The margin of error decreases with an increased sample size and increases with an increase in confidence level.
A. X is the number of years after 2000
2006-200 = 6 years.
Replace x with 6 and solve:
105(6)^2 + 680(6) + 4296 = 12,156
Answer for part a: 12,156
Answer for part B.
There was just over 12,000 in 6 years , to get to 21,500 would be a little over 9,000 more 9/12 = 0.75
6 years x .75 = 4.5 years
6 + 4.5 = 10.5 years round to 10 years for estimating purposes
Answer for part b: about 10 years
Answer:
As ΔABC is an <u>isosceles triangle</u>:
⇒ BA = BC
(the dashes on the line segments indicate they are of equal measure)
⇒ ∠BAC = ∠BCA = 55°
⇒ ∠BCA = ∠BAD = 55°
Angles on a <u>straight line</u> sum to 180°
⇒ ∠ADE + ∠EDC = 180°
⇒ 98° + ∠EDC = 180°
⇒ ∠EDC = 82°
As BE intersects AC, the <u>vertically opposite angles</u> are <em>equal</em>:
⇒ ∠BDC = ∠ADE = 98°
⇒ ∠ADB = ∠EDC = 82°
Interior angles in a triangle sum to 180°
⇒ ∠BAD + ∠ADB + ∠ABD = 180°
⇒ 55° + 82° + ∠ABD= 180°
⇒ ∠ABD = 180° - 55° - 82°
⇒ ∠ABD = 43°
The answer to your question is the last one.
