Mathematical Induction Questions and Answers

A political scientist surveys 21 of the current 98 representatives in a state's congress. What is the size of the sample: What is the size of the population:

A true-false test contains 10 questions. In how many different ways can this test be completed? (Assume we don't care about our scores.) This test can be completed in different ways.

Circle the polynomials below that are in P2. x²+x+2 x³ -x²+x-1 x²+x+1 5 Show that every polynomial in P2 can be written as a linear combination of the following three polynomials. x²+2x+1 (x-1)³ - (x + 1)³ x² + 4x +4

Given its time to maturity the duration of a zero coupon bond is O the same regardless of the discount rate O lowest when the discount rate is equal to the risk free rate O higher when the discount rate is lower O higher when the discount rate is lower

For each of the following differential equations, determine whether it is an exact equation or not. If it is, find a general solution. a. 2y²e²xy dx + ((2xy + 1)e²xy + 2y) dy = 0 b. (xy² - 4y³) dx + (x²y — 12x²y) dy = 0

Perform the given calculations mentally from left to right. Write down a sequence of numbers indicating intermediate steps in your thought process. (a) 647-382 (b) 3.173 (c) 56+36+41+4+75+32 (a) Select the choice below that shows a left to right thought process for 647-382 and fill in the final answer in the answer box in your choice. A. 9, 120, B. 9, 129, C. 200, 182, D. 300, 260,