Roger has 4 gallóns of orange juice. He puts the same amount of juice each of 5 pitchers. How many gallons of orange juice are i
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Answer:
<h2>It must be shown that both j(k(x)) and k(j(x)) equal x</h2>Step-by-step explanation:
Given the function j(x) = 11.6 and k(x) =
, to show that both equality functions are true, all we need to show is that both j(k(x)) and k(j(x)) equal x,
For j(k(x));
j(k(x)) = j[(ln x/11.6)]
j[(ln (x/11.6)] = 11.6e^{ln (x/11.6)}
j[(ln x/11.6)] = 11.6(x/11.6) (exponential function will cancel out the natural logarithm)
j[(ln x/11.6)] = 11.6 * x/11.6
j[(ln x/11.6)] = x
Hence j[k(x)] = x
Similarly for k[j(x)];
k[j(x)] = k[11.6e^x]
k[11.6e^x] = ln (11.6e^x/11.6)
k[11.6e^x] = ln(e^x)
exponential function will cancel out the natural logarithm leaving x
k[11.6e^x] = x
Hence k[j(x)] = x
From the calculations above, it can be seen that j[k(x)] = k[j(x)] = x, this shows that the functions j(x) = 11.6 and k(x) =
are inverse functions.
Options:
A. Both the Highlands and the Lowlands data points are evenly distributed around the center.
B. Both the Highlands and the Lowlands data points are clustered toward the left of the plot.
C. The Highlands data points are evenly distributed around the center, while the Lowlands data points are clustered toward the left of the plot.
D. The Highlands data points are clustered toward the left of the plot, while the Lowlands data points are evenly distributed.
Answer:
B. Both the Highlands and the Lowlands data points are clustered toward the left of the plot.
Step-by-step Explanation:
From the dot plots displaying rainfall totals for highland and lowland areas as shown in the diagram attached below, we can clearly observe that most of the dots on the plot tend to be more concentrated towards the left of the plot, compared to the concentration of dots toward the right of the plot.
Invariably, we can infer that data points for lowlands and Highlands are clustered toward the left of the plot.
Therefore, the statement that is true, comparing the shapes of the dot plot is B. "Both the Highlands and the Lowlands data points are clustered toward the left of the plot."
