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Linear Algebra and Its Applications (5th Edition)
5th Edition
ISBN: 9780321982384
Author: David C. Lay, Steven R. Lay, Judi J. McDonald
Publisher: PEARSON
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Textbook Question
Chapter 2.5, Problem 27E
Design two different ladder networks that each output 9 volts and 4 amps when the input is 12 volts and 6 amps.
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Chapter 2 Solutions
Linear Algebra and Its Applications (5th Edition)
Ch. 2.1 - Since vectors in n may be regarded as n 1...Ch. 2.1 - Let A be a 4 4 matrix and let x be a vector in 4....Ch. 2.1 - Suppose A is an m n matrix, all of whose rows are...Ch. 2.1 - In Exercises 1 and 2, compute each matrix sum or...Ch. 2.1 - In Exercises 1 and 2, compute each matrix sum or...Ch. 2.1 - In the rest of this exercise set and in those to...Ch. 2.1 - Compute A 5I3 and (5I3)A, when A=[913876418].Ch. 2.1 - In Exercises 5 and 6, compute die product AB in...Ch. 2.1 - In Exercises 5 and 6, compute die product AB in...Ch. 2.1 - If a matrix A is 5 3 and the product AB is 5 7,...
Ch. 2.1 - How many rows does B have if BC is a 3 4 matrix?Ch. 2.1 - Let A=[2531] and B=[453k]. What value(s) of k, if...Ch. 2.1 - Let A=[2346], B=[8455], and C=[5231]. Verify that...Ch. 2.1 - Let A=[111123145] and D=[200030005]. Compute AD...Ch. 2.1 - Let A=[3612]. Construct a 2 2 matrix B such that...Ch. 2.1 - Let r1,..., rp be vectors in n, and let Q be an m ...Ch. 2.1 - Let U be the 3 2 cost matrix described in Example...Ch. 2.1 - Exercises 15 and 16 concern arbitrary matrices A,...Ch. 2.1 - a. If A and B are 3 3 and B = [b1 b2 b3], then AB...Ch. 2.1 - If A=[1225] and AB=[121693], determine the first...Ch. 2.1 - Suppose the first two columns, b1 and b2, of B are...Ch. 2.1 - Suppose die third column of B is die sum of die...Ch. 2.1 - Suppose the second column of B is all zeros. What...Ch. 2.1 - Suppose the last column of AB is entirely zero but...Ch. 2.1 - Show that if the columns of B are linearly...Ch. 2.1 - Suppose CA = In (the n n identity matrix). Show...Ch. 2.1 - Suppose AD = Im (the m m identity matrix). Show...Ch. 2.1 - Suppose A is an m n matrix and there exist n m...Ch. 2.1 - Suppose A is a 3 n matrix whose columns span 3....Ch. 2.1 - In Exercises 27 and 28, view vectors in n as n 1...Ch. 2.1 - If u and v are in n. how are uTv and vTu related?...Ch. 2.1 - Prove Theorem 2(b) and 2(c). Use the row-column...Ch. 2.1 - Prove Theorem 2(d). [Hint: The (i, j)-entry in...Ch. 2.1 - Show that ImA = A when A is an m n matrix. You...Ch. 2.1 - Show that AIn = A when A is an m n matrix. [Hint:...Ch. 2.1 - Prove Theorem 3(d). [Hint: Consider the jth row of...Ch. 2.1 - Give a formula for (A Bx)T, where x is a vector...Ch. 2.2 - Use determinants to determine which of the...Ch. 2.2 - Find the inverse of the matrix A = [121156545], if...Ch. 2.2 - If A is an invertible matrix, prove that 5A is an...Ch. 2.2 - Find the inverses of the matrices in Exercises 14....Ch. 2.2 - Find the inverses of the matrices in Exercises 14....Ch. 2.2 - Find the inverses of the matrices in Exercises 14....Ch. 2.2 - Find the inverses of the matrices in Exercises 14....Ch. 2.2 - Use the inverse found in Exercise 1 to solve the...Ch. 2.2 - Use the inverse found in Exercise 3 to solve the...Ch. 2.2 - Let A = [12512], b1 = [13], b2 = [15], b3 = [26],...Ch. 2.2 - Use matrix algebra to show that if A is invertible...Ch. 2.2 - In Exercises 9 and 10, mark each statement True or...Ch. 2.2 - a. A product of invertible n n matrices is...Ch. 2.2 - Let A be an invertible n n matrix, and let B be...Ch. 2.2 - Let