1)probabilitatea =nr cazurilor favorabile/nr cazurilor posibile
nr cazurilor favorabile:15;30;45;60;75;90
p= 6/90= 2/30= 1/15=0,06%
2)f+b=25
40% din 25= 40/100 * 25= 10/25 *25= 2/5 * 25= 2*5=10 baieti
25-10=15 fete
3)ΔABC
mas< ACR= mas<CAB+mas <CBA
mas<ABN= mas <BAC +mas < BCA
mas <SAM= mas <ABC + mas < ACB
mas< CAB +mas< CBA +mas < BCA=180 grade
mas<BAC+mas <ABC +mas< ACB=180 grade
mas <ACR +mas <ABN +mas <SAM=180+180 =360 grade
(vezi mai jos figura)
4)[tex]2^{n+3} +2^{n+2} +2^{n+1} = \\ 2^n *2^3 +2^n* 2^2 +2^n *2 = \\ 2^n(2^3+2^2+2)= \\ 2^n(8+4+2)= \\ 2^n *14= \\ 2^n * 2*7 :7 \ (trebuiau \ 3 \ puncte)[/tex]
5)[tex]\frac{1}{3} * ( \frac{x-1}{2} - \frac{1}{6} ) = \frac{1}{36}+ \frac{1}{36} \\ \frac{1}{3} * ( \frac{x-1}{2} - \frac{1}{6}) = \frac{2}{36} \\ (\frac{x-1}{2}-\frac{1}{6} ) = \frac{1}{18} : \frac{1}{3} \\ \frac{3(x-1)}{6}- \frac{1}{6} = \frac{1}{18}*\frac{3}{1} \\ \frac{3x-3 -1}{6}= \frac{1}{6} \\ 3x-4=1 \\ 3x=1+4 \\ 3x=5 \\ x= \frac{5}{3}[/tex]