U.S. stocks opened mixed Friday after a reading from the Federal Reserve’s preferred inflation gauge showed that the cost of living is still running hot. The blue-chip gauge Dow Jones Industrial Average          DJIA,         +1.82%        rose 0.5% soon after the opening bell, while the S&P 500          SPX,         +1.53%        gained 0.1% and technology-heavy Nasdaq Composite          COMP,         +1.72%        dropped less than 0.1%, according to FactSet data, at last check. U.S. inflation measured by the personal-expenditures-consumption index rose 0.3% in September for an unchanged annual rate of 6.2%, according to a Bureau of Economic Analysis report Friday. Core PCE, which excludes energy and food prices, climbed 0.5% last month, bringing its annual rate to 5.1%, from 4.9% in August.