Consider an ant that is walking on a cartesian grid, starting at (0,0) and ending at (20, 15). the ant always chooses to walk exactly one unit either up or to the right (towards his destination) whenever he arrives at a lattice point. (a lattice point is a point with integer coordinates.) thus, from (0,0) he either walks to (1, 0) or (0, 1). if the ant is not allowed to go to the points (12, 5) and (17, 11), how many different paths can he take on his walk?

Mercury poisoning is dangerous overload of mercury within the body. a major source of mercury within the body, a major source of mercury poisoning is consuming fish that contain mercury. certain fish are more prone to having higher levels of mercury than others. the pie chart shows the distribution of four breeds of fish at a hatchery. the hatchery has approximately 6,000 fish. a biologist from the centers for disease control and prevention randomly test 5% of each breed of fish for mercury content. her findings are shown in the following table. based on the biologist's findings, if a single salmon is randomly selected from those that were tested, what is the probability that this particular fish would have a dangerous mercury level? a) 0.001 b) 0.004 c) 0.02 d) 0.08

Over which interval is the graph of f(x) = x2 + 5x + 6 increasing?

Sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y. draw a typical approximating rectangle and label its height and width. y= 5x, y=7x^2then find the area s of the region.