The correct formula for conducting a dependent-samples \( t \) test is

Approximate each number using a calculator. \( 6^{\sqrt{6}} \)

What is the product of the mean and the median of the first 6 prime numbers? (Note: 2 is the first prime number.) A. 27 B. 37 C. 39 D. 41 E. 42

The electric potential \( V \) at a point is given by \( V(x, y, z)= \) \( A\left(y^{2}-x^{2}\right) \exp \left(-B z^{2}\right) \), where \( A= \) \( 15 \mathrm{Vm}^{-2} \) and \( B=2.5 \mathrm{~m}^{-2} \) (i) Find the magnitude of the electric field vector on the positive \( x \)-axis at at point 1 m from the origin. (ii) Determine the curl of the electric field in part(i) above.

The path of a football is given by the equation \( y=x-\frac{x^{2}}{40}, x \geqslant 0 \). If \( \frac{\mathrm{d} x}{\mathrm{~d} t}=10 \sqrt{2} \) for all \( t \), find \( \frac{\mathrm{d} y}{\mathrm{~d} t} \) when \( x=10 \).

Іайдите значение выражения \( \sqrt{108} \cos ^{2} \frac{\pi}{12}-\sqrt{27} \).