Explanation for Question 37 From the Math (Calc) Section on the 2017 May Sat
The last questions. Um, 37 and 38 are related, 2 but this video will cover question 37. 3 So they give us a graph and it says, or a scatterplot. 4 And it says the scatterplot above shows the average fuel economy for a certain 5 class of car driven at 12 different speeds. 6 The graphical quadratic model for the data is also shown. 7 And then we look at 37, it says for what fraction of the 12 8 speeds does the model overestimate the average fuel economy. 9 So we need to understand which one's the model and which one is the 10 actual value. So between the graph and the points. 11 So they say the scatter plot shows the average fuel economy. 12 And then it says the graph of the quadratic model. 13 Um, well that is the model. 14 So the scatter plot would be the points and that's the average 15 blue economy. That's the real. 16 And then the graph, um, 17 is the model. So the, 18 the outside on parabola is just a model and it says 19 for what fraction of the 12 speeds does the model or the, 20 the graph, the parabola overestimate, 21 the average fuel economy, which is the points. 22 So we just want to see where, 23 or for how many points is the graph higher than the points. 24 We have our graph here, since we're, we want to know how many they're 25 overestimating, that's our graph. 26 So we want to see how many are under this. 27 One's under this one's under, 28 and this one's under. So for those three points, 29 our graph overestimates them and they say there's 12. 30 So we know three are, 31 um, overestimated over 12, 32 which could also simplify, simplify to one fourth, 33 which is our final answer.