Answer :
6 : Margaret has 30 50-cent coins and 26 10-cent coins
let 'x' represent the number of 50-cent coins, then '56-x' represents the number of 10-cent coins
17.60 = 0.5x + 0.1(56-x)
solving for 'x' we have x=30
56-30 = 26
7 : Total money = $29.40
mich money = m dollar,
amy money = (3/4)m dollars,
Total = m + 3m/4 = 29.40,
4m+3m = 4*29.4,
7m = 117.6,
m = 117.6/7 = 16.8
Hence,
Michelle's money = $16.80
Amy money = $12.60
8 : (a) The amount of milk in a carton is normally distributed with a mean of 260 millilitres (mL) and a standard deviation of 8 mL. Every milk carton is labelled with the serving size as 250 mL. (i) What is the probability that a randomly selected carton has more than the labelled serving? [3 marks) (ii) Determine the amount of milk in a carton for which only 7.08% of cartons fall below this amount. [3 marks (iii) Find an interval around the mean y = 260mL such that 95% of all milk cartons fall within this interval. (5 marks)
9 : a=3, b=5
So b+2 = a+4 = 4a-b
b=a+2
3a=b+4
b=2a-1
Hence
2a-1=a+2
10 : original dimensions of rectangle, length = 18cm and width = 10cm
Let length and width = L and W.
from statement "A rectangle has perimeter 56 cm. If 4 cm is taken from the length and added to the width, the rectangle becomes a square", you can deduce
2L + 2W = 56 ( its sides make up its perimeter )
L - 4 = W + 4
L = W + 8
sub L = W + 8 into 2L + 2W = 56
2 ( W + 8 ) + 2W = 56
2W + 16 + 2W = 56
4W = 40
W = 10
sub W = 10 into L = W + 8
L = 10 + 8 = 18
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The answer is 1e + 13 i think
RHS-
(x+y)(x²-xy+y²)
=x(x²-xy+y²)+y(x²-xy+y²)
=x³-x²y+xy²+x²y-xy²+y³
(CANCEL THE POSSIBLE TERMS)
=x³+y³
=LHS
therefore verified
For this you need to expand the brackets first:
3(2x+5)-4(2x-7) = 6x+15-8x-28
And then now you need to add and simplify:
6x+15-8x-28 —> 6x-8x= -2x
15-28= -13
So that leaves
-2x - 13
