Contemporary Mathematics for Business & Consumers
8th Edition
ISBN: 9781305886803
Author: Brechner
Publisher: Cengage
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 15, Problem 8AT
For the month of January. Consolidated Engine Pans. Inc. had the following financial information: merchandise inventory. January 1, $322,000; merchandise inventory, January 31, $316,400; gross purchases. $243,460; purchase returns and allowances. $26,880; and freight in, $3,430.
a. What are Consolidated's goods available for sale?
b. What is the cost of goods sold for January?
c. If net sales were $389,450, what was the gross margin for January?
d. If total operating expenses were $179,800. what was the net profit or loss?
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
5. (a) State the Residue Theorem. Your answer should include all the conditions required
for the theorem to hold.
(4 marks)
(b) Let y be the square contour with vertices at -3, -3i, 3 and 3i, described in the
anti-clockwise direction. Evaluate
に
dz.
You must check all of the conditions of any results that you use.
(5 marks)
(c) Evaluate
L
You must check all of the conditions of any results that you use.
ཙ
x sin(Tx)
x²+2x+5
da.
(11 marks)
3. (a) Lety: [a, b] C be a contour. Let L(y) denote the length of y. Give a formula
for L(y).
(1 mark)
(b) Let UCC be open. Let f: U→C be continuous. Let y: [a,b] → U be a
contour. Suppose there exists a finite real number M such that |f(z)| < M for
all z in the image of y. Prove that
<
||, f(z)dz| ≤ ML(y).
(3 marks)
(c) State and prove Liouville's theorem. You may use Cauchy's integral formula without
proof.
(d) Let R0. Let w € C. Let
(10 marks)
U = { z Є C : | z − w| < R} .
Let f UC be a holomorphic function such that
0 < |ƒ(w)| < |f(z)|
for all z Є U. Show, using the local maximum modulus principle, that f is constant.
(6 marks)
3. (a) Let A be an algebra. Define the notion of an A-module M. When is a module M
a simple module?
(b) State and prove Schur's Lemma for simple modules.
(c) Let AM(K) and M = K" the natural A-module.
(i) Show that M is a simple K-module.
(ii) Prove that if ƒ € Endд(M) then ƒ can be written as f(m) = am, where a
is a matrix in the centre of M, (K).
[Recall that the centre, Z(M,(K)) == {a Mn(K) | ab
M,,(K)}.]
= ba for all bЄ
(iii) Explain briefly why this means End₁(M) K, assuming that Z(M,,(K))~
K as K-algebras.
Is this consistent with Schur's lemma?
Chapter 15 Solutions
Contemporary Mathematics for Business & Consumers
Ch. 15.I - Use the following financial information to prepare...Ch. 15.I - Prob. 2TIECh. 15.I - Prob. 3TIECh. 15.I - Prob. 1RECh. 15.I - Prob. 2RECh. 15.I - Prob. 3RECh. 15.I - Prob. 4RECh. 15.I - Prob. 5RECh. 15.I - Prob. 6RECh. 15.I - Calculate the following values according to the...
