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#14897

A piece of meat weighing 1kg needs to be cooked for one hour. How many hours and minutes would you need to cook a piece of meat weighing 2.6kg?

For every kg, need 1 hour

2.6 × 1 = 2.6hours

convert to hours and minutes using the degrees, minutes, seconds button on your calculator (° ‘ “)
= 2h 36 minutes

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#15244

The average NSW annual water consumption from the residential sector is equal to 90 340 litres per person per year. The Building Sustainability Index (BASIX) uses this as the benchmark to set a target for reducing water consumption by up to 40%. A new building, planned to house 50 people, has been designed to meet a 25% reduction on this water consumption benchmark. How much water per year, to the nearest kilolitre, is this building designed to save when fully occupied?
90 340 × 50 =4 517 000 L	each person uses 90 340L a year and there will be 50 people , multiply to find the number of litres for all the people
4 517 000 × 25% = 1 129 250L	find 25% of the total amount of litres
1 129 250 ÷ 1000 = 1129.25 KL	convert to kilolitres by dividing by 1000 as 1KL = 1000L
= 1129KL	round to nearest KL

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#15248

A tap runs at 9L of water per minute. If you leave the tap on while brushing your teeth for 4.5 minutes each day, how much water would be used in a week brushing your teeth?
= 4.5 × 7 = 31.5 minutes per week	there are 7 days in a week, so find out the total amount of minutes in the week that the water is used
total water = 31.5 × 9 = 283.5L	each minute uses 9L, so multiply the 9L by 31.5 minute

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#15441

A bilge pump on a yacht pumps water at the rate of 10ml per second. How long will it take the pump to empty 12 litres of water?

12L = 12000 ml
if it does 10 per second
12000 ÷ 10 = 1200 seconds
1200 ÷ 60 = 20 minutes

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#15442

A drop of water contains about 1.7 × 10²¹ molecules. A typical waterfall may have a flow of 7.5 × 10¹¹ drops of water per minute. How many molecules of water flow over the waterfall in one minute?

1.7 × 10²¹ × 7.5 × 10¹¹
= 1.275 × 10³³

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#15443

Water flows from an irrigation pipe at the rate of 2.4m³ every minute. How long would it take for 100 litres of water to flow from the pipe? (1000L = 1m³)?

2.4 × 1000
= 2400L           convert 2.4m³ into litres by multiplying by 1000
2400L              per minute flows through this pipe
100 ÷ 2400
= 0.0416 minutes               to find how long it takes for 100L to flow, divide by 2400 as this gives us 0.0416 minutes 0.0416 × 60
= 2.5 secs                              convert to seconds by multiplying by 60
[br]

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#15458

A liquid fertilizer is diluted at a rate of 15ml per 10 litres of water. The label claims that 5L of diluted mixture is required per every 10 square metres of lawn. How many ml of fertilizer is needed to fertilize a 120m2 lawn?
120 ÷ 10 = 12	first we find out how many 10 metres squared are in 120 metres squared by dividing
total amount of litres of mixture = 12 × 5 = 60 Litres	so we need 12 lots of 5 Litres which is 60 Litres of mixture
60 ÷ 10 = 6	each 10 litres of mixture has 15mls of fertilizer in, so we find out how many lots of 10L is in 60L by dividing
6 × 15 = 90ml	we need 6 lots of the fertilizer : which is 6 lots of 15ml

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#15459

If the Earth travels through space at a speed of 106,000km/h then the distance travelled by the Earth (in metres) in 30 days in scientific notation is?
106,000 × 24 × 30 = 76,320,000	Distance = speed × time speed = 106,000 time = 30 days which is 30 × 24 hours
= 76,320,000 × 1000 = 76,320,000,000m	to convert to metres we times the km by 1000
= 7.632 × 1010 m	to convert to scientific notation, we need to move the decimal from the end to in between the 7 and the 6, which is 10 places, hence will be 7.632 times 10 to the power of 10
total mass = 42 + 12 + 6 = 60kg	find the total weight by adding water, protein and bone

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#15494

Goods costing 35c per kg are sold at $420 per tonne. Find the gain as percentage of the cost price.
35c/kg = $0.35/kg 0.35 × 1000 = $350/tonne	first we must convert to same units 1000kg = 1 tonne
gain = 420 – 350 = $70	find the gain
= 70/350 × 100 = 20%	to change to percentage gain = gain/original price × 100

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#18870

Jessica received 1.8 L of fluid over 12 hours. What is the flow rate in ml/h?
1.8 × 1000 = 1800 ml	change the 1.8 L to ml  there are 1000 ml in a litre
1800 ÷ 12 = 150	so she received 1800 ml over 12 hours to find how many ml per hour, divide by the number of hours
∴ 150 ml/h

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#18871

Ariane is given 1.8 litres of fluid over 10 hours by intravenous drip. The fluid is delivered at a rate of 30 drops per mL. What is the required drip rate, in drops per minute?
1.8 L × 1000 = 1800 ml	convert the 1.8 L into ml × 1000
1800 ÷ 10 = 180 ml/h	need 1800 ml over 10 hours, convert to per hour by dividing by 10
180 ÷ 30 = 3 ml/min	convert to per minute by dividing by 60 as there are 60 minutes in an hour
drops = 30 × 3 = 90 drops per minute	if each ml has 30 drops and we need 3 ml per minute, then the drops will be 30 times 3

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#18872

A patient is prescribed 600mg of a painkiller. Calculate how much must be given if the medication is available in the concentrations: a. 20 mg in 5 ml b. 75 mg in 5 ml
a. 600 ÷ 20 = 30	this means for every 20 mg, we need 5 ml of painkiller, so we find out how many lots of 2omg are in 600 mg
8 × 5 ml = 40 ml	we need 8 lots of 20 mg, which means we need 8 lots of 5 ml

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#18874

2.5 g of medicine is used to make a 300 mL solution. What is the concentration of this medicine in mg/mL?
2.5 × 1000 = 2500 mg	this means for every 3oo mL of solution, we need 2.5 g of medicine. first we need to change the g to mg by multiplying 2.5 by 1000
2500 ÷ 300 = 8.333..	we need to find out how much per 1 mL, so we need to divide by 3oo
8.3 mg/mL

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