1. **State the problem:** Calculate the product of $95$ and $3 \times 10^{4}$ and express the answer in scientific notation. 2. **Recall the formula:** When multiplying numbers in scientific notation, multiply the coefficients and add the exponents of 10. 3. **Multiply the coefficients:** $$95 \times 3 = 285$$ 4. **Combine with the power of ten:** $$285 \times 10^{4}$$ 5. **Convert to proper scientific notation:** Scientific notation requires the coefficient to be between 1 and 10. $$285 = 2.85 \times 10^{2}$$ So, $$285 \times 10^{4} = (2.85 \times 10^{2}) \times 10^{4} = 2.85 \times 10^{2+4} = 2.85 \times 10^{6}$$ 6. **Final answer:** $$\boxed{2.85 \times 10^{6}}$$