 49.1: When the product of 0.2 and 0.3 is subtracted from the sum of 0.2 a...
 49.2: Four fifths of a dollar is how many cents? Draw a diagram toillustr...
 49.3: The rectangular, 99piece Nano jigsaw puzzle is only 2.6 incheslong...
 49.4: Find the perimeter of the puzzle described in problem 3.
 49.5: Compare: a. 0.31 0.301 b. 31% 30.1%
 49.6: 0.67 + 2 + 1.33
 49.7: 12(0.25)
 49.8: 0.07 3.5
 49.9: 0.5 12
 49.10: 8 0.14
 49.11: (0.012)(1.5)
 49.12: Find each unknown number:n  618 4 38
 49.13: Find each unknown number:45 x100
 49.14: Find each unknown number:5 m = 1.37
 49.15: Find each unknown number:m 714 = 15
 49.16: Write the decimal number one and twelve thousandths.
 49.17: 5 710 4 910
 49.18: 52 53
 49.19: How much money is 40% of $25.00?
 49.20: There are 24 hours in a day. James sleeps 8 hours each night.a. Eig...
 49.21: What factors do 12 and 18 have in common (that is, the numbersthat ...
 49.22: What is the average of 1.2, 1.3, and 1.7?
 49.23: Jan estimated that 49% of $19.58 is $10. She rounded 49%to 50% and ...
 49.24: a. How many 34 s are in 1? b. Use the answer to part a to find the ...
 49.25: Refer to the number line shown below to answer parts ac.a. Which po...
 49.26: Multiply and divide as indicated:2 3 2 5 72 5 7
 49.27: We can find the number of quarters in three dollars bydividing $3.0...
 49.28: Use a ruler to find the length of each side of this squareto the ne...
 49.29: A papertowel tube is about 4 cm in diameter. The circumferenceof a...
 49.30: Sam was given the following division problem:2.50.5Instead of multi...
Solutions for Chapter 49: Dividing by a Decimal Number
Full solutions for Saxon Math, Course 1  1st Edition
ISBN: 9781591417835
Solutions for Chapter 49: Dividing by a Decimal Number
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Saxon Math, Course 1, edition: 1. Since 30 problems in chapter 49: Dividing by a Decimal Number have been answered, more than 35518 students have viewed full stepbystep solutions from this chapter. Chapter 49: Dividing by a Decimal Number includes 30 full stepbystep solutions. Saxon Math, Course 1 was written by and is associated to the ISBN: 9781591417835.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

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.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

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.

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

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

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.

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.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

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.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

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.

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