1. **State the problem:** Calculate the value of the expression $-228.6\ \text{dBW/Hz} + 10 \log 290$ (K). 2. **Recall the formula and rules:** The expression involves adding a decibel value and a logarithmic term. The logarithm is base 10. 3. **Calculate the logarithm:** $$10 \log 290 = 10 \times \log_{10}(290)$$ Calculate $\log_{10}(290)$: $$\log_{10}(290) \approx 2.4624$$ So, $$10 \log 290 \approx 10 \times 2.4624 = 24.624$$ 4. **Add the values:** $$-228.6 + 24.624 = -203.976$$ 5. **Final answer:** The value of the expression is approximately $$-203.98\ \text{dBW/Hz}$$