A be an invertible n n matrix, and let B be...Ch. 2.2 - Suppose AB = AC. where B and C are n p matrices...Ch. 2.2 - Suppose (B C) D = 0, where B and C are m n...Ch. 2.2 - Suppose A, B, and C are invertible n n matrices....Ch. 2.2 - Suppose A and B are n n, B is invertible, and AB...Ch. 2.2 - Solve the equation AB = BC for A, assuming that A,...Ch. 2.2 - Suppose P is invertible and A = PBP1 Solve for B...Ch. 2.2 - If A, B, and C are n n invertible matrices, does...Ch. 2.2 - Suppose A, B, and X are n n matrices with A, X,...Ch. 2.2 - Explain why the columns of an n n; matrix A are...Ch. 2.2 - Explain why the columns of an n n matrix A span n...Ch. 2.2 - Suppose A is n n and die equation Ax = 0 has only...Ch. 2.2 - Suppose A is n n and the equation Ax = b has a...Ch. 2.2 - Exercises 25 and 26 prove Theorem 4 for A =...Ch. 2.2 - Exercises 25 and 26 prove Theorem 4 for A =...Ch. 2.2 - Exercises 27 and 28 prove special cases of the...Ch. 2.2 - Show that if row 3 of A is replaced by row3(A) 4 ...Ch. 2.2 - Find the inverses of the matrices in Exercises...Ch. 2.2 - Find die inverses of the matrices in Exercises...Ch. 2.2 - Find die inverses of the matrices in Exercises...Ch. 2.2 - Find die inverses of the matrices in Exercises...Ch. 2.2 - Use the algorithm from this section to find the...Ch. 2.2 - Repeat the strategy of Exercise 33 to guess the...Ch. 2.2 - Let A = [279256134]. Find the third column of A1...Ch. 2.2 - [M] Let A = [2592754618053715450149]. Find the...Ch. 2.2 - Let A = [121315]. Constuct a 2 3 matrix C (by...Ch. 2.2 - Let A = [11100111]. Construct a 4 2 matrix D...Ch. 2.2 - Let D = [.005.002.001.002.004.002.001.002.005] be...Ch. 2.3 - Determine if A = [234234234] is invertible.Ch. 2.3 - Suppose that for a certain n n matrix A,...Ch. 2.3 - Suppose that A and B are n n matrices and the...Ch. 2.3 - Unless otherwise specified, assume that all...Ch. 2.3 - Unless otherwise specified, assume that all...Ch. 2.3 - Unless otherwise specified, assume that all...Ch. 2.3 - Unless otherwise specified, assume that all...Ch. 2.3 - Unless otherwise specified, assume that all...Ch. 2.3 - Unless otherwise specified, assume that all...Ch. 2.3 - Unless otherwise specified, assume that all...Ch. 2.3 - Unless otherwise specified, assume that all...Ch. 2.3 - Unless otherwise specified, assume that all...Ch. 2.3 - Unless otherwise specified, assume that all...Ch. 2.3 - In Exercises 11 and 12, the matrices are all n n....Ch. 2.3 - In Exercises 11 and 12, the matrices are all n n....Ch. 2.3 - An m n upper triangular matrix is one whose...Ch. 2.3 - An m n lower triangular matrix is one whose...Ch. 2.3 - Can a square matrix with two identical columns be...Ch. 2.3 - Is it possible for a 5 5 matrix to be invertible...Ch. 2.3 - If A is invertible, then the columns of A1 are...Ch. 2.3 - If C is 6 6 and the equation Cx = v is consistent...Ch. 2.3 - If the columns of a 7 7 matrix D are linearly...Ch. 2.3 - If n n matrices E and F have the property that EF...Ch. 2.3 - If the equation Gx = y has more than one solution...Ch. 2.3 - If the equation Hx = c is inconsistent for some c...Ch. 2.3 - If an n n matrix K cannot be row reduced to In....Ch. 2.3 - If L is n n and the equation Lx = 0 has the...Ch. 2.3 - Verify the boxed statement preceding Example 1.Ch. 2.3 - Explain why the columns of A2 span n whenever the...Ch. 2.3 - Show that if AB is invertible, so is A. You cannot...Ch. 2.3 - Show that if AB is invertible, so is B.Ch. 2.3 - If A is an n n matrix and the equation Ax = b has...Ch. 2.3 - If A is an n n matrix and the transformation x ...Ch. 2.3 - Suppose A is an n n matrix with the property that...Ch. 2.3 - Suppose A is an n n matrix with the property that...Ch. 2.3 - In Exercises 33 and 34, T is a linear...Ch. 2.3 - In Exercises 33 and 34, T is a linear...Ch. 2.3 - Let T : n n be an invertible linear...Ch. 2.3 - Let T be a linear transformation that maps n onto...Ch. 2.3 - Suppose T and U are linear transformations from n...Ch. 2.3 - Suppose a linear transformation T : n n has the...Ch. 2.3 - Let T : n n be an invertible linear...Ch. 2.3 - Suppose T and S satisfy the invertibility...Ch. 2.4 - Show that[I0AI] is invertible and find its...Ch. 2.4 - Compute XTX, where X is partitioned as [X1 X2].Ch. 2.4 - In Exercises 19, assume that the matrices are...Ch. 2.4 - In Exercises 19, assume that the matrices are...Ch. 2.4 - In Exercises 19, assume that the matrices are...Ch. 2.4 - In Exercises 19, assume that the matrices are...Ch. 2.4 - In Exercises 58, find formulas for X, Y, and Z in...Ch. 2.4 - In Exercises 58, find formulas for X, Y, and Z in...Ch. 2.4 - In Exercises 58, find formulas for X, Y, and Z in...Ch. 2.4 - In Exercises 58, find formulas for X, Y, and Z in...Ch. 2.4 - Suppose A11 is an invertible matrix. Find matrices...Ch. 2.4 - The inverse of [I00CI0ABI] is [I00ZI0XYI]. Find X,...Ch. 2.4 - In Exercises 11 and 12, mark each statement True...Ch. 2.4 - In Exercises 11 and 12, mark each statement True...Ch. 2.4 - Let A=[B00C], where B and C are square. Show A is...Ch. 2.4 - Show that the block upper triangular matrix A in...Ch. 2.4 - Suppose A11 is invertible. Find X and Y such that...Ch. 2.4 - Suppose the block matrix A on the left side of (7)...Ch. 2.4 - When a deep space probe is launched, corrections...Ch. 2.4 - Let X be an m n data matrix such that XT X is...Ch. 2.4 - In the study of engineering control of physical...Ch. 2.4 - Suppose the transfer function W(S) in Exercise 19...Ch. 2.4 - a. Verify that A2 = I when A=[1031]. b. Use...Ch. 2.4 - Generalize the idea of Exercise 21(a) [not 21(b)]...Ch. 2.4 - Use partitioned matrices to prove by induction...Ch. 2.4 - Use partitioned matrices to prove by induction mat...Ch. 2.4 - Without using row reduction, find the inverse of...Ch. 2.5 - Find an LU factorization of...Ch. 2.5 - In Exercises 16, solve the equation Ax = b by...Ch. 2.5 - In Exercises 16, solve the equation Ax = b by...Ch. 2.5 - In Exercises 16, solve the equation Ax = b by...Ch. 2.5 - In Exercises 16, solve the equation Ax = b by...Ch. 2.5 - In Exercises 16, solve the equation Ax = b by...Ch. 2.5 - In Exercises 16, solve the equation Ax = b by...Ch. 2.5 - Find an LU factorization of the matrices in...Ch. 2.5 - Find an LU factorization of the matrices in...Ch. 2.5 - Find an LU factorization of the matrices in...Ch. 2.5 - Find an LU factorization of the matrices in...Ch. 2.5 - Find an LU factorization of the matrices in...Ch. 2.5 - Find an LU factorization of the matrices in...Ch. 2.5 - Find an LU factorization of the matrices in...Ch. 2.5 - Find an LU factorization of the matrices in...Ch. 2.5 - Find an LU factorization of the matrices in...Ch. 2.5 - Find an LU factorization of the matrices in...Ch. 2.5 - When A is invertible, MATLAB finds A1 by factoring...Ch. 2.5 - Find A1 as in Exercise 17, using A from Exercise...Ch. 2.5 - Let A be a lower triangular n n matrix with...Ch. 2.5 - Let A = LU be an LU factorization. Explain why A...Ch. 2.5 - Suppose A = BC, where B is invertible. Show that...Ch. 2.5 - (Reduced LU Factorization) With A as in the...Ch. 2.5 - (Rank Factorization) Suppose an m n matrix A...Ch. 2.5 - (QR Factorization) Suppose A = QR, where Q and R...Ch. 2.5 - (Singular Value Decomposition) Suppose A = UDVT,...Ch. 2.5 - (Spectral Factorization) Suppose a 