Shannon manages a small zoo and she has been analyzing the attendance data. Shannon finds that the number of visitors increases
exponentially as the temperature increases, and this situation is represented by the function f(x) = 3x. Shannon also finds a linear equation that models the number of people who leave the park early depending on the change in temperature, and it is represented by f(x) = −x + 4. The graph of the two functions is below. Find the solution to the two functions and explain what the solution represents.
On the graph two functions are joined at (1,3) but I would like to know how to solve it with the visual graph.
On the graph two functions are joined at (1,3) but I would like to know how to solve it with the visual graph.
2 answers:
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.
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Answer:
Step-by-step explanation:
It was noted that a music streaming platform modified its format to highlight previously unreleased tracks from emerging artists. The site manager is now aiming to assess whether the daily unique listener count has changed.
The hypothesis is set
(A two-tailed test for mean difference)
The test statistic is calculated, and the p-value turns out to be 0.0743
Assuming a significance level of 5%, we observe that p-value = 0.0743>0.05Thus, we accept the null hypothesis.i.e. there is no statistically significant alteration in the average number of daily unique listeners
The p-value serves as an indicator of the extremity of the observed data. If p is lower than alpha, we thus reject H0; otherwise, we accept it.