Answer:
f^-1(x)=x-3/2
Step-by-step explanation:
we have f(x)=2x+3
let
y=f(x)
y=2x+3
Exchanges the variables x for y and y for x
x=2y+3
isolate the variable y
2y=x-3
y=x-3/2
let
f^-1(x)=y
f^-1(x)=x-3/2
The answers are x=2 and y=5. 2(2)=4. 4+5=8. y=x-7 then is converted into 5=2-7.
Without trying to list all of them, I just now thought of a way to figure out the number of different possibilities:
The total can be made from:
-- zero, 1, 2, or 3 quarters . . . 4 choices
-- zero, 1, or 2 dimes . . . . . . . 3 choices
-- zero or 1 nickel . . . . . . . . . . 2 choices
and
-- zero, 1, or 2 pennies . . . . . . 3 choices
So there are (4 x 3 x 2 x 3) = 72 different possible combinations of coins
Almost all of the possible combinations appear to be unique. I do
see one possible duplication: 1qtr is the same thing as (2dim + 1nkl).
That reduces the number somewhat, but I don't really know how to handle it.
So the number of different amounts of change is a few less than 72 .
I hope this answer is worth 5 points.
Answer:
0.505 g is <em>more than</em> the advertised amount by 0.005 g.
Step-by-step explanation:
0.5 = 0.500, so 0.505 is <em>more than</em> the advertised amount.
"Too little" or "too much" is a judgment based on some criteria not specified by the problem statement. Usually a supplier will want to ensure the customer receives full measure, so will adjust the capsule-making machine to provide at least the advertised amount. Whether it is "too little" or "too much" depends on your point of view and the dangers or costs of deviating from the advertised amount.
0.505 - 0.500 = 0.005 . . . . the difference between the actual and advertised amounts, in grams.