3 3 matrix A...Ch. 2.5 - Design two different ladder networks that each...Ch. 2.5 - Show that if three shunt circuits (with...Ch. 2.5 - Prob. 29ECh. 2.5 - Find a different factorization of the A in...Ch. 2.6 - Suppose an economy has two sectors: goods and...Ch. 2.6 - Exercises 14 refer to an economy that is divided...Ch. 2.6 - Exercises 14 refer to an economy that is divided...Ch. 2.6 - Exercises 14 refer to an economy that is divided...Ch. 2.6 - Exercises 14 refer to an economy that is divided...Ch. 2.6 - Consider the production model x = Cx + d for an...Ch. 2.6 - Repeat Exercise 5 with C=[.1.6.5.2], and d=[1811]....Ch. 2.6 - Let C and d be as in Exercise 5. a. Determine the...Ch. 2.6 - Let C be an n n consumption matrix whose column...Ch. 2.6 - Solve the Leontief production equation for an...Ch. 2.6 - The consumption matrix C for the U.S. economy in...Ch. 2.6 - The Leontief production equation, x = Cx + d, is...Ch. 2.6 - Let C be a consumption matrix such that Cm 0 as m...Ch. 2.7 - Rotation of a figure about a point p in 2 is...Ch. 2.7 - What 3 3 matrix will have the same effect on...Ch. 2.7 - Use matrix multiplication to find the image of the...Ch. 2.7 - In Exercises 38, find the 3 3 matrices that...Ch. 2.7 - In Exercises 38, find the 3 3 matrices that...Ch. 2.7 - In Exercises 38, find the 3 3 matrices that...Ch. 2.7 - In Exercises 38, find the 3 3 matrices that...Ch. 2.7 - In Exercises 38, find the 3 3 matrices that...Ch. 2.7 - In Exercises 38, find the 3 3 matrices that...Ch. 2.7 - A 2 200 data matrix D contains the coordinates of...Ch. 2.7 - Consider the following geometric 2D...Ch. 2.7 - Prob. 11ECh. 2.7 - A rotation in 2 usually requires four...Ch. 2.7 - The usual transformations on homogeneous...Ch. 2.7 - Prob. 14ECh. 2.7 - What vector in 3 has homogeneous coordinates...Ch. 2.7 - Are (1. 2, 3, 4) and (10, 20, 30, 40) homogeneous...Ch. 2.7 - Give the 4 4 matrix that rotates points in 3...Ch. 2.7 - Give the 4 4 matrix that rotates points in 3...Ch. 2.7 - Let S be the triangle with vertices (4.2, 1.2,4),...Ch. 2.7 - Let S be the triangle with vertices (9,3,5),...Ch. 2.7 - [M] The actual color a viewer sees on a screen is...Ch. 2.7 - [M] The signal broadcast by commercial television...Ch. 2.8 - Let A=[115207353] and u=[732] Is u in Nul A? Is u...Ch. 2.8 - Given A=[010001000], find a vector in Nul A and a...Ch. 2.8 - Suppose an n n matrix A is invertible. What can...Ch. 2.8 - Exercises 14 display sets in 2. Assume the sets...Ch. 2.8 - Exercises 14 display sets in 2. Assume the sets...Ch. 2.8 - Exercises 14 display sets in 2. Assume the sets...Ch. 2.8 - Exercises 1-4 display sets in 2. Assume the sets...Ch. 2.8 - Let v1 = [235], v2 = [458], and w = [829]....Ch. 2.8 - Let v1 = [1243], v2 = [4797], v3 = [5865], and u =...Ch. 2.8 - Let v1 = [286], v2 = [387], v3 = [467], p =...Ch. 2.8 - Let v1 = [306], v2 = [223], v3 = [063], and p =...Ch. 2.8 - With A and p as in Exercise 7, determine if p is...Ch. 2.8 - With u = (2, 3, 1) and A as in Exercise 8,...Ch. 2.8 - In Exercises 11 and 12. give integers p and q such...Ch. 2.8 - In Exercises 11 and 12. give integers p and q such...Ch. 2.8 - For A as in Exercise 11, find a nonzero vector in...Ch. 2.8 - For A as in Exercise 12, find a nonzero vector in...Ch. 2.8 - Determine which sets in Exercises 15-20 are bases...Ch. 2.8 - Determine which sets in Exercises 15-20 are bases...Ch. 2.8 - Determine which sets in Exercises 15-20 are bases...Ch. 2.8 - Determine which sets in Exercises 15-20 are bases...Ch. 2.8 - Determine which sets in Exercises 15-20 are bases...Ch. 2.8 - Determine which sets in Exercises 15-20 are bases...Ch. 2.8 - In Exercises 21 and 22, mark each statement True...Ch. 2.8 - a. A subset H of n is a subspace if the zero...Ch. 2.8 - Exercises 23-26 display a matrix A and an echelon...Ch. 2.8 - Exercises 23-26 display a matrix A and an echelon...Ch. 2.8 - Exercises 23-26 display a matrix A and an echelon...Ch. 2.8 - Exercises 23-26 display a matrix A and an echelon...Ch. 2.8 - Construct a nonzero 3 3 matrix A and a nonzero...Ch. 2.8 - Construct a nonzero 3 3 matrix A and a vector b...Ch. 2.8 - Construct a nonzero 3 3 matrix A and a nonzero...Ch. 2.8 - Suppose the columns of a matrix A = [a1 ap] are...Ch. 2.8 - In Exercises 31-36, respond as comprehensively as...Ch. 2.8 - In Exercises 31-36. respond as comprehensively as...Ch. 2.8 - In Exercises 31-36, respond as comprehensively as...Ch. 2.8 - In Exercises 31-36, respond as comprehensively as...Ch. 2.8 - In Exercises 31-36, respond as comprehensively as...Ch. 2.8 - In Exercises 31-36, respond as comprehensively as...Ch. 2.8 - [M] In Exercises 37 and 38, construct bases for...Ch. 2.8 - [M] In Exercises 37 and 38, construct bases for...Ch. 2.9 - Determine the dimension of the subspace H of 3...Ch. 2.9 - Prob. 2PPCh. 2.9 - Could 3 possibly contain a four-dimensional...Ch. 2.9 - In Exercises 1 and 2, find the vector x determined...Ch. 2.9 - In Exercises 1 and 2, find the vector x determined...Ch. 2.9 - In Exercises 3-6, the vector s is in a subspace H...Ch. 2.9 - In Exercises 1 and 2, find the vector x determined...Ch. 2.9 - In Exercises 3-6, the vector x is in a subspace H...Ch. 2.9 - In Exercises 3-6, the vector x is in a subspace H...Ch. 2.9 - Let b1 = [30], b2 = [12], w = [72], x = [41], and...Ch. 2.9 - Let b1 = [02], b2 = [21], x = [23], y = [24], z =...Ch. 2.9 - Exercises 9-12 display a matrix A and an echelon...Ch. 2.9 - Exercises 9-12 display a matrix A and an echelon...Ch. 2.9 - Exercises 9-12 display a matrix A and an echelon...Ch. 2.9 - Exercises 9-12 display a matrix A and an echelon...Ch. 2.9 - In Exercises 13 and 14, find a basis for the...Ch. 2.9 - In Exercises 13 and 14, find a basis for the...Ch. 2.9 - Suppose a 3 5 matrix A has three pivot columns....Ch. 2.9 - Suppose a 4 7 matrix A has three pivot columns....Ch. 2.9 - In Exercises 17 and 18, mark each statement True...Ch. 2.9 - In Exercises 17 and 18, mark each statement True...Ch. 2.9 - If the subspace of all solutions of Ax = 0 has a...Ch. 2.9 - What is the rank of a 4 5 matrix whose null space...Ch. 2.9 - If the tank of a 7 6 matrix A is 4, what is the...Ch. 2.9 - Show that a set of vectors {v1, v2, , v5} in n is...Ch. 2.9 - If possible, construct a 3 4 matrix A such that...Ch. 2.9 - Constructa4 3 matrix with tank 1.Ch. 2.9 - Let A be an n p matrix whose column space is...Ch. 2.9 - Suppose columns 1, 3, 5, and 6 of a matrix A are...Ch. 2.9 - Suppose vectors b1, bp span a subspace W, and let...Ch. 2.9 - Use Exercise 27 to show that if A and B are bases...Ch. 2.9 - Prob. 29ECh. 2.9 - [M] Let H = Span {v1, v2, v3} and B= {v1, v2,...Ch. 2 - Assume that the matrices mentioned in the...Ch. 2 - Find the matrix C whose inverse is C1 = [4567].Ch. 2 - Show that A = [000100010]. Show that A3 = 0. Use...Ch. 2 - Suppose An = 0 for some n 1. Find an inverse for...Ch. 2 - Suppose an n n matrix A satisfies the equation A2...Ch. 2 - Prob. 6SECh. 2 - Let A = [1382411125] and B = [351534]. Compute A1B...Ch. 2 - Find a matrix A such that the transformation x Ax...Ch. 2 - Suppose AB =[5423] and B = [7321]. Find A.Ch. 2 - Suppose A is invertible. Explain why ATA is also...Ch. 2 - Let x1, , xn, be fixed numbers. The matrix below,...Ch. 2 - Prob. 12SECh. 2 - Given u in n with uTu = 1, Let P = uuT (an outer...Ch. 2 - Prob. 14SECh. 2 - Prob. 15SECh. 2 - Let A be an n n singular matrix Describe how to...Ch. 2 - Let A be a 6 4 matrix and B a 4 6 matrix. Show...Ch. 2 - Suppose A is a 5 3 matrix and mere exists a 3 5...Ch. 2 - Prob. 19SECh. 2 - [M] Let An be the n n matrix with 0s on the main...
