You are given a \( 1.0 \mathrm{~mol} / \mathrm{L} \) solution of KOH . Using this solution, you must prepare 100 mL of a diluted solution that will have a concentration of \( 0.25 \mathrm{~mol} / \mathrm{L} \). \( \begin{array}{ll}\text { a) What volume of the initial solution should be used? } & \text { b) How much water should be added? }\end{array} \)

Factor the trinomial completely. \[ 6 x^{2} y+90 x y-66 y \]

Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of \( \mu=1.1 \mathrm{~kg} \) and a standard deviation of \( \sigma=4.9 \mathrm{~kg} \). Complete parts (a) through (c) below. a. If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year. The probability is (Round to four decimal places as needed.)

\( \begin{array}{ll}\text { C } \cos \left(\frac{\pi}{4}\right) & \text { a. } \frac{1}{2} \\ \text { - } \sin \pi & \text { b. }-1 \\ \text { - } \cos \pi & \text { c. } \frac{\sqrt{2}}{2} \\ \cos \left(\frac{\pi}{6}\right) & \text { d. } 0 \\ \text { ( } \sin \left(\frac{\pi}{6}\right) & \text { e. } \frac{\sqrt{3}}{}\end{array} \)

1) \( \frac{x+6}{x+1}<2 \)

Use substitution to determine whether the given \( x \)-value is a solution of the equation. \[ \cos x=\sin 3 x, x=\frac{\pi}{6} \]