1. **State the problem:** Calculate the value of $2.75(0.35+0.15)\times 2$. 2. **Apply the order of operations:** First, solve the expression inside the parentheses. $$0.35 + 0.15 = 0.50$$ 3. **Substitute back:** $$2.75 \times 0.50 \times 2$$ 4. **Multiply step-by-step:** $$2.75 \times 0.50 = 1.375$$ 5. **Multiply the result by 2:** $$1.375 \times 2 = 2.75$$ 6. **Final answer:** $$2.75$$ The value of the expression is $2.75$.