Researchers want to determine if caffeine affects reaction time. They divide a sample of 150 people into 3 groups. Group 1 gets a regular drink with no caffeine, group 2 gets a drink with 95 mg of caffeine, and group 3 gets a drink with 250 mg of caffeine. Each group is then given a test to gauge their reaction time. What is the appropriate test to use?

One-way ANOVA

Step-by-step explanation:

One-way ANOVA(analysis of variance) a testing method in statistics that is used to compare the means of two or more independent samples, to check if the differences are statistically significant.

In this case, we have three groups which their various reaction time to caffeine is to be tested using the same testing method (amount of caffeine). Hence the appropriate test to use here is the one-way ANOVA

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240