Concept explainers
Temperature The table shows the temperatures y (in degrees Fahrenheit) in a city over a 24-hour period. Let x represent the time of day, where
Time, x | Temperature, y |
0 | 34 |
2 | 50 |
4 | 60 |
6 | 64 |
8 | 63 |
10 | 59 |
12 | 53 |
14 | 46 |
16 | 40 |
18 | 36 |
20 | 34 |
22 | 37 |
24 | 45 |
These data can be approximated by the model
(a) Use a graphing utility to create a
(b) How well does the model fit the data?
(c) Use the graph to approximate the times when the temperature was increasing and decreasing.
(d) Use the graph to approximate the maximum and minimum temperature during this 24-hour period.
(e) Could this model predict the temperatures in the city during the next 24-hour period? Why or why not?
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
PRECALCULUS-WEBASSIGN EPIN K12 ACCESS
- The Kelvin Temperature Scale Physicists and chemists often use the Kelvin temperature scale. In order to determine the relationship between the Fahrenheit and Kelvin temperature scales, a lab assistant put Fahrenheit and Kelvin thermometers side by side and took readings at various temperatures. The following data were recorded. K = kelvins F = degrees Fahrenheit 200 -99.67 220 -63.67 240 -27.67 260 8.33 280 44.33 300 80.33 a. Show that the temperature F in degrees Fahrenheit is a linear function of the temperature K in kelvins. b. What is the slope of this linear function? Note: Be sure to take into account that the table lists kelvins in jumps of 20 rather than in jumps of 1. c. Find a formula for the linear function. d. Normal body temperature is 98.6 degrees Fahrenheit. What is that temperature in kelvins? e. If temperature increases by 1 kelvin, by how many degrees Fahrenheit does it increase? If temperature increases by 1 degree Fahrenheit, by how many kelvins does it increase? f. The temperature of 0 kelvins is known as absolute zero. It is not quite accurate to say that all molecular motion ceases at absolute zero, but at that temperature the system has its minimum possible total energy. It is thought that absolute zero cannot be attained experimentally, although temperatures lower than 0.0000001 kelvin have been attained. Find the temperature of absolute zero in degrees Fahrenheit.arrow_forwardRunning Speed A man is running around a circular track that is 200 m in circumference. An observer uses a stopwatch to record the runner’s time at the each of each lap, obtaining the data in the following table. (a) What was the man’s average speed (rate) between 68 s and 152 s? (b) What was the man’s average speed between 263 s and 412 s? (c) Calculate the man’s speed for cadi lap, Is he slowing down, speeding up, or neither?arrow_forwardMortgage Rates The following table is taken from the website of Freddie Mac. It shows rates for 30-year fixed-rate mortgages since 1970. y=Year r=Mortgagerate 1975 9.05 1980 13.74 1985 12.43 1990 10.13 1995 7.93 2000 8.05 2005 5.87 2010 4.69 2015 3.84 a. Explain in practical terms the meaning of r(2003). b. Use the table to estimate the value of r(2003).arrow_forward
- Running Speed A man is running around a circular track that is 200 m in circumference. An observer uses a stopwatch to record the runners time at the end of each lap, obtaining the data in the following table. aWhat was the mans average speed rate between 68 s and 152 s? bWhat was the mans average speed between 263 s and 412 s? cCalculate the mans speed for each lap. Is he slowing down, speeding up or neither? Time s Distance m 32 200 68 400 108 600 152 800 203 1000 263 1200 335 1400 412 1600arrow_forwardaylor Swift wants to know the proportion of her fans who listened to her new single ME! within the first hour of it being released. In order to estimate this, she takes a sample of 150 of her fans and asks them if they listened to the song in this time period. Of the 150 fans, 135 of them (90%) responded that they did listen to the song during this time period. What is the parameter and what is its value? a. The parameter is the proportion of the 150 sampled Taylor Swift fans who listened to ME! within the first hour after it released, which is 135. b. The parameter is the group of Taylor Swift fans who were surveyed, which is 150. c. The parameter is the proportion of all Taylor Swift fans who listened to ME! within the first hour after it released, which is unknown. d. The parameter is the proportion of all Taylor Swift fans who listened to ME! within the first hour after it released, which is 0.9. e. The parameter is the…arrow_forwardThe geoemetric mean of 2, 4 & 8.arrow_forward
- Nate is investigating how long his phone's battery lasts (in hours) for various brightness levels (on a scale of 0- 100). His data is displayed in the table and graph below. 89 Brightness Level (x) Hours (y) 26 30 52 55 68 68 79 5.1 6. 3.9 4.5 1.8 5.7 2.8 2.3 +6 积 3. 70 80 90 100 11 60 Brightness Level 10 30 40 50 What is the residual for the point (68,5.7)? Round to 3 decimal places. hours Question Help: D Video D Post to forum Submit Question EGO 20arrow_forwardStatistics Questionarrow_forwardEach row represents an experimental “run” (in this case, averaged sample of mango wine). Column A shows the run number; Column B shows the percentage of ethanol; Column C shows the amount of glycerol (in g/L); Column D shows the amount of acid (in g/L); Column E shows the temperature of the run (in °C); and Column F shows the pH of the run. Y represents Ethanol of mango wine. 1. Create a scatterplot of the ethanol data for all 20 runs a. Draw a graphical representation of the model that you chose to use. b. Comparing the model to your data, evaluate its fit in one or two sentences. (Not sure what this question is getting at. I've provided all the information given) c. Replace the generic Yi = β0 + ε with the information you have here. Please help. I have no idea what this even means or where to start. HERE is the attached dataset to start with; a b c d e f Run Ethanol Glycerol Acidity Temp pH 1 4.8 3.5 0.84 24 3.8 2 9.6…arrow_forward
- Frank is investigating how long his phone's battery lasts (in hours) for various brightness levels (on a scale of 0-100). His data is displayed in the table and graph below. Brightness Level (x) Hours (y) 37 4.7 39 4.6 42 5.5 50 5.9 64 3.8 71 1.8 82 3.1 93 2.3 6. 8. 71 6. 5- 10 20 30 40 50 60 70 80 90 100 ll -14 Brightness Level a) Find the equation for the line of best fit. Keep at least 3 decimals for each parameter in the equation. b) Interpret the slope in context. O Frank should expect -0.0566 hours per brightness level. O Frank should expect -0.0566 brightness level per hour. c) What does the equation predict for the number of hours the phone will last at a brightness level of 55? hoursarrow_forwardAn experiment is performed to determine the % elongation of electrical conducting 1 material as a function of temperature. The relating data is - Temp C % elongation Use the above da:a to interpolate the % elongation for a temperature of 400°C. 200 250 300 375 425 475 525 500 13 13 15 17 19 20 23arrow_forwardOcean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent The distance from point of release to point of recovery in km/100. The following data a representative of one study using drift bottles to study ocean currents. x day 72 79 32 96 203 y km/100 14.8 19.6 5.3 11.8 35.1 Σx=482 Σy=86.6 Σx2=62874 Σy2=2002.54 Σxy=11041.7 r=.93787 use a 1% level of significance to test the claim p>0.(use 2 decimal places) t=critical t= Se=4.4913 a=1.4966 b=.1641 D) find the predicted distance (km/100) when a drift bottle has been floating for 80 days.(use 2 decimal places) find a 90% confidence interval for your prediction of part D. (use 2 decimal places) lower limit=___km/100upper limit=___km/100 he was a 1% level of…arrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill