What fraction of members were between 150 and 160 cm tall?

Mathematics
What fraction of members were between 150 and 160 cm tall?

ScanSolve AI Answer

Answer

\dfrac{5}{19}

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:

\begin{tabular}{|c|c|} \hline Height (cm) & Frequency \\ \hline 150--160 & 105 \\ 160--170 & 189 \\ 170--180 & 105 \\ \hline \end{tabular}

Total frequency = 105+189+105=399105 + 189 + 105 = 399 members.

Step 3: Calculate the fraction of members between 150 cm and 160 cm tall.

Fraction=Frequencyfor150−−160cmTotalfrequency=105399Fraction = \frac{Frequency for 150--160 cm}{Total frequency} = \frac{105}{399}

Step 4: Simplify the fraction 105399\frac{105}{399}.
First, divide numerator and denominator by 3:

105÷3399÷3=35133\frac{105 \div 3}{399 \div 3} = \frac{35}{133}

Next, divide numerator and denominator by 7:

35÷7133÷7=519\frac{35 \div 7}{133 \div 7} = \frac{5}{19}

The fraction of members between 150 cm and 160 cm tall is 519\dfrac{5}{19}.

\dfrac{5{19}}

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Quick Answer

Identify the frequency for members between 150 cm and 160 cm tall. From the frequency table, this interval has a frequency of 105 members.

What fraction of members were between 150 and 160 cm tall?
Mathematics

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)