Mathematics for the Trades: A Guided Approach (11th Edition) (What's New in Trade Math)
11th Edition
ISBN: 9780134756967
Author: Hal Saunders, Robert Carman
Publisher: PEARSON
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Chapter 2, Problem 25DPS
D. Practical Applications
Automotive Trades On a certain vehicle, each turn of the tie-rod sleeve changes the toe-in setting by
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Module Code: MATH380202
3. (a) Let {} be a white noise process with variance σ2.
Define an ARMA(p,q) process {X} in terms of {+} and state (without proof)
conditions for {X} to be (i) weakly stationary and (ii) invertible.
Define what is meant by an ARIMA (p, d, q) process. Let {Y} be such an ARIMA(p, d, q)
process and show how it can also be represented as an ARMA process, giving the
AR and MA orders of this representation.
(b) The following tables show the first nine sample autocorrelations and partial auto-
correlations of X and Y₁ = VX+ for a series of n = 1095 observations. (Notice
that the notation in this part has no relationship with the notation in part (a) of
this question.)
Identify a model for this time series and obtain preliminary estimates for the pa-
rameters of your model.
X₁
= 15.51, s² = 317.43.
k
1
2
3
4
5
6
7
Pk
0.981
0.974
0.968
akk 0.981 0.327
8
9
0.927
0.963 0.957 0.951 0.943 0.935
0.121 0.104 0.000 0.014 -0.067 -0.068 -0.012
Y₁ = VX : y = 0.03, s² = 11.48.
k
1…
Let G be a graph with n ≥ 2 vertices x1, x2, . . . , xn, and let A be the adjacency matrixof G. Prove that if G is connected, then every entry in the matrix A^n−1 + A^nis positive.
Module Code: MATH380202
1. (a) Define the terms "strongly stationary" and "weakly stationary".
Let {X} be a stochastic process defined for all t € Z. Assuming that {X+} is
weakly stationary, define the autocorrelation function (acf) Pk, for lag k.
What conditions must a process {X+) satisfy for it to be white noise?
(b) Let N(0, 1) for t€ Z, with the {+} being mutually independent. Which of
the following processes {X+} are weakly stationary for t> 0? Briefly justify your
answers.
i. Xt for all > 0.
ii. Xo~N(0,) and X₁ = 2X+-1+ &t for t > 0.
(c) Provide an expression for estimating the autocovariance function for a sample
X1,..., X believed to be from a weakly stationary process. How is the autocor-
relation function Pk then estimated, and a correlogram (or acf plot) constructed?
(d) Consider the weakly stationary stochastic process ✗+ = + + +-1+ +-2 where
{E} is a white noise process with variance 1. Compute the population autocorre-
lation function Pk for all k = 0, 1, ....
Chapter 2 Solutions
Mathematics for the Trades: A Guided Approach (11th Edition) (What's New in Trade Math)
Ch. 2.1 - What fraction of the box does the shaded region...Ch. 2.1 - Reduce 48 to lowest terms.Ch. 2.1 - Write as a mixed number. 174Ch. 2.1 - Write as a mixed number. 85Ch. 2.1 - Write as a mixed number. 118Ch. 2.1 - Write as a mixed number. 4016Ch. 2.1 - Write as a mixed number. 32Ch. 2.1 - Prob. 6AECh. 2.1 - Prob. 7AECh. 2.1 - Prob. 8AE
