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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Here are the solutions to the problems you've provided: 1. Given the statements P and Q: P: He is strong Q: He is handsome Write in ordinary English: a. P This symbol means "not P". He is not strong. b. P Q This symbol means "P or Q". He is strong or he is handsome. c. P Q This symbol means "P and Q". He is strong and he is handsome. 2. Figure 3 shows a circle with radius, r=2.5 cm inside a rectangle PQRS. Given that PQ = 9 cm, PS = 7 cm, taking = (22)/(7). Calculate the area of: a. the rectangle Step 1: Identify the formula for the area of a rectangle. Area_rectangle = length × width Step 2: Substitute the given values for length (PQ) and width (PS). Area_rectangle = 9 cm × 7 cm Step 3: Calculate the area. Area_rectangle = 63 cm^2 The area of the rectangle is 63 cm^2. b. the circle Step 1: Identify the formula for the area of a circle. Area_circle = r^2 Step 2: Substitute the given values for and r. Area_circle = (22)/(7) × (2.5 cm)^2 Step 3: Calculate r^2. (2.5)^2 = 6.25 Step 4: Substitute and calculate the area. Area_circle = (22)/(7) × 6.25 cm^2 Area_circle = (137.5)/(7) cm^2 Area_circle ≈ 19.64 cm^2 The area of the circle is 19.64 cm^2. c. the shaded region Step 1: The area of the shaded region is the area of the rectangle minus the area of the circle. Area_shaded = Area_rectangle - Area_circle Step 2: Substitute the calculated areas. Area_shaded = 63 cm^2 - (137.5)/(7) cm^2 Step 3: Perform the subtraction. Area_shaded = (63 × 7 - 137.5)/(7) cm^2 Area_shaded = (441 - 137.5)/(7) cm^2 Area_shaded = (303.5)/(7) cm^2 Area_shaded ≈ 43.36 cm^2 The area of the shaded region is 43.36 cm^2. 3. Figure 1 represents the height of a boy, PQ, and his shadow RQ, 2.4m long on a flat ground. This problem is incomplete. It provides the length of the shadow (RQ = 2.4 m) but does not provide the height of the boy (PQ) or the angle of elevation. To calculate the distance PQ or the angle of elevation, one of these missing values is required. That's 2 down. 3 left today — send the next one.