Step-by-step explanation:
∑⁴ₙ₌₁ -144 (½)ⁿ⁻¹
This represents a finite geometric series where n equals 4, a₁ is -144, and r is ½.
S = a₁ (1 − rⁿ) / (1 − r)
S = -144 (1 − (½)⁴) / (1 − ½)
S = -270
If you wish to calculate the infinite sum (n = ∞):
S = a₁ / (1 − r)
S = -144 / (1 − ½)
S = -288
Multiplying 3 × 5 × 2 × 4 × 3 × 2 × 1 × 1 results in 720
The function
represents a parabola positioned at the vertex (5, 3).
Attached here is the graph depicting this function.
The least number of times that two planes can cross is zero, since parallel planes do not intersect. A good example would be a floor and a ceiling, which run parallel, hence they do not meet. Conversely, if two planes occupy the same space, they can intersect at infinitely many points, as could happen with a line within that plane.
<span>P(black socks): 24/42 or 12/21
P(black socks without replacement): 23/41. Consequently, the chance of randomly selecting 2 black socks, without replacement, from the basket is 12/21×23/41=276/861, equivalent to 32%. Hope this helps!</span>
