Prove: If a chord of a circle has a common end point with a diameter and makes an angle of 30° with it, prove that the distance from the center to the chord is one-fourth the length of the diameter.

Step-by-step explanation:

The perpendicular distance between the chord and the center of the circle forms a right triangle with the chord and the radius.  Using trig:

sin 30° = x / (D/2)

sin 30° = 2x / D

1/2 = 2x / D

x = D/4

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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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answer: $13,622.84

step-by-step explanation: check the picture for info and stats : )