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: Identify the frequency for members between 150 cm and 160 cm tall. From the frequency table, this interval has a frequency of 105 members. Step 2: Determine the total number of members in the swimming club. The frequency table shows: |c|c| Height (cm) & Frequency \\ 150--160 & 105 \\ 160--170 & 189 \\ 170--180 & 105 \\ Total frequency = 105 + 189 + 105 = 399 members. Step 3: Calculate the fraction of members between 150 cm and 160 cm tall. Fraction = Frequency for 150--160 cmTotal frequency = (105)/(399) Step 4: Simplify the fraction (105)/(399). First, divide numerator and denominator by 3: (105 ÷ 3)/(399 ÷ 3) = (35)/(133) Next, divide numerator and denominator by 7: (35 ÷ 7)/(133 ÷ 7) = (5)/(19) The fraction of members between 150 cm and 160 cm tall is (5)/(19). (5)/(19)