This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — let's break these down. 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 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 = (y_2 - y_1)/(x_2 - x_1) Substitute the coordinates: m_CD = (2 - (-1))/(0 - 2) m_CD = (2 + 1)/(-2) m_CD = (3)/(-2) m_CD = -(3)/(2) Step 2: Calculate the angle of inclination . The angle of inclination is related to the slope m by the formula = m. Since the slope is negative, the angle will be in the second quadrant. We first find the reference angle . = |m_CD| = |-(3)/(2)| = 1.5 = (1.5) ≈ 56.31^ For a negative slope, the angle of inclination is 180^ - . = 180^ - 56.31^ = 123.69^ The angle is 123.69^. What's next?