Odpowiedź:
1
[tex] \overline{x} = \frac{ \sum2*20+3*40+4*70+5*90+6*80}{300} = \frac{ \sum40 + 120 + 280 + 450 + 480}{300} = \frac{1370}{300} = 4.5(6) \approx \: 4.57[/tex]
Odp. średni czas spędzany na zakupach to 4,57 godz.
2
[tex]a_{n} = a_{1} + (n - 1) \times r \\ 346 = 3 + (n - 1) \times 7 \\ 346 =3 + 7n - 7 \\ 7n = 350 \\ n = 50[/tex]
[tex]S_{n} = \frac{a_{1}+ a_{n} }{2} \cdot \: n = \frac{3 + 346}{2} \times 50 = 349 \times 25 = 8725[/tex]
3
[tex]a = 4 \\ \\ P= \frac{1}{2} ab \\ 12 = \frac{1}{2} \times 4 \times b \\ b = 6 \\ \\ c = \sqrt{ {a}^{2} + {b}^{2} } = \sqrt{ {4}^{2} + {6}^{2} } = \sqrt{16 + 36} = \sqrt{52} = 2 \sqrt{13} [/tex]
4.
[tex]81 {x}^{2} + 16 = 0 \\ \Delta = {b}^{2} - ac = 0 - 4 \times 81 \times 16 = - 5184[/tex]
∆<0 - brak rozwiązań rzeczywistych
