This is an example of a piecewise defined function. It means that the function has not a unique formula to represent it, but it depends on "where" you want to compute it.
So, if you choose any input
, you have two alternative:
- If
(i.e., if you've chosen any input that is not 3), the output will be the opposite of the input you've chosen (
) - If
, the ouput will be -1.
So, let's forget about
for a moment. For any input
you choose, the answer is
. The graph of this function is the bisector of the second and fourth quadrant.
Now remember that there is our special case: you have to "carve a hole" in our line, at
, and assing to this point the value -1, instead of what we would expect, i.e. -3.
So, the graph of this function is the line
, except for one point (
), where we reassign the value to be -1.
Answer:
38.46%
Step-by-step explanation:
there are a total of 6 + 7 + 10 + 3 = 26 stamps in marge's collection
out of these 26 stamps, 10 are from the United States (Marge's home country) and 16 are from foreign countries. If she picks a random stamp, the probability that it is from the United States = 10/26 = 5/13 = 0.3846 = 38.46%
Answer:
A
Step-by-step explanation:
a and d look similar but I'm quite sure it's a
Answer:
Part A: Kimberly
Part B:
Becca = 22.5 miles, Kimberly = 25 miles
Step-by-step explanation:
Part A:
Given that Becca runs at a constant speed of 4.5 miles per hour, use the table to find the constant speed that Kimberly runs, and compare who runs faster.
Let x = time
y = distance
k = speed = y/x
Equation for each person can be written as: y = kx
Therefore:
✔️Equation for Becca if k = 4.5
y = 4.5x
✔️Find k (speed) of Kimberly using (2, 10):
Speed (k) = y/x
k = 10/2
k = 5 miles per hour
Equation for Kimberly would be:
y = 5x
Comparing their speed, Kimberly runs faster because she covers more miles per hour than Becca does.
Part B:
For Becca, substitute x = 5 into Becca's equation, y = 4.5x
Thus:
y = 4.5*5 = 22.5 miles
For Kimberly, substitute x = 5 into Kimberly's equation, y = 5x
Thus:
y = 5*5 = 25 miles
Answer:
176 of 12% vinegar
44 of 7% vinegar
Step-by-step explanation:
Percentage vinegar required = 11%
Volume = 220 mL
First brand % = 7%
Second brand % = 12%
Let p = volume of 12% vinegar material
Mixture :
0.12p + 0.07(220 - p) = 220 * 0.11
0.12p + 15.4 - 0.07p = 24.2
0.05p = 8.8
p = 8.8 / 0.05
p = 176
176 of 12% vinegar and
220 - 176 = 44
44 of 7% vinegar