Question

1. during a basketball game, mia made 9 out of 12 free throws. mallory made 16 out 20. both girls believe they shot better. select all true statements below: if mallory had made one more free throw, she would have beaten mia. mallorys percentage was higher. mias percentage was higher. mallorys percentage was 80%. if mia had made one more free throw, she would have beaten mallory. mias percentage was 80%.

Explanation:

Step1: Calculate Mia's percentage

Mia made 9 out of 12 free - throws. The formula for percentage is \(\frac{\text{number of successful throws}}{\text{total number of throws}}\times100\%\). So, Mia's percentage is \(\frac{9}{12}\times100\% = 75\%\).

Step2: Calculate Mallory's percentage

Mallory made 16 out of 20 free - throws. Using the percentage formula \(\frac{\text{number of successful throws}}{\text{total number of throws}}\times100\%\), Mallory's percentage is \(\frac{16}{20}\times100\%=80\%\).

Step3: Analyze each statement

• Mia's percentage was 80%: Since Mia's percentage is \(75\%\), this statement is false.
• If Mia had made one more free throw, she would have beaten Mallory: If Mia made \(9 + 1=10\) out of \(12\) free - throws, her percentage would be \(\frac{10}{12}\times100\%\approx83.3\%\). Since \(83.3\%>80\%\), this statement is true.
• Mallory's percentage was 80%: As calculated above, Mallory's percentage is \(80\%\), so this statement is true.
• Mia's percentage was higher: Since \(75\%<80\%\), this statement is false.
• Mallory's percentage was higher: Since \(80\%>75\%\), this statement is true.
• If Mallory had made one more free throw, she would have beaten Mia: Mallory already has a higher percentage (\(80\%\) vs \(75\%\)), and making one more free throw would only increase her percentage further. But the key is that she already has a higher percentage. However, if we calculate, if Mallory made \(16 + 1 = 17\) out of \(20\), her percentage is \(\frac{17}{20}\times100\% = 85\%\), but this is just an extra check. The main point is that Mallory's original percentage (\(80\%\)) is already higher than Mia's (\(75\%\)). But the statement "If Mallory had made one more free throw, she would have beaten Mia" is a bit of a misnomer because she already beats Mia. But if we consider the strict calculation of the new percentage, it's still valid in terms of percentage increase.

Answer:

If Mia had made one more free throw, she would have beaten Mallory; Mallory's percentage was 80%; Mallory's percentage was higher.