[tex]6)A=\left\{0,2,4,6,8\right\} = > cardA=5[/tex]
Numărul tuturor submulțimilor lui A este:
[tex] {2}^{cardA} = {2}^{5} = 32[/tex]
=>număr cazuri posibile=32
Numărul tuturor submulțimilor lui A cu 3 elemente este :
[tex]C_{5}^{3}=\frac{5!}{3!(5-3)!}=\frac{5!}{3!\times2!} = \frac{1 \times 2 \times 3 \times 4 \times 5}{1 \times 2 \times 3 \times 1 \times 2} = \frac{4 \times 5}{2} = \frac{20}{2} = 10[/tex]
=>număr cazuri favorabile=10
[tex]P = \frac{nr. \: cazuri \: favorabile}{nr. \: cazuri \: posibile} = \frac{10}{32} = \frac{10}{ {2}^{5} } [/tex]
[tex]=>D. \: \frac{10}{ {2}^{5} } [/tex]
[tex]8) \alpha \: \in \: (\pi, \frac{3\pi}{2} ) = > cadranul \: III[/tex]
[tex]cos \alpha = - \frac{3}{5} [/tex]
[tex] {sin}^{2} \alpha + {cos}^{2} \alpha = 1[/tex]
[tex] {sin}^{2} \alpha + {( - \frac{3}{5}) }^{2} = 1[/tex]
[tex] {sin}^{2} \alpha + \frac{9}{25} = 1[/tex]
[tex] {sin}^{2} \alpha = 1 - \frac{9}{25} [/tex]
[tex] {sin}^{2} \alpha = \frac{16}{25} = > sin \alpha = \pm \sqrt{ \frac{16}{25} } = \pm \frac{4}{5} [/tex]
[tex] \alpha \: \in \: (\pi, \frac{3\pi}{2} ) = > sin \alpha < 0 = > sin \alpha = - \frac{4}{5} [/tex]
[tex]sin2 \alpha = 2sin \alpha cos \alpha = 2 \times ( - \frac{4}{5} ) \times ( - \frac{3}{5} ) = \frac{24}{25} [/tex]
[tex] = > B. \: \frac{24}{25} [/tex]
