Answer:
31 games
Step-by-step explanation:
round 1 has 32 teams ÷2=16games
round 2 has 16 teams ÷2=8games
round 3 has 8 teams ÷2=4games
round 4 has 4 teams ÷ 2=2games
round 5 has 2 teams ÷2=1games
16+8+4+2+1
Answer: Third option
Step-by-step explanation:
For this exercise it is important to remember the following:
1. By definition, the Associative property of addition states that it does not matter how you grouped the numbers, you will always obtained the same sum.
2. The rule for the Associative property of addition is the following (given three numbers "a", "b" and "c"):
Knowing the information shown before, you can identify in the picture attached that the option that illustrates the Associative property of addition is the third one. This is:
As you can notice that you will always get the same result:
Answer:
50
Step-by-step explanation:
im not that sure sorry
For (2), start with the base case. When n = 2, we have
(n + 1)! = (2 + 1)! = 3! = 6
2ⁿ = 2² = 4
6 > 4, so the case of n = 2 is true.
Now assume the inequality holds for n = k, so that
(k + 1)! > 2ᵏ
Under this hypothesis, we want to show the inequality holds for n = k + 1. By definition of factorial, we have
((k + 1) + 1)! = (k + 2)! = (k + 2) (k + 1)!
Then by our hypothesis,
(k + 2) (k + 1)! > (k + 2) 2ᵏ = k•2ᵏ + 2ᵏ⁺¹
and k•2ᵏ ≥ 2•2² = 8, so
k•2ᵏ + 2ᵏ⁺¹ ≥ 8 + 2ᵏ⁺¹ > 2ᵏ⁺¹
which proves the claim.
Unfortunately, I can't help you with (3). Sorry!
