Determine whether the argument is inductive or deductive reasoning.

______________1. All books written by J.K. Rowling make the best seller list. The bookHarry Potter and the Deathly Hallows is a J.K Rowling book. Therefore, the bookHarry Potter and the Deathly Hallowsmade the best seller list.

______________2. Samantha got an A on each of her first four math tests, so she will get an A on the next Math test.

_______________3. We had rain each day for the last five days, so it will rain today.

_______________4. All amoeba multiply b dividing. I have named the amoeba shown in my microscope Amelia. Therefore, Amelia multiplies by dividing.

_______________5. Find the counterexample to show that the following conjecture is false.

Conjecture: For all numbers x, x⁴ > x.

_______________6. Find the counterexample to show that the following conjecture is false.

Conjecture: For all counting numbers n,n3+5n+66 is an even counting number.

______________7. Find counterexample to show that the following conjecture is false.

Conjecture: For numbers a and b, (a + b)³ = x² + 16.

B. Solve each problem using Polya's four step problem-solving strategies. Label your work so that each of Polya's four steps is identified.

1. A rancher decides to enclose a rectangular region by using an existing fence along one side of the region and 2240 feet of new fence on the other three sides. The rancher wants the length rectangular region to be five times as long as its width. What will be the dimensions of the rectangular region?
2. An investor bought 20 shares of stock for a total cost of $1200 and them sold all the shares for $1400. A few months later, the investor bought 25 shares of the same stock for a total cost for a total cost of $1800 and then sold all the shares for $1900. How much money did the investor earn on these investments?
3. Two perpendicular line segments partition the interior of a rectangle into four smaller rectangles. The areas of these smaller rectangles are x, 2, 5 and 10 square inches. Find all possible values of x.