Response:
2(3-n)+5.
Clarification:
Twice a number plus five equals three times the difference between that number and two. "More" indicates addition, hence twice the number is represented as multiplying N (or whatever variable) with the determination that it equals three times the reduction of that number and two.
2ab x cos(C) = 7 since
a^2 + b^2 - 2ab x cos(C) = c^2
2ab x cos(C) = a^2 + b^2 - c^2
2ab x cos(C) = 2^2 + 2^2 - 1^2
2ab x cos(C) = 7
c) Step-by-step breakdown: The collision rate is 1.2 incidents per 4 months, which can be expressed as 0.3 incidents monthly. Therefore, the Poisson distribution for the variable X representing monthly collisions is defined as P(X = x) =... for x ∈ N ∪ {0} = 0 otherwise. (1) Where X = 0 denotes no collisions during a 4-month timeframe, substituting gives P(X = 0) =... (2). For a 4-month period, P(No collision in 4 month period) =... (3). Two collisions in a 2-month span translate to 1 per month, thus P(X =1) =... (4). Over 2 months, P(2 collisions in a 2 month period) =... (5). One collision over a 6-month period equates to P(1 collision in 6 months period) =... (6). Consequently, P(1 collision in 6 month period) results in... (7). For no collisions in a 6-month period, P(No collision in 6 months period) =... (8). Finally, the probability of 1 or fewer collisions over six months is P(1 or fewer collision in 6 months period) = (8) + (7) = 0.0785 + 0.1653.
Clarification:
To accomplish the next steps, we simply need to determine the factors of each quadratic expression:
Factors of 
:
To identify factors, we must find two numbers whose product equals 4, with a difference of 3 (the difference is crucial since both resulting factors carry opposing signs). Those numbers are 4 and 1.
So, 
The initial factor
is negative reflecting the sign of the quadratic expression's second term which is negative. The subsequent factor
is positive due to the product from the second term sign (-) and the third term sign (+).
Next, we repeat this process with 
:
Finally, we substitute each factor pair with its corresponding quadratic expression as illustrated:
We can see that the Least Common Denominator is , which incidentally turns out to be the sole common factor.