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- What operations can be performed on a linear system to arrive at an equivalent system?arrow_forwardThe amount of nitrogen (in lb/acre), phosphate (in lb/acre), and labor (in hr/acre) needed to grow honeydews, yellow onjons, and lettuce is given by the table to the right. Complete parts a and b. OA. Yes, the farmer should allot B. No, it is not possible to use all resources completely. acres for honeydew, for yellow onions, and acres for lettuce. Honeydews 120 Nitrogen Phosphate 180 Labor 5 a) If the farmer has 230 acres, 30,300 lb of nitrogen, 34,400 lb of phosphate, and 400 hours of labor, is it possible to use all resources completely? If so, how many acres should he allot for each crop? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. ⒸA. Yes, the farmer should allot acres for honeydew, OB. No, it is not possible to use all resources completely. Yellow onions 150 acres for lettuce. 80 6 Lettuce b) Suppose everything is the same as in part a, except that 1180 hours of labor are available. Is it possible to use all resources…arrow_forwardSuppose that 5 bulldozers can load 8 trucks full of gravel in 40 minutes. Assume all bull dozers work at the same steady pace and that all trucks hold the same amount of gravel. Find out what A,B,C, and D are in the tables below. The left table is when the job takes 40 minutes. Find out how many trucks 10 bulldozers and 4 bulldozers can fill up. This job will take 40 minutes Bulldozer 4 5 10 Trucks A 8 13 The right table is when the job is filling 6 trucks. Find out how long it takes 10 bulldozers and 4 bulldozers to complete the job. This job to fill 8 trucks with gravel. bulldozers 4 5 10 time needed. C 40 D What are A, B,C,Darrow_forward
- Ron and Tim both work as landscapers during the summer months. Due to the heat, thescheduled start time is 7am. Typically though, the crew leader is late and most days they do notactually start work until 7:30 or 8am. Ron likes to catch a quick nap while he waits, however Timusually will pick up a broom or clean to pass the time. What time would his “compensabletime” begin for Ron and Tim (assume that 7:45 is the average start timarrow_forwardANSWER THE FOLLOWING A company produces two types of tables, T1 and T2. It takes 2 hours to produce the parts of one unit of T1, 1 hour to assemble and 2 hours to polish. It takes 4 hours to produce the parts of one unit of T2, 2.5 hour to assemble and 1.5 hours to polish. Per month, 7000 hours are available for producing the parts, 4000 hours for assembling the parts and 5500 hours for polishing the tables. The profit per unit of T1 is $90 and per unit of T2 is $110. Set T1 = X1 ; T2 =X2 ; Z=Profit Profit Equation would be: a. Z= 90 x1 + 110 x2 b. Z= 1.5 x1 + 2.5 x2 c. Z= 2 x1 + 3 x2 d. Z= 110 x1 + 90 x2 (2) The solution set of the system of inequalities are the following, except? a. x1+2.5x2≥4000 b. 2x1+1.5x2≤5500 c. x1≥0 d. 2x1+4x2≤7000 (3) How many of type A of tables should be produced in order to maximize the total monthly profit? a. 2,300 b. 2,750 c. 1,750 d. 1,500 (4) How many of type B of tables should be produced in order to maximize the total…arrow_forwardAssume that each gallon of Deluxe Vanilla uses 2 quarts of milk, 2 quarts of cream, and 3 ounces of vanilla; each gallon of Regular Vanilla uses 3 quarts of milk, 1 