Question

question
theres 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 + 31 ), 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 = 77 )?
answer
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 77
times per minute. its ( 77^{circ}f ).
the number of times the cricket could
be expected to chirp in one minute if

Explanation:

Step1: Analyze the linear equation

The given formula is \( T = 0.27c+31 \), where \( T \) is temperature and \( c \) is the number of chirps. We need to find \( c \) when \( T = 77 \).

Step2: Substitute \( T = 77 \) into the equation

Substitute \( T = 77 \) into \( T = 0.27c + 31 \), we get \( 77=0.27c + 31 \).

Step3: Solve for \( c \)

First, subtract 31 from both sides: \( 77 - 31=0.27c \), so \( 46 = 0.27c \). Then divide both sides by 0.27: \( c=\frac{46}{0.27}\approx170.37 \). But in the context of the problem, \( c \) represents the number of chirps per minute.

Answer:

The number of times the cricket chirps in one minute.