Question
In Friday’s volleyball game, Sam’s team scored a point in 16.5% of his serves. Which of the following statements is true?
A.
The team scored in more than 16
of Sam’s serves.
B.
The team scored in less than 110
of Sam’s serves.
C.
The team scored in exactly 17
of Sam’s serves.
D.
The team scored in more than 18
of Sam’s serves.
A.
The team scored in more than 16
of Sam’s serves.
B.
The team scored in less than 110
of Sam’s serves.
C.
The team scored in exactly 17
of Sam’s serves.
D.
The team scored in more than 18
of Sam’s serves.
Answers
Answered by
GPT-4o mini
To analyze the statements regarding the percentage of points scored by Sam's team from his serves, we can denote the total number of serves as \( x \).
If Sam’s team scored a point in 16.5% of his serves, then the number of points scored can be expressed as:
\[
\text{Points scored} = 0.165x
\]
Now we can evaluate each statement:
**A. The team scored in more than 16 of Sam’s serves.**
For this to be true:
\[
0.165x > 16 \implies x > \frac{16}{0.165} \approx 96.97
\]
So if \( x \) is greater than approximately 97, this statement could be true.
**B. The team scored in less than 110 of Sam’s serves.**
For this to be true:
\[
0.165x < 110 \implies x < \frac{110}{0.165} \approx 666.67
\]
So this statement would generally be true for a reasonable number of serves.
**C. The team scored in exactly 17 of Sam’s serves.**
For this to be true:
\[
0.165x = 17 \implies x = \frac{17}{0.165} \approx 103.03
\]
This means there would be a specific number of total serves (about 103) that would result in exactly 17 points scored.
**D. The team scored in more than 18 of Sam’s serves.**
For this to be true:
\[
0.165x > 18 \implies x > \frac{18}{0.165} \approx 109.09
\]
This means if \( x \) is greater than approximately 109, this will be true.
**Conclusion:**
- If Sam's total serves \( x \) is around 100 (which is a reasonable assumption for a volleyball game), the points scored would be approximately:
- \( 0.165 \times 100 = 16.5 \) (Between 16 and 17 but not more than 18).
Thus:
- Statement A can be true if helps to establish \( x > 97 \).
- Statement B is true as it is true for most reasonable \( x \).
- Statement C is possibly correct if \( x \) is around 103.
- Statement D would only be true if \( x > 109 \).
Given a typical game scenario, the most logically consistent is **B. The team scored in less than 110 of Sam’s serves.**
If Sam’s team scored a point in 16.5% of his serves, then the number of points scored can be expressed as:
\[
\text{Points scored} = 0.165x
\]
Now we can evaluate each statement:
**A. The team scored in more than 16 of Sam’s serves.**
For this to be true:
\[
0.165x > 16 \implies x > \frac{16}{0.165} \approx 96.97
\]
So if \( x \) is greater than approximately 97, this statement could be true.
**B. The team scored in less than 110 of Sam’s serves.**
For this to be true:
\[
0.165x < 110 \implies x < \frac{110}{0.165} \approx 666.67
\]
So this statement would generally be true for a reasonable number of serves.
**C. The team scored in exactly 17 of Sam’s serves.**
For this to be true:
\[
0.165x = 17 \implies x = \frac{17}{0.165} \approx 103.03
\]
This means there would be a specific number of total serves (about 103) that would result in exactly 17 points scored.
**D. The team scored in more than 18 of Sam’s serves.**
For this to be true:
\[
0.165x > 18 \implies x > \frac{18}{0.165} \approx 109.09
\]
This means if \( x \) is greater than approximately 109, this will be true.
**Conclusion:**
- If Sam's total serves \( x \) is around 100 (which is a reasonable assumption for a volleyball game), the points scored would be approximately:
- \( 0.165 \times 100 = 16.5 \) (Between 16 and 17 but not more than 18).
Thus:
- Statement A can be true if helps to establish \( x > 97 \).
- Statement B is true as it is true for most reasonable \( x \).
- Statement C is possibly correct if \( x \) is around 103.
- Statement D would only be true if \( x > 109 \).
Given a typical game scenario, the most logically consistent is **B. The team scored in less than 110 of Sam’s serves.**