For what value of b will the system of equations shown below have no solution? y= x^2 - 3
y = b

(1) -5
(2) 4
(3) -3
(4) 0

Researchers were interested in whether relaxation training decreases the number of headaches a person experiences. they randomly assigned 20 participants to a control group or a relaxation training group and noted the change in number of headaches each group reported from the week before training to the week after training. which statistical analysis should be performed to answer the researchers' question?

In each diagram, line p is parallel to line f, and line t intersects lines p and f. based on the diagram, what is the value of x? ( provide explanation)

Anita has a success rate of 80% on free throws in basketball. she wants to know the estimated probability that she can make exactly four of five free throws in her next game. how can she simulate this scenario? categorize each simulation of this scenario as correct or incorrect.