The path of a race will be drawn on a coordinate grid like the one shown below. The starting point of the race will be at (−5.5, 2). The finishing point will be at (2, −5.5). A four-quadrant coordinate grid is drawn from negative 4 to positive 4. Quadrant I is labeled Quadrant P, Quadrant II is labeled Quadrant Q, Quadrant III is labeled Quadrant R, and Quadrant IV is labeled Quadrant S. Part A: Use the grid to determine in which quadrants the starting point and the finishing point are located. Explain how you determined the locations. (6 points) Part B: A checkpoint will be at (5.5, 2). In at least two sentences, describe the differences between the coordinates of the starting point and the checkpoint, and explain how the points are related. (4 points)

Suppose there is a simple index of three stocks, stock abc, stock xyz, and stock qrs. stock abc opens on day 1 with 4000 shares at $3.15 per share. stock xyz opens on day 1 with 5000 shares at $4.30 per share. stock qrs opens on day 1 with 6000 shares at $4.60 per share. the price of stock abc on day 8 begins at $3.50. the price of stock xyz on day 8 begins at $3.90. stock qrs opens on day 8 with a price of $4.50 per share. assume that each stock has the same number of shares that it opened with on day 1. what is the rate of change of this simple index over 1 week?

Browning labs is testing a new growth inhibitor for a certain type of bacteria. the bacteria naturally grows exponentially each hour at a rate of 6.2%. the researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. the sample currently contains 100 bacteria.the container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. however, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. they would like to determine the possible number of bacteria in the container over time.create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

Orly uses 2 cups of raisins for every 12 cups of trail mix she makes. how many cups of trail mix will she make if she uses 8 cups of raisins?