 75.1: What is the reciprocal of two and three fifths?
 75.2: What time is one hour thirtyfive minutes after 2:30 p.m.?
 75.3: A 1pound box of candy cost $4.00. What was the cost per ounce(1 po...
 75.4: Freda bought a sandwich for $4.00 and a drink for 94. Hergrandson o...
 75.5: If the chance of rain is 50%, then what is the chance it will not r...
 75.6: Draw a cube. How many edges does a cube have?
 75.7: a. Write 34 as a decimal number. b. Write the answer to part a as a...
 75.8: a. Write 3 4 as a fraction with a denominator of 100. b. Write 34 a...
 75.9: Write 12% as a reduced fraction. Then write the fraction as adecima...
 75.10: Find each unknown number:710 n100
 75.11: Find each unknown number:5 m 318
 75.12: Find each unknown number:1 w = 0.95
 75.13: Find each unknown number:m + 123 316
 75.14: Find each unknown number:(12 13b 16
 75.15: Find each unknown number:312 113 112
 75.16: Find each unknown number:(0.43)(2.6)
 75.17: Find each unknown number:0.26 5
 75.18: Nathan correctly answered 17 of the 20 questions on the test. Whatp...
 75.19: The diameter of the big tractor tire was about 5 feet. As thetire r...
 75.20: Which digit in 4.87 has the same place value as the 9 in0.195?
 75.21: Write the prime factorization of both the numerator and denominator...
 75.22: What is the greatest common factor of 18 and 30?
 75.23: If the product of two numbers is 1, then the two numbers are which ...
 75.24: Why is every rectangle a quadrilateral?
 75.25: If b equals 8 and h equals 6, what does bh2 equal?
 75.26: Find the prime factorization of 400 using a factor tree. Thenwrite ...
 75.27: Draw a coordinate plane on graph paper. Then draw arectangle with v...
 75.28: Refer to the rectangle drawn in problem 27 to answer parts aand b b...
 75.29: a. What is the perimeter of thisparallelogram? b. What is the area ...
 75.30: Draw two parallel segments of different lengths. Then form aquadril...
Solutions for Chapter 75: Writing Fractions and Decimals as Percents, Part 1
Full solutions for Saxon Math, Course 1  1st Edition
ISBN: 9781591417835
Solutions for Chapter 75: Writing Fractions and Decimals as Percents, Part 1
Get Full SolutionsSaxon Math, Course 1 was written by and is associated to the ISBN: 9781591417835. This textbook survival guide was created for the textbook: Saxon Math, Course 1, edition: 1. Since 30 problems in chapter 75: Writing Fractions and Decimals as Percents, Part 1 have been answered, more than 33783 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 75: Writing Fractions and Decimals as Percents, Part 1 includes 30 full stepbystep solutions.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

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.)

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.

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

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.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

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.

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

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

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.

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 .

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).

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

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

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

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

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·