A student prepares for an exam by studying a lut of 5 problems che can volve six of them. For the exam the ingtructor colects fire guestion's at a random from the list of 15 . a) What is the probobility that the student can volve exactly 3 prablems onthe the exam. b) Find e nean and standard deriabon of the number of stucto problems that student can volve on the exam

A car completes a 200 km journey at an average speed of \( x \mathrm{~km} / \mathrm{h} \). The car completes the return journey of 200 km at an average speed of \( (x+10) \mathrm{km} / \mathrm{h} \). i) Show that the difference between the time taken for each of the two journeys is \( \frac{2000}{x(x+10)} \) hours. ii) Find the difference between the time taken for each of the two journeys when \( x=80 \). Give your answer in minutes and seconds.

1 Jessica is making metal sculptures to sell. A metal sculpture costs \( \$ 24 \) to make and Jessica sells it to a retailer for a profit of \( 175 \% \). If the retailer then marks up the sculpture by another \( 120 \% \), how much will it cost someone to buy a sculpture in the shop? ( 3 marks)

9 For a soccer carnival, Derek is mixing the cordial which uses a ratio of 40 mL cordial to 750 mL of water. If he needs to add cordial to 10 litres of water, how much cordial is needed? State your answer in millilitres, correct to one decimal place. ( 3 marks)

2) Estimate: \( 2,491 \div 48 \)

ii) \( \quad 4 y^{2}-81 \) iii) \( \quad t^{2}-6 t+8 \)