Suppose that \( 30 \% \) of bottles produced in a certain plant are defective. If a bottle is defective, the probability is 0.9 that an inspector will notice it and remove it from the filing line. If a bottle is not defective, the probability is 0.2 that the inspector will think it is defective and remove it from the line. (i) If a bottle is removed from the line, what is the probability that it is defective? (ii) if a customer buys a bottle that has not been removed from the line, what is the probability that it is defective? (iii) If a customer buys one bottle at a time until two defective bottles are found, find the probability that he needs to buy 10 bottles.

\( 2 \frac { 1 } { 2 } l = \square ml \)

Solve the following system of equations. \[ \begin{array}{l}4 x-8 z=32 \\ 6 x-y+3 z=-5 \\ 2 x+y=-45\end{array} \] Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. There is one solution. The solution is ( (Type integers or simplified fractions.) B. There are infinitely many solutions. The solution set is \( \{(x, y, z) \mid 2 x+y=-45\} \). The solution set is \( \varnothing \).

Solve the system of equations by the substitution method. \( \left\{\begin{array}{l}4 x-y=5 \\ 7 x-2 y=11\end{array}\right. \) A. The solution is \( \square \). (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions; \( \{(x, y) \mid 4 x-y=5\} \) or \( \{(x, y) \mid 7 x-2 y=11\} \). C. There is no solution; \( \} \) or \( \varnothing \).

1. \( \frac{1}{2} a-\frac{2}{3} b \) pur \( \frac{2}{5} a^{2}= \)

Solve the following system of equations. \[ \begin{aligned} x+4 z=0 \\ 7 x+y=0 \\ y-3 z=0\end{aligned} \] A. There is one solution. The solution is (Type integers or simplified fractions.) B. There are infinitely many solutions. The solution set is \( \{(x, y, z) \mid 7 x+y=0\} \). C. The solution set is \( \varnothing \).