Jennifer bought a $1,038.99 dining room set for her home in Cincinnati. She calculated the sales tax to be exactly $67.53435. a. Round the sales tax to the nearest penny.

b. Round the sales tax to the nearest dollar.

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).

Avery’s piggy bank has 300 nickels, 450 pennies, and 150 dimes. she randomly picks three coins. each time she picks a coin, she makes a note of it and puts it back into the piggy bank before picking the next coin.

Aclassroom is made up of 11 boys and 14 girls. the teacher has four main classroom responsibilities that she wants to hand out to four different students (one for each of the four students). if the teacher chooses 4 of the students at random, then what is the probability that the four students chosen to complete the responsibilities will be all boys?