 Chapter 1: REVIEW OF WHOLE NUMBERS AND INTEGERS
 Chapter 11: PLACE VALUE AND OUR NUMBER SYSTEM
 Chapter 12: OPERATIONS WITH WHOLE NUMBERS AND INTEGERS
 Chapter 10: PAYROLL
 Chapter 101: GROSS PAY
 Chapter 102: PAYROLL DEDUCTIONS
 Chapter 103: THE EMPLOYERS PAYROLL TAXES
 Chapter 11: SIMPLE INTEREST AND SIMPLE DISCOUNT
 Chapter 111: THE SIMPLE INTEREST FORMULA
 Chapter 112: ORDINARY AND EXACT INTEREST
 Chapter 113: PROMISSORY NOTES
 Chapter 12: CONSUMER CREDIT
 Chapter 121: INSTALLMENT LOANS AND CLOSEDEND CREDIT
 Chapter 122: PAYING A LOAN BEFORE IT IS DUE: THE RULE OF 78
 Chapter 123: OPENEND CREDIT
 Chapter 13: COMPOUND INTEREST, FUTURE VALUE, AND PRESENT VALUE
 Chapter 131: COMPOUND INTEREST AND FUTURE VALUE
 Chapter 132: PRESENT VALUE
 Chapter 14: ANNUITIES AND SINKING FUNDS
 Chapter 141: FUTURE VALUE OF AN ANNUITY
 Chapter 142: SINKING FUNDS AND THE PRESENT VALUE OF AN ANNUITY
 Chapter 15: BUILDING WEALTH THROUGH INVESTMENTS
 Chapter 151: STOCKS
 Chapter 152: BONDS
 Chapter 153: MUTUAL FUNDS
 Chapter 16: MORTGAGES
 Chapter 161: MORTGAGE PAYMENTS
 Chapter 162: AMORTIZATION SCHEDULES AND QUALIFYING RATIOS
 Chapter 17: DEPRECIATION
 Chapter 171: DEPRECIATION METHODS FOR FINANCIAL STATEMENT REPORTING
 Chapter 172: DEPRECIATION METHODS FOR IRS REPORTING
 Chapter 18: INVENTORY
 Chapter 181: INVENTORY
 Chapter 182: TURNOVER AND OVERHEAD
 Chapter 19: INSURANCE
 Chapter 191: LIFE INSURANCE
 Chapter 192: PROPERTY INSURANCE
 Chapter 193: MOTOR VEHICLE INSURANCE
 Chapter 2: REVIEW OF FRACTIONS
 Chapter 21: FRACTIONS
 Chapter 22: ADDING AND SUBTRACTING FRACTIONS
 Chapter 23: MULTIPLYING AND DIVIDING FRACTIONS
 Chapter 20: TAXES
 Chapter 201: SALES TAX AND EXCISE TAX
 Chapter 202: PROPERTY TAX
 Chapter 203: INCOME TAXES
 Chapter 21: FINANCIAL STATEMENTS
 Chapter 211: THE BALANCE SHEET
 Chapter 212: INCOME STATEMENTS
 Chapter 213: FINANCIAL STATEMENT RATIOS
 Chapter 3: DECIMALS
 Chapter 31: DECIMALS AND THE PLACEVALUE SYSTEM
 Chapter 32: OPERATIONS WITH DECIMALS
 Chapter 33: DECIMAL AND FRACTION CONVERSIONS
 Chapter 4: BANKING
 Chapter 41: CHECKING ACCOUNT TRANSACTIONS
 Chapter 42: BANK STATEMENTS
 Chapter 5: EQUATIONS
 Chapter 51: EQUATIONS
 Chapter 52: USING EQUATIONS TO SOLVE PROBLEMS
 Chapter 53: FORMULAS
 Chapter 6: PERCENTS
 Chapter 61: PERCENT EQUIVALENTS
 Chapter 62: SOLVING PERCENTAGE PROBLEMS
 Chapter 63: INCREASES AND DECREASES
 Chapter 7: BUSINESS STATISTICS
 Chapter 71: GRAPHS AND CHARTS
 Chapter 72: MEASURES OF CENTRAL TENDENCY
 Chapter 73: MEASURES OF DISPERSION
 Chapter 8: TRADE AND CASH DISCOUNTS
 Chapter 81: SINGLE TRADE DISCOUNTS
 Chapter 82: TRADE DISCOUNT SERIES
 Chapter 83: CASH DISCOUNTS AND SALES TERMS
 Chapter 9: MARKUP AND MARKDOWN
 Chapter 91: MARKUP BASED ON COST
 Chapter 92: MARKUP BASED ON SELLING PRICE AND MARKUP COMPARISONS
 Chapter 93: MARKDOWN, SERIES OF MARKDOWNS, AND PERISHABLES
Business Math, 9th Edition  Solutions by Chapter
Full solutions for Business Math,  9th Edition
ISBN: 9780135108178
Business Math,  9th Edition  Solutions by Chapter
Get Full SolutionsThis textbook survival guide was created for the textbook: Business Math, , edition: 9. The full stepbystep solution to problem in Business Math, were answered by Patricia, our top Math solution expert on 03/08/18, 08:36PM. Business Math, was written by Patricia and is associated to the ISBN: 9780135108178. Since problems from 77 chapters in Business Math, have been answered, more than 8039 students have viewed full stepbystep answer. This expansive textbook survival guide covers the following chapters: 77.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Column space C (A) =
space of all combinations of the columns of A.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Solvable system Ax = b.
The right side b is in the column space of A.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.