 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 12967 students have viewed full stepbystep answer. This expansive textbook survival guide covers the following chapters: 77.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

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).

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

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].

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!).

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Iterative method.
A sequence of steps intended to approach the desired solution.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.