Decide what number must be added to both sides of the equation to make the left side a perfect square trinomial, then factor the left side. \( x^{2}-6 x=3 \) Add a number to both sides of the equation to make the left side a perfect square trinomial. \( x^{2}-6 x+\square=3+\square \) (Simplify your answers.)

\( ( \exists a > 0 ) \ln - \frac { \pi } { 2 } ) @ \)

33. A factory makes low cost soccer balls with diameters that are normally distributed with mean \( \mu \mathrm{cm} \) and standard deviation 0.25 cm . (a) Estimate the number of balls in a random sample of 200 balls that have diameters within 0.3 cm of the mean diameter. (b) The diameters of \( 80 \% \) of the soccer balls produced by this factory have diameters within \( k \mathrm{~cm} \) of the mean diameter. Find the value of \( k \). (c) \( 25 \% \) of the balls have diameters less than 21.832 cm . Find \( \mu \).

2. Determine the equation of the parabola after being transformed from \( f(x)=x^{2} \) by a vertical stretch of factor 4 , and a horizontal stretch of factor \( \frac{1}{3} \) reflected on the \( y \)-axis, and translations of 4 units to the right and 3 units up.

How many hours on average does it take for \( 50 \% \) of emails to be opened? Select the correct answer then click confirm.

Give the center and radius of the circle represented by the equation. \[ x^{2}+y^{2}-12 x+6 y=-44 \] The center of the circle is \( \square \). (Type an ordered pair, using integers or fractions.) The radius of the circle is \( \square \). (Type an integer or a simplified fraction.)