 16.1: In 112, evaluate each expression.6!
 16.2: In 112, evaluate each expression.5P5
 16.3: In 112, evaluate each expression.5C5
 16.4: In 112, evaluate each expression.8P6
 16.5: In 112, evaluate each expression.8C6
 16.6: In 112, evaluate each expression.8C0
 16.7: In 112, evaluate each expression.8C8
 16.8: In 112, evaluate each expression.106R
 16.9: In 112, evaluate each expression.5049R
 16.10: In 112, evaluate each expression.12!10!
 16.11: In 112, evaluate each expression.12!5! 7!
 16.12: In 112, evaluate each expression.40C39
 16.13: In how many different ways can 8 students choose a seat if there ar...
 16.14: In how many different ways can 8 students choose a seat if there ar...
 16.15: Randy is trying to arrange the letters T, R, O, E, E, M to form dis...
 16.16: A buffet offers six flavors of ice cream, four different syrups, an...
 16.17: A dish contains eight different candies. How many different choices...
 16.18: At a carnival, the probability that a person will win a prize at th...
 16.19: A fair coin is tossed 12 times. What is the probability of the coin...
 16.20: A convenience store makes over $200 approximately 75% of the days i...
 16.21: The math portion of the SAT is designed so that the scores are norm...
 16.22: In 2225, write the expansion of each binomial.x + y)
 16.23: In 2225, write the expansion of each binomial.2a 1 1)7
 16.24: In 2225, write the expansion of each binomial.3 2 x)6
 16.25: In 2225, write the expansion of each binomial.A b 2 1b B8
 16.26: When i = , express (1 1 i)5 in a 1 bi form.
 16.27: Write in simplest form the fourth term of (x 2 y)9
 16.28: Write in simplest form the seventh term of (a 1 3)10.
 16.29: Write in simplest form the middle term of (2x 2 1)12.
Solutions for Chapter 16: PROBABILITY AND THE BINOMIAL THEOREM
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 16: PROBABILITY AND THE BINOMIAL THEOREM
Get Full SolutionsThis textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1. Amsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 16: PROBABILITY AND THE BINOMIAL THEOREM includes 29 full stepbystep solutions. Since 29 problems in chapter 16: PROBABILITY AND THE BINOMIAL THEOREM have been answered, more than 29357 students have viewed full stepbystep solutions from this chapter.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

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

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

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

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

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

Dimension of vector space
dim(V) = number of vectors in any basis for V.

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.

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.

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.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

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

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

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).

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

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 picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

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

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.