We know that Boeing currently produces five models of airplanes for commercial sale. The airline that Lauren works for is rapidly expanding and would like to purchase three airplanes of different models to service various routes. We calculate the number of combinations will she have to analyze.

$C^5_3=\frac{5!}{3!(5-3)!}=\frac{5\cdot 4\cdot 3!}{3!\cdot 2\cdot 1}=10$

The number of combinations will she have to analyze is 10.

4 0

3 years ago

Given that f(x)=x^2-4x -3 and g(x)=x+3/4 solve for f(g(x)) when x=9

SSSSS [86.1K]

Answer:

f(g(9)) = 945/16

Step-by-step explanation:

To find f(g(x)), you have to substitute g(x) wherever there is an x in f(x).

g(x) = x + 3/4

f(x) = x² - 4x - 3

f(g(x)) = (x + 3/4)² - 4(x + 3/4) - 3

f(g(x)) = x² + 3/2x + 9/16 - 4x + 3 - 3

f(g(x)) = x² - 5/2x + 9/16 + 3 - 3

f(g(x)) = x² - 5/2x + 9/16

Now, put a 9 wherever there is an x in f(g(x)).

f(g(9)) = (9)² - 5/2(9) + 9/16

f(g(9)) = 81 - 5/2(9) + 9/16

f(g(9)) = 81 - 45/2 + 9/16

f(g(9)) = 117/2 + 9/16

f(g(9)) = 945/16

7 0

3 years ago