You are a researcher interested in the relationship between alcohol consumption and grade-point average (GPA). You set out to conduct a hypothesis test. You draw a random sample of 12 college juniors and ask them, "on average, how many drinks do you have per week?" You also record the students current GPA. Calculate Pearson's r to determine if there is a relationship (Show all of your work). Indicate what you are doing at each step (i. e. Step Two: Pearson's Correlation)

1) in triangle the, what is the measure of angle t (in degrees)? 2) in triangle bat, the measure of angle b is 66∘, and the measure of angle t is 77∘.what is the measure of the exterior angle at a (in degrees)?

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?

The functions f(x) and g(x) are shown in the graph f(x)=x^2 what is g(x) ?