Linear Algebra Questions and Answers

A population numbers 12 000 organisms initially and grows by 8 each year Suppose P represents population and t represents the number of years of growth An exponential model for the population can be written in the form P ab where P Question Help Video 1 Video 2

2 Find the perimeter 3 Find the volume 4 Find the area 5 Find the perimeter

18 This graph shows the profit P dollars on a company s sale of n baseball caps Profit S 2400 1600 800 0 800 P f n n 200 400 600 Number sold a How many baseball caps have to be sold before the company begins to make a profit b What is the profit on the sale of each baseball cap c How many caps have to be sold to make each profit i 600 ii 1200 d In part c when the profit doubles why does the number of baseballs caps sold not double

3 Which sets of ordered pairs represent functions What strategies did you use to find out a 4 3 4 2 4 1 4 0 b 2 4 2 4 3 9 3 9 c 2 8 3 12 4 16 5 20 d 5 5 5 5 5 5 5 5

California renews the registration for an automobile the bar graph shown below is included with the bill Use this bar graph to answer the question The following statement is ncluded with the graph There is no safe way to drive after drinking These charts show that a few drinks can make you an unsafe driver They show that drinking affects your BLOOD ALCOHOL CONCENTRATION BAC The BAC zones for various numbers of drinks and time periods are printed in white gray and red HOW TO USE THESE CHARTS First find the chart that includes your weight For example if you weigh 160 lbs use the 150 to 169 chart Then look under Total Drinks at the 2 on this 150 to 169 chart Now look below the 2 drinks in the row for 1 hour You l your BAC is in the gray shaded zone This means that if you drive after 2 drinks in 1 hour you could be arrested In the gray zone your chances of having an accident are 5 times higher t you had no drinks But if you had 4 drinks in 1 hour your BAC would be in the red shaded area and your chances of having an accident 25 times higher BAC Zones 90 to 109 lbs TOTAL DRINKS 110 to 129 lbs TOTAL DRINKS 130 to 149 lbs TOTAL DRINKS TIME FROM 1st DRINK 12345678123456781234567812345678 1 hr 2 hrs 3 hrs 4 hrs 190 to 209 lbs TOTAL DRINKS BAC Zones 170 to 189 lbs TIME FROM 1st TOTAL DRINKS DRINK 12345678123456781234567812345678 1 hr 2 hrs 3 hrs 4 hrs SHADINGS IN THE CHARTS ABOVE MEAN 01 04 Seldom illegal 150 to 169 lbs TOTAL DRINKS 210 to 229 lbs TOTAL DRINKS 05 09 May be illegal 05 09 Illegal if under 18 yrs old Blood alcohol concentration BAC charts ou weigh 140 pounds how many drinks in four hours would you need to drink to 230 lbs up TOTAL DRINKS 10 Up Definitely illegal

For each of the graphs given below determine how many spanning trees that graph has 1 The graph G shown below Fo A F E A BO 2 The graph G shown below E D B C D C

aggregate supply curve LRAS for the United States The economy is initially at long run equilibrium at point A The Great Depression was unusual because it was so deep and lasted so long In fact it was actually two separate recessions August 1929 to March 1933 and May 1937 to June 1938 The Great Depression was also characterized by another striking condition Prices across the economy declined throughout the course of the decade In fact at the end of the 1930s the general price level as measured by the GDP deflator was 20 lower than it had been in 1929 Due to the decline in the price level it is evident that the primary cause of the Great Depression was a decline in aggregate In the figure below shift the appropriate curve to reflect your answer choice which would create the outcome of declining prices during the Great Depression To refer to the graphing tutorial for this question type please click here B Price Level P LRASS SRASI AD2

1 point Determine whether each of the following statements is true or false 1 Every graph contains a spanning tree as a subgraph 2 For m n 0 the complete bipartite graph Kmn has nm 1m spanning trees 3 For n 2 the complete graph Kn has n spanning trees 4 Every connected graph contains a spanning tree as a subgrph

V8 V7 5 G 07 H 1 8 V1 V6 V2 V5 V3 V4 3 Let S V V4 V8 Which of the following vertices are in N S A V1 B V2 C V3 D V4 E 05 F 06

1 point Let V 4 00 For u v E V and a R define vector addition by uvuv 4 u v 20 and scalar multiplication by au u 4 4 It can be shown that V B O is a vector space over the scalar field R Find the following the sum 125 12 the scalar multiple 10 12 12 the additive inverse of 12 B12 0 the zero vector 0 4 the additive inverse of Br X

Assignment 8 Problem 22 1 point Let V R For 2 1 2 EV and a ER define vector addition by u 2 B v v2 0 1 U2 U 2 and scalar multiplication by a au a 1 auz 2a 2 It can be shown that V BB C is a vector space over the scalar field R Find the following the sum 8 7 1 3 10 12 the scalar multiple 0 8 7 1 2 the zero vector 0y 12 the additive inverse of x y B x y 2x 2y Note You can earn partial credit on this problem

