The correct answer is:
She can ascertain that while there exists an association between the variables, a correlation does not exist, and causation cannot be established.
Explanation:
Due to the arch shape of her graph, it indicates that as one variable varies, the other also changes. This indicates an association exists between these variables.
Nonetheless, given that the graph does not follow a linear pattern, no correlation can be claimed. As there is no correlation, causation cannot be determined.
The distance from the bottom of the wheel to a point on the ground can be expressed using the sine function h(t) = a*sin(kt) + b, where b represents the height of the wheel at 4m. The radius a is calculated as 50/2 = 25m. Since it takes 6 minutes for 3 complete rotations, the period can be derived from 2π/k, giving us k = π. Thus, h(t) = 25*sin(π*t) + 4.
The paraboloid intersects the x-y plane when x²+y²=9, defining a circle with a radius of 3, centered at the origin.
<span>Utilizing cylindrical coordinates (r,θ,z), the paraboloid transforms into z = 9−r² and f = 5r²z. </span>
<span>If F represents the average of f over the area R then F ∫ (R)dV = ∫ (R)fdV </span>
<span>∫ (R)dV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] rdrdθdz </span>
<span>= ∫∫ [θ=0,2π, r=0,3] r(9−r²)drdθ = ∫ [θ=0,2π] { (9/2)3² − (1/4)3⁴} dθ = 81π/2 </span>
<span>∫ (R)fdV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] 5r²z.rdrdθdz </span>
<span>= 5∫∫ [θ=0,2π, r=0,3] ½r³{ (9−r²)² − 0 } drdθ </span>
<span>= (5/2)∫∫ [θ=0,2π, r=0,3] { 81r³ − 18r⁵ + r⁷} drdθ </span>
<span>= (5/2)∫ [θ=0,2π] { (81/4)3⁴− (3)3⁶+ (1/8)3⁸} dθ = 10935π/8 </span>
<span>Thus, F = 10935π/8 ÷ 81π/2 = 135/4</span>
To create algebraic expressions that represent quantities, translate the verbal description into mathematical terms following the sentence’s structure. For example, “one minus a number equals zero” becomes
1. 1 – n = 0.
Another example: John bought 25 apples and Julia bought 15. If Niccole bought twice as many as Julia, how many apples did Niccole buy?<span><span>
Steps:</span>First, restate the situation clearly so you can identify the relationship and how to form the expression.</span>
<span><span>
Solution:</span>Julia = 15 apples
Niccole = 2Julia
</span>Thus, 2Julia = 2(15) = 30 apples.
P(f | weekend) = p(f & weekend)/p(weekend)
.. = 10%/25%
.. = 0.4 = 2/5