Ch. 2.1 - Write as a mixed number. 8032Ch. 2.1 - Write as a mixed number. 52Ch. 2.1 - Write as an improper fraction. 213Ch. 2.1 - Write as an improper fraction. 712Ch. 2.1 - Write as an improper fraction. 838Ch. 2.1 - Prob. 4BECh. 2.1 - Prob. 5BECh. 2.1 - Prob. 6BECh. 2.1 - Prob. 7BECh. 2.1 - Prob. 8BECh. 2.1 - Write as an improper fraction. 456Ch. 2.1 - Prob. 10BECh. 2.1 - Complete. 78=?16Ch. 2.1 - Complete. 34=?16Ch. 2.1 - Complete. 18=?64Ch. 2.1 - Prob. 4CECh. 2.1 - Complete. 114=?16Ch. 2.1 - Complete. 278=?32Ch. 2.1 - Prob. 7CECh. 2.1 - Complete. 1116=?32Ch. 2.1 - Prob. 9CECh. 2.1 - Prob. 10CECh. 2.1 - Prob. 11CECh. 2.1 - Prob. 12CECh. 2.1 - Write in lowest terms. 416Ch. 2.1 - Write in lowest terms. 46Ch. 2.1 - Write in lowest terms. 616Ch. 2.1 - Prob. 4DECh. 2.1 - Write in lowest terms. 410Ch. 2.1 - Prob. 6DECh. 2.1 - Prob. 7DECh. 2.1 - Prob. 8DECh. 2.1 - Prob. 9DECh. 2.1 - Prob. 10DECh. 2.1 - Prob. 11DECh. 2.1 - Write in lowest terms. 1035Ch. 2.1 - Prob. 13DECh. 2.1 - Prob. 14DECh. 2.1 - Write in lowest terms. 3824Ch. 2.1 - Prob. 1EECh. 2.1 - Prob. 2EECh. 2.1 - Prob. 3EECh. 2.1 - Prob. 4EECh. 2.1 - E. Which is larger? 78or56Ch. 2.1 - Prob. 6EECh. 2.1 - Prob. 7EECh. 2.1 - Prob. 8EECh. 2.1 - Prob. 9EECh. 2.1 - E. Which is larger? 312or274Ch. 2.1 - Prob. 11EECh. 2.1 - Prob. 12EECh. 2.1 - F. Practical Applications Carpentry An apprentice...Ch. 2.1 - F. Practical Applications Electrical Trades An...Ch. 2.1 - F. Practical Applications The numbers 227, 196,...Ch. 2.1 - F. Practical Applications Sheet Metal Trades Which...Ch. 2.1 - F. Practical Applications Plumbing Is it possible...Ch. 2.1 - F. Practical Applications Sheet Metal Trades...Ch. 2.1 - F. Practical Applications Printing A printer has...Ch. 2.1 - F. Practical Applications Machine Trades A...Ch. 2.1 - F. Practical Applications Landscaping Before it...Ch. 2.1 - F. Practical Applications Roofing A ridge beam...Ch. 2.1 - F. Practical Applications Construction A 34-in....Ch. 2.1 - Prob. 12FECh. 2.1 - F. Practical Applications General Trades The...Ch. 2.2 - What is half of 18?Ch. 2.2 - Write 2416 as a mixed number in lowest terms.Ch. 2.2 - Multiply and write the answer in lowest terms....Ch. 2.2 - Multiply and write the answer in lowest terms....Ch. 2.2 - Multiply and write the answer in lowest terms....Ch. 2.2 - Multiply and write the answer in lowest terms. 612Ch. 2.2 - Multiply and write the answer in lowest terms. 893Ch. 2.2 - Prob. 6AECh. 2.2 - Multiply and write the answer in lowest terms....Ch. 2.2 - Multiply and write the answer in lowest terms....Ch. 2.2 - Multiply and write the answer in lowest terms....Ch. 2.2 - Multiply and write the answer in lowest terms....Ch. 2.2 - Multiply and write the answer in lowest terms....Ch. 2.2 - Multiply and write the answer in lowest terms....Ch. 2.2 - Multiply and write the answer in lowest terms....Ch. 2.2 - Multiply and write the answer in lowest terms....Ch. 2.2 - Multiply and write the answer in lowest terms....Ch. 2.2 - Multiply and write the answer in lowest terms....Ch. 2.2 - Multiply and write the answer in lowest terms....Ch. 2.2 - Multiply and write the answer in lowest terms....Ch. 2.2 - Prob. 19AECh. 2.2 - Prob. 20AECh. 2.2 - Prob. 21AECh. 2.2 - Prob. 22AECh. 2.2 - Prob. 23AECh. 2.2 - Prob. 24AECh. 2.2 - Prob. 25AECh. 2.2 - Prob. 1BECh. 2.2 - Prob. 2BECh. 2.2 - Prob. 3BECh. 2.2 - Prob. 4BECh. 2.2 - Find. 12 of 112Ch. 2.2 - Prob. 6BECh. 2.2 - Prob. 7BECh. 2.2 - Prob. 8BECh. 2.2 - Find. 43 of 34Ch. 2.2 - Prob. 10BECh. 2.2 - Prob. 11BECh. 2.2 - B. Find. 35of4Ch. 2.2 - B. Find. 716of6Ch. 2.2 - Prob. 14BECh. 2.2 - Prob. 15BECh. 2.2 - Prob. 16BECh. 2.2 - Practical Applications Flooring and Carpeting Find...Ch. 2.2 - Prob. 2CECh. 2.2 - Practical Applications Roofing Shingles are laid...Ch. 2.2 - Prob. 4CECh. 2.2 - Prob. 5CECh. 2.2 - Prob. 6CECh. 2.2 - Prob. 7CECh. 2.2 - Practical Applications Machine Trades What is the...Ch. 2.2 - Practical Applications Manufacturing How many...Ch. 2.2 - Practical Applications Plumbing A plumber cut...Ch. 2.2 - Practical Applications Machine Trades How far will...Ch. 2.2 - Practical Applications Landscaping A landscaping...Ch. 2.2 - Practical Applications Drafting If 38 in. on a...Ch. 2.2 - Practical Applications Manufacturing What is the...Ch. 2.2 - Practical Applications Machine Trades How long...Ch. 2.2 - Prob. 16CECh. 2.2 - Prob. 17CECh. 2.2 - Prob. 18CECh. 2.2 - Practical Applications Photography A photograph...Ch. 2.2 - Prob. 20CECh. 2.2 - Prob. 21CECh. 2.2 - Practical Applications Water/Wastewater Treatment...Ch. 2.2 - Prob. 23CECh. 2.2 - Practical Applications Plumbing To find the degree...Ch. 2.2 - Prob. 25CECh. 2.2 - Prob. 26CECh. 2.2 - Prob. 27CECh. 2.2 - Prob. 28CECh. 2.2 - Prob. 29CECh. 2.2 - Prob. 30CECh. 2.2 - Prob. 31CECh. 2.2 - C. Practical Applications Carpentry A carpenter is...Ch. 2.2 - C. Practical Applications Retail Merchandising...Ch. 2.3 - Prob. 1LCCh. 2.3 - Prob. 2LCCh. 2.3 - Prob. 1AECh. 2.3 - Prob. 2AECh. 2.3 - Prob. 3AECh. 2.3 - Prob. 4AECh. 2.3 - Prob. 5AECh. 2.3 - Prob. 6AECh. 2.3 - Prob. 7AECh. 2.3 - Prob. 8AECh. 2.3 - Prob. 9AECh. 2.3 - Prob. 10AECh. 2.3 - Prob. 11AECh. 2.3 - Prob. 12AECh. 2.3 - Prob. 13AECh. 2.3 - Prob. 14AECh. 2.3 - Prob. 15AECh. 2.3 - Prob. 16AECh. 2.3 - Prob. 17AECh. 2.3 - Prob. 18AECh. 2.3 - Prob. 19AECh. 2.3 - Prob. 20AECh. 2.3 - Prob. 21AECh. 2.3 - Prob. 22AECh. 2.3 - Prob. 23AECh. 2.3 - Divide and write the answer in lowest terms....Ch. 2.3 - Drafting How many feet are represented by a 4-in....Ch. 2.3 - Drafting If 14in. on a drawing represents 1 ft 0...Ch. 2.3 - Flooring and Carpeting How many boards 458 in....Ch. 2.3 - Construction How many supporting columns 8812in....Ch. 2.3 - Construction How many pieces of 12in. plywood are...Ch. 2.3 - Masonry The front side of a standard brick...Ch. 2.3 - Prob. 7BECh. 2.3 - Prob. 8BECh. 2.3 - Prob. 9BECh. 2.3 - Prob. 10BECh. 2.3 - Prob. 11BECh. 2.3 - Prob. 12BECh. 2.3 - Prob. 13BECh. 2.3 - Prob. 14BECh. 2.3 - Prob. 15BECh. 2.3 - Prob. 16BECh. 2.3 - Prob. 17BECh. 2.3 - Prob. 18BECh. 2.3 - Prob. 19BECh. 2.3 - Prob. 20BECh. 2.3 - Landscaping An agricultural supply yard sells...Ch. 2.4 - Write 18 as a product of its prime factors.Ch. 2.4 - What is the smallest number that 8 and 12 both...Ch. 2.4 - Prob. 1AECh. 2.4 - Add or subtract as shown. 512+1112Ch. 2.4 - Prob. 3AECh. 2.4 - Prob. 4AECh. 2.4 - Add or subtract as shown. 3414Ch. 2.4 - Prob. 6AECh. 2.4 - Prob. 7AECh. 2.4 - Add or subtract as shown. 512212Ch. 2.4 - Add or subtract as shown. 516+316+716Ch. 2.4 - Add or subtract as shown. 18+38+78Ch. 2.4 - Add or subtract as shown. 17838Ch. 2.4 - Add or subtract as shown. 39161516Ch. 2.4 - Add or subtract as shown. 14+12Ch. 2.4 - Add or subtract as shown. 