Answer:
D) 1541
Step-by-step explanation:
I like to answer it w without deriving the formula of f(g(x)). So, we go this way, you firstly have to find g(7) which will be equal to 3 * 7 - 5 = 16.
And then you find f(16) = 6*16*16+5 = 1541. That's all.
Answer:
Percentage of balls which are red = 80%.
Step-by-step explanation:
Let the probability of drawing a red ball be x then the probability of drawing a white ball is 1-x.
There are 5C3 = 10 ways of getting 3 reds in 5 draws so the probability of this is 10* x^3 * (1 - x)^2.
The probability of getting 1 red in 5 draws = 5C1 * x (1-x)^4.
The first probability is 32 times the last.
So we have the equation:
10x^3(1 - x)^2 / 5x(1 - x)^4 = 32
2x^2 / (1 - x)^2 = 32
2x^2 = 32(1 -x)^2
2x^2 = 32( 1 - 2x + x^2)
2x^2 = 32 - 64x + 32x^2
30x^2 - 64x + 32 = 0
15x^2 - 32x + 16 = 0
(5x - 4)(3x - 4) = 0
x = 0.8, 1.333...
The probability must be < 1 so x = 0.8 = 80%.
Answer:
Step-by-step explanation:
The average rate of change over a given interval is the slope of the secant line through the endpoints of the interval.
![m = \dfrac{f(b)-f(a)}{b-a} = \dfrac{f(103)-f(100)}{103-100}\\\\ = \dfrac{(103)^2-2500-[(100)^2-2500]}{103-100} = \dfrac{609}{3}=203](https://tex.z-dn.net/?f=m%20%3D%20%5Cdfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D%20%3D%20%20%5Cdfrac%7Bf%28103%29-f%28100%29%7D%7B103-100%7D%5C%5C%5C%5C%20%3D%20%5Cdfrac%7B%28103%29%5E2-2500-%5B%28100%29%5E2-2500%5D%7D%7B103-100%7D%20%3D%20%20%5Cdfrac%7B609%7D%7B3%7D%3D203)
$203/unit.The instantaneous rate of change at a certain point is the slope of the tangent line.
We differentiate C to get 2x. We substitute 100 for x to get that the instantaneous rate of change at 100 is
$200/unit.
6. Brand A is .15 per ounce / Brand B is .12 per ounce / Brand C is .14 per ounce
7. Brand B
8. Regular is .21 per ounce / Family Size is .19 per ounce
9. Family Size