Ch. 15.I - Prob. 8RECh. 15.I - Calculate the missing balance sheet items for...Ch. 15.I - Prob. 10RECh. 15.I - Prob. 11RECh. 15.I - Prob. 12RECh. 15.I - Prob. 13RECh. 15.I - For the following balance sheet items, check the...Ch. 15.I - For the following balance sheet items, check the...Ch. 15.I - Prob. 16RECh. 15.I - Prob. 17RECh. 15.I - Prob. 18RECh. 15.I - Prob. 19RECh. 15.I - Prob. 20RECh. 15.I - Prob. 21RECh. 15.I - For the following balance sheet items, check the...Ch. 15.I - Prob. 23RECh. 15.I - Prob. 24RECh. 15.I - Prob. 25RECh. 15.I - For the following balance sheet items, check the...Ch. 15.I - Prob. 27RECh. 15.I - Prob. 28RECh. 15.I - Prob. 29RECh. 15.I - Prob. 30RECh. 15.I - Prob. 31RECh. 15.I - Prob. 32RECh. 15.I - Prob. 33RECh. 15.I - Prepare the following statements on separate...Ch. 15.I - a. Use the following financial information to...Ch. 15.II - Prob. 4TIECh. 15.II - Prob. 5TIECh. 15.II - Prob. 6TIECh. 15.II - Prob. 1RECh. 15.II - Prob. 2RECh. 15.II - Prob. 3RECh. 15.II - Prob. 4RECh. 15.II - Calculate the missing information based on the...Ch. 15.II - Prob. 6RECh. 15.II - Prob. 7RECh. 15.II - Prob. 8RECh. 15.II - Prob. 9RECh. 15.II - Prob. 10RECh. 15.II - Prob. 11RECh. 15.II - 12. For the third quarter. Micro Tech had gross...Ch. 15.II - For August, Island Traders, Inc. had the following...Ch. 15.II - Prepare the following statements on separate...Ch. 15.II - Prepare the following statements on separate...Ch. 15.III - Use the balance sheet and income statement on...Ch. 15.III - Prob. 8TIECh. 15.III - Prob. 1RECh. 15.III - Prob. 2RECh. 15.III - Prob. 3RECh. 15.III - Prob. 4RECh. 15.III - Prob. 5RECh. 15.III - Prob. 6RECh. 15.III - Prob. 7RECh. 15.III - Prob. 8RECh. 15.III - Prob. 9RECh. 15.III - Prob. 10RECh. 15.III - Prob. 11RECh. 15.III - Prob. 12RECh. 15.III - Prob. 13RECh. 15.III - Prob. 14RECh. 15.III - Calculate the average inventory and inventory...Ch. 15.III - Prob. 16RECh. 15.III - Prob. 17RECh. 15.III - Prob. 18RECh. 15.III - Prob. 19RECh. 15.III - Prob. 20RECh. 15.III - Prob. 21RECh. 15.III - Prob. 22RECh. 15.III - Prob. 23RECh. 15.III - Prob. 24RECh. 15.III - Calculate the gross and net profits and the two...Ch. 15.III - Prob. 26RECh. 15.III - Prob. 27RECh. 15.III - Prob. 28RECh. 15.III - Prob. 29RECh. 15.III - Prob. 30RECh. 15.III - Prob. 31RECh. 15.III - Prob. 32RECh. 15.III - Prob. 33RECh. 15 - 1. In accounting, economic resources owned by a...Ch. 15 - 2. The financial statement that illustrates the...Ch. 15 - 3. The balance sheet is a visual presentation of...Ch. 15 - Prob. 4CRCh. 15 - 5. A financial statement prepared with the data...Ch. 15 - Prob. 6CRCh. 15 - Prob. 7CRCh. 15 - Prob. 8CRCh. 15 - Prob. 9CRCh. 15 - Prob. 10CRCh. 15 - Prob. 11CRCh. 15 - Prob. 12CRCh. 15 - Prob. 13CRCh. 15 - Prob. 14CRCh. 15 - Prob. 1ATCh. 15 - Prob. 2ATCh. 15 - Prob. 3ATCh. 15 - Prob. 4ATCh. 15 - a. Use the following financial information to...Ch. 15 - a. Use the following financial information to...Ch. 15 - For the second quarter. Evergreen Plant Nursery...Ch. 15 - 8. For the month of January. Consolidated Engine...Ch. 15 - Prob. 9ATCh. 15 - a. Use the following financial information to...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - As the accounting manager of Spring Creek...Ch. 15 - Prob. 22ATCh. 15 - Prob. 23ATCh. 15 - 24. From the following consolidated statements of...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- (a) State, without proof, Cauchy's theorem, Cauchy's integral formula and Cauchy's integral formula for derivatives. Your answer should include all the conditions required for the results to hold. (8 marks) (b) Let U{z EC: |z| -1}. Let 12 be the triangular contour with vertices at 0, 2-2 and 2+2i, parametrized in the anticlockwise direction. Calculate dz. You must check the conditions of any results you use. (d) Let U C. Calculate Liz-1ym dz, (z - 1) 10 (5 marks) where 2 is the same as the previous part. You must check the conditions of any results you use. (4 marks)arrow_forward(a) Suppose a function f: C→C has an isolated singularity at wЄ C. State what it means for this