5. When do we describe the histogram as symmetric? A) A histogram is symmetric if it is identical on both sides of its central poin B) A histogram is symmetric when it is skewed to the left. C) A histogram is symmetric when it is skewed to the right. D) A histogram is symmetric when probability is equal to zero.

Exercice 2: (1) Montrer les implications suivantes: a \( (\forall \mathrm{x}, \mathrm{y} \in \mathbb{R}) ; \quad \mathrm{Si} \quad(|\mathrm{x}| \leq 1 \) et \( |\mathrm{y}| \leq 1) \quad \) alors \( \sqrt{1-\mathrm{x}^{2}}+\sqrt{1-\mathrm{y}^{2}} \leq 2 \sqrt{1-\left(\frac{\mathrm{x}+\mathrm{y}}{2}\right)^{2}} \) b \( \left(\forall \mathrm{x}, \mathrm{y} \in \mathbb{R}^{*}\right) ; \quad 2 \mathrm{x}+4 \mathrm{y}=1 \Rightarrow \frac{1}{\mathrm{x}^{2}+\mathrm{y}^{2}} \leq 20 \) (2) En utilisant "Le raisonnement par les équivalences successives", montrer que: a \( \left(\forall \mathrm{x}, \mathrm{y} \in \mathbb{R}^{+}\right) ; \quad \mathrm{x} \sqrt{\mathrm{x}^{2}+1}=\mathrm{y} \sqrt{\mathrm{y}^{2}+1} \Longleftrightarrow \mathrm{x}=\mathrm{y} \) b \( \left(\forall \mathrm{x}, \mathrm{y} \in \mathbb{R}_{+}^{*}\right) ; \quad \mathrm{x} \prec \mathrm{y} \Longleftrightarrow \frac{\mathrm{x}}{\mathrm{y}} \prec \frac{2 \mathrm{x}+5 \mathrm{y}}{5 \mathrm{x}+2 \mathrm{y}} \prec \frac{\mathrm{y}}{\mathrm{x}} \)

7. Representa cada situación como una multiplicación de números racionales. Luego resuélvela En un colegio, \( \operatorname{los} \frac{2}{5} \) de estudiantes son hom- bres y de ellos \( \frac{1}{2} \) están en bachillerato. :Qué fracción representa a los hombres que hay en bachillerato?

a) \( \frac{0,3}{0,5}=\frac{1,5}{x} \)

2. Calcula el área lateral, el área total y el volumen de los cilindros, teniendo en cuenta las condiciones dadas. a. El radio de la base del cilindro es \( 0,9 \mathrm{~m} \) y su altura es 30 cm . b. El diámetro de la base del cilindro es 14 cm y su altura es 7 cm . c. El área de la base es \( 144 \pi \mathrm{~cm}^{2} \) y la altura es 10 cm . d. El valor del área lateral es igual al valor del volumen y la altura mide 5 cm .

(1 point) Monday's lecture went over a logistic equation: \( f(t)=\frac{1000}{1+999 e^{-0.603 t}} \) which models how many people \( f \) have had the flu \( t \) days after an initial infection in a community of 1000 people. According to the model, how many people will have had the flu after 10 days? \( \square \) According to the model, how many people will have had the flu after 20 days? \( \square \) According to the model, how many days until 500 people have had the flu? \( \square \) According to the model, how many days until 700 people have had the flu? \( \square \) According to the model, how many days until 2000 people have had the flu? \( \square \) Hint: One of your answers should be "never"