Thomas' Calculus and Linear Algebra and Its Applications Package for the Georgia Institute of Technology, 1/e
5th Edition
ISBN: 9781323132098
Author: Thomas, Lay
Publisher: PEARSON C
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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
Thomas' Calculus and Linear Algebra and Its Applications Package for the Georgia Institute of Technology, 1/e
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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- A diesel engine uses Type A filter and high-grade lubricating oil costing P5.50 per liter. With this filter, the oil and the filter have to be changed every 500 hours of operation, and 5 liters of coil have to be added every 100 hours. This filter costs P148 a piece. Eighty liters of coil fill the engine. Another type, filter B, costing P120 may be used with a lower grade of oil costing P4.80 per liter. However, if this filter is used, the oil and filter have to be changed every 300 hours, and 10 liters are added after each 150 hours the engine is used. Which type of filter and oil would you recommend?arrow_forwardExplain why A and -A always have the same reduced echelon form R.arrow_forwardImagine that you took a tennis racket and tennis ball out to a Golf Course. Is it possible to stand at the start of one of the holes and get a hole in one with the tennis ball and racket?arrow_forward
- Suppose 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_forwardConsider a block of wood in the shape of a cube, 3 feet on an edge. It is desired to cut the cube into 27 smaller cubes, 1 foot on an edge. One way to do this is to make 6 cuts, 2 in each direction, while keeping the cube in one block. Is it possible to use fewer cuts if the pieces can be rearranged between cuts?arrow_forwardA bathroom tub will fill in 15 minutes with both faucets open and the stopper in place. With both faucets closed and the stopper removed, the tub will empty in 20 minutes. How long will it take for the tub to fill if both faucets are open and the stopper is removed?arrow_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_forwardLeah Peschel is the bottling department manager for a bottling company that produces various soft drinks and juices. The company uses two different machines from different manufacturers to fill the bottles of its popular cola. Leah periodically verifies that the amount of cola in the bottles filled by Machine 1 is the same as the amount in the bottles filled by Machine 2. The manufacturers calibrated the machines at the time of installation and provided that information to the bottling company. Leah knows that the population standard deviation for Machine 1 is 0.021 ounce and the population standard deviation for Machine 2 is 0.019 ounce. Leah randomly selects samples of bottles filled by Machine 1 and Machine 2. The amount of cola in each bottle is recorded for both samples, and the results are shown in the table. Let α=0.05, μ1 be the population mean amount of cola in bottles filled by Machine 1, and μ2 be the population mean amount of cola in bottles filled by Machine 2. The test…arrow_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_forward
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