quart(s) of cream, and 1 ounces of vanilla; and each gallon of Deluxe Chocolate uses 2.75 quarts of milk, 1.25 quarts of cream, and 5 ounces of cacao. Assume also that the shop has on hand 115 gallons of milk, 77 gallons of cream, 19 pounds of vanilla, and 25 pounds of cacao. How many gallons of each type of ice cream should the shop make to use up all of these ingredients? When you setup a system of linear equations to solve this problem, how many variables and how many equations should you have.?Number of variables: Number of equations:arrow_forward
- Akira is running around a circular track. Akira runs counterclockwise. From where he starts, it takes him 22 seconds to reach the easternmost point of the track. It takes him 95 seconds to run one complete lap.Bob starts running at the same time as Akira. Bob starts from the northernmost point and runs clockwise. Bob and Akira pass each other for the first time after 26 seconds. How long does Bob take to run one lap of the track? The answer to this question should be the amount of time in seconds rounded to four decimal places that it takes for Bob to run a complete lap around the circular track.arrow_forwardThe Reception of the Laweh Graduate School receives external telephone calls. Due to certain difficulties, it is only one person who is taking care of the Reception Area. Ms. Jennifer, the receptionist wants to vacate her post for lunch between the hours of 1 and 2 pm. She knows that, the average number of phone calls received on the switchboard per hour is 2. However, what she does not know is the number of calls she will miss during the period. You can help her to determine the probability that during that one particular break hour: (i) No call will be received on the switchboard (ii) At least three calls will be received on the switchboardarrow_forwardA scientist investigated the effect of cross-fertilization on the heights of plants. In one study, the scientist planted 15pairs of a species of plant. Each pair consisted of one cross-fertilized plant and one self-fertilized plant grown in the same pot. The table available below gives the height differences, in eighths of an inch, for the 15 pairs. Each difference is obtained by subtracting the height of the self-fertilized plant from that of the cross-fertilized plant. Use the paired t-interval procedure to determine a 99% confidence interval for the difference between the mean heights of cross-fertilized and self-fertilized plants. Interpret the result. (Note: d=19.00 and sd=35.50.) The 99%confidence interval is from ____ eighths of an inch to_____ eighths of an inch. (Round to two decimal places as needed. Use ascending order.) Which statement below best interprets the confidence interval? A. There is 99%confidence that the difference between the…arrow_forward
- Solve step by step in digital format 3. Graph and conclude according to the variable under study, productions were taken in tons of corn, sorghum and beans in three different regions of the country and the following was found in the northern zone: 500, 400, 200, respectively, for the central region the following 700,500,500 were found and for the southern region the following 1000,700,300.arrow_forwardIn a very simple computer chip, 8 wires go from one transistor to a second transistor. For the computer to function, instructions must be sent between these 2 transistors. In how many ways can 4 different instructions be sent between the 2 transistors if no 2 instructions can be sent along the same wire?arrow_forwardAsap. In 10 min. Else i will Dislike. Plzarrow_forward
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