Can someone help me out? I’m studying for my test tomorrow, and I get it for the most part. I’m just confused on a couple of things. I understand how my teacher got all the way to the sinx = -root 2 over 2 but how did they get 5 pi over 4 + 2n pi and 7 pi over 4 + 2n pi?

Astudent draws two parabolas on graph paper. both parabolas cross the x-axis at (–4, 0) and (6, 0). the y-intercept of the first parabola is (0, –12). the y-intercept of the second parabola is (0, –24). what is the positive difference between the a values for the two functions that describe the parabolas? write your answer as a decimal rounded to the nearest tenth

The price of a visit to the dentist is \$50$50. if the dentist fills any cavities, an additional charge of \$100$100 per cavity gets added to the bill. if the dentist finds nn cavities, what will the cost of the visit be?

Abottled water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company. the water bottling company’s specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. a random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.995 gallon a. construct a 99% confidence interval estimate for the popula-tion mean amount of water included in a 1-gallon bottle. b. on the basis of these results, do you think that the distributor has a right to complain to the water bottling company? why? c. must you assume that the population amount of water per bottle is normally distributed here? explain. d. construct a 95% confidence interval estimate. how does this change your answer to (b)?