Ann and Bill play rock-paper-scissors. Each has a strategy of choosing uniformly at random out of the three possibilities every
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To plot the two functions, you need to assign values for x. By selecting various x values, corresponding y values are calculated. You then plot the points as shown. The blue line illustrates the function f(x) = 3x, while the orange line indicates f(x) = -x + 4.
These two lines intersect at the coordinates (1,3). To solve for this analytically, we establish the system of equations:
y = 3x
y = -x + 4
By setting these two equations for y equal to each other:
3x = -x + 4
4x = 4
x = 1
Next, substituting x into one of the original equations gives us: y = 3x = 3(1) = 3. Therefore, the solution is (1,3), meaning at a temperature of 3 units, the number of visitors entering matches those exiting the zoo, indicating a balance of one person entering for each one leaving.
These two lines intersect at the coordinates (1,3). To solve for this analytically, we establish the system of equations:
y = 3x
y = -x + 4
By setting these two equations for y equal to each other:
3x = -x + 4
4x = 4
x = 1
Next, substituting x into one of the original equations gives us: y = 3x = 3(1) = 3. Therefore, the solution is (1,3), meaning at a temperature of 3 units, the number of visitors entering matches those exiting the zoo, indicating a balance of one person entering for each one leaving.