Finding the coefficient a of the term in the expansion of the binomial.

3,247,695

Step-by-step explanation:

We want the coefficient of  the term with  x^8

So  Use Newton's Binomial Expansion formula

Formula is  (x + y) ^n  =   Sum for i=0 to n     (n choose i)   x^(n-i)*y^i

here   (x^2  + 3) ^ 12

( 12 choose i) *  (x^2)^(12-i) * (3)^i

i needs to equal 8  for us to get  x^8

(12 choose 8) * (x^2)^(12-8) * (3^8)

= (12 choose 8) * x^8  * (3^8)

so  a = (12 choose 8) *

a =  (12! /(8! * 4!) ) *

a = ( 12*11*10*9/  4*3*2*1)  *

a =  (11*5*9) *

a = 11*5*9 * 6561

a = 3,247,695

Vitamin C levels

Step-by-step explanation:

In order to identify which is the dependent variable in a experiment, it is useful think which is the variable being tested in the experiment. Whereas for the independent variable you need to check which is the variable that is usually controlled to test its effects on the dependent variable.

In this case you are measuring vitamina C levels (dependent variable) which you expect that depends on the fruit which you are testing (variable independent).

Note that the environmental conditions are factors which can affect also your dependent variable but you are not controlling that. They could be independent variables if you manipulate them.