3. 5. 6. ty = f(x) (2, 8) y fy= f(x) 4. f(1.5. 5) 5 %3D 6- y = g(x) (-2, 8) 3 (-2, 0) (2, 0) -3 3 (-1, 0) (4, 0) (-3, –12) (1, -3) -3 (3,-12) -4 -2 2 (1, 2) -12- y = f(x) 4 x -5 y = g(x) -4 y = g(x) (a) f(x) > 0 (b) f(x) s 0 (a) g(x) < 0 (b) g (x) 2 0 (a) g(x) = f(x) (b) f(x) > g(x) (a) f(x) < g(x) (b) f(x) = g(x)
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In Problems 3–6, use the figure to solve each inequality.
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- What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
- The U.S. Bureau of the Census prediction for the percentage of the population 65 years and older can be modeled as p(x) = −0.00022x3 + 0.014x2 − 0.0033x + 12.236 percent where x is the number of years since 2000, data from 0 ≤ x ≤ 50. 1. Determine the value of x in the domain 0 ≤ x ≤ 50 for which the percentage is predicted to be increasing most rapidly (Round your answer to three decimal places). 2. Thus, in which year is the percentage is predicted to be increasing most rapidly? 3. Calculate the percentage at that time. (Round your answer to two decimal places.) 4. Calculate the rate of change of the percentage at that time. (Round your answer to three decimal places.)A positive value of the correlation coefficient "r" means_________ Group of answer choices that when x increases, y tends to increase and when x decreases, y tends to decrease that when x increases, y tends to increase and when x increases, y tends to decrease that when x increases, y tends to decrease and when x decreases, y tends to increase15. For several years researchers have noticed that thereappears to be a regular, year-by-year increase in theaverage IQ for the general population. Thisphenomenon is called the Flynn effect after theresearcher who first reported it (Flynn, 1984, 1999),and it means that psychologists must continuouslyupdate IQ tests to keep the population mean at 100. To evaluate the size of the effect, aresearcher obtained a 10-year-old IQ test that wasstandardized to produce a mean IQ of 100 for thepopulation 10 years ago. The test was then given to asample of n 64 of today’s 20-year-old adults. Theaverage score for the sample was M 107 with astandard deviation of s 12.a. Based on the sample, is the average IQ for today’spopulation significantly different from the average10 years ago, when the test would have producesa mean of 100? Use a two-tailed test with.01.b. Make an 80% confidence interval estimate oftoday’s population mean IQ for the 10-year-old test.
- A chemical reaction is run 12 times, and the temperature xi (in °C) and the yield yi (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded: x⎯⎯=65.0, y⎯⎯=29.03,∑ni=1(xi−x⎯⎯)2=6032.0,∑ni=1(yi−y⎯⎯)2=835.42,∑ni=1(xi−x⎯⎯)(yi−y⎯⎯)=1988.6x¯=65.0, y¯=29.03,∑i=1n(xi−x¯)2=6032.0,∑i=1n(yi−y¯)2=835.42,∑i=1n(xi−x¯)(yi−y¯)=1988.6 Let β0 represent the hypothetical yield at a temperature of 0°C, and let β1 represent the increase in yield caused by an increase in temperature of 1°C. Assume that assumptions 1 through 4 for errors in linear models hold. Find a 95% prediction interval for the yield of a particular reaction at a temperature of 40°C. Round the answers to three decimal places. The 95% prediction interval is ( , ).A chemical reaction is run 12 times, and the temperature xi (in °C) and the yield yi (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded: x⎯⎯=65.0, y⎯⎯=29.03,∑ni=1(xi−x⎯⎯)2=6032.0,∑ni=1(yi−y⎯⎯)2=835.42,∑ni=1(xi−x⎯⎯)(yi−y⎯⎯)=1988.6x¯=65.0, y¯=29.03,∑i=1n(xi−x¯)2=6032.0,∑i=1n(yi−y¯)2=835.42,∑i=1n(xi−x¯)(yi−y¯)=1988.6 Let β0 represent the hypothetical yield at a temperature of 0°C, and let β1 represent the increase in yield caused by an increase in temperature of 1°C. Assume that assumptions 1 through 4 for errors in linear models hold. Compute the error variance estimate s2. Round the answer to three decimal places.A chemical reaction is run 12 times, and the temperature xi (in °C) and the yield yi (in percent of a theoretical maximum) is recorded each time. The following summary statistics are recorded: x⎯⎯=65.0, y⎯⎯=29.03,∑ni=1(xi−x⎯⎯)2=6032.0,∑ni=1(yi−y⎯⎯)2=835.42,∑ni=1(xi−x⎯⎯)(yi−y⎯⎯)=1988.5x¯=65.0, y¯=29.03,∑i=1n(xi−x¯)2=6032.0,∑i=1n(yi−y¯)2=835.42,∑i=1n(xi−x¯)(yi−y¯)=1988.5 Let β0 represent the hypothetical yield at a temperature of 0°C, and let β1 represent the increase in yield caused by an increase in temperature of 1°C. Assume that assumptions 1 through 4 for errors in linear models hold. Find 95% confidence intervals for β0 and β1. Round the answers to three decimal places. The 95% confidence interval for β0 is ( , ). The 95% confidence interval for β1 is ( , ).
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