Trigonometry (11th Edition)
11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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Textbook Question
Chapter 4, Problem 43RE
(Modeling) Monthly Temperatures A set of temperature data (in °F) is given for a particular location. (Source: www.weathcrbasc.com)
(a) Plot the data over a two-year interval.
(b) Use sine regression to determine a model for the two-year interval. Let x = 1 represent January of the first year.
(c) Graph the equation from part (b) together with the data on the same coordinate axes.
Average Monthly Temperature. Auckland, New Zealand
Jan | Feb | Mar | Apr | May | Jun | Jul | Aug | Sept | Oct | Nov | Dec |
67.6 | 68.5 | 65.8 | 61.3 | 57.2 | 53.2 | 51.6 | 52.9 | 55.4 | 58.1 | 61.2 | 64.9 |
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Dataset temperature is available here.
The average January temperatures (y) and geographic latitudes (x) of 20 cities in the United States are given in the dataset. The regression equation for these data is
ŷ = 126 − 2.34x.
Use the regression equation given above to answer the following question.
(a)
What is the slope of the line?
Interpret the slope in terms of how mean January temperature is related to change in latitude.
The slope gives the average January temperature at the equator.The slope gives the average latitude of cities with an average January temperature is 0 degrees. The slope gives the average change in average January temperature for each one unit increase in latitude.The slope gives the average change in latitude for each one degree increase in the average January temperature.
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microorganisms that break down these compounds. BOD is hard to measure accurately. Total organic carbon (TOC) is easy to
measure, so it is common to measure TOC and use regression to predict BOD. A typical regression equation for water entering a
municipal treatment plant is
BOD= -55.42 + 1.507 TOC
Both BOD and TOC are measured in milligrams per liter of water.
(a) What does the slope of this line say about the relationship between BOD and TOC?
O TOC rises (falls) by 1.507 mg/l for every 1 mg/l increase (decrease) in BOD
O BOD rises (falls) by 1.507 mg/l for every 1 mg/l increase (decrease) in TOC
O TOC rises (falls) by 1.507 mg/l for every 55.42 mg/l increase (decrease) in BOD
O BOD rises (falls) by 55.42 mg/l for every 1 mg/l increase (decrease) in TOC
(b) What is the predicted BOD when TOC = 0?
Values of BOD less than 0 are impossible. Why do you think the prediction gives an impossible value?
This arises from extrapolation; the data used to find this regression formula must not…
The data provided give the number of standby hours based on total staff present, X₁, and remote hours, X₂. Perform a multiple regression analysis using the data
provided and determine the VIF for each independent variable in the model. Is there reason to suspect the existence of collinearity?
Click the icon to view the data.
Determine the VIF for each independent variable in the model.
|
VIF ₂2 =
VIF₁ =
(Round to three decimal places as needed.)
Is there reason to suspect the existence of collinearity?
OA. No. The VIF for each independent variable is less than 5.
B. Yes. The VIF for each independent variable is greater than 5.
OC. No. The VIF for each independent variable is greater than 5.
OD. Yes. The VIF for each independent variable is less than 5.
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Table of Data
Standby Total Staff
Hours Present
245
330
274
358
195
197
117
153
115
275
200
236
336
339
321
303
286
329
352
323
Remote
Hours
417
655
524
385
349
350
388
153
278
479
Print
Done
Chapter 4 Solutions
Trigonometry (11th Edition)
Ch. 4.1 - CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 4.1 -
CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 4.1 - CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 4.1 - CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 4.1 -
5. The least positive number x for which cos x =...Ch. 4.1 - CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 4.1 - Concept Check Match each function with its graph...Ch. 4.1 - Concept Check Match each function with its graph...Ch. 4.1 -
Concept Check Match each function with its graph...Ch. 4.1 - Concept Check Match each function with its graph...
