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 side length of the cubic-shaped packet. The volume of the cubic-shaped packet is given as 2744 cm^3. The formula for the volume of a cube is Volume = side × side × side = side^3. To find the side length, we need to take the cube root of the volume. side = [3]Volume side = [3]2744 cm^3 side = 14 cm The side length of the cubic-shaped packet is 14 cm. Step 2: Determine the number of pink or yellow sweets. From Table 2: Number of pink sweets = 8 Number of yellow sweets = 7 The total number of pink or yellow sweets is the sum of these two values. Number of pink or yellow sweets = 8 + 7 = 15 Step 3: Determine the total number of sweets. The problem states there are 35 different coloured sweets in each packet. We can also verify this by summing the numbers in Table 2: Total sweets = 4 (Blue) + 5 (Purple) + 8 (Pink) + 11 (Orange) + 7 (Yellow) Total sweets = 35 Step 4: Calculate the probability of choosing a pink or yellow sweet. The probability is the ratio of the number of favorable outcomes (pink or yellow sweets) to the total number of possible outcomes (total sweets). P(Pink or Yellow) = Number of pink or yellow sweetsTotal number of sweets P(Pink or Yellow) = (15)/(35) Simplify the fraction: P(Pink or Yellow) = (3)/(7) Convert the fraction to a decimal: P(Pink or Yellow) ≈ 0.4285714... Rounding to a reasonable number of decimal places (e.g., three decimal places): P(Pink or Yellow) ≈ 0.429 The probability of randomly choosing a pink or a yellow sweet is 0.429. That's 2 down. 3 left today — send the next one.