716+38Ch. 2.4 - Add or subtract as shown. 58+112Ch. 2.4 - Add or subtract as shown. 512+316Ch. 2.4 - Add or subtract as shown. 1238Ch. 2.4 - Add or subtract as shown. 516332Ch. 2.4 - Add or subtract as shown. 151612Ch. 2.4 - Add or subtract as shown. 716132Ch. 2.4 - Add or subtract as shown. 35+18Ch. 2.4 - Add or subtract as shown. 23+45Ch. 2.4 - Add or subtract as shown. 7825Ch. 2.4 - Add or subtract as shown. 4914Ch. 2.4 - Add or subtract as shown. 12+1418Ch. 2.4 - Prob. 26AECh. 2.4 - Prob. 27AECh. 2.4 - Prob. 28AECh. 2.4 - Prob. 29AECh. 2.4 - Prob. 30AECh. 2.4 - Add or subtract as shown. 213+115Ch. 2.4 - Add or subtract as shown. 178+14Ch. 2.4 - Prob. 33AECh. 2.4 - Prob. 34AECh. 2.4 - Add or subtract as shown. 3152112Ch. 2.4 - Prob. 36AECh. 2.4 - Add or subtract as shown. 8278Ch. 2.4 - Prob. 2BECh. 2.4 - Prob. 3BECh. 2.4 - Add or subtract as shown. 12+13+14+15Ch. 2.4 - Prob. 5BECh. 2.4 - Prob. 6BECh. 2.4 - Prob. 7BECh. 2.4 - Prob. 8BECh. 2.4 - B. Add or subtract as shown. 2316lessthan478Ch. 2.4 - Prob. 10BECh. 2.4 - B. Add or subtract as shown. 235 less than 612Ch. 2.4 - Prob. 12BECh. 2.4 - C. Practical Applications Construction The...Ch. 2.4 - C. Practical Applications Carpentry A countertop...Ch. 2.4 - Prob. 3CECh. 2.4 - Prob. 4CECh. 2.4 - Prob. 5CECh. 2.4 - Prob. 6CECh. 2.4 - Prob. 7CECh. 2.4 - Prob. 8CECh. 2.4 - Prob. 9CECh. 2.4 - Prob. 10CECh. 2.4 - Prob. 11CECh. 2.4 - Prob. 12CECh. 2.4 - Prob. 13CECh. 2.4 - Prob. 14CECh. 2.4 - Prob. 15CECh. 2.4 - Prob. 16CECh. 2.4 - Prob. 17CECh. 2.4 - Prob. 18CECh. 2.4 - Prob. 19CECh. 2.4 - Prob. 20CECh. 2.4 - Prob. 21CECh. 2.4 - Prob. 22CECh. 2.4 - Prob. 23CECh. 2.4 - Prob. 24CECh. 2.4 - Prob. 25CECh. 2 - Work with fractions. (a) Write as a mixed number...Ch. 2 - Multiply and divide fractions. (a) 78532 (b) 41223...Ch. 2 - Add and subtract fractions. (a) 716+316 (b)...Ch. 2 - Solve practical problems involving fractions....Ch. 2 - A. Write as an improper fraction. 118Ch. 2 - A. Write as an improper fraction. 415Ch. 2 - A. Write as an improper fraction. 123Ch. 2 - A. Write as an improper fraction. 2316Ch. 2 - A. Write as an improper fraction. 3332Ch. 2 - Prob. 6APSCh. 2 - A. Write as an improper fraction. 158Ch. 2 - Prob. 8APSCh. 2 - A. Write as a mixed number. 104Ch. 2 - Prob. 10APSCh. 2 - A. Write as a mixed number. 253Ch. 2 - Prob. 12APSCh. 2 - Prob. 13APSCh. 2 - Prob. 14APSCh. 2 - A. Write as a mixed number. 354Ch. 2 - A. Write as a mixed number. 73Ch. 2 - A. Write in lowest terms. 632Ch. 2 - A. Write in lowest terms. 832Ch. 2 - A. Write in lowest terms. 1232Ch. 2 - Prob. 20APSCh. 2 - A. Write in lowest terms. 520Ch. 2 - Prob. 22APSCh. 2 - A. Write in lowest terms. 11620Ch. 2 - Prob. 24APSCh. 2 - A. Complete these. 34=?12Ch. 2 - Prob. 26APSCh. 2 - A. Complete these. 234=?16Ch. 2 - Prob. 28APSCh. 2 - A. Complete these. 523=?12Ch. 2 - Prob. 30APSCh. 2 - A. Complete these. 114=?12Ch. 2 - A. Complete these. 235=?10Ch. 2 - A. Circle the larger number. 716or215Ch. 2 - Prob. 34APSCh. 2 - A. Circle the larger number. 1316or78Ch. 2 - Prob. 36APSCh. 2 - A. Circle the larger number. 1332or35Ch. 2 - A. Circle the larger number. 210or316Ch. 2 - A. Circle the larger number. 1716 or 74Ch. 2 - Prob. 40APSCh. 2 - B. Multiply 12316Ch. 2 - Prob. 2BPSCh. 