Ch. 4.1 - Concept Check Match each function with its graph...Ch. 4.1 - Concept Check Match each function with its graph...Ch. 4.1 -
Graph each function over the interval [ –2π, 2π]....Ch. 4.1 - Graph each function over the interval [ 2, 2]....Ch. 4.1 - Graph each function over the interval [2, 2]. Give...Ch. 4.1 -
Graph each function over the interval [–2π, 2π]....Ch. 4.1 - Graph each function over the interval [2,2]. Give...Ch. 4.1 -
Graph each function over the interval [–2π,2π]....Ch. 4.1 -
Graph each function over the interval [–2 π,2π]....Ch. 4.1 - Graph each function over the interval [–2π,2π]....Ch. 4.1 - Graph each function over the interval [2,2 ]. Give...Ch. 4.1 - Prob. 22ECh. 4.1 - Graph each function over a two-period interval....Ch. 4.1 -
Graph each function over a two-period interval....Ch. 4.1 -
Graph each function over a two-period interval....Ch. 4.1 - Graph each function over a two-period interval....Ch. 4.1 - Graph each function over a two-period interval....Ch. 4.1 - Graph each function over a two-period interval....Ch. 4.1 - Graph each function over a two-period interval....Ch. 4.1 -
Graph each function over a two-period interval....Ch. 4.1 - Graph each function over a two-period interval....Ch. 4.1 -
Graph each function over a two-period interval....Ch. 4.1 - Graph each function over a two-period interval....Ch. 4.1 -
Graph each function over a two-period interval....Ch. 4.1 -
Graph each function over a two-period interval....Ch. 4.1 -
Graph each function over a two-period interval....Ch. 4.1 -
Graph each function over a two-period interval....Ch. 4.1 -
Graph each function over a two-period interval....Ch. 4.1 - Graph each function over a two-period interval....Ch. 4.1 - Graph each function over a two-period interval....Ch. 4.1 - Connecting Graphs with Equations Determine an...Ch. 4.1 - Connecting Graphs with Equations Determine an...Ch. 4.1 - Connecting Graphs with Equations Determine an...Ch. 4.1 - Connecting Graphs with Equations Determine an...Ch. 4.1 - Connecting Graphs with Equations Determine an...Ch. 4.1 - Connecting Graphs with Equations Determine an...Ch. 4.1 - Average Annual Temperature Scientists believe that...Ch. 4.1 - Blood Pressure Variation The graph gives the...Ch. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Prob. 53ECh. 4.1 - Activity of a Nocturnal Animal Many activities of...Ch. 4.1 -
55. Atmospheric Carbon Dioxide At Mauna Loa....Ch. 4.1 - Atmospheric Carbon Dioxide Refer to Exercise 55....Ch. 4.1 -
57. Average Daily Temperature The temperature in...Ch. 4.1 - 58. Fluctuation in the Solar Constant The solar...Ch. 4.1 -
Musical Sound Waves Pure sounds produce single...Ch. 4.1 - Musical Sound Waves Pure sounds produce single...Ch. 4.1 - Prob. 61ECh. 4.1 - Prob. 62ECh. 4.1 - Prob. 63ECh. 4.1 - Prob. 64ECh. 4.1 - Prob. 65ECh. 4.1 - Prob. 66ECh. 4.2 - CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 4.2 - CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 4.2 - CONCEPT PREVIEW Fill in the blanks to correctly...Ch. 4.2 - CONCEPT PREVIEW Fill in the blanks to correctly...Ch. 4.2 -
CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 4.2 - CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 4.2 -
CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 4.2 - CONCEPT PREVIEW Fill in the blanks to correctly...Ch. 4.2 - Concept Check Match each function with its graph...Ch. 4.2 - Concept Check Match each function with its graph...Ch. 4.2 - Concept Check Match each function w ith its graph...Ch. 4.2 - Concept Check Match each function w ith its graph...Ch. 4.2 - Concept Check Match each function with its graph...Ch. 4.2 - Concept Check Match each function with its graph...Ch. 4.2 - Concept Check Match each function with its graph...Ch. 4.2 - Concept Check Match each function with its graph...Ch. 4.2 - The graphs of y = sin x + 1 and y = sin(x + 1) are...Ch. 4.2 - Concept Check Refer to Exercise 17. Which one of...Ch. 4.2 -
