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Choice C is correct. It’s given that the cost of renting a tent is $\$11$ per day for $d$ days. Multiplying the rental cost by the number of days yields $\$11d$, which represents the cost of renting the tent for $d$ days before the insurance is added. Adding the onetime insurance fee of $\$10$ to the rental cost of $\$11d$ gives the total cost $c$, in dollars, which can be represented by the equation $c=11d+10$.

Choice A is incorrect. This equation represents the total cost to rent the tent if the insurance fee was charged every day.

Choice B is incorrect. This equation represents the total cost to rent the tent if the daily fee was $\$\left(d+11\right)$ for $10$ days.

Choice D is incorrect. This equation represents the total cost to rent the tent if the daily fee was $\$10$ and the onetime fee was $\$11$.