 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 , our top Math solution expert on 03/08/18, 08:36PM. Business Math, was written by and is associated to the ISBN: 9780135108178. Since problems from 77 chapters in Business Math, have been answered, more than 10788 students have viewed full stepbystep answer. This expansive textbook survival guide covers the following chapters: 77.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

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 .

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)ยท(b  Ax) = o.

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

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.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

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

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.