Answer: The graph is shown below
The solution to the system is (x,y) = (2,3)
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Explanation:
To graph 
, we need two points. Generating any (x,y) point involves picking a random x value to find its paired y value. For instance, if you plugged in x = 0, you should get to y = -2 which is the y intercept. Then trying something like x = 2 will lead to y = 3. This line goes through (0,-2) and (2,3). This line is shown in red below.
The blue line is horizontal and goes through 3 on the y axis. Every point on this horizontal line has the same y coordinate of 3. The x value doesn't matter, so it's not part of the equation y = 3.
The intersection of the red and blue line is the solution to the system. That intersection occurs at (x,y) = (2,3). This means x = 2 and y = 3 pair up together to make both original equations true.
Since this system has at least one solution, we consider it a consistent system.
9514 1404 393
Answer:
x = 2
Step-by-step explanation:
To find g(x), we can start with the inverse of f(x).
f(y) = x . . . . . . . solve this to find f^-1(x)
3y -2 = x
3y = x +2 . . . . add 2
y = (x +2)/3 = f^-1(x) . . . . divide by 3
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Now, we can find g(x):
f^-1(f(g(x)) = g(x)
f^-1(6x -2) = ((6x -2) +2)/3 = g(x)
6x/3 = g(x) = 2x
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Now, we want g(f(x)) = 8
g(3x -2) = 8
2(3x -2) = 8
6x -4 = 8
6x = 12
x = 2 . . . . makes g(f(x)) = 8
5/9 (fraction simplified)
Answer:
A = P * a / 2
A = 81.25
Step-by-step explanation:
We have that there is a corresponding formula for a regular decagon, which depends on the apothem and the perimeter, it is the following:
A = P * a / 2
In this case, the perimeter is the sum of all the sides, that is, 10 sides, therefore:
P = 10 * 3.25
P = 32.5 meters
We replace:
A = 32.5 * 5/2
A = 81.25
Which means that for that regular decagon, the area is 81.25 square meters.
This kind of experiments are ruled by Bernoulli's formula. If you have probability p of "success", and you want k successes in n trials, the probability is
It's easier to compute the first probability by difference: instead of computing the probability of the event "at least one of the surveyed eats breakfast", let's compute the probability of its contrary: none of them eats breakfast. So, we want 0 successes in 4 trials, with probability of success 0.34. The formula yields
Since the contrary has probability 17%, our event "at least one of the surveyed eats breakfast" has probability 83%.
As for the second question, the event "at least three of the surveyed eats breakfast" is the union of the events "exactly three of the surveyed eats breakfast" and "exactly four of the surveyed eats breakfast". So, we just need to sum their probabilities:
