Which of the following statements best defines independent events?
a.
two events are independent events if it is impossible for the two events to occur simultaneously.
b.
two events are independent events if the occurrence of one event has no effect on the probability of the other.
c.
two events are independent events if the intersection between the sample spaces of the two events is not empty.
d.
two events are independent events if the union of the sample spaces of the two events is not empty.

For the right triangle shown, the lengths of two sides are given. find the third side. leave your answer in simplified, radical form.

Which of the following is not a solution to the inequality graphed below? (-2, -4)(-1, -5)(0, -3)(2, -1)which of the following is a solution to the inequality graphed below? select all that apply.(-3, -3)(-1, -1)(-3, -1)(2, 2)

Stu and ambrose are working together on a study of whether diet is related to students' mental health. first, they randomly select 10 students from the student center and 10 students from the office of counseling and psychological services. then, they ask students to rate their diet in terms of healthiness on a scale of 1-100 before completing a 20-item mental health survey. a) name one of the constructs being studied b) how was the construct you named above operationally defined in this experiment? e) was the variable you described above their independent variable, their dependent variable, or a controlled variable? d) what is a confounding variable? what is a potential confound in this study?