Let P(x) be the statement "x is a duck", let Q(x) be the statement "x is one of my poultry", let R(x) be the statement "x is an officer", and let S(x) be the statement "x is willing to waltz". Express each of the following statements in terms of P(x), Q(x), R(x) and S(x), quantifiers, and logical connectives. Let the universe of discourse consist of all living creatures. Put the appropriate letter next to the corresponding symbolic form.

Asocial networking site currently has 400,000 active members, and that figure is predicted to increase by 32% each year. the following expression represents the number of active members on the site after t years.

What is the next step in the given proof? choose the most logical approach. a. statement: m 1 + m 2 + 2(m 3) = 180° reason: angle addition b. statement: m 1 + m 3 = m 2 + m 3 reason: transitive property of equality c. statement: m 1 = m 2 reason: subtraction property of equality d. statement: m 1 + m 2 = m 2 + m 3 reason: substitution property of equality e. statement: 2(m 1) = m 2 + m 3 reason: substitution property of equality

Percent increase and decrease. original number: 45 new number: 18