- 8-3.1: How much was the cash discount?
- 8-3.2: What is the net amount Ken will pay?
- 8-3.3: How much would Jim pay 7 days after the invoice date? Jim Bettendor...
- 8-3.4: How much would Jim pay 15 days after the invoice date?
- 8-3.5: Find the amount due if the bill is paid on or before April 16. Alex...
- 8-3.6: What amount is due if the bill is paid on or between April 17 and A...
- 8-3.7: What amount is due if Alexa pays on or between April 22 and May 6?
- 8-3.8: If Alexa pays on or after May 7, how much must she pay?
- 8-3.9: How much would Jim pay 25 days after the invoice date?
- 8-3.10: If the net price of the invoice is $1,296.45, how much cash discoun...
- 8-3.11: What is the net amount Chloe will need to pay?
- 8-3.12: Charlene Watson received a bill for $800 dated July 5, with sales t...
- 8-3.13: Ruby Wossum received an invoice for $798.53 dated February 27 with ...
- 8-3.14: An invoice for a camcorder that cost $1,250 is dated August 1, with...
- 8-3.15: Sylvester Young received an invoice for a leaf blower for $493 date...
- 8-3.16: How much is due if the bill is paid October 27? An invoice for $900...
- 8-3.17: How much is due if the bill is paid on November 3?
- 8-3.18: Sharron Smith is paying an invoice showing a total of $5,835 and da...
- 8-3.19: Kariem Salaam is directing the accounts payable office and is train...
- 8-3.20: Clordia Patterson-Nathanial handles all accounts payable for her co...
- 8-3.21: David Wimberly has an invoice for a complete computer system for $3...
- 8-3.22: Lacy Dodd has been directed to pay all invoices in time to receive ...
- 8-3.23: Dorothy Rogers Bicycle Shop received a shipment of bicycles via tru...
- 8-3.24: Joseph Denatti is negotiating the freight payment for a large shipm...
- 8-3.25: Charlotte Oakley receives a shipment with the bill of lading marked...
- 8-3.26: Explain the difference in the freight terms FOB shipping point and ...
Solutions for Chapter 8-3: CASH DISCOUNTS AND SALES TERMS
Full solutions for Business Math, | 9th Edition
Tv = Av + Vo = linear transformation plus shift.
Column space C (A) =
space of all combinations of the columns of A.
Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.
Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).
A = S-1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k S-I.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n - 1)/2 edges between nodes. A tree has only n - 1 edges and no closed loops.
Hilbert matrix hilb(n).
Entries HU = 1/(i + j -1) = Jd X i- 1 xj-1dx. Positive definite but extremely small Amin and large condition number: H is ill-conditioned.
Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b - Ax is orthogonal to all columns of A.
Left inverse A+.
If A has full column rank n, then A+ = (AT A)-I AT has A+ A = In.
Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.
Length II x II.
Square root of x T x (Pythagoras in n dimensions).
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.
= Xl (column 1) + ... + xn(column n) = combination of columns.
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.
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.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.
Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.
Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.
Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.
Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.