1. **State the problem:** Calculate the value of $$r = \frac{7 \times 2495 - 113 \times 161}{\sqrt{(7 \times 1889 - 113^2)(7 \times 3883 - 161^2)}}$$ 2. **Calculate the numerator:** $$7 \times 2495 = 17465$$ $$113 \times 161 = 18193$$ $$\text{Numerator} = 17465 - 18193 = -728$$ 3. **Calculate the first bracket in the denominator:** $$7 \times 1889 = 13223$$ $$113^2 = 12769$$ $$7 \times 1889 - 113^2 = 13223 - 12769 = 454$$ 4. **Calculate the second bracket in the denominator:** $$7 \times 3883 = 27181$$ $$161^2 = 25921$$ $$7 \times 3883 - 161^2 = 27181 - 25921 = 1260$$ 5. **Calculate the product inside the square root:** $$454 \times 1260 = 572040$$ 6. **Calculate the square root:** $$\sqrt{572040} \approx 756.32$$ 7. **Calculate the final value of $r$:** $$r = \frac{-728}{756.32} \approx -0.9625$$ **Final answer:** $$r \approx -0.9625$$