[tex]1) probabilitatea = \frac{nr. \ cazurilor \ favorabile}{nr.\ cazurilor \ posibile} \\ \\ nr.\ cazurilor \ posibile: \\ |1|=1\\ |2|=2 \\........... \\ |9|=9 \\|-1|=1 \\ |-2|=2 \\ ................ \\ |-9|=9 \\\\ sunt \ in \ total \ 18 \\ \\ nr. \ cazurilor posibile: \\ |3|=3 \\ |6|=6 \\ |9|=9 \\ |-3| =3 \\ |-6|=6 \\ |-9|=9 \\ sunt \ in \ total \ 6 \\ \\ \boxed{p= \frac{6}{18}=\frac{1}{3}}[/tex]
[tex]2) 2,5= 2 \frac{5}{10}= 2\frac{1}{2}= \frac{5}{2} \\ \\ 0,5= \frac{5}{10}= \frac{1}{2} \\ \\ \frac{2x}{5}= \frac{16*2}{1} => x= \frac{5*16*2}{2} \\\\ \boxed{x=80}[/tex]
[tex]3)cp= \frac{md}{ms} *100 \\ cp-\ concentratia \ procentuala \ \\ md-masa \ substantei \ dizolvate \\ ms-masa \ solutiei \\ \\ \frac{25}{100}=\frac{30}{ms}*100 <=> \frac{1}{4} = \frac{30*100}{ms} => \\ \\ => ms=4*3000 \\ \\ \boxed{ms=12000g}[/tex]
[tex]4)x-suma \ initiala \ \\ \\ \frac{1}{2} \ din\ x= \frac{1}{2} * x= \frac{x}{2} - \ prima \ data\ \\ \\ x^{(2}- \frac{x}{2}= \frac{2x-x}{2}= \frac{x}{2} - restul \\ \\ \frac{2}{3}\ din \ \frac{x}{2} = \frac{2}{3} * \frac{x}{2}= \frac{x}{3} \ -a \ 2a \ oara \\ \\ \frac{x}{2}^{(3}- \frac{x}{3}^{(2}= \frac{3x-2x}{6}= \frac{x}{6} -a \ 3a \ oara\ \\ \\ \frac{x}{6}=120 \\ \\ \boxed{x=720 \lei}[/tex]
5)ΔABC ≡ ΔMNP
ΔABC; ΔMNP -echilaterale
[AB]=[BC]=[AC]=l
[MN]=[NP]=[MP]=l =>P ΔMNP= P ΔABC=3l= 3*8=24 cm
