Question
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).
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).
Answers
GPT-4o mini
To analyze the scenario described by the equation \( t = c + 40 \), where \( t \) is the temperature in degrees Fahrenheit and \( c \) is the number of cricket chirps heard in 14 seconds, let's evaluate the given options:
1. **The graph is continuous.** - This is **not true**. The number of cricket chirps (c) can only take on non-negative integer values (0, 1, 2, ...). Therefore, the graph will consist of discrete points rather than being a continuous line.
2. **All values of t must be positive.** - This statement is **not necessarily true**. The minimum chirp count c is 0, which gives \( t = 0 + 40 = 40 \). Thus, \( t \) must be at least 40 degrees Fahrenheit, so this option is correct in the context of the problem.
3. **A viable solution is (–2, 38).** - This is **not true**. If c = -2, then according to the equation \( t = -2 + 40 = 38 \). However, \( c \) must be non-negative (c cannot be negative), so this solution is invalid.
4. **A viable solution is (0.5, 40.5).** - This is **not true**. Since \( c \) must be a non-negative integer, \( c = 0.5 \) is invalid.
5. **A viable solution is (10, 50).** - This is **true**. If \( c = 10 \), then \( t = 10 + 40 = 50 \). This satisfies the equation with valid non-negative integer chirps.
Given these evaluations, the true statements about the graph representing this real-world scenario are:
- All values of t must be positive.
- A viable solution is (10, 50).
1. **The graph is continuous.** - This is **not true**. The number of cricket chirps (c) can only take on non-negative integer values (0, 1, 2, ...). Therefore, the graph will consist of discrete points rather than being a continuous line.
2. **All values of t must be positive.** - This statement is **not necessarily true**. The minimum chirp count c is 0, which gives \( t = 0 + 40 = 40 \). Thus, \( t \) must be at least 40 degrees Fahrenheit, so this option is correct in the context of the problem.
3. **A viable solution is (–2, 38).** - This is **not true**. If c = -2, then according to the equation \( t = -2 + 40 = 38 \). However, \( c \) must be non-negative (c cannot be negative), so this solution is invalid.
4. **A viable solution is (0.5, 40.5).** - This is **not true**. Since \( c \) must be a non-negative integer, \( c = 0.5 \) is invalid.
5. **A viable solution is (10, 50).** - This is **true**. If \( c = 10 \), then \( t = 10 + 40 = 50 \). This satisfies the equation with valid non-negative integer chirps.
Given these evaluations, the true statements about the graph representing this real-world scenario are:
- All values of t must be positive.
- A viable solution is (10, 50).