50 points. Only solve 6-10. And show work

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

someone already answered it i just wanted points thanks