piece of wire 8 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. (a) How much wire should be used for the square in order to maximize the total area

piece of wire 8 m long

one piece is bent into square:

the square has four equal sides , so at least 4 m has to be cut from the wire to form a square with side=1 m.

the perimeter of the square =2L+2W=2(1)+2(1)=4 m

that is the max. amount can be cut from the wire, since the other part is bent into a circle.

( note if you cut more, the square will take the whole wire)

Perimeter=2L+2W=2(2)=2(2)=8 m and the area=2*2=4 m²)

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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step-by-step explanation: