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Singapore
A train travels 400 km between Tokyo and Osaka. Renee searches the Internet and finds that the average speed of the Nozomi train is greater than that of t Hikari train by \( 30 \mathrm{~km} / \mathrm{h} \), and the faster train reduces the travelling time by 30 minutes. Find the average speed of the Nozomi train based on Renee's research.
Algebra Jan 22, 2025
A train travels 400 km between Tokyo and Osaka. Renee searches the Internet and finds that the average speed of the Nozomi train is greater than that of t Hikari train by \( 30 \mathrm{~km} / \mathrm{h} \), and the faster train reduces the travelling time by 30 minutes. Find the average speed of the Nozomi train based on Renee's research.
Algebra Jan 22, 2025
A train travels 400 km between Tokyo and Osaka. Renee searches the Internet and finds that the average speed of the Nozomi train is greater than that of t Hikari train by \( 30 \mathrm{~km} / \mathrm{h} \), and the faster train reduces the travelling time by 30 minutes. Find the average speed of the Nozomi train based on Renee's research.
Algebra Jan 22, 2025
3. Rudi, Sam and Teh had 162 stickers altogether. Rudi gave \( \frac{3}{10} \) of his stickers to Sam and \( \frac{1}{4} \) of his stickers to Ted. After that, all three boys had the same number of stickers Who had more stickers at first, Sam or Ted, and how many more?
Algebra Jan 22, 2025
Form the smallest 5-digit odd number with the digits. Use each digit only once. \[ 5,6,2,3,7 \]
Arithmetic Jan 22, 2025
** 13) Show that \( x^{2}(x+2)^{2}-1=(x+1)^{2}(x+1+\sqrt{2})(x+1-\sqrt{2}) \). Hence, without using a calculator, solve the inequality \( \frac{1}{(x+2)^{2}} \geq x^{2} \) Deduce the range of values of x for which \( \frac{1}{\left(e^{x}+2\right)^{2}} \geq e^{2 x} \).
Algebra Jan 22, 2025
** 12. Solve the following inequality \( \frac{x(x+3)(x-3)+16}{(x+3)(x-2)} \geq-2 \). Hence without the use of graphic calculator, solve the inequality \( \frac{2^{x}\left(2^{x}+3\right)\left(2^{x}-3\right)+16}{2^{2 x}+2^{x}-6} \geq-2 \) where \( x \neq 1 \).
Algebra Jan 22, 2025
before it hits the gr 15. Profit function. The profit, \( \$ y \), of a company can \( b_{e} \) approximated by \( y=-\frac{1}{20} x^{2}+75 x-600 \), where \( x \) is the number of goods sold. (i) Explain the meaning of " -600 " in the equation. (ii) How many goods must be sold in order for the company to yield the maximum profit? What is this maximum profit?
Algebra Jan 22, 2025
10. Given the prime factorisation of each of the following numbers, find its square root without using a calculator. \( \begin{array}{ll}\text { (a) } 9801=3^{4} \times 11^{2} & \text { (b) } 35721=3^{6} \times 7^{2}\end{array} \)
Arithmetic Jan 22, 2025
A data set consist of the following 6 values: The range is 6 . The median is 5 . The lower quartile is 4 . The interquartile range is 3 . Given that \( x<y<z \), find the values of \( x, y \) and \( z \).
Statistics Jan 22, 2025
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