b. Whole number ii. Truncate to; a. 2 decimal places b. Whole number State the type of matrix P and matrix Q, giving a reason for

5. Aplique o Princípio de Indução Finita para demonstrar que para \( n \geq 1 \) vale: a) \( 1^{2}+2^{2}+\cdots+n^{2}=\frac{n(n+1)(2 n+1)}{6} \) b) \( 1+3+5+\cdots+(2 n-1)=n^{2} \) c) \( 1 \cdot 2+2 \cdot 3+3 \cdot 4+\cdots+n \cdot(n+1)=\frac{n(n+1)(n+2)}{3} \) d) \( 1^{2}+3^{2}+5^{2}+\cdots+(2 n-1)^{2}=\frac{n\left(4 n^{2}-1\right)}{3} \)

2. Utilice diagramas de Venn para resolver los siguientes problemas. (a) En una competencia de atletismo conformada por 15 pruebas participaron 50 atletas. Al finalizar la competencia se determinó lo siguiente: cuatro atletas conquistaron medallas de oro, plata y bronce; siete conquistaron medallas de oro y plata; seis de ellos plata y bronce; ocho conquistaron oro y bronce. Determine: ¿Cuántos de los atletas no conquistaron medallas?, ¿Cuántos solo oro?, ¿Cuántos solo plata? y ¿Cuántos solo plata y bronce?.

Tre numeri naturali sono tali che il secondo è la somma degli altri due aumentata di 7 . La differenza tra il secondo eil primo è tre volte la metá del terzo, mentre la differenza tra il terzo e il doppio del primo èi \( \frac{2}{13} \) del secondo. Trova i tre numeri. Rapporti \& rapporti La somma di tre numerie 70

22. The measure of \( \angle G \) is six more than twice the measure of \( \angle H \). If \( \angle G \) and \( \angle H \) are complementary angles, find \( m \angle H \).

Assume that there is a \( 10 \% \) rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. If copies of all your computer data are stored on three independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive? a. With two hard disk drives, the probability that catastrophe can be avoided is (Round to four decimal places as needed.)