Let's address each part of the question step-by-step.
### Part 1: Simplifying the Win:Loss Ratio
We are given the win:loss ratio for a baseball team as [tex]\(48:16\)[/tex]. To simplify this ratio, we need to divide both numbers by their greatest common divisor (GCD).
Step-by-Step:
1. Identify the GCD of 48 and 16. The GCD is the largest number that divides both 48 and 16 without leaving a remainder.
2. Divide both the numerator (48) and the denominator (16) by the GCD.
After calculations, the simplified ratio of wins to losses is [tex]\(3:1\)[/tex].
### Part 2: Band Members Who Do Not Play the Flute
We are given that 20% of the members in the band play the flute, and the total number of band members is 40.
Step-by-Step:
1. Calculate the number of members who play the flute:
[tex]\[
\text{Members who play the flute} = 20\% \text{ of } 40 = 0.20 \times 40 = 8
\][/tex]
2. Calculate the number of members who do not play the flute:
[tex]\[
\text{Members who do not play the flute} = \text{Total band members} - \text{Members who play the flute}
\][/tex]
[tex]\[
\text{Members who do not play the flute} = 40 - 8 = 32
\][/tex]
Summary:
1. The simplified win:loss ratio is [tex]\(3:1\)[/tex].
2. There are 8 band members who play the flute.
3. There are 32 band members who do not play the flute.
