
Precalculus
11th Edition
ISBN: 9780135189405
Author: Michael Sullivan
Publisher: PEARSON
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Textbook Question
Chapter 13.3, Problem 54AYU
Doctorate Degrees According to the National Science Foundation, in 2016 there was a 17.2% probability that a doctoral degree awarded at a U.S. university was awarded in engineering. If a 2016 U.S. doctoral recipient is randomly selected, what is the probability that his or her degree was not in engineering?
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Please solve 14 and 15
1. Consider the following system of equations:
x13x2 + 4x3 - 5x4 = 7
-2x13x2 + x3 - 6x4 = 7
x16x213x3 - 21x4 = 28
a) Solve the system. Write your solution in parametric and vector form.
b) What is a geometric description of the solution.
7
c) Is v =
7 in the span of the set S=
[28.
1
HE
3
-5
3
·6
? If it is, write v
6
as a linear combination of the vectors in S. Justify.
d) How many solutions are there to the associated homogeneous system for
the system above? Justify.
e) Let A be the coefficient matrix from the system above. Find the set of all
solutions to Ax = 0.
f) Is there a solution to Ax=b for all b in R³? Justify.
4. Suppose that A is made up of 5 column vectors in R³, and suppose that the
rank(A)=3.
a. How many solutions are there to Ax=0? Justify.
b. What is a geometric description for the nullspace(A)? Justify.
c. Do the column vectors of A span R³? Justify.
d. Is A invertible? Justify.
Chapter 13 Solutions
Precalculus
Ch. 13.1 - Prob. 1AYUCh. 13.1 - Prob. 2AYUCh. 13.1 - True or false The intersection of two sets is...Ch. 13.1 - Prob. 4AYUCh. 13.1 - Prob. 5AYUCh. 13.1 - Prob. 6AYUCh. 13.1 - True or False If a task consists of a sequence of...Ch. 13.1 - Prob. 8AYUCh. 13.1 - Prob. 9AYUCh. 13.1 - Prob. 10AYU
Ch. 13.1 - If n( A )=15 , n( B )=20 , and n( AB )=10 , find...Ch. 13.1 - If n( A )=30 , n( B )=40 , and n( AB )=45 , find...Ch. 13.1 - If n( AB )=50 , n( AB )=10 , and n( B )=20 , find...Ch. 13.1 - If n( AB )=60 , n( AB )=40 , and n( A )=n( B ) ,...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - A man has shirts and ties. How many different...Ch. 13.1 - Blouses and Skirts A woman has 5 blouses and 8...Ch. 13.1 - Four-digit Numbers How many four-digit numbers can...Ch. 13.1 - Five-digit Numbers How many five-digit numbers can...Ch. 13.1 - Analyzing Survey Data In a consumer survey of ...Ch. 13.1 - Analyzing Survey Data In a student survey, 200...Ch. 13.1 - Analyzing Survey Data In a survey of 100 investors...Ch. 13.1 - Classifying Blood Types Human blood is classified...Ch. 13.1 - Demographics The following data represent the...Ch. 13.1 - Demographics The following data represent the...Ch. 13.1 - Stock Portfolios As a financial planner, you are...Ch. 13.1 - Prob. 34AYUCh. 13.1 - Prob. 36AYUCh. 13.1 - Prob. 37AYUCh. 13.1 - Prob. 38AYUCh. 13.1 - Prob. 39AYUCh. 13.1 - Prob. 40AYUCh. 13.1 - Prob. 41AYUCh. 13.1 - Prob. 42AYUCh. 13.1 - Determine whether the infinite series converges or...Ch. 13.1 - If f(x)=23(x2)13+13(x2)23, find where f(x)=0 f(x)...Ch. 13.1 - Find the partial fraction decomposition:...Ch. 13.2 - 0!= ; 1!= . (p. 642)Ch. 13.2 - Prob. 2AYUCh. 13.2 - A(n) __________ is an ordered arrangement of r...Ch. 13.2 - A(n) ___________ is an arrangement of r objects...Ch. 13.2 - P( n,r )= __________________.Ch. 13.2 - C( n,r )= _______________________.Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - List all the ordered arrangements of 5 objects a ,...Ch. 13.2 - List all the ordered arrangements of 5 objects a ,...Ch. 13.2 - List all the ordered arrangements of 4 objects 1,...Ch. 13.2 - List all the ordered arrangements of 6 objects 1,...Ch. 13.2 - List all the combinations of 5 objects a , b , c ,...Ch. 13.2 - List all the combinationss of 5 objects a , b , c...Ch. 13.2 - List all the combinations of 4 objects 1, 2, 3,...Ch. 13.2 - List all the combinationss of 6 objects 1, 2, 3,...Ch. 13.2 - Forming Codes How many two-letter codes can be...Ch. 13.2 - Forming Codes How many two-letter codes can be...Ch. 13.2 - Forming Numbers How many three-digit numbers can...Ch. 13.2 - Forming Numbers How many three-digit numbers can...Ch. 13.2 - Lining People Up In how many ways can 4 people be...Ch. 13.2 - Stacking Boxes In how many ways can 5 different...Ch. 13.2 - Forming Codes How many different three-letter...Ch. 13.2 - Forming Codes How many different four-letter codes...Ch. 13.2 - Stocks on the NYSE Companies whose stocks are...Ch. 13.2 - Stocks on the NASDAQ Companies whose stocks are...Ch. 13.2 - Establishing Committees In how many ways can a...Ch. 13.2 - Establishing Committees In how many ways can a...Ch. 13.2 - Possible Answers on a True/False Test How many...Ch. 13.2 - Possible Answers on a Multiple-choice Test How...Ch. 13.2 - Arranging Books Five different mathematics books...Ch. 13.2 - Prob. 46AYUCh. 13.2 - Birthday Problem In how many ways can 2 people...Ch. 13.2 - Prob. 48AYUCh. 13.2 - Prob. 49AYUCh. 13.2 - Prob. 50AYUCh. 13.2 - Forming Words How many different 9-letter words...Ch. 13.2 - Prob. 52AYUCh. 13.2 - Selecting Objects An urn contains 7 white balls...Ch. 13.2 - Prob. 54AYUCh. 13.2 - Prob. 55AYUCh. 13.2 - Prob. 56AYUCh. 13.2 - Prob. 57AYUCh. 13.2 - Prob. 58AYUCh. 13.2 - Prob. 59AYUCh. 13.2 - Prob. 60AYUCh. 13.2 - Prob. 61AYUCh. 13.2 - Prob. 62AYUCh. 13.2 - Combination Locks A combination lock displays 50...Ch. 13.2 - Challenge Problem Passwords Suppose a password...Ch. 13.2 - Prob. 65AYUCh. 13.2 - Prob. 66AYUCh. 13.2 - Prob. 67AYUCh. 13.2 - Problems 67-70 are based on material learned...Ch. 13.2 - Prob. 69AYUCh. 13.2 - Prob. 70AYUCh. 13.2 - Prob. 71AYUCh. 13.2 - Prob. 72AYUCh. 13.2 - Prob. 73AYUCh. 13.2 - Prob. 74AYUCh. 13.2 - Prob. 75AYUCh. 13.2 - Find the partial fraction decomposition:...Ch. 13.2 - Prob. 77AYUCh. 13.3 - When the same probability is assigned to each...Ch. 13.3 - Prob. 2AYUCh. 13.3 - Prob. 3AYUCh. 13.3 - Prob. 4AYUCh. 13.3 - In a probability model, which of the following...Ch. 13.3 - Prob. 6AYUCh. 13.3 - Determine whether the following is a probability...Ch. 13.3 - Prob. 8AYUCh. 13.3 - Prob. 9AYUCh. 13.3 - Prob. 10AYUCh. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - Prob. 14AYUCh. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 23-26, consider the experiment of...Ch. 13.3 - In Problems 23-26, consider the experiment of...Ch. 13.3 - Prob. 25AYUCh. 13.3 - Prob. 26AYUCh. 