26. The table below shows the values of the function {(X) for different values of x. What is the average rate of change in f(x) between X : 1 and X : 5? Enter your answer in the box. \f29. The polynomial function p(x) = x3 - 4x2 + ax + 20 has (x + 1) as one of its factors. What would be the remainder when p(x) is divided by (x + 2)? O A. 42 O B. 15 O C. -22 O D. -3430. A researcher surveyed 220 residents of a city about the number of hours they spend watching news on television each day. The mean of the sample was 1.8 with a standard deviation of 0.35. The researcher can be 95% confident that the mean number of hours all the residents of the city are watching news on television is 1.8 with what margin of error? (Use the formula M = 1.96 x O A. +4.62% O B. +3.88% O C. +0.31% O D. +2.5%31. A researcher surveyed two different samples of a town's population to determine whether the residents support building a new sports complex. The first sample was made up of 160 people randomly chosen from a list of all the residents of that town. The second sample was made up of 190 residents who graduated from the local university. Sample Sample In Favor of Size the Proposal 160 125 2 190 110 Which sample best fulfills the purpose of the survey? O A. Sample 1 because its makeup is more representative of the town population. O B. Sample 1 because more people were in favor of the proposal. O C. Sample 2 because it involved more people. O D. Sample 2 because it involved residents with a college degree.32. A teacher gave her class two functions, f(x) : Ix 5| + 4 and g(x) : -X2 + 21, and asked for the solution(s) of the equation f(x) : g(x). The answers given by four students are shown below: Betty: only 4 Donna: only 5 Edward: 12 and 5 Gary: -3 and 4 Who found the solution correctly and why? 0 A. Edward, the solutions are the yvalues of the points of intersection of the graphs of {(x) and g(x). I O B. Donna, the solutions are the yvalues of the points of intersection of the graphs of {(X) and g(x) but solutions paired with negative X i values must be discarded because f(x) is an absolute value function. 0 C. Gary, the solutions are the xvalues of the points of intersection of the _ I graphs of {(x) and g(x). O D. Betty, because the solutions are the xvalues of the points of intersection of the graphs of {(x) and g(x) but the negative solutions I must be discarded because {(x) is an absolute value function. 33. A researcher claims that reading information aloud affects students' ability to retain the information. To test this hypothesis, he asked thirty students to memorize two lists of names, one written and the other read aloud. The number of names from each list remembered by students was recorded. The data has a tvalue of 2.879 and the critical value is 2.462. Because the t value is greater than the critical value, what can the researcher conclude? O A. The null hypothesis cannot be rejected and the difference in __ performance is significant with 99% confidence. I O B. The null hypothesis cannot be rejected and the difference in __ I performance is not significant with 99% confidence. 0 C. The null hypothesis can be rejected and the difference in performance __ is not significant with 99% confidence. 0 D. The null hypothesis can be rejected and the difference in performance __ is significant with 99% confidence. 34. A study was conducted to determine whether the difference in fuel economy (miles per gallon) for two different brands of tires was statistically significant. The data has a tyalue of 0.755 and the critical value is 1.729. The null hypothesis is that there will be no difference between the two brands of tires. Because the tvalue is less than the critical value, what can the researcher conclude? O A. The null hypothesis can be rejected and the difference in performance is significant with 95% confidence. 0 B. The null hypothesis cannot be rejected and the difference in performance is not significant with 95% confidence. 0 C. The null hypothesis can be rejected and the difference in performance is not significant with 95% confidence. 0 D. The null hypothesis cannot be rejected and the difference in performance is significant with 95% confidence