If \({u_{10}} = 100\)  and  \({u_{15}} = 175\),   find \({u_{100}}\) of the arithmetic sequence.

Solve \({\log _{10}}x = – 5\), correcting to one significant figures.

The amount in an investment account is initially \($4500 \) at the beginning of January 2019 and decrease by 5% per annum due to deflation. At which year and month the amount becomes half.

Find \(\theta \), correcting to the nearest degree, if the area of the triangle is 12 cm². Ensure  \(\theta \)  is an obtuse angle.

Find the smallest angle in the triangle, correcting to the nearest degree.

Find the interquartile range of the data represented in the box-and-whisker plot.

\( \begin{array}{c|cccccc}
1 & 0 & 1 &&&& \\
2 & 1 & 2 & 6 &&& \\
3 & 2 & 4 & 7 & 7 && \\
4 & 3 &&&&& \\
\end{array} \)

Find the probability that a randomly chosen student plays rugby given that he plays soccer.

Daniel is a marathon runner. On the Olympic course in the northern hemisphere, the meantime is 2 hours 16 minutes with a standard deviation of 5 minutes. On the southern hemisphere, the meantime is 2 hours 20 minutes with a standard deviation of 4 minutes. In the northern hemisphere, Daniel’s time was 2 hours 18 minutes and in the southern hemisphere, his time was 2 hours 21 minutes. By writing these \(z\)-scores, determine the better performance.

For what values of  \(x\)  is  \(y = \dfrac{{{x^2}}}{{2{x^2} + x + 1}}\)  decreasing?

Find the value of  \(k\)    if   \(\int_{ – 1}^2 {\left( {3{x^2} + 4x + k} \right)dx} = 30\).