For A it is 6240 / 20% for B it is 6240 x 15%
We start with 3: it stays unchanged
3.
then the first decimal place also remains unchanged:
3.6
now the second decimal place:
3.61
does it remain unchanged? No! the number AFTER is is 5 or bigger (it's 7), so we need to round it up. the answer is this:
3.62
Step-by-step explanation:
The Taylor series expansion is:
Tₙ(x) = ∑ f⁽ⁿ⁾(a) (x − a)ⁿ / n!
f(x) = 1/x, a = 4, and n = 3.
First, find the derivatives.
f⁽⁰⁾(4) = 1/4
f⁽¹⁾(4) = -1/(4)² = -1/16
f⁽²⁾(4) = 2/(4)³ = 1/32
f⁽³⁾(4) = -6/(4)⁴ = -3/128
Therefore:
T₃(x) = 1/4 (x − 4)⁰ / 0! − 1/16 (x − 4)¹ / 1! + 1/32 (x − 4)² / 2! − 3/128 (x − 4)³ / 3!
T₃(x) = 1/4 − 1/16 (x − 4) + 1/64 (x − 4)² − 1/256 (x − 4)³
f(x) = 1/x has a vertical asymptote at x=0 and a horizontal asymptote at y=0. So we can eliminate the top left option. That leaves the other three options, where f(x) is the blue line.
Now we have to determine which green line is T₃(x). The simplest way is to notice that f(x) and T₃(x) intersect at x=4 (which makes sense, since T₃(x) is the Taylor series centered at x=4).
The bottom right graph is the only correct option.
The answer will be D) 75
To find this it’s easiest to find how many animals there are per percent. So to find this you simply have to divide 30 (the number of cats) by 40 (the percent that makes up) to find the number of animals per percent.
30/40
.75
Then you multiply this by 100 to find how many animals there are total.
.75(100)
75
