 12.1: Determine the probability of each event if you randomly select a cu...
 12.2: Determine the probability of each event if you randomly select a cu...
 12.3: Determine the probability of each event if you randomly select a cu...
 12.4: GAMES Paul is going to roll a game cube with 3 sides painted red, t...
 12.5: Find each product.
 12.6: Find each product.
 12.7: Find each product.
 12.8: Find each product.
 12.9: Find each product.
 12.10: Find each product.
 12.11: Write each fraction as a percent. Round to the nearest tenth.
 12.12: Write each fraction as a percent. Round to the nearest tenth.
 12.13: Write each fraction as a percent. Round to the nearest tenth.
 12.14: Write each fraction as a percent. Round to the nearest tenth.
 12.15: CONCERTS At a local concert, 585 of 2000 people were under the age ...
 12.16: MULTIPLE CHOICE A teacher took a survey of his class of 28 students...
 12.17: Evaluate each expression. (7C1)(6C3)
 12.18: Evaluate each expression. (7P3)(7P2)
 12.19: Evaluate each expression. (3C2)(4P1)
 12.20: CLASS PHOTO For Exercises 20 and 21, use the following information....
 12.21: CLASS PHOTO For Exercises 20 and 21, use the following information....
 12.22: A bag of colored paper clips contains 30 red clips, 22 blue clips, ...
 12.23: A bag of colored paper clips contains 30 red clips, 22 blue clips, ...
 12.24: One card is randomly drawn from a standard deck of 52 cards. Find e...
 12.25: One card is randomly drawn from a standard deck of 52 cards. Find e...
 12.26: BASEBALL Travis Hafner of the Cleveland Indians has a batting avera...
 12.27: ACTIVITIES The table shows the probability distribution for the num...
 12.28: ACTIVITIES The table shows the probability distribution for the num...
 12.29: ACTIVITIES The table shows the probability distribution for the num...
 12.30: BIOLOGY While studying flower colors in biology class, students are...
 12.31: BIOLOGY While studying flower colors in biology class, students are...
 12.32: BIOLOGY While studying flower colors in biology class, students are...
Solutions for Chapter 12: Statistics and Probability
Full solutions for Algebra 1, Student Edition (MERRILL ALGEBRA 1)  1st Edition
ISBN: 9780078738227
Solutions for Chapter 12: Statistics and Probability
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 32 problems in chapter 12: Statistics and Probability have been answered, more than 35143 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. Algebra 1, Student Edition (MERRILL ALGEBRA 1) was written by and is associated to the ISBN: 9780078738227. Chapter 12: Statistics and Probability includes 32 full stepbystep solutions.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

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

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

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

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

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.

Graph G.
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.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

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 columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

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

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

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

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.