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There are design specifications for the minimum sight distance that a driver stopped at a stop sign must have to safely cross the roadway where vehicles do not stop. The sight distance is the distance to see an approaching vehicle measured along the roadway from the intersection of the two roadways.

**Major Roadway Design Speed (DS) vs. Sight Distance (SD):**

| Design Speed (DS) [mph] | Sight Distance (SD) [ft] |
|-------------------------|--------------------------|
| 25 | 240 |
| 30 | 290 |
| 35 | 335 |
| 40 | 385 |
| 45 | 430 |
| 50 | 480 |
| 60 | 575 |
| 65 | 625 |
| 70 | 670 |
| 75 | 720 |

Tasks:
(a) Plot a graph with design speed as the independent variable.
(b) Determine the equation of the relationship using the method of selected points.
(c) Determine the equation of the relationship using computer-assisted methods.
(d) Predict the sight distance required at 55 mph.

Answer :

(a) A graph that represents the data set is shown in the picture below.

(b) An equation of the relationship using the method of selected points is y = 9.5x + 5.

(c) An equation of the relationship using computer-assisted methods is y = 9.58x + 0.91.

(d) The predicted sight distance required at 55 mph is 528 feet.

Part a.

In this scenario, we would plot a graph that represents the data set by making design speed the independent variable and sight distance the dependent variable, as shown in the picture below.

Part b.

An equation of the relationship using the method of selected points can be determined by using these points (30, 290) and (50, 480);

Slope (m) = (480 - 290)/(50 - 30)

Slope (m) = 9.5

At data point (30, 290) and a slope of 9.5, an equation for this line can be calculated by using the point-slope form as follows:

[tex]y - y_1 = m(x - x_1)[/tex]

y - 290 = 9.5(x - 30)

y = 9.5x - 285 + 290

y = 9.5x + 5

Part c.

By using computer-assisted methods, an equation of the relationship between DS and SD is given by;

y = 9.58x + 0.91.

Part d.

The predicted sight distance required at 55 mph can be caculated as follows;

y = 9.58(55) + 0.91

y = 526.9 + 0.91

y = 527.81 ≈ 528 feet.

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