A binary operation ∆ is defined on the set of real numbers R, by \(x∆y = \sqrt{x+y-\frac{xy}{4}}\), where x, yER. Find the value of \(4∆3\)

The functions \(f:x \to 2x^2 + 3x -7\) and \(g:x \to 5x^2 + 7x - 6\) are defined on the set of real numbers, R. Find the values of \(x\) for which \(3f(x) = ...

If \( \log_{10}(3x+1) + \log_{10}4 = \log_{10}(9x+2) \), find the value of x

\[ \left(\frac{3\sqrt{6}}{\sqrt{5}}+\frac{\sqrt{54}}{3\sqrt{5}}\right)^{-1} \]

Which of the following is the semi-interquartile range of a distribution?

Express \( \frac{4\pi}{2} \) radians in degrees.

Consider the following statement: x: All wrestlers are strong y: Some wresters are not weightlifters. Which of the following is a valid conclusion?

Simplify \( \frac{9 \ast 3^{n+1}-3^{n+2}}{3^{n+1}-3^n} \)

A straight line makes intercepts of -3 and 2 on the x and y axes respectively. Find the equation of the line.