Which graph represents a function with direct variation?
1 answer:
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Let m∠CLN = x. Then m∠ALM = 3x, and m∠A = 90°-x, m∠C = 90°-3x.
The sum of angles of ∆ABC is 180°, so we have
... 180° = 40° + m∠A + m∠C
Using the above expressions for m∠A and m∠C, we can write ...
... 180° = 40° + (90° -x) + (90° -3x)
... 4x = 40° . . . . . . . . . add 4x-180°
... x = 10°
From which we conclude ...
... m∠C = 90°-3x = 90° - 3·10° = 60°
The ratio of CN to CL is
... CN/CL = cos(∠C) = cos(60°)
... CN/CL = 1/2
so ...
... CN = (1/2)CL
Answer: 0.813
Step-by-step explanation:
Let A be the event describes the number of residents believed that the amount of violent television programming had increased over the past 10 years.
& B be the event describes the number of residents believed that the amount of violent television programming had decreased over the past 10 years.
Given : n(A)=721 ; n(B)=454 ; n(A∩B)=362
We know that ,
i.e.
Also, the total number of U.S. residents surveyed n(S)= 1,000
Then, the proportion of the 1,000 U.S. residents believed that either the amount of violent programming had increased or the overall quality of programming had decreased over the past 10 years will be :-
Hence, the required answer = 0.813
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."
