Tonya and Pearl each completed a separate proof to show that alternate interior angles AKL and FLK are congruent. Who completed the proof incorrectly? Explain.

The triangles are similar. what is the value of x? show your work.

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?

Two friends are reading books. jimmy reads a book with 21,356 words. his friend bob reads a book with one-and-a-half times as many words. which expression represents the number of words bob reads?