Concept Check Match each function in Column I...Ch. 4.2 - Concept Check Match each function in Column I with...Ch. 4.2 -
Concept Check Match each function in Column I...Ch. 4.2 - Concept Check Match each function in Column I with...Ch. 4.2 - Concept Check Fill in each blank with the word...Ch. 4.2 - Prob. 24ECh. 4.2 - Connecting Graphs with equations Each function...Ch. 4.2 - Connecting Graphs with Equations Each function...Ch. 4.2 -
Connecting Graphs with Equations Each function...Ch. 4.2 - Prob. 28ECh. 4.2 -
Find the amplitude, the period, any vertical...Ch. 4.2 -
Find the amplitude, the period, any vertical...Ch. 4.2 -
Find the amplitude, the period, any vertical...Ch. 4.2 -
Find the amplitude, the period, any vertical...Ch. 4.2 - Find the amplitude, the period, any vertical...Ch. 4.2 -
Find the amplitude, the period, any vertical...Ch. 4.2 - Find the amplitude, the period, any vertical...Ch. 4.2 - Find the amplitude, the period, any vertical...Ch. 4.2 - Graph each function over a two-period interval....Ch. 4.2 - Graph each function over a two-period interval....Ch. 4.2 - Graph each function over a two-period interval....Ch. 4.2 - Graph each function over a two-period interval....Ch. 4.2 -
Graph each function over a two-period interval....Ch. 4.2 - Graph each function over a two-period interval....Ch. 4.2 -
Graph each function over a one-period interval....Ch. 4.2 -
Graph each function over a one-period interval....Ch. 4.2 - Graph each function over a one-period interval....Ch. 4.2 - Graph each function over a one-period interval....Ch. 4.2 - Graph each function over a one-period interval....Ch. 4.2 -
Graph each function over a one-period interval....Ch. 4.2 - Graph each function over a two-period interval....Ch. 4.2 - Graph each function over a two-period interval....Ch. 4.2 -
Graph each function over a two-period interval....Ch. 4.2 -
Graph each function over a two-period interval....Ch. 4.2 - Graph each function over a two-period interval....Ch. 4.2 -
Graph each function over a two-period interval....Ch. 4.2 -
Graph each function over a two-period interval....Ch. 4.2 - Graph each function over a two-period interval....Ch. 4.2 -
Graph each function over a two-period interval....Ch. 4.2 - Graph each function over a one-period interval....Ch. 4.2 -
Graph each function over a one-period interval....Ch. 4.2 - Prob. 60ECh. 4.2 - Average Monthly Temperature The average monthly...Ch. 4.2 - Prob. 62ECh. 4.2 - Prob. 63ECh. 4.2 - Prob. 64ECh. 4.2 - Prob. 65ECh. 4.2 - Prob. 66ECh. 4.2 - Prob. 1QCh. 4.2 - Graph each function over a two-period interval....Ch. 4.2 - Prob. 3QCh. 4.2 - Prob. 4QCh. 4.2 - Prob. 5QCh. 4.2 - Graph each function over a two-period interval....Ch. 4.2 - Prob. 7QCh. 4.2 - Prob. 8QCh. 4.2 - Prob. 9QCh. 4.2 - Prob. 10QCh. 4.2 - Prob. 11QCh. 4.2 - Prob. 12QCh. 4.3 - 1. The least positive value x for which tan x = 0...Ch. 4.3 - The least positive value x for which cot x = 0 is...Ch. 4.3 - Concept Check Fill in each blank with the word...Ch. 4.3 - Concept Check Fill in each blank with the word...Ch. 4.3 - The negative value k with the greatest value for...Ch. 4.3 - CONCEPT PREVIEW Fill in the blank(s) to correctly...Ch. 4.3 - Concept Check Match each function with its graph...Ch. 4.3 - Concept Check Match each function with its graph...Ch. 4.3 -
Concept Check Match each function with its...Ch. 4.3 - Concept Check Match each function with its graph...Ch. 4.3 - Concept CheckMatch each function with its graph...Ch. 4.3 - Concept Check Match each function with its graph...Ch. 4.3 - Graph each function over a one-period interval....Ch. 4.3 -
