Risk and return 2 doubt

Hey ! I am just having a hard time comprehending this question.

When a risk-free asset is combined with a portfolio of risky assets, which of the following is least accurate?

A. The standard deviation of the return for the newly created portfolio is the standard deviation of the returns of the risky asset portfolio multiplied by its portfolio weight.

B. The expected return for the newly created portfolio is the weighted average of the return on the risk-free asset and the expected return on the risky asset portfolio.

C. The variance of the resulting portfolio is a weighted average of the returns variances of the risk-free asset and of the portfolio of risky assets.

I don’t understand why std deviation is taken as a weighted average. since weighted avg was not the right way to calculate the risk that’s why we have the formula sqrt(w1s1)^2 +(w2s2)^2 + 2w1w2s1s2corr1,2 . So even though this formula has weights it’s not quite similar to the way we calculate returns. Can someone help me understand the flaw in my understanding?

Thanks !