Sample response: The student did not distribute the negative when subtracting. Distributing the negative,
the expression is equal to 6b + 4r – 2b – r. Then use
the commutative property to rewrite it as 6b – 2b + 4r
- r. Then you can use the distributive property to write
Which did you consider in your response? Check all
that apply.
When subtracting an expression in parentheses,
you need to distribute the negative.
You can use properties of operations to rearrange
the expression and group like terms in order to
combine them.

Find the balance at the end of 4 years if 1000 is deposited at the rate of

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.

(50 ) mrs. julien’s and mrs. castillejo’s classes are selling cookie dough for a school fundraiser. customers can buy packages of macadamia nut chip cookie dough and packages of triple chocolate cookie dough. mrs. julien’s class sold 25 packages of macadamia nut chip cookie dough and 30 packages of triple chocolate cookie dough for a total of $221.25. mrs. castillejo’s class sold 5 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $191.25. (a) write the system of equations that model the problem. be sure to explain which equation represents which situation. (b) find the cost of each type of cookie. show your work. (c) explain which method you used to solve the system and why you chose that method.