1) This is a combination, so use ⁴⁰C₂.
⁴⁰C₂ = 780
There are 780 handshakes in total.
2) I got my solution by using the combinations formula. Or another way you could do this is to add up... 39 + 38 + 37 + 36 + 35 + 34 + 33 + 32 + 31... +1. You will end up with 780 (I did this to double check my work).
3) The quickest way to figure this out if Drake invited 1,000 people is to use the natural numbers formula = n(n+ 1)/2.
Plug the numbers in: 999(1000)/2 = 499,500
If Drake invited 1,000 people, there would be 499,500 handshakes.
Answer:
The answer is B. hope this helps
I attached a photo of the work.
If you have any further questions feel free to ask.
Hope this helps
Option B: 1.6 s.
Although the equation is not included, you can obtain it by physical considerations
H(t) = -16.t^2 + 52t + 16
The maximum point is at the vertex and the vertex is in the middle of the roots.
The roots are when H(t) = 0,
So you have to solve 0 =-16t^2 + 52t + 16
Use the quadratic formula and you will find t = 3.53 and t =-0.28
Then the vertex is at the middle point = (3.53 -.028)/2 =1.63 s and the answer is option B: 1.6 s.
