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
Step 1: Calculate the total number of learners. Total learners = 18 + 12 + 10 + 9 + 11 = 60 learners. Step 2: Calculate the angle for each game in the pie chart. The total angle in a circle is 360^. The angle for each category is calculated as: Angle = (Number of learners for gameTotal learners) × 360^ Football: Angle_Football = ((18)/(60)) × 360^ = 0.3 × 360^ = 108^ Netball: Angle_Netball = ((12)/(60)) × 360^ = 0.2 × 360^ = 72^ Volleyball: Angle_Volleyball = ((10)/(60)) × 360^ = (1)/(6) × 360^ = 60^ Handball: Angle_Handball = ((9)/(60)) × 360^ = 0.15 × 360^ = 54^ Basketball: Angle_Basketball = ((11)/(60)) × 360^ = 11 × 6^ = 66^ Step 3: Verify the sum of angles. 108^ + 72^ + 60^ + 54^ + 66^ = 360^. The angles for the pie chart are: Football: 108^ Netball: 72^ Volleyball: 60^ Handball: 54^ Basketball: 66^ 40. Step 1: List all possible numbers. The numbers from 10 to 20 are \10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\. The total number of possible outcomes is 20 - 10 + 1 = 11. a) Determine the probability that the number of the card picked is a prime number. Step 2: Identify prime numbers in the list. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The prime numbers in the list are \11, 13, 17, 19\. There are 4 prime numbers. Step 3: Calculate the probability. P(prime number) = Number of prime numbersTotal number of outcomes = (4)/(11) The probability of picking a prime number is (4)/(11). b) Determine the probability that the number of the card picked is an even number. Step 4: Identify even numbers in the list. The even numbers in the list are \10, 12, 14, 16, 18, 20\. There are 6 even numbers. Step 5: Calculate the probability. P(even number) = Number of even numbersTotal number of outcomes = (6)/(11) The probability of picking an even number is (6)/(11). That's 2 down. 3 left today — send the next one.