j) Your friend starts selling at three farmer's markets each week. They earn \( \$(10+6 w) \) at each market and their weekly expenses for all three markets are \( \$(4 w+100) \). Write and solve a break-even equation. Show all work for full credit. ( 10 points) (Hint: Your equation should require the use of the Distributive Property.)

2) \( \frac{10 x-8}{4}=\frac{1}{4} \)

\( \left. \begin{array} { c } { a = 3 , b = - 4 , c = - 2 } \\ { \frac { 3 a - b } { 2 c } + \frac { 3 a - c } { c - b } } \end{array} \right. \)

Sea \( A=\left[\begin{array}{cccc}-2 & 0 & 0 & 7 \\ 1 & 2 & -1 & 4 \\ 3 & 0 & -1 & 5 \\ 4 & 2 & 3 & 0\end{array}\right] \) Encontrar: a) \( \operatorname{det}(A) \)

12. Risolvi i seguenti problemi. a. Una circonferenza di centro \( O \) ha il raggio di \( 6,5 \mathrm{~cm} \) e una sua corda \( A B \) dista \( 3,9 \mathrm{~cm} \) dal centro. Calcola il perimetro e l'area del triangolo \( A O B \).

Harry is bored in class and decided to write the word MATHEMATICS over and over. e.g. MATHEMATICSMATHEMATICSMAT.... 7.1 If Harry continues this pattern, determine the \( 2014^{\text {th }} \) letter he will write. 7.2 Determine the probability of the letter 'M' being selected out of the 2014 letters. Leave your answer as a fraction in its simplest form.