Alvin and Simon shared £540 in the ratio 4:5. Alvin gave half of his share to Theo. Simon gave a tenth of his share to Theo. What fraction of the £540 did Theo receive.

Step-by-step explanation:

sum the parts of the ratio, 4 + 5 = 9 parts

Divide the amount by 9 to find the value of one part of the ratio

£540 ÷ 9 = £60 ← value of 1 part of the ratio , thus

4 parts = 4 × £60 = £240 ← Alvin's share

5 parts = 5 × £60 = £300 ← Simon's share

× £240 = £120

× £300 = £30

Theo receives £120 + £30 = £150 , which as a fraction is

( divide numerator/ denominator by 30 )

= ← in simplest form

answer: bearing in mind that a rectangle has a perimeter of length + length + width + width.

step-by-step explanation:

p = perimeter

l = length

x=width

p = 2l + 2x

p = 2(l+x)     < ==== perimeter of the base of the box.

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm