For the following exercise, j ∥ k and △ABC is given.
Given:
m∠3 = 52°
m∠2 = 77°
Find: m∠1, m∠4, and m∠5 in degrees

Find csc x if sin x + cot x cos x =√3 a. 9 b. 3 c. √(3)/2 d. √(3)

Abby is preparing fruit punch for her party. she starts with a bowl filled with liquid that has 1/2 fruit juice and 1/2 sprite, but she decides it's too fruity. so she pours out 1/4 of the liquid, and then fills the bowl up again with sprite. what fraction of the punch is now sprite?

Assume that 1400 births are randomly selected and 1378 of the births are girls. use subjective judgment to describe the number of girls as significantly high, significantly low, or neither significantly low nor significantly high. choose the correct answer below. a. the number of girls is neither significantly low nor significantly high. b. the number of girls is significantly high. c. the number of girls is significantly low. d. it is impossible to make a judgment with the given information.