To determine the correct explanation for calculating the number of advertisements that will run with a program that is 334 hours, we need to understand the relationship between advertisements and programming hours.
From the given information, the television station runs 2 advertisements (a) for every 14 hours of programming (p).
To find a, the relationship can be expressed with the ratio:
- If there are 2 ads for every 14 hours, then for each hour, the station runs \(\frac{2}{14} = \frac{1}{7}\) advertisements.
Thus, the equation that describes the number of advertisements \(a\) in terms of hours \(p\) can be represented as: \[ a = \frac{1}{7}p \text{ or equivalently } a = \frac{1}{7} \times 334 \]
Now, since we want to find the total number of ads for 334 hours: \[ a = 2 \times \left(\frac{334}{14}\right) \]
Calculating the number of 14-hour segments in 334 hours: \[ \frac{334}{14} = 23.857 \text{ (approximately)} \]
Therefore, \[ a = 2 \times 23.857 \approx 47.714 \text{ or rounded appropriately to 48 ads, depending on whether the station rounds up.} \]
Let’s review the options given:
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The situation can be represented by the equation a=18p. Since the program, p, will run for 334 hours, calculate 334=18⋅p to find the number of advertisements that will run with the program.
- Incorrect. The ratio is not correct.
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The situation can be represented by the equation a=8p. Since the program, p, will run for 334 hours, calculate a=8334 to find the number of advertisements that will run with the program.
- Incorrect. Again, the ratio is not correct.
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The situation can be represented by the equation a=18p. Since the program, p, will run for 334 hours, calculate a=18⋅334 to find the number of advertisements that will run with the program.
- Incorrect. The ratio is not correct.
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The situation can be represented by the equation a=8p. Since the program, p, will run for 334 hours, calculate a=8⋅334 to find the number of advertisements that will run with the program.
- Incorrect ratio once more.
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The situation can be represented by the equation a=18p. Since the program, p, will run for 334 hours, calculate a=18⋅334 to find the number of advertisements that will run with the program.
- Incorrect. Again, incorrect ratio.
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The situation can be represented by the equation a=8p. Since the program, p, will run for 334 hours, calculate a=8⋅334 to find the number of advertisements that will run with the program.
- Incorrect ratio once again.
None of the responses appear to reflect the correct calculations and ratios based on the information given. The correct relationship based on \(a = \frac{1}{7}p\) needs to be established to yield the correct number of advertisements for 334 hours of programming. The most logical representation would be using \(a = \frac{2}{14}p\).
If any of the answers had used \(a = \frac{1}{7}p\) or noted \(a = 2 \times (334/14)\), that would have been the correct choice.
1 answer