Energy saving

Three independent inventions were released, each saving 15%, 17%, and 16% of energy respectively. Some people assumed that using all three would save 15% + 17% + 16% = 48% of energy. Is this correct? What is the actual total percentage of energy saved by all three inventions used together?

Final Answer:

p =  40.7 %

Step-by-step explanation:

$$\begin{gathered} q_1=100\%-15\%=1-\frac{15}{100}=0.85 \\ {q}_2=100\%-17\%=1-\frac{17}{100}=0.83 \\ {q}_3=100\%-16\%=1-\frac{16}{100}=0.84 \\ q=1-q_1\cdot q_2\cdot q_3=1-0.85\cdot 0.83\cdot 0.84\doteq 0.4074 \\ p=100\cdot q=100\cdot 0.4074=40.7\% \end{gathered}$$

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