The sum of Joy's age and her brother's age is 24 . Her brother's age is 3 years older than twice Joy's age. What is the difference, in years, between Joy's age and her brother's age?

Danielle has $127.02 in her account before making any transactions. over the course of a week, danielle makes the following transactions: transaction debit ($) credit ($) birthday check 75.00 night out 66.14 garage sale proceeds 121.58 charitable donation 42.25 doctor’s appointment 115.30 at the end of the week, how much money is in danielle’s account? a. $99.91 b. $27.11 c. $184.41 d. $142.16 select the best answer from the choices provided a b c d

The distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of $235 and a standard deviation of $20. according to the standard deviation rule, how much did almost all (99.7%) of the students spend on textbooks in a semester?

Can someone me with #s 8, 9, and 11. with just one of the three also works. prove using only trig identities.