2 - B. Multiply 71643Ch. 2 - Prob. 4BPSCh. 2 - B. Multiply 11256Ch. 2 - B. Multiply 311615Ch. 2 - B. Multiply 316512Ch. 2 - Prob. 8BPSCh. 2 - B. Multiply 3410Ch. 2 - Prob. 10BPSCh. 2 - B. Multiply or divide as shown. 18112Ch. 2 - Prob. 12BPSCh. 2 - B. Multiply or divide as shown. 223438Ch. 2 - Prob. 14BPSCh. 2 - Multiply or divide as shown. 1214Ch. 2 - Prob. 16BPSCh. 2 - Multiply or divide as shown. 418Ch. 2 - Multiply or divide as shown. 834Ch. 2 - Multiply or divide as shown. 234Ch. 2 - Prob. 20BPSCh. 2 - Multiply or divide as shown. 3125Ch. 2 - Prob. 22BPSCh. 2 - Multiply or divide as shown. 234118Ch. 2 - Prob. 24BPSCh. 2 - C. Add or subtract as shown. 38+78Ch. 2 - Prob. 2CPSCh. 2 - C. Add or subtract as shown. 332+18Ch. 2 - Prob. 4CPSCh. 2 - C. Add or subtract as shown. 35+56Ch. 2 - Prob. 6CPSCh. 2 - Prob. 7CPSCh. 2 - Prob. 8CPSCh. 2 - Prob. 9CPSCh. 2 - Prob. 10CPSCh. 2 - C. Add or subtract as shown. 78310Ch. 2 - Prob. 12CPSCh. 2 - C. Add or subtract as shown. 218+114Ch. 2 - Prob. 14CPSCh. 2 - C. Add or subtract as shown. 6112Ch. 2 - Prob. 16CPSCh. 2 - C. Add or subtract as shown. 323178Ch. 2 - Prob. 18CPSCh. 2 - C. Add or subtract as shown. 12+13+15Ch. 2 - Prob. 20CPSCh. 2 - C. Add or subtract as shown. 312213Ch. 2 - C. Add or subtract as shown. 2351415Ch. 2 - C. Add or subtract as shown. 2135Ch. 2 - Prob. 24CPSCh. 2 - D. Practical Applications Welding In a welding...Ch. 2 - D. Practical Applications Machine Trades How many...Ch. 2 - D. Practical Applications Welding A piece of metal...Ch. 2 - D. Practical Applications Automotive Trades A...Ch. 2 - D. Practical Applications Machine Trades A shaft...Ch. 2 - D Practical Applications Machine Trades A bar...Ch. 2 - D. Practical Applications Manufacturing A cubic...Ch. 2 - D. Practical Applications Manufacturing Find the...Ch. 2 - D. Practical Applications Machine Trades What...Ch. 2 - D. Practical Applications Machine Trades The Ace...Ch. 2 - D. Practical Applications Carpentry What is the...Ch. 2 - D. Practical Applications Construction For the...Ch. 2 - D. Practical Applications Carpentry Find the...Ch. 2 - D. Practical Applications Masonry Find the height...Ch. 2 - D. Practical Applications Masonry If the wall in...Ch. 2 - D. Practical Applications Electrical Trades An...Ch. 2 - D. Practical Applications Printing An invitation...Ch. 2 - D. Practical Applications Printing As a rule of...Ch. 2 - D. Practical Applications Welding A 46-in. bar...Ch. 2 - D. Practical Applications Construction If an...Ch. 2 - D. Practical Applications Machine Trades If a...Ch. 2 - Prob. 22DPSCh. 2 - D. Practical Applications Landscaping A...Ch. 2 - D. Practical Applications Machine Trades A machine...Ch. 2 - D. Practical Applications Automotive Trades On a...Ch. 2 - D. Practical Applications Automotive Trades A...Ch. 2 - D. Practical Applications Allied Health One bottle...Ch. 2 - D. Practical Applications Construction The...Ch. 2 - Prob. 29DPSCh. 2 - Prob. 30DPSCh. 2 - Flooring and Carpeting In the United States carpet...Ch. 2 - D. Practical Applications Retail Merchandising In...Ch. 2 - D. Practical Applications Retail Merchandising The...Ch. 2 - D. Practical Applications Carpentry A carpenter...
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