To determine the inequality that can be used to find \( p \), the number of pies the class needs to sell, we start by breaking down the information given:
- The cost of the field trip is \( 386 \).
- The principal has given the class \( 75 \) dollars.
- The students earn \( 5 \) dollars for each pie sold.
Let \( p \) represent the number of pies sold. The total money raised from selling pies will be \( 5p \).
The total amount of money the class will have after selling the pies and receiving the principal's contribution is:
\[ 75 + 5p \]
To find out how many pies they need to sell to at least cover the cost of the trip (which is \( 386 \)), we need to set up the inequality:
\[ 75 + 5p \geq 386 \]
This means that the total funds from the pies and the principal need to be at least \( 386 \).
Now, let's analyze the inequality options provided:
A. \( 5p + 75 \leq 386 \) is incorrect because we want to ensure the money is at least \( 386 \).
B. \( 5p + 75 \geq 386 \) is correct because it fits our derived inequality.
C. \( 75p + 5 \geq 386 \) is incorrect as it improperly correlates the principal's contribution with the wrong factor of the pies sold.
D. \( 75p + 5 \leq 386 \) is incorrect as it suggests they should stay under the budget, which does not apply here.
Thus, the correct inequality that can be used to find \( p \) is:
\[ \boxed{B} \quad 5p + 75 \geq 386 \]