Practice
1. samuel is remodeling his basement. one part of the planning involves the flooring. he knows that he
would like both carpet and hardwood, but isn't sure how much of each he will use. the most amount
of flooring area he can cover is 2000 square feet. the carpet is $4.50 per square foot and the
hardwood is $8.25 per square foot. both prices include labor costs. samuel has budgeted $10,000
for the flooring.
a. write a system of inequalities to represent the maximum amount of flooring needed and the
maximum amount of money samuel wants to spend.
b. one idea samuel has is to make two rooms-one having 400 square feet of carpeting and the other
having 1200 square feet of hardwood. determine whether this amount of carpeting and hardwood are
solutions to the system of inequalities. explain your reasoning in terms of the problem situation.
c. graph this system of inequalities.
d. determine the intersection point of the two lines. is this a solution to this system of inequalities in
terms of the problem situation?
e. identify two different solutions to the system of inequalities. explain what the solutions represent

F(x) = (x^2 + 3x − 4) and g (x) = (x+4) find f/g and state the domain.

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

Name and describe the three most important measures of central tendency. choose the correct answer below. a. the mean, sample size, and mode are the most important measures of central tendency. the mean of a data set is the sum of the observations divided by the middle value in its ordered list. the sample size of a data set is the number of observations. the mode of a data set is its highest value in its ordered list. b. the sample size, median, and mode are the most important measures of central tendency. the sample size of a data set is the difference between the highest value and lowest value in its ordered list. the median of a data set is its most frequently occurring value. the mode of a data set is sum of the observations divided by the number of observations. c. the mean, median, and mode are the most important measures of central tendency. the mean of a data set is the product of the observations divided by the number of observations. the median of a data set is the lowest value in its ordered list. the mode of a data set is its least frequently occurring value. d. the mean, median, and mode are the most important measures of central tendency. the mean of a data set is its arithmetic average. the median of a data set is the middle value in its ordered list. the mode of a data set is its most frequently occurring value.