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Two-variable data: Models and scatterplots SAT question

Math · Problem-Solving and Data Analysis · Easy · Answer it here, explanation included.

A study was done to determine a new car’s stopping distance when it was traveling at different speeds. The study was done on a dry road with good surface conditions. The results are shown below, along with the graph of a quadratic function that models the data.

The figure presents a graph in the x y-plane titled “Vehicle Stopping Distance.” The x-axis is labeled “Speed, in miles per hour,” and the numbers zero through 80, in increments of 20, are indicated. The y-axis is labeled “Stopping Distance, in feet” and the numbers zero through 350, in increments of 50, are indicated. In the graph, there are six data points indicated from left to right with each point strictly to the right and above the preceding point. From left to right, the approximate coordinates of the six points are as follows. Point 1: 20 comma 40. Point 2: 30 comma 75. Point 3: 40 comma 120. Point 4: 50 comma 185. Point 5: 60 comma 240. Point 6: 70 comma 315. A quadratic curve is shown on the graph. The curve begins at point 1 and curves upward and to the right, passing through point 2 and point 3. It then passes slightly below point 4 and slightly above point 5, ending at point 6.

According to the model, which of the following is the best estimate for the stopping distance, in feet, if the vehicle was traveling 55 miles per hour?

ExplanationShow

Correct Answer Rationale
Choice C is correct. According to the model, the stopping distance, in feet, of a vehicle traveling 55 miles per hour is about 200 feet. Of the choices given, the best estimate of the stopping distance for a car traveling 55 miles per hour is 210 feet.

Incorrect Answer Rationale
Choices A, B, and D are incorrect and may be the result of incorrectly reading the given quadratic model. The corresponding x-values to the y-values of 25 and 30 are not part of the model. The corresponding x-value to a y-value of 250 is approximately 60 mph, not 55 mph.

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