Questions asked by Yukina A.

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• Charlotte is a librarian who has a taxable income of $69410. The tax payable on the first $37000 is $3572 and the balance was taxed at the rate of 32.5%. How much does Charlotte have to pay in tax, to the nearest dollar?
  
• The maximum Youth Allowance is reduced by $1 for every $4 that the youth's parents income is over $31 400. By how much is Hannah's Youth Allowance reduced if her parents earn a combined income of $35 624?
  
• A survey of showed that 6% of families-1 child, 38% -2, 42%-3 and 10%-3 or more. A family is selected at random. What is the probability that it has some children?
  
• A drawer contains 8 black socks and 8 white. Two are pulled out randomly: I) probability that it is the same colour? II) how many will have to be pulled out for matching pairs?
  
• A card is selected at random from a normal pack of cards. The cards are replaced each time. What is the expected number of times you would select a king from 260 trials?
  
• A fair coin is tossed 3 times. The probability of throwing 3 tails = 0.125, two tails = 0.375 and 1 tails = 0.375. What is the probability of throwing 1 head?
  
• PQ= x cm PR= 2xcm Angle QPR= 30 degrees The area of the triangle PQR= Acm squared Show that x = square root 2A?
  
• BCDE is a square with side lengths of 10cm , The other faces of the pyramids are equilateral triangles with side lengths of 10cm. a) calculate the volume of the pyramid? (3 s.f) (Apex= A , front triangles areB&C, back are E&D)
  
• The image below displays that the water leakage happens from the bottom of the trough at a constant rate. 2hrs later, the level of the water has fallen by 20cm. How many more mins will it take for the trough to empty completely?
  
• Please help with the image below.(?)
  
• 1) what proportion of boys and girls should be selected? 2) How many boys and girls should be selected for a stratified random sample of 30 students? Explain how to obtain this sample question.