 6.1: Write the decimal as a percent 0.23
 6.2: Write the decimal as a percent 0.82
 6.3: Write the decimal as a percent 0.03
 6.4: Write the decimal as a percent 0.34
 6.5: Write the decimal as a percent 0.601
 6.6: Write the decimal as a percent 1
 6.7: Write the decimal as a percent 3
 6.8: Write the decimal as a percent 0.37
 6.9: Write the decimal as a percent 0.2
 6.10: Write the decimal as a percent 4
 6.11: Write the fraction or mixed number as a percent. Round to the neare...
 6.12: Write the fraction or mixed number as a percent. Round to the neare...
 6.13: Write the fraction or mixed number as a percent. Round to the neare...
 6.14: Write the fraction or mixed number as a percent. Round to the neare...
 6.15: Write the fraction or mixed number as a percent. Round to the neare...
 6.16: Write the fraction or mixed number as a percent. Round to the neare...
 6.17: Write the percent as a decimal 0.25%
 6.18: Write the percent as a decimal 98%
 6.19: Write the percent as a decimal 256%
 6.20: Write the percent as a decimal 91.70%
 6.21: Write the percent as a decimal 0.50%
 6.22: Write the percent as a decimal 6%
 6.23: Write the percent as a decimal 10%
 6.24: Write the percent as a decimal 6%
 6.25: Write the percent as a decimal 89%
 6.26: Write the percent as a decimal 45%
 6.27: Write the percent as a decimal 225%
 6.28: 3313% ___ ____
 6.29: ___ ____ 0.125
 6.30: ___ ____ 0.8
 6.31: Find P, R, or B using the percentage formula or one of its forms. R...
 6.32: Find P, R, or B using the percentage formula or one of its forms. R...
 6.33: Find P, R, or B using the percentage formula or one of its forms. R...
 6.34: Find P, R, or B using the percentage formula or one of its forms. R...
 6.35: Find P, R, or B using the percentage formula or one of its forms. R...
 6.36: Find P, R, or B using the percentage formula or one of its forms. R...
 6.37: Find P, R, or B using the percentage formula or one of its forms. R...
 6.38: Find P, R, or B using the percentage formula or one of its forms. R...
 6.39: Jaime McMahan received a 7% pay increase. If he was earning $2,418 ...
 6.40: Eighty percent of one stores customers paid with credit cards. Fort...
 6.41: Seventy percent of a towns population voted in an election. If 1,58...
 6.42: Thirtyseven of 50 shareholders attended a meeting. What percent of...
 6.43: The financial officer allows $3,400 for supplies in the annual budg...
 6.44: Chloe Denleys rent of $940 per month was increased by 8%. What is h...
 6.45: The price of a wireless phone increased by 14% to $165. What was th...
 6.46: Global wind energy had a record growth in a recent year, achieving ...
Solutions for Chapter 6: PERCENTS
Full solutions for Business Math,  9th Edition
ISBN: 9780135108178
Solutions for Chapter 6: PERCENTS
Get Full SolutionsThis textbook survival guide was created for the textbook: Business Math, , edition: 9. Chapter 6: PERCENTS includes 46 full stepbystep solutions. Business Math, was written by and is associated to the ISBN: 9780135108178. Since 46 problems in chapter 6: PERCENTS have been answered, more than 19344 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

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!

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.)

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

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.

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].

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

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

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

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

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij 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.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

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

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).