At a coffee shop, 70% of the customers buy a coffee drink, 30% buy food, and 20% buy both a coffee drink and food. Are buying food and buying a coffee drink independent events? How do you know?

Find the roots of the polynomial function f(x) = x^3 + 2x^2 + x

Which scenarios are most effectively explored by conducting an experiment? there is more than one correct answer. select all that apply. researchers want to study the effectiveness of a particular drug for treating migraines. they want to know which dosage of the drug yields the best results with the least side effects. to ensure fair results, the researchers want to ensure that participants and dosage administrators do not know which dosage participants receive. a teacher wants to plan a class fieldtrip and quickly determine where students prefer to go for the class fieldtrip. a car mechanic wants to know which of two engine brands makes better-performing engines. he wants to test the engines in identical situations and rate their performance in a way that can be fairly measured. a chemist studies the properties of a metal compound. she wants to know how the sample size of the metal affects its ability to conduct electricity. she wants to conduct the research in a controlled environment to minimize bias. a realty company wants to know the average income of its clients. the company wants to gather data income from current clients.

Anew test for ra is being developed. the test is administered to 750 patients with ra and 750 without ra. for the sake of the question, assume the prevalence of ra in this population is 50%. of the 750 patients with ra, 575 have a positive result. of the 750 patients without ra, 150 have a positive result. what is the positive predictive value of the new test? a575/(575+150) b. 600/(600+ 150) c. 575/(575+125) d. 600/(600+ 125)