Two state parks, Elm Grove and Cathedral Rock, each recorded the number of visitors to the park each day for 15 days. The parks
made line plots from the data recorded.
What statement about the two plots’ distributions is true?
There is no overlap between the two distributions.
The degree of overlap between the two distributions is high.
The degree of overlap between the two distributions is moderate.
The degree of overlap between the two distributions is low.
Two line plots with the same scale and interval, from zero to six hundred, with tick marks every fifty units. The plots are stacked vertically for comparison. Values appear as x marks above the line. Each plot has fourteen data values. Upper plot is labeled Elm Grove. Upper plot data values are one x mark above fifty, two x marks above one hundred, three x marks above one hundred fifty, four x marks above two hundred, three x marks above two hundred fifty, one x mark above three hundred, and one x mark above three hundred fifty. Lower plot is labeled Cathedral Rock. Lower plot data values are one mark above three hundred, one makr above three hundred fifty, two marks above four hundred, three marks above four hundred fifty, four marks above five hundred, three marks above five hundred fifty, and one mark above six hundred.
What statement about the two plots’ distributions is true?
There is no overlap between the two distributions.
The degree of overlap between the two distributions is high.
The degree of overlap between the two distributions is moderate.
The degree of overlap between the two distributions is low.
Two line plots with the same scale and interval, from zero to six hundred, with tick marks every fifty units. The plots are stacked vertically for comparison. Values appear as x marks above the line. Each plot has fourteen data values. Upper plot is labeled Elm Grove. Upper plot data values are one x mark above fifty, two x marks above one hundred, three x marks above one hundred fifty, four x marks above two hundred, three x marks above two hundred fifty, one x mark above three hundred, and one x mark above three hundred fifty. Lower plot is labeled Cathedral Rock. Lower plot data values are one mark above three hundred, one makr above three hundred fifty, two marks above four hundred, three marks above four hundred fifty, four marks above five hundred, three marks above five hundred fifty, and one mark above six hundred.
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The problem statement tells you ∠MLK is 61°, so ∠LMK = 180° -68° -61° = 51°. Since a tangent is always perpendicular to a radius, triangles LJM and LJK are right triangles.
Trigonometry tells you ...
tangent = opposite / adjacent
so you can write two relations involving LJ.
tan(51°) = LJ/JM
tan(68°) = LJ/JK
The second equation can be used to write an expression for LJ that can be substituted into the first equation.
LJ = JK*tan(68°) = 3*tan(68°)
Substituting, we have
tan(51°) = 3*tan(68°)/JM
Multiplying by JM/tan(51°), we get
JM = 3*tan(68°)/tan(51°)
JM ≈ 6.01
The radius of circle M is about 6.01.
Trigonometry tells you ...
tangent = opposite / adjacent
so you can write two relations involving LJ.
tan(51°) = LJ/JM
tan(68°) = LJ/JK
The second equation can be used to write an expression for LJ that can be substituted into the first equation.
LJ = JK*tan(68°) = 3*tan(68°)
Substituting, we have
tan(51°) = 3*tan(68°)/JM
Multiplying by JM/tan(51°), we get
JM = 3*tan(68°)/tan(51°)
JM ≈ 6.01
The radius of circle M is about 6.01.