9514 1404 393
Answer:
f(4) -g(4) = 2
Step-by-step explanation:
Fill in the given values for x and do the arithmetic.
f(4) = 9·4 -2 = 34
g(4) = 2·4^2 = 32
Then ...
f(4) -g(4) = 34 -32
f(4) -g(4) = 2
Town A starts with 2in and has a rate of accumulation of 6in every 1 hour
Town B starts with 9in and has a rate of accumulation of 3in every 1 hour
If X is number of hours then:
2+ 6X= 9+3X
6x-3x=9-2
3x=7
X=7/3 is about 2 hours
Answer:
The expected volume of the box is 364 cubic inches.
Step-by-step explanation:
Since the die is fair, then P(X=k) = 1/6 for any k in {1,2,3,4,5,6}. Let Y represent the volume of the box in cubic inches. For how the box is formed, Y = X²*24. Thus, the value of Y depends directly on the value of X, and we have
- (When X = 1) Y = 1²*24 = 24, with probability 1/6 (the same than P(X=1)
- (When X = 2) Y = 2²*24 = 96, with probability 1/6 (the same than P(X=2)
- (When X = 3) Y = 3²*24 = 216, with probability 1/6 (the same than P(X=3)
- (When X = 4) Y = 4²*24 = 384, with probability 1/6 (the same than P(X=4)
- (When X = 5) Y = 5²*24 = 600, with probability 1/6 (the same than P(X=5)
- (When X = 6) Y = 6²*24 = 864, with probability 1/6 (the same than P(X=6)
As a consequence, the expected volume of the box in cubic inches is
E(Y) = 1/6 * 24 + 1/6*96 + 1/6*216+ 1/6*384+ 1/6*600+1/6*864 = 364
