Option A:
The equation for the trend line is y = 82x + 998.
Solution:
The points on the line are (2, 1162) and (11, 1900).
Here, 
Slope of the line:
m = 82
Point-slope formula:
Add 1162 on both sides of the equation.
The equation for the trend line is y = 82x + 998.
Hence Option A is the correct answer.
Answer:
the first selection is so shaded
Step-by-step explanation:
Each strip is divided into 10 parts. 1/5 will be represented by 2 of those parts, so 2/5 will be represented by 4 of the 10 parts. The 3/10 used on the other gift will be represented by 3 additional parts. So, a total of 7 of the 10 parts of the strip need to be colored to represent the ribbon used.
Answer:
r = sqrt(16/pi)
Step-by-step explanation:
Cylinder formula = r^2 x pi x height
176 pi/11pi = 16
16 = r^2 x pi
16/ pi = r^2
r = sqrt(16/pi)
Answer: x = -1, -3
Step-by-step explanation:
By definition of tangent,
tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)
Recall the double angle identities:
sin(2<em>θ</em>) = 2 sin(<em>θ</em>) cos(<em>θ</em>)
cos(2<em>θ</em>) = cos²(<em>θ</em>) - sin²(<em>θ</em>) = 2 cos²(<em>θ</em>) - 1
where the latter equality follows from the Pythagorean identity, cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1. From this identity we can solve for the unknown value of sin(<em>θ</em>):
sin(<em>θ</em>) = ± √(1 - cos²(<em>θ</em>))
and the sign of sin(<em>θ</em>) is determined by the quadrant in which the angle terminates.
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We're given that <em>θ</em> belongs to the third quadrant, for which both sin(<em>θ</em>) and cos(<em>θ</em>) are negative. So if cos(<em>θ</em>) = -4/5, we get
sin(<em>θ</em>) = - √(1 - (-4/5)²) = -3/5
Then
tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)
tan(2<em>θ</em>) = (2 sin(<em>θ</em>) cos(<em>θ</em>)) / (2 cos²(<em>θ</em>) - 1)
tan(2<em>θ</em>) = (2 (-3/5) (-4/5)) / (2 (-4/5)² - 1)
tan(2<em>θ</em>) = 24/7