Assignment 8 Problem 21 1 point Let V R For u v V and a ER define vector addition by uv u v 2 and scalar multiplication by a u au 2a 2 It can be shown that V B C is a vector space over the scalar field R Find the following the sum 74 5 the scalar multiple 50 7 43 the zero vector 0 2 the additive inverse of Bz 2

6 21 Capital asset pricing model MFI Inc has a beta of 0 86 If the expected mar ket return is 11 5 percent and the risk free rate is 3 percent what is the appropriate required return of MFI using the CAPM

Identify the sentence where the verb tense is consistent O Martin picked up the phone and dials the number Martin pick up the phone and dialed the number O Martin picked up the phone and dialed the number O Martin picks up the phone and dialed the number

10 of 13 Solve the equation reporting your answer in degrees 2 cos x 1 Choose the correct solution s where k represents any integer 120 k360 60 k360 2 3 2kt 2kz 120 k360 330 k360

Macmillan Lea A B A Let the length of side B 6 and the length of side C 11 Find the length of the side A Give an exact answer Use symbolic notation and fractions where needed Cauder et al Preparation for Cal SZ Find the measure of angles s and 1 Use decimal notation Give your answers to two decimal places Include the degree symbol in your answers

A saleswoman wants to visit eastern cities New York City Boston Cleveland and Washington D C Driving distances are as shown in the figure below what is the shortest trip starting in New York that visits each of these cities if r1 493 r2 560 Find the solution using the sorted edge method Cleveland 375 667 r1 12 Wash Boston 235 216 NYC

1 point Consider the matrix blem 18 a The determinant of the matrix is b Does the matrix have an inverse 1 0 37 0 4 3 3 0 0

1 point Use determinants to determine if the matrix below is singular A 244 det A 05 3 435

Assignm 7 Problem 11 1 point Evaluate the following 3 x 3 determinant Use the properties of determinants to your advantage 17 3 2 1 2 13 3 2 13

2 A 12 Moot ladder leans against a wall The foot of the ladder is 5 feet from the wall How much would the foot of the ladder have to be pulled away from the wall so that the top of the ladder would slide down the wall by the same amount Round to the nearest tenth

When a seller breaches a contract for the sale of goods to a buyer the buyer is entitled to specific performance of the contract if the goods are unique market cost of goods has increased goods can be purchased in any city buyer s customers will be disappointed

Jeremy caught 8 fish in a contest The mean weight of the fish was 4 3 kg He forgot to make his own record of the weight of the last fish but the first 7 were 4 1 kg 5 5 kg 6 7 kg 2 kg 3 9 kg 4 6 kg and 4 3 What was the weight of the last fish kg 2

21 Median Work out the median for each group of numbers 3 5 8 9 10 11 12 12 13 13 12 12 15 16 10 14 11 2 3 5 6 7 8 9 11 11 46 48 53 45 46 49 43 52 43 42 1 1 2 2

Assume that math test scores are normally distributed with a mean of 300 and a standard deviation of 60 If you were to score 180 on this exam what percentage of those taking the test scored below you Click the icon to view the standard normal distribution table What percentage of those taking the test scored below you Round to two decimal places as needed

roblem 3 A Ferris wheel is built such that the height h in feet above ground of a seat on the wheel at time 5 in seconds can be modeled by h t 53 50 sin G t a Find the period of the model What does the period tell you about the ride b Find the amplitude and the range of the model What can we say about the ride c Find and interpret the average rate of change of h t on the time interval 2 2 5

Write the ordered pair for each point that is plotted A B C 5 4 3 2 1 D D 5 4 3 2 1 1 2 3 4 5 Be sure to give answers as ordered pairs including parentheses 1 2 3 4

A bag is filled with green and blue marbles There are 89 marbles in the bag If there are 9 more green marbles than blue marbles find the number of green marbles and the number of blue marbles in the bag The number of blue marbles is The number of green marbles is Question Help Video Submit Question

1 point Net earnings are the total earnings less all of payroll deductions

Give three different points that lie on the line y 52 3 by choosing different values for Note that you must answer all three questions in order for you responses to be scored correctly then the point on the line is If a is If a is If a is 1 then the point on the line is then the point on the line is

In problems 9 and 10 find the exact value of the expressions using the following conditions 15 4 9 sin 20 sin 20 10 sin 0 3 and 0 1

0 0 College enrollments in the United States are projected to increase from 2012 to 2022 The models below give the projected enrollments among men and women in thousands where t O represents the year 2012 Number of Students Men m x 80t 8998 Women w x 212t 11 970 A Find m w B Sketch graphs of all three functions c Evaluate m w for the year 2018 28000 26000 24000 22000 20000 18000 16000 14000 12000 10000 8000 6000 1 D Create a function to represent how many more woman are enrolled in college than

