1+4=5, 2+5=12, 3+6=21,8+11=

Define the unit vectors along the x and y axes as correspondingly.

Consequently, the vector from P to Q is

In terms of components, vector PQ is represented as (-8,5).

The magnitude of vector PQ can be calculated as
√[(-8)² + 5²] = √(89) = 9.434

Answer:
Thus, vector PQ is (-8, 5), and its magnitude equals √89 (or 9.434).

Answer:

E 240

Step-by-step explanation:

Mean of the geometric distribution = (1- p) / p

16 = (1 - p) / p

16p = 1 - p;  17p = 1; thus, p = 1/17 = 0.058  

Standard Deviation = (1 - p) / p^2

= (1 - 0.058) / (0.058)^2

0.942 / 0.003364

= 280, which is closest to 240

<span>Given that each individual can receive a single prize, there are 50*49*48= 117600 different ways to allocate the prizes. The first award can be given to any of the 50 participants, the second to one of the remaining 49, and the last to one of the leftover 48. Multiplying these options together provides the solution.</span>