Answer:
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
Answer:
$1,152 Mort will make if he sells 36 necklaces at the local art fair.
Step-by-step explanation:
Unit rates are expressed as the rates as a quantity 1 such that 4 miles per hour or 3 meter per seconds.
As per the given statement: Mort makes beaded necklaces that he sells for $32 each.
⇒ Unit rate per necklace = $32
It is also given that if he sells 36 necklaces at the local art fair.
by definition of unit rate;
Substitute the given values we have;
Therefore, $1,152 Mort will make if he sells 36 necklaces at the local art fair.