 124.1: BUSINESS For Exercises 13, use the following information. Mr. Salye...
 124.2: BUSINESS For Exercises 13, use the following information. Mr. Salye...
 124.3: BUSINESS For Exercises 13, use the following information. Mr. Salye...
 124.4: A bin contains colored chips as shown in the table. Find each proba...
 124.5: A bin contains colored chips as shown in the table. Find each proba...
 124.6: A bin contains colored chips as shown in the table. Find each proba...
 124.7: A bin contains colored chips as shown in the table. Find each proba...
 124.8: A student is selected at random from a group of 12 male and 12 fema...
 124.9: A student is selected at random from a group of 12 male and 12 fema...
 124.10: A student is selected at random from a group of 12 male and 12 fema...
 124.11: A student is selected at random from a group of 12 male and 12 fema...
 124.12: STANDARDIZED TEST PRACTICE At the basketball game, 50% of the fans ...
 124.13: A die is rolled and a spinner like the one at the right is spun. Fi...
 124.14: A die is rolled and a spinner like the one at the right is spun. Fi...
 124.15: A die is rolled and a spinner like the one at the right is spun. Fi...
 124.16: A die is rolled and a spinner like the one at the right is spun. Fi...
 124.17: BIOLOGY For Exercises 1719, use the diagram and following informati...
 124.18: BIOLOGY For Exercises 1719, use the diagram and following informati...
 124.19: BIOLOGY For Exercises 1719, use the diagram and following informati...
 124.20: SAFETY For Exercises 2023, use the following information. A carbon ...
 124.21: SAFETY For Exercises 2023, use the following information. A carbon ...
 124.22: SAFETY For Exercises 2023, use the following information. A carbon ...
 124.23: SAFETY For Exercises 2023, use the following information. A carbon ...
 124.24: A bag contains 2 red, 6 blue, 7 yellow, and 3 orange marbles. Once ...
 124.25: A bag contains 2 red, 6 blue, 7 yellow, and 3 orange marbles. Once ...
 124.26: A bag contains 2 red, 6 blue, 7 yellow, and 3 orange marbles. Once ...
 124.27: A bag contains 2 red, 6 blue, 7 yellow, and 3 orange marbles. Once ...
 124.28: ECONOMICS For Exercises 2830, use the table below that compares the...
 124.29: ECONOMICS For Exercises 2830, use the table below that compares the...
 124.30: ECONOMICS For Exercises 2830, use the table below that compares the...
 124.31: Raffle tickets numbered 1 through 30 are placed in a box. Tickets f...
 124.32: Raffle tickets numbered 1 through 30 are placed in a box. Tickets f...
 124.33: Raffle tickets numbered 1 through 30 are placed in a box. Tickets f...
 124.34: Raffle tickets numbered 1 through 30 are placed in a box. Tickets f...
 124.35: GEOMETRY For Exercises 3537, use the figure and the following infor...
 124.36: GEOMETRY For Exercises 3537, use the figure and the following infor...
 124.37: GEOMETRY For Exercises 3537, use the figure and the following infor...
 124.38: RESEARCH Use the Internet or other reference to investigate various...
 124.39: A dart is thrown at a dartboard like the one at the right. If the d...
 124.40: A dart is thrown at a dartboard like the one at the right. If the d...
 124.41: A dart is thrown at a dartboard like the one at the right. If the d...
 124.42: A dart is thrown at a dartboard like the one at the right. If the d...
 124.43: OPEN ENDED Explain how dependent events are different from independ...
 124.44: FIND THE ERROR On the school debate team, 6 of the 14 girls are sen...
 124.45: REASONING Find a counterexample for the following statement. If two...
 124.46: CHALLENGE For Exercises 4649, use the following information. A samp...
 124.47: CHALLENGE For Exercises 4649, use the following information. A samp...
 124.48: CHALLENGE For Exercises 4649, use the following information. A samp...
 124.49: CHALLENGE For Exercises 4649, use the following information. A samp...
 124.50: Writing in Math Refer to the information on page 663 to explain how...
 124.51: A bag contains 8 red marbles, 5 blue marbles, 4 green marbles, and ...
 124.52: REVIEW The sum of a number x and 12 is 64. Which equation shows th...
 124.53: CIVICS For Exercises 53 and 54, use the following information. Stra...
 124.54: CIVICS For Exercises 53 and 54, use the following information. Stra...
 124.55: BUSINESS A real estate developer built a strip mall with seven diff...
 124.56: Find each quotient. Assume that no denominator has a value of 0. _s...
 124.57: Find each quotient. Assume that no denominator has a value of 0. 2m...
 124.58: Simplify. 45
 124.59: Simplify. 128
 124.60: Simplify. 40b4
 124.61: Simplify. 120a3b
 124.62: Simplify. 3 7 6 2
 124.63: Simplify. 3 (3 + 6
 124.64: PREREQUISITE SKILL Express each fraction as a decimal. Round to the...
 124.65: PREREQUISITE SKILL Express each fraction as a decimal. Round to the...
 124.66: PREREQUISITE SKILL Express each fraction as a decimal. Round to the...
 124.67: PREREQUISITE SKILL Express each fraction as a decimal. Round to the...
 124.68: PREREQUISITE SKILL Express each fraction as a decimal. Round to the...
 124.69: PREREQUISITE SKILL Express each fraction as a decimal. Round to the...
 124.70: PREREQUISITE SKILL Express each fraction as a decimal. Round to the...
 124.71: PREREQUISITE SKILL Express each fraction as a decimal. Round to the...
Solutions for Chapter 124: Probability of Compound Events
Full solutions for Algebra 1, Student Edition (MERRILL ALGEBRA 1)  1st Edition
ISBN: 9780078738227
Solutions for Chapter 124: Probability of Compound Events
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Algebra 1, Student Edition (MERRILL ALGEBRA 1) was written by and is associated to the ISBN: 9780078738227. Chapter 124: Probability of Compound Events includes 71 full stepbystep solutions. Since 71 problems in chapter 124: Probability of Compound Events have been answered, more than 34578 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Algebra 1, Student Edition (MERRILL ALGEBRA 1) , edition: 1.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Column space C (A) =
space of all combinations of the columns of A.

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

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

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

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

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

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

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).

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

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

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.