Ưna pirâmide reta possui como base um quadrado cujo lado mede \( 6 \sqrt{ } 2 \mathrm{~cm} \). Se a sua altura è 10 cm , então o seu volume, em \( \mathrm{cm}^{2} \), é de: A) 240 B) 340 C) 480 D) 500 E) 720

24 Consider the equation of the second degree in \( x: x^{2}-(m+3) x+m=0 \), where \( m \) is a real parameter. Show that there is between the roots, when they exist, an independent relation from \( m \). (Eliminate \( m \) between \( S \) and \( P) \).

32 What is the simplest form of \( \frac{2 a-(a+b)}{a^{2}-b^{2}} \) ? \( \begin{array}{ll}\text { A } a+b & \text { B } a-b \\ \text { C } \frac{1}{a+b} & \text { D } \frac{1}{a-b}\end{array} \)

ercice 5 . Soit \( n \in \mathbb{N}^{*} \). On définit la relation \( \mathcal{R} \) sur \( \mathbb{C} \) par: \( z \mathcal{R} z^{\prime} \Leftrightarrow z^{n}=z^{\prime n} \) Montrer que \( \mathcal{R} \) cst unc relation d'équivalence. Soit a \( \in \mathbb{C}^{*} \). Déterminer la classe d'équivalence de a note \( \mathrm{cl}(\mathrm{a}) \). En déduire les classes \( \mathrm{cl}(1+\mathrm{i}) \) et \( \mathrm{cl}(-1+i \sqrt{3}) \) pour \( n=3 \) et \( n=4 \).

Lesson 14: What Do You Know About Polynomials? Cool Down: How Would You Factor? A polynomial \( D(x)=3 x^{3}-2 x^{2}-15 x+14 \) has known factors \( (x-2) \) and \( (x-1) \). Would you use a diagram, long division, or some other method to rewrite the expression for D in factored form? Explain your reasoning.

Exercise \#3. Calculate confidence intervals for proportion. Use the following information to complete the calculations. \[ \text { Formula: } P \pm Z \sqrt{\left(\frac{p(1-P)}{n}\right)} \] (3a) You are polling San Marcos to check support for a proposition that citizens will be voting on next election. The sample, \( n=500 \), indicates that the proportion of San Martians who support the proposition is 0.67 . Calculate the \( 95 \% \) and \( 99 \% \) confidence intervals for the proportion of San Martians who support the proposition.