discovered that when we use n in the denominator of the variance calculation for a sample the sample variance tends to underestimate the population variance Since many times we do not know the true population variance Bessel s correction for a point estimate of the population variance is very useful

Macmillan Learning Find the standardized value z such that the probability is 0 8 that a randomly selected observation falls below z Enter your answer rounded to two decimal places Approximation of 7 b c 2 1 01 2

Find the value of 7 O O OA 42 OB 823 543 O O C 5040 D 49

A and B are independent events What is P AIB P A 0 3 P B 0 5 O A 0 15 OB Not enough information O C 0 5 D 0 3

A building has three elevators Each elevator is out of order 30 of the time The following set of random numbers represents 20 simulations of the elevators with 0 1 and 2 representing a broken elevator and 3 4 5 6 7 8 and 9 representing a working elevator In how many of the simulations were all three elevators working 931 188 763 841 404 396 011 843 OA 8 OB 10 OC 11 D 9 559 144 652 277 653 673 599 797 414 761 273 844

SOA OB 10X 10

What is the third quartile of the following data set A 29 OB 26 OC 24 OD 34 15 18 20 21 23 24 26 29 34 37 40

You roll two number cubes Let event A The number rolled on the first cube is 6 Let event B The sum of the numbers rolled is 11 What does P BA represent A The probability that the sum is not 11 B The probability that the first number cube shows a 6 given that th sum is 11 C The probability that the first cube does not show a 6 D The probability that the sum is 11 given that the first number cub shows a 6

7 Match each polynomial with its end behavior 32 7x 8 2 3x 9x 2x 8x 5 x 8x 2x 5 DRAG DROP THE ANSWER Asz co f x o and As o 2 0 Asz o f z o and As o f x o As 2 f z and As o f x o As T 00 f x and As a too f x 0

Task Classify each polynomial based on the the degree of the polynomial DRAG DROP THE ANSWER 3 x 12x 6x 7y 12y 3y 17 9 6 4x 16 X 9 3x 9x 12 Quadratic Linear Cubic Constant

Classify each polynomial by its terms DRAG DROP THE ANSWER 2p p 1 5n 10n 10 10a 8n 5n 2n 8n 9n 10 4 2a 8a Monomial Trinomial Binomial Other

Which type of polynomial is the following 3x 5 7y A binomial B trinomial c monomial

a Which statement describes the end behavior of the function f x 2a 16x 32x As a o f a o and as a f x 0 B As a o f x co and as a o f a As a f a oo and as a f a DAs a o f a oo and as a o f a 0 b Part B Based on its end behavior which graph represents f x 2a 16x 32x A 25 20 15 10 5 s 10

Directions Multiply the binomials using the box metho 3x 2x x 5

Let event A You buy a new umbrella on Friday Which event is most likely to be independent of A A You had a math test on Thursday B You visited the school lost and found on Thursday afternoon C It rained on Thursday D The weather forecast says it will rain on Saturday

Which situation can be considered a binomial experiment O A Drawing one marble from a bag containing 10 red and 7 blue marbles replacing after each draw until you have drawn 4 blue marbles B Asking 15 students how tall they are and recording their answers C Rolling a single number cube until you get a 3 D Tossing a coin 10 times and recording the number of times it lands on heads

A prize of 100 200 400 or 800 will be randomly awarded to a game show contestant with the probabilities of winning each prize shown in the table below What is the expected value of the prize that will be awarded A 320 B 375 OC 340 O D 380 Prize 100 200 400 800 Probability 0 2 0 2 0 4 0 2

According to the table below what is the probability that the grade of a student chosen at random will be a B or higher O A 47 O B 7 217 D 3 O C 17 1 7 A Grade Probability 6 B C D F 4 12 9 4 35 35 35 35 35

A school knows that 11 of its students are left handed What is the probability that there will be between 33 and 45 left handed students in a randomly selected group of 400 Use your calculator and this formula Plas x b binomcdf n p b binomcdf n p a 1 Round your answer to three decimal places OA 0 602 OB 0 043 OC 0 029 OD 0 573

lan often takes his dog to the park He estimates that 30 of the other dogs he sees are retrievers 20 are terriers and 20 are German shepherds He designs a simulation Let 0 1 and 2 represent retrievers Let 3 and 4 represent terriers Let 5 and 6 represent German shepherds Let 7 8 and 9 represent other dogs The table shows the simulation results 01611 49003 63777 91971 26343 49116 OA 0 60 OB 0 75 OC 0 70 71890 58647 87208 98444 01595 39440 58889 34845 90500 28893 58822 67970 43938 51995 According to this simulation what is the probability that at least one of the next five dogs he sees is a retriever

This table shows how many sophomores and juniors attended two school events Sophomore Junior Total OA 0 56 OB 0 31 C 0 26 Jazz band concert 35 D 0 48 36 71 Volleyball game 42 24 66 Total 77 60 What is the probability that a randomly chosen person from this group is a sophomore and attended the volleyball game Round your answer to two decimal places 137

Suppose the following set of random numbers is being used to simulate the event of a basketball player making two free throws in a row How should the numbers be rearranged 502666 346453 524366 387026 704473 775061 350054 771009 621563 762199 OA 5026 6634 6453 5243 6638 7026 7044 7377 5061 3500 5477 1009 6215 6376 2199 OB 50266 63464 53524 36638 70267 04473 77506 13500 54771 00962 15637 62199 C 502 666 346 453 524 366 387 026 704 473 775 061 350 054 771 009 621 563 762 199 OD 50 26 66 34 64 53 52 43 66 38 70 26 70 44 73 77 50 61 35 00 54 77 10 09 62 15 63 76 21 99

group of students was randomly divided into two subgroups One subgroup took a test in the morning and the other took the same test in the afternoon This table shows the results Morning Afternoon Total Pass 28 36 64 Fail 22 14 36 Total 50 50 100 Compare the probability that a student will pass the test in the morning with the probability that a student will pass the test in the afternoon Draw a conclusion based on your results OA P pass morning 0 28 P pass afternoon 0 36 Conclusion A student taking the test in the morning has a greater chance of passing it than a student taking it in the afternoon OB P pass morning 0 56 P pass afternoon 0 72 Conclusion A student taking the test in the afternoon has a greater chance of passing it than a student taking it in the morning OC P pass morning 0 56 P pass afternoon 0 72 Conclusion A student taking the test in the morning has a greater chance of passing it than a student taking it in the afternoon O D P pass morning 0 28 P pass afternoon 0 36 Conclusion A student taking the test in the afternoon has a greater chance of passing it than a student taking it in the morning

Two classmates Aisha and Brandon want to attend two school over the coming weekend They have one parking pass between them The probabilities that the classmates will attend each event are shown in the table Probability of attending the Saturday activity Probability of attending the Sunday activity Alsha 0 65 0 80 Brandon 0 94 0 43 They decide to let the person more likely to attend both events have the parking pass Assuming that attendance at one activity is independent of attendance at the other who is more likely to attend both activities A Aisha She has a 0 65 probability of attending both activities O B Brandon He has a 0 40 probability of attending both activities C Aisha She has a 0 52 probability of attending both activities O D Brandon He has a 0 69 probability of attending both activities