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
Welcome back God's — been a while! Let's pick up where you left off. 10 (a) Step 1: Identify the given probability and the event for which the probability is required. The probability of Kasukulu waking up late is P(late) = 0.3. The probability of waking up early is the complement of waking up late. Step 2: Use the complementary probability formula. The sum of the probability of an event and its complement is 1. P(early) = 1 - P(late) P(early) = 1 - 0.3 P(early) = 0.7 The probability that she will wake up early is 0.7. 10 (b) Step 1: State the formula for the area of a sector and identify the given values. The area of a sector A with radius r and angle (in degrees) is given by: A = ()/(360^) r^2 Given: A = 24.2 cm^2 r = 6 cm = (22)/(7) Step 2: Substitute the given values into the formula. 24.2 = ()/(360^) × (22)/(7) × (6 cm)^2 24.2 = ()/(360^) × (22)/(7) × 36 Step 3: Simplify the equation and solve for . 24.2 = × (22 × 36)/(360 × 7) 24.2 = × (792)/(2520) Divide both the numerator and denominator of the fraction by their greatest common divisor, which is 72: 24.2 = × (11)/(35) Now, isolate : = 24.2 × (35)/(11) = (242)/(10) × (35)/(11) = (22 × 11)/(10) × (35)/(11) = (22)/(10) × 35 = 2.2 × 35 = 77 The value of is 77^. Send me the next one 📸