Answer:
Step-by-step explanation:
Note*
To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations. To evaluate, substitute 3 for x in the expression, and then simplify.
the answer i got was 5% , because all you have to do is perform a proportion . you put $400 which is what avery made over the total money of the sale which is $8,000 . then you put n the variable over 100 so you can find the percentage of her commission . now you have to cross multiply , so you would multiply $400 and 100 . & $8,000 with the variable n . in the end you'll get 400*100= 40,000 and 8,000n= 8,000n . now you would divide 40,000 by 8,000 to get rid of the 8,000 off the variable . so 40,000/8,000= 5 . so the percentage of her sale is actually hers is only 5% .
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!
Step-by-step explanation:
200...............................
