Answer :
To express that a cat’s temperature is normally within $1.3^\circ F$ of the average temperature $101.2^\circ F$, we write the inequality
$$
|t - 101.2| \leq 1.3.
$$
Here’s how we derive this step-by-step:
1. The average temperature is given as $101.2^\circ F$.
2. The temperature can vary by up to $1.3^\circ F$. This means the absolute difference between the actual temperature $t$ and the average is at most $1.3^\circ F$.
3. In mathematical terms, this is written using the absolute value inequality:
$$
|t - 101.2| \leq 1.3.
$$
Thus, the inequality that represents the normal temperature range is
$$
|t-101.2| \leq 1.3.
$$
$$
|t - 101.2| \leq 1.3.
$$
Here’s how we derive this step-by-step:
1. The average temperature is given as $101.2^\circ F$.
2. The temperature can vary by up to $1.3^\circ F$. This means the absolute difference between the actual temperature $t$ and the average is at most $1.3^\circ F$.
3. In mathematical terms, this is written using the absolute value inequality:
$$
|t - 101.2| \leq 1.3.
$$
Thus, the inequality that represents the normal temperature range is
$$
|t-101.2| \leq 1.3.
$$
