<h1>12 Got this right, but just wondering if there's a more efficient method than simply seeing that the line passes through (3, 25) and cost/oz is thus 300/25 = 12 cents.</h1>
<h1>14 I get LN is either 15 or 1. I'm physically drawing out the lines, but I'm missing something here.</h1>
<h1>18 How are you supposed to do this other than draw out circles? Seeing that 1 and 3 points of intersection are possible is easy to do, but it's harder to tell that 4 points are possible (the only circle I can think of passes though A, C, BC, and AB).</h1>
<h1>12. Right on! The average y/x is the slope of the line of the best fit; the point (25, 3) gives you the slope 3/25=.06.</h1>
<h1>14. The power of assumption: L, M, and N don’t have to be collinear, do they? :)</h1>
<h1>18. You mark 4 points you want you circle pass through and see if you can make it happen with some tweaking.</h1>
<p>Point A is fixed.
You chose C and one point on each BC and AB.
You can also choose B and one point on each BC and AC.
Or you can choose one point (besides A) on each AB, BC, and AC - in this case the circle has to be tangent to BC.</p>
<h1>14 Ah I see! They don’t have to be collinear! So we can let LM and MN be the two smaller sides of an obtuse triangle, with LN being the largest side. The largest LN could be is 15 if the obtuse angle were made 180 degrees. The only choice less than 15 is 14, E.</h1>
<p>Also could’ve done it using the fact that side 1 + side 2 > side 3. So LM + MN > LN, or LN < 15.</p>