Answer:
See below
Step-by-step explanation:
We shall prove that for all 
. This tells us that 3 divides 4^n+5 with a remainder of zero.
If we let 
, then we have 
, and evidently, 
.
Assume that 
is divisible by 
for 
. Then, by this assumption, 
.
Now, let 
. Then:
Since 
, we may conclude, by the axiom of induction, that the property holds for all 
.
Answer:
b
Step-by-step explanation:
Answer:
2000 bars, or $1200
Explanation:
Let x represent the number of candy bars that are sold. Since they are sold for $0.60 each, this gives us the expression
0.60x
to represent the profit.
The factor has $0.10 per candy bar additional expense; this gives us the expression
0.10x.
However the factory also has $1000 fixed costs; this gives us
0.10x + 1000
to represent the costs.
The break-even point is the point where these two expressions are equal; this gives us the equation
0.60x = 0.10x + 1000
Subtract 0.10x from each side:
0.60x - 0.10x = 0.10x + 1000 - 0.10x
0.50x = 1000
Divide both sides by 0.50:
0.50x/0.50 = 1000/0.50
x = 2000
The break-even point is 2000 candy bars, which would sell for
0.60(2000) = $1200
The ratio of yellow to total is 2 to 8, or 1:4 if you divide both by 2. So the answer is B.
Answer:
Ummmm I Cannot remember use your caculator
