A clothing manufacturer produces 120 garments per hour, of which 5 are damaged. How many garments without damage would the manufacture except to produce in 8 hours?

First we have to found all the clothes that the manufacturer produces in 8 hours,

As given    120 clothes = produce in 1 hour

                  X clothes  = produce in 8 hour

By cross multiplication, we get

X= 120*8

X= 960  total clothes produced in 8 hours

As also given that in each hour 5 clothes damaged ,so we can write as

 5 clothes = damaged in 1 hour

Y clothes = Damaged in 8 hour

By cross multiplication we get

Y=  40 clothes damaged in 8 hour

So the total clothes that manufacturer produce with out damage clothe will be ,

Total normal clothes = X-Y   = 960 - 40  = 920 clothes

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).