13.3 - Assigning Probabilities A coin is weighted so that...Ch. 13.3 - Assigning Probabilities A coin is weighted so that...Ch. 13.3 - Assigning Probabilities A die is weighted so that...Ch. 13.3 - Assigning Probabilities A die is weighted so that...Ch. 13.3 - For Problems 31-34, the sample space is S={...Ch. 13.3 - For Problems 31-34, the sample space is S={...Ch. 13.3 - For Problems 31-34, the sample space is S={...Ch. 13.3 - For Problems 31-34, the sample space is S={...Ch. 13.3 - For Problems 35 and 36, an urn contains 5 white...Ch. 13.3 - For Problems 35 and 36, an urn contains 5 white...Ch. 13.3 - In Problems 37-40, assume equally likely outcomes....Ch. 13.3 - In Problems 37-40, assume equally likely outcomes....Ch. 13.3 - In Problems 37-40, assume equally likely outcomes....Ch. 13.3 - In Problems 37-40, assume equally likely outcomes....Ch. 13.3 - Prob. 41AYUCh. 13.3 - Prob. 42AYUCh. 13.3 - Prob. 43AYUCh. 13.3 - Prob. 45AYUCh. 13.3 - In Problems 45-48, find the probability of the...Ch. 13.3 - Prob. 47AYUCh. 13.3 - Prob. 48AYUCh. 13.3 - Prob. 49AYUCh. 13.3 - Prob. 50AYUCh. 13.3 - Automobile Theft According to the Insurance...Ch. 13.3 - Prob. 52AYUCh. 13.3 - Cat Ownership According to the American Pet...Ch. 13.3 - Doctorate Degrees According to the National...Ch. 13.3 - Prob. 55AYUCh. 13.3 - For Problems 57-60, a golf ball is selected at...Ch. 13.3 - Prob. 57AYUCh. 13.3 - Prob. 58AYUCh. 13.3 - Prob. 59AYUCh. 13.3 - Prob. 60AYUCh. 13.3 - Prob. 61AYUCh. 13.3 - Prob. 62AYUCh. 13.3 - Prob. 63AYUCh. 13.3 - Prob. 64AYUCh. 13.3 - Prob. 65AYUCh. 13.3 - Prob. 66AYUCh. 13.3 - Surveys In a survey about the number of TV sets in...Ch. 13.3 - Prob. 68AYUCh. 13.3 - Prob. 69AYUCh. 13.3 - Prob. 70AYUCh. 13.3 - Prob. 71AYUCh. 13.3 - Prob. 72AYUCh. 13.3 - Prob. 73AYUCh. 13.3 - Challenge Problem If 3 six-sided dice are tossed,...Ch. 13.3 - To graph g( x )=E| x+2 |3 , shift the graph of f(...Ch. 13.3 - Prob. 76AYUCh. 13.3 - Prob. 77AYUCh. 13.3 - Prob. 78AYUCh. 13.3 - Prob. 79AYUCh. 13.3 - Prob. 80AYUCh. 13.3 - Problems 75-84 are based on material learned...Ch. 13.3 - Prob. 82AYUCh. 13.3 - Problems 75-84 are based on material learned...Ch. 13.3 - Problems 75-84 are based on material learned...Ch. 13 - Prob. 1RECh. 13 - Prob. 2RECh. 13 - Prob. 3RECh. 13 - Prob. 4RECh. 13 - Prob. 5RECh. 13 - Prob. 6RECh. 13 - Prob. 7RECh. 13 - Prob. 8RECh. 13 - Prob. 9RECh. 13 - Prob. 10RECh. 13 - Prob. 11RECh. 13 - Prob. 12RECh. 13 - Baseball On a given day, the American Baseball...Ch. 13 - Choosing Seats If 4 people enter a bus that has 9...Ch. 13 - Choosing a Team In how many ways can a squad of 4...Ch. 13 - Baseball In how many ways can 2 teams from 14...Ch. 13 - Prob. 17RECh. 13 - Prob. 18RECh. 13 - Prob. 19RECh. 13 - Arranging Flags How many different vertical...Ch. 13 - Prob. 21RECh. 13 - Prob. 22RECh. 13 - Unemployment According to the U.S. Bureau of Labor...Ch. 13 - Prob. 24RECh. 13 - Prob. 25RECh. 13 - Prob. 26RECh. 13 - Prob. 1CTCh. 13 - In Problems, a survey of college freshmen asked...Ch. 13 - In Problems 14, a survey of 70college freshmen...Ch. 13 - In Problems 14, a survey of 70college freshmen...Ch. 13 - Prob. 5CTCh. 13 - Prob. 6CTCh. 13 - Prob. 7CTCh. 13 - MMs offers customers the opportunity to create...Ch. 13 - Prob. 9CTCh. 13 - Prob. 10CTCh. 13 - On February 20, 2004, the Ohio Bureau of Motor...Ch. 13 - Kiersten applies for admission to the University...Ch. 13 - A cooler contains 8 bottles of Pepsi, 5 bottles of...Ch. 13 - Prob. 14CTCh. 13 - Prob. 15CTCh. 13 - Prob. 16CTCh. 13 - Prob. 1CRCh. 13 - Prob. 2CRCh. 13 - Prob. 3CRCh. 13 - Prob. 4CRCh. 13 - Prob. 5CRCh. 13 - Prob. 6CRCh. 13 - Prob. 7CRCh. 13 - Prob. 8CRCh. 13 - Prob. 9CRCh. 13 - Prob. 10CRCh. 13 - Graph: y=3sin(2x+)Ch. 13 - Prob. 12CR
