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Batteries and supercapacitors are complementary: batteries have a high energy-to-weight ratio but are limited in the power levels they can support; supercapacitors can provide high levels of power while they have a much lower energy-to-weight ratio. A battery-supercapacitor duo can therefore prove useful in embedded systems serving sporadic, energy-intensive, tasks: the battery charges the capacitor at a low, fairly steady, rate which maximizes the energy that can be drawn from it, while the supercapacitor satisfies the impulse power demands of the application. In this letter, we characterize such energy sources by means of two performance measures: expected time before the first task failure and the fraction of tasks that fail before the battery dies. or the case of rare (but energy-intensive) sporadic tasks, we present semi-Markov models to evaluate these measures. For more frequent task arrivals, we provide simulation results. This letter demonstrates the impact of various parameters on our performance measures: power draw, capacitor sizing, and the battery rest scheduling policy.