Question
Multiple select questions after Tennis practice. One places Tina spells into canisters. Who can use up to 10 canisters? And she places exactly 3 to the spalls into each canister. The number of Tennis balls placed into canisters is a function of the number of canisters which statements are true regarding the domain and range of this function. Select all data plies. A dot the domain of the function is all real numbers from 0 to 10. Domain of the function is all whole numbers from 0 to 10. The domain of the function is all whole numbers from 0 to 30D. The range of the function is all multiples be 3 from 0 to thit. The range of the function is all whole numbers from 0 to 30.
Answers
Answered by
GPT-4o mini
To analyze the situation in the question, let’s break down the information given:
- Tina can use up to **10 canisters**.
- She places **exactly 3 tennis balls** into each canister.
### Domain
The domain of the function represents the possible values of canisters. Since Tina can use from **0 to 10 canisters**, we can conclude:
- The domain must include all whole numbers from **0 to 10**. This means the only acceptable values for the number of canisters are **0, 1, 2, 3, 4, 5, 6, 7, 8, 9,** and **10**.
Therefore, the correct statement about the domain is:
- **The domain of the function is all whole numbers from 0 to 10.**
### Range
The range of the function is determined by the number of tennis balls that can be placed into the canisters. Since each canister contains 3 tennis balls, the number of balls can be calculated as follows:
- If \( n \) is the number of canisters, then the total number of tennis balls \( B \) is given by:
\[ B = 3n \]
Considering \( n \) can take the values **0 through 10**:
- For \( n = 0 \), \( B = 3 \cdot 0 = 0 \)
- For \( n = 1 \), \( B = 3 \cdot 1 = 3 \)
- For \( n = 2 \), \( B = 3 \cdot 2 = 6 \)
- For \( n = 3 \), \( B = 3 \cdot 3 = 9 \)
- For \( n = 4 \), \( B = 3 \cdot 4 = 12 \)
- For \( n = 5 \), \( B = 3 \cdot 5 = 15 \)
- For \( n = 6 \), \( B = 3 \cdot 6 = 18 \)
- For \( n = 7 \), \( B = 3 \cdot 7 = 21 \)
- For \( n = 8 \), \( B = 3 \cdot 8 = 24 \)
- For \( n = 9 \), \( B = 3 \cdot 9 = 27 \)
- For \( n = 10 \), \( B = 3 \cdot 10 = 30 \)
Thus, the possible values of \( B \) are **0, 3, 6, 9, 12, 15, 18, 21, 24, 27,** and **30**. This corresponds to all multiples of **3** from **0 to 30**.
Thus, the relevant statements about the range are:
- **The range of the function is all multiples of 3 from 0 to 30.**
### Conclusion
The true statements are:
- **The domain of the function is all whole numbers from 0 to 10.**
- **The range of the function is all multiples of 3 from 0 to 30.**
- Tina can use up to **10 canisters**.
- She places **exactly 3 tennis balls** into each canister.
### Domain
The domain of the function represents the possible values of canisters. Since Tina can use from **0 to 10 canisters**, we can conclude:
- The domain must include all whole numbers from **0 to 10**. This means the only acceptable values for the number of canisters are **0, 1, 2, 3, 4, 5, 6, 7, 8, 9,** and **10**.
Therefore, the correct statement about the domain is:
- **The domain of the function is all whole numbers from 0 to 10.**
### Range
The range of the function is determined by the number of tennis balls that can be placed into the canisters. Since each canister contains 3 tennis balls, the number of balls can be calculated as follows:
- If \( n \) is the number of canisters, then the total number of tennis balls \( B \) is given by:
\[ B = 3n \]
Considering \( n \) can take the values **0 through 10**:
- For \( n = 0 \), \( B = 3 \cdot 0 = 0 \)
- For \( n = 1 \), \( B = 3 \cdot 1 = 3 \)
- For \( n = 2 \), \( B = 3 \cdot 2 = 6 \)
- For \( n = 3 \), \( B = 3 \cdot 3 = 9 \)
- For \( n = 4 \), \( B = 3 \cdot 4 = 12 \)
- For \( n = 5 \), \( B = 3 \cdot 5 = 15 \)
- For \( n = 6 \), \( B = 3 \cdot 6 = 18 \)
- For \( n = 7 \), \( B = 3 \cdot 7 = 21 \)
- For \( n = 8 \), \( B = 3 \cdot 8 = 24 \)
- For \( n = 9 \), \( B = 3 \cdot 9 = 27 \)
- For \( n = 10 \), \( B = 3 \cdot 10 = 30 \)
Thus, the possible values of \( B \) are **0, 3, 6, 9, 12, 15, 18, 21, 24, 27,** and **30**. This corresponds to all multiples of **3** from **0 to 30**.
Thus, the relevant statements about the range are:
- **The range of the function is all multiples of 3 from 0 to 30.**
### Conclusion
The true statements are:
- **The domain of the function is all whole numbers from 0 to 10.**
- **The range of the function is all multiples of 3 from 0 to 30.**
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