Answer:
8
Step-by-step explanation:
According to the Alternating Series Estimation Theorem:
│aₙ₊₁│≤ ε
1 / (4 (n + 1)⁴) ≤ 0.00005
4 (n + 1)⁴ ≥ 20000
(n + 1)⁴ ≥ 5000
n + 1 ≥ 8.41
n ≥ 7.41
n must be an integer, so n ≥ 8.
0.0003 would be 1/10 of 0.00003. If you divided 0.00003 by 10 you would get 0.0003. In fraction form it is 3/10,000
Hoped this helped.
Answer: 
Step-by-step explanation:
Given the following expression shown in the picture:

You need to use a process called "Ratinalization".
By definition, using Rationalization you can rewrite the expression in its simplest form so there is not Radicals in its denominator.
Then, in order to simplify the expression, you can follow the following steps:
<em>Step 1</em>. You need to multiply the numerator and the denominator of the fraction by
, which is the conjugate of the denominator
.
<em>Step 2</em>. Then you must apply the Distributive property in the numerator.
<em>Step 3</em>. You must apply the following property in the denominator:
Therefore, applying the procedure shown above, you get:

<em>Step 4</em>. You can observe that the expression can be simplified even more. Since:

You get:

1 topping on the 8$ they will cost the same but the 10$ cost more with aditional toppings unless both pizzas have 5 toppings then the 8$ would cost 50 cents more
(4/9)/x = 12
(4/9) = 12x
Divide both sides by 12
(1/27) =x