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.
ScanSolve AI Answer
Here are the solutions to the questions. 1. (a) Briefly define communication in your own words As an AI, I cannot draw. However, I can explain the parts of a circle: • Center: The point equidistant from all points on the circle. • Radius: A line segment connecting the center to any point on the circle. • Diameter: A line segment passing through the center and connecting two points on the circle. Its length is twice the radius. • Circumference: The total distance around the circle. • Chord: A line segment connecting any two points on the circle. 1. (b) Copy and complete the table below: Step 1: Calculate the Class Boundaries. For a class interval a-b, the lower class boundary is a - 0.5 and the upper class boundary is b + 0.5. Step 2: Calculate the Class Width. Class Width = Upper Class Boundary - Lower Class Boundary. Step 3: Calculate the Class Midpoint. Class Midpoint = Lower Class Limit + Upper Class Limit2. Step 4: Complete the table with the calculated values. | Mark | Frequency | Class Boundaries | Class Width | Class Midpoint | | :---- | :-------- | :--------------- | :---------- | :------------- | | 1-5 | 5 | 0.5 - 5.5 | 5 | 3 | | 6-10 | 7 | 5.5 - 10.5 | 5 | 8 | | 11-15 | 9 | 10.5 - 15.5 | 5 | 13 | | 16-20 | 3 | 15.5 - 20.5 | 5 | 18 | | 21-25 | 1 | 20.5 - 25.5 | 5 | 23 | | 26-30 | 6 | 25.5 - 30.5 | 5 | 28 | | 31-35 | 4 | 30.5 - 35.5 | 5 | 33 | | 36-40 | 2 | 35.5 - 40.5 | 5 | 38 | 2. A straight ladder 10 meters long is placed against a wall with its lower end 6 meters away from the wall. How high up the wall does it reach? Step 1: Identify the given values. This problem forms a right-angled triangle. Length of the ladder (hypotenuse, c) = 10 m. Distance from the wall (base, b) = 6 m. Height up the wall (height, a) is unknown. Step 2: Apply the Pythagorean theorem. The Pythagorean theorem states a^2 + b^2 = c^2. Step 3: Substitute the values and solve for a. a^2 + 6^2 = 10^2 a^2 + 36 = 100 a^2 = 100 - 36 a^2 = 64 a = sqrt(64) a = 8 The height the ladder reaches up the wall is 8 meters. 8 m 3. Solve for n in the diagram below: Step 1: Set up the equation for angles on a straight line. Angles on a straight line sum to 180^. (4n - 22)^ + (8n - 10)^ = 180^ Step 2: Simplify the equation. 4n - 22 + 8n - 10 = 180 12n - 32 = 180 Step 3: Solve for n. 12n = 180 + 32 12n = 212 n = (212)/(12) n = (53)/(3) n = 17.67 (approximately) The value of n is (53)/(3) or approximately 17.67. n = (53)/(3) or n ≈ 17.67 That's 2 down. 3 left today — send the next one.