 8.2.1: In 12, find the gross income, the adjusted gross income, and the ta...
 8.2.2: In 12, find the gross income, the adjusted gross income, and the ta...
 8.2.3: In 34, find the gross income, the adjusted gross income, and the ta...
 8.2.4: In 34, find the gross income, the adjusted gross income, and the ta...
 8.2.5: In 514, use the 2012 marginal tax rates in Table 8.1 on page 501 to...
 8.2.6: In 514, use the 2012 marginal tax rates in Table 8.1 on page 501 to...
 8.2.7: In 514, use the 2012 marginal tax rates in Table 8.1 on page 501 to...
 8.2.8: In 514, use the 2012 marginal tax rates in Table 8.1 on page 501 to...
 8.2.9: In 514, use the 2012 marginal tax rates in Table 8.1 on page 501 to...
 8.2.10: In 514, use the 2012 marginal tax rates in Table 8.1 on page 501 to...
 8.2.11: In 514, use the 2012 marginal tax rates in Table 8.1 on page 501 to...
 8.2.12: In 514, use the 2012 marginal tax rates in Table 8.1 on page 501 to...
 8.2.13: In 514, use the 2012 marginal tax rates in Table 8.1 on page 501 to...
 8.2.14: In 514, use the 2012 marginal tax rates in Table 8.1 on page 501 to...
 8.2.15: In 1518, use the 2012 marginal tax rates in Table 8.1 on page 501 t...
 8.2.16: In 1518, use the 2012 marginal tax rates in Table 8.1 on page 501 t...
 8.2.17: In 1518, use the 2012 marginal tax rates in Table 8.1 on page 501 t...
 8.2.18: In 1518, use the 2012 marginal tax rates in Table 8.1 on page 501 t...
 8.2.19: In 1924, use the 2012 FICA tax rates in Table 8.2 on page 503.If yo...
 8.2.20: In 1924, use the 2012 FICA tax rates in Table 8.2 on page 503.If yo...
 8.2.21: In 1924, use the 2012 FICA tax rates in Table 8.2 on page 503.If yo...
 8.2.22: In 1924, use the 2012 FICA tax rates in Table 8.2 on page 503.If yo...
 8.2.23: In 1924, use the 2012 FICA tax rates in Table 8.2 on page 503.To he...
 8.2.24: In 1924, use the 2012 FICA tax rates in Table 8.2 on page 503.To he...
 8.2.25: You decide to work parttime at a local supermarket. The job pays $...
 8.2.26: You decide to work parttime at a local veterinary hospital. The jo...
 8.2.27: What is income tax?
 8.2.28: What is gross income?
 8.2.29: What is adjusted gross income?
 8.2.30: What are exemptions?
 8.2.31: What are deductions?
 8.2.32: Under what circumstances should taxpayers itemize deductions?
 8.2.33: How is taxable income determined?
 8.2.34: What are tax credits?
 8.2.35: What is the difference between a tax credit and a tax deduction?
 8.2.36: What are FICA taxes?
 8.2.37: How do you determine your net pay?
 8.2.38: Make Sense? In 3842, determine whether each statement makes sense o...
 8.2.39: Make Sense? In 3842, determine whether each statement makes sense o...
 8.2.40: Make Sense? In 3842, determine whether each statement makes sense o...
 8.2.41: Make Sense? In 3842, determine whether each statement makes sense o...
 8.2.42: Make Sense? In 3842, determine whether each statement makes sense o...
 8.2.43: Suppose you are in the 10% tax bracket. As a college student, you c...
 8.2.44: A common complaint about income tax is I cant afford to work more b...
 8.2.45: Because of the mortgage interest tax deduction, is it possible to s...
 8.2.46: The following topics are appropriate for either individual or group...
 8.2.47: The following topics are appropriate for either individual or group...
 8.2.48: The following topics are appropriate for either individual or group...
 8.2.49: The following topics are appropriate for either individual or group...
Solutions for Chapter 8.2: Income Tax
Full solutions for Thinking Mathematically  6th Edition
ISBN: 9780321867322
Solutions for Chapter 8.2: Income Tax
Get Full SolutionsThinking Mathematically was written by and is associated to the ISBN: 9780321867322. Chapter 8.2: Income Tax includes 49 full stepbystep solutions. This textbook survival guide was created for the textbook: Thinking Mathematically, edition: 6. Since 49 problems in chapter 8.2: Income Tax have been answered, more than 70953 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

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.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

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!).

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

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 .

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

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.

Outer product uv T
= column times row = rank one matrix.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

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.

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

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.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.