Let c(n) be the constant term in the expansion of (x + 4)n. prove by induction that c(n) = 4n for all n is in n. (induction on n.) the constant term of (x + 4)1 is = 4 . suppose as inductive hypothesis that the constant term of (x + 4)k − 1 is for some k > 1. then (x + 4)k = (x + 4)k − 1 · , so its constant term is · 4 = , as required.

Even if a person is in very good shape, applying to be a police officer requires commitment to fitness. applicants must pass a physical fitness test. in order to prepare for the test, janet purchases an activity tracker to court her steps. her goal is to walk 10,000 steps each day. she measures heard average step length to be 30 inches. play janet runs, her average steps length increases to 36 in. how many steps would she have to take to run 1 mile 50280 round to the nearest step

Which of the following best describes the graph below? + + 2 + 3 + 4 1 o a. it is not a function. o b. it is a one-to-one function. o c. it is a many-to-one function. o d. it is a function, but it is not one-to-one.

Atravel agent is booking a trip to england, scotland, ireland, and france for a group of senior citizens. the agent sent surveys to the group, asking which countries they would like to visit, in order, and created the shown preference schedule (e = england, i = ireland, s = scotland, f = france). which country is the condorcet winner? number of votes 15 12 16 19 1st f e e i 2nd e s i s 3rd s i s e 4th i f f f 1. scotland 2. england 3. france 4.ireland