Calculate the angle of inclination of the line segment CD given the coordinates of the vertices A, B, C, and D.

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Question 2.4 and 2.5
To determine and interpret the correlation between productivity and hours training, the specific data points for these variables are required. This information is not provided in the image. Without the data, it is not possible to calculate the correlation coefficient or comment on its nature.

Question 3
ABCD is a quadrilateral with vertices A(-3; 0), B(-1; -3), C(2; -1) and D(0; 2). The diagram shows an angle $\theta$ which is the angle of inclination of the line segment CD with the positive x-axis.

• Step 1: Calculate the slope of the line segment CD. The coordinates of C are $(x_1, y_1) = (2; -1)$ and D are $(x_2, y_2) = (0; 2)$. The formula for the slope $m$ is:

  $$m = \frac{y_2 - y_1}{x_2 - x_1}$$

  Substitute the coordinates:

  $$m_{CD} = \frac{2 - (-1)}{0 - 2}$$ $$m_{CD} = \frac{2 + 1}{-2}$$ $$m_{CD} = \frac{3}{-2}$$ $$m_{CD} = -\frac{3}{2}$$

• Step 2: Calculate the angle of inclination $\theta$. The angle of inclination $\theta$ is related to the slope $m$ by the formula $\tan \theta = m$. Since the slope is negative, the angle will be in the second quadrant. We first find the reference angle $\alpha$.

  $$\tan \alpha = |m_{CD}|$$ $$\tan \alpha = \left|-\frac{3}{2}\right|$$ $$\tan \alpha = 1.5$$ $$\alpha = \arctan(1.5)$$ $$\alpha \approx 56.31^\circ$$

  For a negative slope, the angle of inclination $\theta$ is $180^\circ - \alpha$.

  $$\theta = 180^\circ - 56.31^\circ$$ $$\theta = 123.69^\circ$$

The angle $\theta$ is $\boxed{\text{123.69}^\circ}$.