Graph each function over a one-period interval....Ch. 4.3 - Graph each function over a one-period interval....Ch. 4.3 - Graph each function over a one-period interval....Ch. 4.3 - Graph each function over a one-period interval....Ch. 4.3 - Graph each function over a one-period interval....Ch. 4.3 - Graph each function over a one-period interval....Ch. 4.3 - Graph each function over a one-period interval....Ch. 4.3 -
Graph each function over a one-period...Ch. 4.3 - Graph each function over a one-period interval....Ch. 4.3 - Graph each function over a one-period interval....Ch. 4.3 -
Graph each function over a one-period interval....Ch. 4.3 - Graph each function over a two-period interval....Ch. 4.3 -
Graph each function over a two-period interval....Ch. 4.3 -
Graph each function over a two-period...Ch. 4.3 -
Graph each function over a two-period...Ch. 4.3 - Graph each function over a two-period interval....Ch. 4.3 - Graph each function over a two-period interval....Ch. 4.3 - Prob. 31ECh. 4.3 - Graph each function over a two-period interval....Ch. 4.3 - Graph each function over a two-period interval....Ch. 4.3 - Prob. 34ECh. 4.3 - Graph each function over a two-period interval....Ch. 4.3 - Prob. 36ECh. 4.3 - Graph each function over a two-period interval....Ch. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - Prob. 40ECh. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Prob. 44ECh. 4.3 - Concept Check Decide whether each statement is...Ch. 4.3 - Concept CheckDecide whether each statement is true...Ch. 4.3 -
Concept Check Decide whether each statement is...Ch. 4.3 - Prob. 48ECh. 4.3 - Concept Check If c is any number, then how many...Ch. 4.3 - Prob. 50ECh. 4.3 - 51. Show that tan(–x) = –tan x by writing tan(–x)...Ch. 4.3 - 52. Show that cot (–x) = –cot x by writing cot...Ch. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.4 - CONCEPT PREVIEW Match each description in Column I...Ch. 4.4 -
CONCEPT PREVIEW Match each description in...Ch. 4.4 -
CONCEPT PREVIEW Match each description in Column...Ch. 4.4 -
CONCEPT PREVIEW Match each description in Column...Ch. 4.4 -
CONCEPT PREVIEW Match each description in Column...Ch. 4.4 -
CONCEPT PREVIEW Match each description in Column...Ch. 4.4 - Concept Check Match each function with its graph...Ch. 4.4 - Concept Check Match each function with its graph...Ch. 4.4 - Concept Check Match each function with its graph...Ch. 4.4 - Concept Check Match each function with its graph...Ch. 4.4 - Graph each function over a one-period interval....Ch. 4.4 - Graph each function over a one-period interval....Ch. 4.4 - Graph each function over a one-period interval....Ch. 4.4 - Graph each function over a one-period interval....Ch. 4.4 -
Graph each function over a one-period interval....Ch. 4.4 - Graph each function over a one-period interval....Ch. 4.4 - Graph each function over a one-period interval....Ch. 4.4 - Graph each function over a one-period interval....Ch. 4.4 - Graph each function over a one-period interval....Ch. 4.4 - Graph each function over a one-period interval....Ch. 4.4 - Graph each function over a one-period interval....Ch. 4.4 - Graph each function over a one-period interval....Ch. 4.4 - Graph each function over a one-period interval....Ch. 4.4 - Graph each function over a one-period interval....Ch. 4.4 - Connecting Graphs with EquationsDetermine an...Ch. 4.4 - Connecting Graphs with Equations Determine an...Ch. 4.4 - Connecting Graphs with Equations Determine an...Ch. 4.4 - Connecting Graphs with Equations Determine an...Ch. 4.4 - Connecting Graphs with Equations Determine an...Ch. 4.4 - Prob. 30ECh. 4.4 - Concept CheckDecide whether each statement is true...Ch. 4.4 - Concept Check Decide whether each statement is...Ch. 4.4 - Concept CheckDecide whether each statement is true...Ch. 4.4 - Prob. 34ECh. 4.4 - 35. Concept Check If c is any number such that -1...Ch. 4.4 - Prob. 36ECh. 4.4 - 37. Show that sec (–x) = sec x by writing sec (–x)...Ch. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - (Modeling) Distance of a Rotating Beacon The...Ch. 4.4 - Prob. 41ECh. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4.4 - Prob. 44ECh. 4.4 - Prob. 45ECh. 4.4 - Prob. 46ECh. 4.4 - Prob. 1SECh. 4.4 - Prob. 2SECh. 4.4 - These summary exercises provide practice with the...Ch. 4.4 - Prob. 4SECh. 4.4 - Prob. 5SECh. 4.4 - Prob. 6SECh. 4.4 - Prob. 7SECh. 4.4 -
Graph each function over a two-period...Ch. 4.4 - Prob. 9SECh. 4.4 - Graph each function over a two-period...Ch. 4.5 - CONCEPT PREVIEW Refer to the equations in the...Ch. 4.5 - Prob. 2ECh. 4.5 - CONCEPT PREVIEW Refer to the equations in the...Ch. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.5 - Prob. 6ECh. 4.5 - Spring Motion An object is attached to a coiled...Ch. 4.5 - Spring Motion Repeat Exercise 7, but assume that...Ch. 4.5 - 9. Voltage of an Electrical Circuit The voltage E...Ch. 4.5 - Prob. 10ECh. 4.5 - Particle Movement Write the equation and then...Ch. 4.5 - Prob. 12ECh. 4.5 -
13. Pendulum Motion What are the period P and...Ch. 4.5 - Prob. 14ECh. 4.5 - Spring Motion The formula for the up and down...Ch. 4.5 - Spring Motion (See Exercise 15.) A spring with...Ch. 4.5 - Spring Motion The position of a weight attached to...Ch. 4.5 - Spring Motion The position of a weight attached to...Ch. 4.5 - Spring Motion A weight attached to a spring is...Ch. 4.5 -
20. Spring Motion A weight attached to a spring...Ch. 4.5 -
(Modeling) Springs A weight on a spring has...Ch. 4.5 - Prob. 22ECh. 4.5 -
(Modeling) Springs A weight on a spring has...Ch. 4.5 -
(Modeling) Springs A weight on a spring has...Ch. 4.5 - Prob. 25ECh. 4.5 - Prob. 26ECh. 4.5 - Prob. 27ECh. 4.5 - Prob. 28ECh. 4.5 -
(Modeling) Spring Motion Consider the spring in...Ch. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - (Modeling) Spring Motion Consider the spring in...Ch. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4 - Concept Check Which one of the following...Ch. 4 - Prob. 2RECh. 4 - Prob. 3RECh. 4 - Prob. 4RECh. 4 - Prob. 5RECh. 4 - Prob. 6RECh. 4 - Prob. 7RECh. 4 - Prob. 8RECh. 4 -
For each function, give the amplitude, period,...Ch. 4 - Prob. 10RECh. 4 - Prob. 11RECh. 4 - Prob. 12RECh. 4 - Prob. 13RECh. 4 -
For each function, give the amplitude, period,...Ch. 4 - Prob. 15RECh. 4 - Prob. 16RECh. 4 - Prob. 17RECh. 4 - Prob. 18RECh. 4 - Prob. 19RECh. 4 - Prob. 20RECh. 4 - Prob. 21RECh. 4 - Prob. 22RECh. 4 - Prob. 23RECh. 4 - Prob. 24RECh. 4 - Prob. 25RECh. 4 - Prob. 26RECh. 4 - Prob. 27RECh. 4 - Prob. 28RECh. 4 - Prob. 29RECh. 4 - Prob. 30RECh. 4 - Prob. 31RECh. 4 - Prob. 32RECh. 4 - Graph each function over a one-period...Ch. 4 -
Graph each function over a one-period...Ch. 4 -
Graph each function over a one-period...Ch. 4 - Prob. 36RECh. 4 -
Graph each function over a one-period...Ch. 4 - Prob. 38RECh. 4 - Prob. 39RECh. 4 - Prob. 40RECh. 4 - Prob. 41RECh. 4 - Prob. 42RECh. 4 - (Modeling) Monthly Temperatures A set of...Ch. 4 - Prob. 44RECh. 4 - Prob. 45RECh. 4 - Prob. 46RECh. 4 - Prob. 47RECh. 4 - Prob. 48RECh. 4 - Prob. 49RECh. 4 - Prob. 50RECh. 4 - Prob. 51RECh. 4 - Prob. 52RECh. 4 - Prob. 53RECh. 4 - Prob. 54RECh. 4 - Prob. 55RECh. 4 - Prob. 56RECh. 4 - Prob. 57RECh. 4 - Prob. 58RECh. 4 - Prob. 1TCh. 4 - Prob. 2TCh. 4 - Prob. 3TCh. 4 - Prob. 4TCh. 4 - Prob. 5TCh. 4 - Prob. 6TCh. 4 - Prob. 7TCh. 4 - Prob. 8TCh. 4 - Prob. 9TCh. 4 - Prob. 10TCh. 4 - Prob. 11TCh. 4 - Prob. 12TCh. 4 - Average Monthly Temperature The average monthly...Ch. 4 -
14. Spring Motion The position of a weight...Ch. 4 - Prob. 15T
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