Question
Home - LPAD Viaiona in Educatio. Inbox (40) - 105449. Maihupace HM hotline Home Home - Google Dive Grade 9 Agenda - 20 .. IM Sanveer Singh Integrated Math 1 B (IS895) \#90179 | Mastery Assess It-1 Due: Tomorrow 8. A basketball tournament starts with 64 teams each year. After each round of play, half the teams are eliminated. How many teams are left after four rounds? one team four teams eight teams two teams
Ask by Kelly Thornton. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
After four rounds, there are 4 teams left.
Solution
To solve the problem of how many teams are left after four rounds of a basketball tournament that starts with 64 teams and eliminates half of the teams after each round, we can follow these steps:
1. **Identify the initial number of teams**:
- We start with \( T_0 = 64 \) teams.
2. **Determine the number of teams after each round**:
- After the first round, half of the teams are eliminated:
\[
T_1 = \frac{T_0}{2} = \frac{64}{2} = 32
\]
- After the second round:
\[
T_2 = \frac{T_1}{2} = \frac{32}{2} = 16
\]
- After the third round:
\[
T_3 = \frac{T_2}{2} = \frac{16}{2} = 8
\]
- After the fourth round:
\[
T_4 = \frac{T_3}{2} = \frac{8}{2} = 4
\]
3. **Final count of teams**:
- After four rounds, there are \( T_4 = 4 \) teams left.
Thus, the answer is **four teams**.
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Mind Expander
After one round, 64 teams are cut in half, leaving 32 teams. After the second round, 32 becomes 16, then 16 becomes 8 in the third round, and finally, after the fourth round, you're left with 4 teams. It’s like a thrilling game of musical chairs but with basketball! This is a classic example of exponential decay—each round reduces the number of teams by half. It's fascinating how quickly the numbers dwindle. Understanding these concepts can really help you appreciate tournament structures and even play strategic games on your own!