In their report, the researchers stated that "after adjusting for various demographic and lifestyle variables, daily consumption of two or more servings was associated with a 30% reduced prevalence of high cholesterol." why was it important to adjust for these variables? a. the researchers wanted to ensure that the study was representative of the entire population, so they were likely to adjust the responses to match actual data collected for the entire population. b. the researchers were sure that various demographic and lifestyle variables had greater influence than daily consumption of two or more servings. c. the researchers wanted to ensure that the sample was large enough in order to perform inference. d. the researchers may be concerned with confounding that occurs when the effects of two or more explanatory variables are not separated or when there are some explanatory variables that were not considered in a study, but that affect the value of the response variable. click to select your answer.

Which math sentence can be used to determine if the triangle is a right triangle?

Use composition to determine if (x) or h(x) is the inverse of f(x) for the limited domain x2-1.

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.