singularity to be a pole of order k. (2 marks) (b) Let f have a pole of order k at wЄ C. Prove that the residue of f at w is given by 1 res (f, w): = Z dk (k-1)! >wdzk−1 lim - [(z — w)* f(z)] . (5 marks) (c) Using the previous part, find the singularity of the function 9(z) = COS(πZ) e² (z - 1)²' classify it and calculate its residue. (5 marks) (d) Let g(x)=sin(211). Find the residue of g at z = 1. (3 marks) (e) Classify the singularity of cot(z) h(z) = Z at the origin. (5 marks)arrow_forward1. Let z = x+iy with x, y Є R. Let f(z) = u(x, y) + iv(x, y) where u(x, y), v(x, y): R² → R. (a) Suppose that f is complex differentiable. State the Cauchy-Riemann equations satisfied by the functions u(x, y) and v(x,y). (b) State what it means for the function (2 mark) u(x, y): R² → R to be a harmonic function. (3 marks) (c) Show that the function u(x, y) = 3x²y - y³ +2 is harmonic. (d) Find a harmonic conjugate of u(x, y). (6 marks) (9 marks)arrow_forward
- Please could you provide a step by step solutions to this question and explain every step.arrow_forwardCould you please help me with question 2bii. If possible could you explain how you found the bounds of the integral by using a graph of the region of integration. Thanksarrow_forwardLet A be a vector space with basis 1, a, b. Which (if any) of the following rules turn A into an algebra? (You may assume that 1 is a unit.) (i) a² = a, b² = ab = ba = 0. (ii) a²=b, b² = ab = ba = 0. (iii) a²=b, b² = b, ab = ba = 0.arrow_forward
- No chatgpt pls will upvotearrow_forward= 1. Show (a) Let G = Z/nZ be a cyclic group, so G = {1, 9, 92,...,g" } with g": that the group algebra KG has a presentation KG = K(X)/(X” — 1). (b) Let A = K[X] be the algebra of polynomials in X. Let V be the A-module with vector space K2 and where the action of X is given by the matrix Compute End(V) in the cases (i) x = p, (ii) xμl. (67) · (c) If M and N are submodules of a module L, prove that there is an isomorphism M/MON (M+N)/N. (The Second Isomorphism Theorem for modules.) You may assume that MON is a submodule of M, M + N is a submodule of L and the First Isomorphism Theorem for modules.arrow_forward(a) Define the notion of an ideal I in an algebra A. Define the product on the quotient algebra A/I, and show that it is well-defined. (b) If I is an ideal in A and S is a subalgebra of A, show that S + I is a subalgebra of A and that SnI is an ideal in S. (c) Let A be the subset of M3 (K) given by matrices of the form a b 0 a 0 00 d Show that A is a subalgebra of M3(K). Ꮖ Compute the ideal I of A generated by the element and show that A/I K as algebras, where 0 1 0 x = 0 0 0 001arrow_forward
- (a) Let HI be the algebra of quaternions. Write out the multiplication table for 1, i, j, k. Define the notion of a pure quaternion, and the absolute value of a quaternion. Show that if p is a pure quaternion, then p² = -|p|². (b) Define the notion of an (associative) algebra. (c) Let A be a vector space with basis 1, a, b. Which (if any) of the following rules turn A into an algebra? (You may assume that 1 is a unit.) (i) a² = a, b²=ab = ba 0. (ii) a² (iii) a² = b, b² = abba = 0. = b, b² = b, ab = ba = 0. (d) Let u1, 2 and 3 be in the Temperley-Lieb algebra TL4(8). ገ 12 13 Compute (u3+ Augu2)² where A EK and hence find a non-zero x € TL4 (8) such that ² = 0.arrow_forwardQ1: Solve the system x + x = t², x(0) = (9)arrow_forwardCo Given show that Solution Take home Су-15 1994 +19 09/2 4 =a log суто - 1092 ж = a-1 2+1+8 AI | SHOT ON S4 INFINIX CAMERAarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Use of ALGEBRA in REAL LIFE; Author: Fast and Easy Maths !;https://www.youtube.com/watch?v=9_PbWFpvkDc;License: Standard YouTube License, CC-BY
Compound Interest Formula Explained, Investment, Monthly & Continuously, Word Problems, Algebra; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=P182Abv3fOk;License: Standard YouTube License, CC-BY
Applications of Algebra (Digit, Age, Work, Clock, Mixture and Rate Problems); Author: EngineerProf PH;https://www.youtube.com/watch?v=Y8aJ_wYCS2g;License: Standard YouTube License, CC-BY