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 questions: 3.1.1 To complete the tree diagram: The food options are porridge, bread, or cereal. Since "Porridge" and "Cereal" are given, (a) must be Bread*. The drink options are tea or coffee. For porridge, "Tea" and "Coffee" are shown. For bread, "Tea" is shown, so (b) must be Coffee*. For cereal, "Tea" is shown, so (c) must be Coffee*. 3.1.2 Step 1: Identify the number of choices for each category. There are 3 food choices (porridge, bread, cereal) and 2 drink choices (tea, coffee). Step 2: Multiply the number of choices to find the total possible outcomes. Total outcomes = (Number of food choices) × (Number of drink choices) = 3 × 2 = 6 Akani can have 6 possible outcomes for breakfast. 3.1.3 Step 1: Identify the probability of eating porridge from the tree diagram. The probability of eating porridge is given as (1)/(3). Step 2: Convert the probability to a percentage. (1)/(3) × 100\% = 33.33\% The probability of eating porridge is 33.33%. 3.1.4 Step 1: Identify the probability of drinking tea for each food option. The probability of drinking tea, regardless of the food choice, is (1)/(2). Step 2: Calculate the probability of drinking tea by summing the probabilities of all paths leading to tea. P(Tea) = P(Porridge and Tea) + P(Bread and Tea) + P(Cereal and Tea) P(Tea) = P(Porridge) × P(Tea) + P(Bread) × P(Tea) + P(Cereal) × P(Tea) P(Tea) = ((1)/(3) × (1)/(2)) + ((1)/(3) × (1)/(2)) + ((1)/(3) × (1)/(2)) P(Tea) = (1)/(6) + (1)/(6) + (1)/(6) P(Tea) = (3)/(6) = (1)/(2) The probability of drinking tea is (1)/(2). 3.1.5 Step 1: Review the available drink options. Akani can choose to drink tea or coffee. "Cool drink" is not listed as an option. Step 2: Determine the probability of an event that is not an option. Since "cool drink" is not an option, the probability of Akane drinking a cool drink is 0. The probability that Akani will eat porridge and drink cool drink is 0. 3.2.1 The instrument used to measure the weight (mass) of potatoes in a bag is a weighing scale (or simply a scale). 3.2.2 The instrument used to measure an angle in a triangle is a protractor. 3.3.1 The most suitable unit of measurement for the distance between two towns is kilometers (km). 3.3.2 The most suitable unit of measurement for time taken by an athlete to run 100 m is seconds (s). Send me the next one 📸