Matthew neem 'n lening uit van R175 000 , teen \( 18 \% \) p.j. kwartaalliks saamgestel. Hy betaal die lening terug oor 'n tydperk van 4 jaar, en begin 3 maande nadat die lening toegestaan is. Bereken (1) Matthew se kwartaallikse paaiement. (2) die totale rente op die lening.

\( \frac { 2 } { x ^ { 3 } } + 5 = 21 \quad ( x \neq 0 ) \)

If \( \bar{x}=7.5 \) hours and margin of error \( =0.33 \) hours for \( 95 \% \) confidence, what is the \( 95 \% \) confidence interval for \( \mu \) ? \( (7.17,7.83) \) Cannot be determined based on information given. \( (-12.5,27.5) \)

Let \( x, y \in \mathbb{R}^{+} \). Prove that: if \( x \leq y \), then \( \sqrt{x} \leq \sqrt{y} \)

\( \frac{3 j^{6}-j^{16}}{1-2 j} \) and express it in form of: \( a+j b \)

A different size rectangular box to part (i) has height 15 cm . The box will also contain 12 cylindrical tins, which are all just touching each other and the sides of the box. The layout of the 12 tins within this box will be the same as in part (i). Each tin is 15 cm high, and with radius \( p \mathrm{~cm} \). Show that the proportion of the volume in the box that is NOT occupied by the tins is \( \frac{(4-\pi)}{4} \).