Question

choosing solutions based on the context of the problem
the temperature, t, in degrees fahrenheit, can be found by counting the number of cricket chirps, c, heard in 14 seconds and then adding 40. the equation t = c + 40 models the relationship between the temperature and the number of cricket chirps.
what is true about the graph that represents this real - world scenario? select two options.
the graph is continuous.
all values of t must be positive.
a viable solution is (-2, 38).
a viable solution is (0.5, 40.5).
a viable solution is (10, 50).

Explanation:

1. Continuous graph check: The number of cricket chirps \(c\) is a whole number (you can't hear a fraction of a chirp), so the graph is discrete, not continuous.
2. Positive \(t\) check: Temperature \(t = c + 40\). Since \(c\) (chirps) can't be negative, \(t\) will always be at least 40, so all \(t\) values are positive.
3. Viable solution check: \(c\) must be a non-negative whole number (you can't have negative or fractional chirps in this real-world context):

• \((-2, 38)\): \(c=-2\) is invalid (negative chirps)
• \((0.5, 40.5)\): \(c=0.5\) is invalid (fractional chirp)
• \((10, 50)\): \(c=10\) is a valid non-negative whole number, and \(t=10+40=50\), so this works.

Answer:

All values of \(t\) must be positive.
A viable solution is (10, 50).