Concept explainers
Weight of Car: Miles per Gallon Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). The following information is based on data taken from Consumer Reports (Vol. 62, No. 4).
x | 27 | 44 | 32 | 47 | 23 | 40 | 34 | 52 |
y | 30 | 19 | 24 | 13 | 29 | 17 | 21 | 14 |
Complete parts (a) through (e), given
(f) Suppose a car weighs
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Chapter 4 Solutions
Understanding Basic Statistics
- Planetary Velocity The following table gives the mean velocity of planets in their orbits versus their mean distance from the sun. Note that 1AU astronomical unit is the mean distance from Earth to the sun, abut 93 million miles. Planet d=distance AU v=velocity km/sec Mercury 0.39 47.4 Venus 0.72 35.0 Earth 1.00 29.8 Mars 1.52 24.1 Jupiter 5.20 13.1 Saturn 9.58 9.7 Uranus 19.20 6.8 Neptune 30.05 5.4 Astronomers tell us that it is reasonable to model these data with a power function. a Use power regression to express velocity as a power function of distance from the sun. b Plot the data along with the regression equation. c An asteroid orbits at a mean distance of 3AU from the sun. According to the power model you found in part a, what is the mean orbital velocity of the asteroid?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_forwardRunning 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_forward
- Energy ConsumptionThe monthly residential consumption of energy in the U.S. for 2012 is found in the following table. Source: Energy Information Administration. Month Energytrillion BTU January 990.527 February 833.163 March 560.826 April 412.426 May 297.500 June 253.015 July 240.486 August 248.035 September 249.354 October 378.094 Number 631.203 December 838.265 Plot the data, letting t=1 correspond to January, t=2 to February, and so on. Is it reasonable to assume that the monthly consumption of energy is periodic? Find the trigonometric function of the form C(t)=asin(bt+c)+d that models these data when t is the month of the year and C(t) is the energy consumption. Graph the function on the same calculator window as the data. Estimate the total energy consumption for the year for residential customers in the United States and compare it to the actual value. Calculate the period of the function found in part b. Is this period reasonable?arrow_forwardWeight Versus Height The following data show the height h, in inches, and weight w, in pounds, of an average adult male. h 61 62 66 68 70 72 74 75 w 131 133 143 149 155 162 170 175 a Make a power model for weight versus height. b According to the model from part a, what percentage increase in weight can be expected if height is increased by 10?arrow_forward
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