Question

there’s a roughly linear relationship between the number of times a species of cricket will chirp in one minute and the temperature outside. for a certain type of cricket, this relationship can be expressed using the formula ( t = 0.27c + 40 ), where ( t ) represents the temperature in degrees fahrenheit and ( c ) represents the number of times the cricket chirps in one minute. what is the meaning of the ( c )-value when ( t = 76 )?
answer
the number of times the cricket could be expected to chirp in one minute if it’s ( 76^circ ) f.
the change in temperature in degrees fahrenheit for each additional cricket chirp in one minute.
the expected temperature in degrees fahrenheit if the cricket has chirped 0 times per minute.
the expected temperature in degrees fahrenheit if the cricket has chirped 76 times per minute.
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Explanation:

Step1: Start with the given formula

We have the formula \( T = 0.27c + 40 \), and we know that \( T = 76 \). So we substitute \( T \) with 76 in the formula:
\( 76 = 0.27c + 40 \)

Step2: Subtract 40 from both sides

To isolate the term with \( c \), we subtract 40 from both sides of the equation.
\( 76 - 40 = 0.27c + 40 - 40 \)
\( 36 = 0.27c \)

Step3: Solve for \( c \)

Now we divide both sides of the equation by 0.27 to find the value of \( c \).
\( c=\frac{36}{0.27} \)
Calculating the right - hand side, \( \frac{36}{0.27}=\frac{36\times100}{0.27\times100}=\frac{3600}{27}=\frac{400}{3}\approx144.44 \) (but we can also think about the meaning). The value of \( c \) when \( T = 76 \) represents the number of times the cricket chirps per minute when the temperature is 76 degrees Fahrenheit. Looking at the options, the correct interpretation is "The expected number of times the cricket chirps per minute when the temperature is 76 degrees Fahrenheit" (the option that says "The expected temperature in degrees Fahrenheit if the cricket has chirped 76 times per minute" is wrong, the correct one is about finding \( c \) when \( T = 76 \), so the interpretation is the number of chirps per minute when temperature is 76°F, among the options, the one that matches is "The expected number of times the cricket chirps per minute if the temperature is 76 degrees Fahrenheit" (assuming the option is worded as such, from the given options, the correct interpretation is that \( c \) is the number of chirps per minute when \( T = 76 \), so when \( T = 76 \), we solve for \( c \), and the meaning of \( c \) in this context is the number of chirps per minute at 76°F. So the correct option is the one that says the expected number of chirps per minute when temperature is 76°F.

Answer:

The expected number of times the cricket chirps per minute if the temperature is 76 degrees Fahrenheit (the option corresponding to this interpretation, e.g., if the options are as per the text, the correct one is the one that describes \( c \) as the number of chirps per minute when \( T = 76 \))