df 500 g of mince meat costs \( \$ 4.50 \), how much would 4 kg of mince meat cost? Solve the following ratio problems, a The required staff to student ratio for an excursion is \( 2: 15 \). If 10 teachers attend the excursion, what is the maximum number of students who can attend? b The ratio of commercials to actual show time for a particular TV channel is \( 2: 3 \). How many minutes of actual show were there in 1 hour? c A rectangle has length and width dimensions in a ratio of \( 3: 1 \). If a particular rectangle has a length of 21 m , what is its width? dalter and William have a height ratio of \( 7: 8 \). If William has a height of 152 cm , how tall is Walter?

A jar of fruit punch contains \( 15 \% \) lemon juice, \( 30 \% \) orange juice and \( 55 \% \) apple juice. If the volume of lemon juice increases by \( 30 \% \), the volume of orange juice increases by \( 15 \% \) and \( t \) volume of apple juice decreases by \( 20 \% \), find the percentage change in the volume of the fru punch.

Considerar la recta \( r:(x, y)=(2,-1)+\lambda(1,4), \operatorname{con} \lambda \in \mathbb{R} \). a) Estudiar la posición relativa de \( r \) con respecto a cada una de las siguientes rectas: \[ r_{1}:(x, y)=(0,3)+\mu_{1}(-2,8) \quad \text { con } \mu_{1} \in \mathbb{R} \] \( r_{2}:\left\{\begin{array}{l}x=1+\frac{1}{2} \mu_{2} \\ y=-5+2 \mu_{2}\end{array}\right. \) con \( \mu_{2} \in \mathbb{R} \)

Marca un punto de solución de la siguiente inecuación: \( x+2 y>7 \)

Solve the system of equations using the substitution method. \[ \begin{aligned} 8 x-6 y & =-2 \\ 4 x+12 y & =9\end{aligned} \]

The value of \( \sin ^{-1}\left(\tan \left(-\frac{\pi}{4}\right)\right) \sin ^{-1}\left(\tan \left(-\frac{\pi}{4}\right)\right)_{\text {is }} \)