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- 3. Suppose that A is 5 x 5 and rank(A)=4. Use this information to answer the following. a. Give a geometric description of nullspace(A). Justify. b. Is A invertible? Justify. c. Give a geometric description of the span of the column vectors of A. What space are the column vectors of A in? Justify. d. What is determinant of A? Justify.arrow_forward2. Consider the matrix: A || 1 1 -3 14 2 1 01 4 1 2 2 -26 1 -3 1 5] a) What is rank(A)? b) Is A invertible? Justify. c) Find the nullspace(A). Justify. d) Is the trivial solution the only solution to Ax=0? Justify. e) What is the span of the column vectors of A? Justify.arrow_forwardE 5. Suppose that S={v € R²: v = [2x² - 3]}. Is S a subspace of R²? Prove or disprovearrow_forward
- 6. Suppose that V1, V2 ER", show that span{v1, v2} is a subspace of Rn.arrow_forwardRa X 2) slots per pole per phase 3/31 180 Ko Sin (1) Kdl 1 sin (4) sin(3) Sin (30) اذا مرید شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 Fo lasa! G s.1000-950 20:05 1000 Capper losses: 5kw Rotor input lookw 0.05 ined sove in peaper I need a detailed solution on paper please 6) 1 ۳/۱ وه اذا ميريد شرح الكتب فقط look DC 7) rotov Find the general solution of the following equations: +4y=tan2x 3 7357 Find the general solution of the following equations: - Qll y + y (³) = 0. 101arrow_forwardB: 18060 msl Kd Ka, Sin (n) I sin () sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 G 5005 1000 s = 1000-950 Copper bosses 5kW /0001 Rotor input 5 : loo kw 0.05 6) 1 اذا ميريد شرح الكتب فقط ١٥٠ 7) rotov DC ined sove in Deaper I need a detailed solution on paper please dy x+2y-4 = dx 2x-y-3 Find the general solution of the following equations: 02//yl-4y+13y=esinarrow_forward
- 1) R₂ = X2 2) slots per pole per phase = 3/31 B msl kd 180 60 Kal Sin (1) I sin () sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 G 5005 1000 s = 1000-950 Copper bosses 5kW Rotor input: 5 0.05 loo kw 6) 1 /0001 اذا ميريد شرح الكتب فقط look 7) rotov DC ined sove in peaper I need a detailed solution on paper please Q1// Find the solution of: 'y' = x² +376 x4+316 xyo Q2 Find the solution of the initial-valued problems: ex-y y' +exarrow_forwardR₂ = X2 2) slots per pole per phase = 3/31 B-18060 msl kd Kasi Sin (1) I sin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed s = 1000-950 1000 Copper losses: 5kw Rotor input 5 0.05 6) 1 120 x 50 G loo kw ined sove in peaper I need a detailed solution on paper please Q3// x²y// +xy/ + (x² - ½) y = x³/². اذا ميريد شرح الكتب فقط look 7) rotor DC Q4// x²y// - (2x+x²)y/ + (2 + x)y = x³. dy 2x+2y+4 = dx 2x-y-3arrow_forward۳/۱ R2X2 2) slots per pole per phase = 3/31 B, 18060 msl Kas Sin() 1sin() sin(30) Sin (30) kd اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speeds S = 1000-950 1000 Copper bosses 5kw 120*50 loca G Rotor input 5 loo kw 6) 1 0.05 اذا ميريد شرح الكتب فقط lookw 7) rotor DC ined sove in peaper I need a detailed solution on paper please 064 Q1// Find the solution of QI/Find the solution of Inxy= 7357 x+2y³ y' = xy3arrow_forward
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