10 Suppose a student drew a graph of each function described below For which graphs should the student connect the points Justify your answers a The cost of a custom made T shirt is a function of the number of letters on the T shirt b The altitude of a plane is a function of the time it is in the air c The mass of a baby is a function of her age d The cube root of a real number is a function of the number

9 Determine the domain and range of the graph of each function a c 6 4 2 y f x 2 y 0 X 2 2 y N 4 2 0 2 2 4 y h x b d 4 N lo 0 y 2 0 y j x y g x N

Use Newton s method with initial approximation x 2 to find x2 the second approximation to the root of the equation x x 7 0 Round your answer to four decimal places x2

14 The two graphs below have the same shape but different vertical axes Copy each graph and include numbers and units on both axes Write and justify a possible situation that it represents a Distance Graph A Time b Speed Graph B Time 18 t t e

Use the savings plan formula to answer the following question At age 45 you start saving for retirement If your investment plan pays an APR of 6 and you want to have 1 3 million when you retire in 20 years how much should you deposit mor You should invest each month Do not round until the final answer Then round to two decimal places as needed COLO

Find the range and the standard deviation correct to two decimal places 6 7 8 9 10 range standard deviation Need Help Read It

A class obtained the following scores on a test Test Score Frequency 90 1 80 6 70 9 60 4 50 3 40 2 Find the mean the median the mode and the range for the class If an answer does not exist enter DN mean median mode range

Find the three measures of central tendency the mean median and mode If an answer does not exist enter DNE 5 6 7 8 9 mean median mode

Given a railroad curve with the following parameters Dc 2 00 00 C 1 18 00 00 PI Station 25 50 00 ft Compute the curve parameters Length of the arc L O 1014 56 O452 71 900 04

Let S A be sets in a universe U and suppose z S satisfies z A Which of the following statements must be true DA ZE AC OB ZE S A OC ZE A S OD 2 2 E SXS 4

Micromedia offers computer training seminars on a variety of topics In the seminars each student works at a personal computer practicing the particular activity that the instructor is presenting Micromedia is currently planning a two day seminar on the use of Microsoft Excel in statistical analysis The projected fee for the seminar is 675 per student The cost for the conference room instructor compensation lab assistants and promotion is 9600 per 2 days Micromedia rents computers for its seminars at a cost of 115 per computer per day a Develop a model for the total cost to put on the seminar Let x represent the number of students who enroll in the seminar Round your answers to the nearest whole number For subtractive or negative num use a minus sign even if there is a sign before the blank Example 300 Total cost 9 600 b Develop a model for the total profit if x students enroll in the seminar Round your answers to the nearest whole number For subtractive or negative number use a minus sign even if there is a sign before blank Example 300 Total profit Total profit 230 X 615 X X 9 600 c Micromedia has forecasted an enrollment of 30 students for the seminar How much profit will be earned if their forecast is accurate Round your answer to the nearest dollar 8 850 X d Compute the breakeven point Round your answer to the nearest whole number The breakeven point is 15 X students

According to a particular test a normal score is 600 It can be with a score that satisfies the inequality 600 2 54 has an unusual score Determine the scores that would be considered unusual Only test scores less than 564 44 would be considered unusual Test scores between 564 44 and 635 56 would be considered unusual Test scores less than 564 44 or greater than 635 56 would be considered nusual Jy test scores greater than 635 56 would be considered unusual ge Next Fl

Question 5 1 point Listen For the polynomial list each real zero and its multiplicity Determine whether th graph crosses or touches the x axis at each x intercept f x x 3 4 x 815 O multiplicity 4 crosses x axis 8 multiplicity 5 touches x axis O multiplicity 4 crosses x axis 8 multiplicity 5 touches x axis multiplicity 4 touches x axis 8 multiplicity 5 crosses x axis multiplicity 4 touches x axis 8 multiplicity 5 crosses x axis

4 Licen Construct a polynomial function that might have the give 27 2 1 1 11 2 2 Wo Which of the following is a polynomial function that might have the given graph Of x x 2 x 1 x 1 2 x 2 1 1

di Listen The graph of the function hole and a horizontal asymptote The vertical asymptote equation is H T A Type an integer or a simplified fraction The X coordinate of the hole is A pe an integer or a simplified fraction orizontal asymptote nauti 32 15 25 2 has one vertical asymptote on

4 Listen Give the equation of the oblique asymptote if any of the function x2 2x 8 x 4 f x x2 Oy x 6 no oblique asymptote y x 10 x y 2

Listen Solve the inequality Express your answer using 5x 2 3 01 13 O 1 or 00 1 or a 1

If 3 x 6 7 5x are consecutive terms of a geometric progression G P with constan ratior 0 find the i value of x ii constant ratio