Answer: 90%
Step-by-step explanation: To write a fraction as a percent, first remember that a percent is a ratio of a number to 100.
So to write 9/10 as a percent, we need to find a fraction
equivalent to 9/10 that has a 100 in the denominator.
We can do this by setting up a proportion.
So we have 
.
Now, we can use cross-products to find the missing value.
So we have (9)(100) which is 900 <em>is equal</em> to (10)(n) or 10n.
So we have 900 = 10n.
Next, dividing both sides of the equation by 10, we have <em>90 = n</em>.
So, 9/10 is equal to 90/100 or 90%.
Answer:
Decimal expansion of 1/5 = 0.2
Answer:
$6.50
Step-by-step explanation:
SET UP A SYSTEM OF EQUATIONS WHERE SANDWHICHES IS REPRESENTED BY S AND DRINKS BY D:
6S+4D = 53
4S+6D=47
ADD THEM TOGETHER
10S+10D=100
SOLVE FOR D
10D = 100 - 10S
D = 10-S
SUBSTITUTE THAT VALUE INTO ONE OF THE ORIGINAL EQUATIONS
4S + 6(10-S) = 47
4S + 60 - 6S = 47
COMBINE LIKE TERMS
-2S + 60 = 47
SUBTRACT 60 FROM BOTH SIDES
-2S = -13
DIVIDE BY -2
S = 13/2
S = $6.50
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!
