 94.1: Ten of the thirty students on the bus were boys. What percentof the...
 94.2: On the Celsius scale water freezes at 0C and boils at100C. What tem...
 94.3: If the length of segment AB is 13 the length of segment AC,and if s...
 94.4: What percent of this group is shaded?
 94.5: Change 1 23 to a percent by multiplying 1 23 by 100%.
 94.6: Change 1.5 to a percent by multiplying 1.5 by 100%.
 94.7: 6.4 614 (Begin by writing 614 as a decimal number.)
 94.8: 104 103
 94.9: How much is 34 of 360?
 94.10: Tommy placed a cylindrical can of spaghetti sauceon the counter. He...
 94.11: Tommy placed a cylindrical can of spaghetti sauceon the counter. He...
 94.12: 312 134 458
 94.13: 910 56 89
 94.14: Write 250,000 in expanded notation using exponents.
 94.15: $8.47 + 95 + $12
 94.16: 37.5 100
 94.17: 37 21x
 94.18: 33 , 13 100
 94.19: If ninety percent of the answers were correct, then what percent we...
 94.20: Write the decimal number one hundred twenty and threehundredths.
 94.21: Arrange these numbers in order from least to greatest:2.5, 25,52 5.2
 94.22: A pyramid with a square base has how many edges?
 94.23: What is the area of this parallelogram?
 94.24: The parallelogram in problem 23 is divided into twocongruent triang...
 94.25: During the year, the temperature ranged from 37F in winter to 103Fi...
 94.26: The coordinates of the three vertices of a triangle are (0, 0),(0, ...
 94.27: Margies first nine test scores are shown below.21, 25, 22, 19, 22, ...
 94.28: 23 225 3 42 24
 94.29: Sandra filled the aquarium with 24 quarts of water. How many gallon...
 94.30: A bag contains lettered tiles, two for each letter of the alphabet....
Solutions for Chapter 94: Writing Fractions and Decimals as Percents, Part 2
Full solutions for Saxon Math, Course 1  1st Edition
ISBN: 9781591417835
Solutions for Chapter 94: Writing Fractions and Decimals as Percents, Part 2
Get Full SolutionsThis textbook survival guide was created for the textbook: Saxon Math, Course 1, edition: 1. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 94: Writing Fractions and Decimals as Percents, Part 2 includes 30 full stepbystep solutions. Since 30 problems in chapter 94: Writing Fractions and Decimals as Percents, Part 2 have been answered, more than 35247 students have viewed full stepbystep solutions from this chapter. Saxon Math, Course 1 was written by and is associated to the ISBN: 9781591417835.

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

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

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

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.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

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

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!).

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

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.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

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.

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.

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).

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

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

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.