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2 answers:
Answer:
R'(-1,3) , S'(0,2) , T'(-1,1), U'(-3,1)
Step-by-step explanation:
To find the vertices of a point after a dilation simply multiply the x and y values of each given coordinate by the scale factor.
So to find the vertices of Trapezoid RSTU after a dilation centered at the origin with a scale factor of 1/5 we would multiply the x and y values of the given coordinates of Trapezoid RSTU by 1/5.
Given Coordinates: R(-5, 15), S(0, 10), T(-5, 5) and U(-15, 5)
Scale Factor: 1/5
R(-5, 15) -----> ( -5 * 1/5 = -1 , 15 * 1/5 = 3 ) -----> (-1,3)
S(0,10) -----> ( 0 * 1/5 = 0 , 10 * 1/5 = 2 ) -----> (0,2)
T(-5,5) -----> ( -5 * 1/5 = -1 , 5 * 1/5 = 1 ) -----> (-1,1)
U(-15,5) -----> (-15 * 1/5 = -3 , 5 * 1/5 = 1 ) -----> (-3,1)
So the coordinates of Trapezoid RSTU after a dilation with a scale factor of 1/5 are R'(-1,3) , S'(0,2) , T'(-1,1), U'(-3,1)
Refer to the attached image for more validation
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Answer:
The probability that a randomly selected student likes jazz or country but not rock is 0.422.
Step-by-step explanation:
The information provided is:
Total number of students selected, <em>N</em> = 500.
The number of students who like rock, <em>n</em> (<em>R</em>) = 198.
The number of students who like country, <em>n</em> (<em>C</em>) = 152.
The number of students who like jazz, <em>n</em> (<em>J</em>) = 113.
The number of students who like rock and country, <em>n</em> (<em>R </em>∩ <em>C</em>) = 21.
The number of students who like rock and Jazz, <em>n</em> (<em>R </em>∩ <em>J</em>) = 22.
The number of students who like country and jazz, <em>n</em> (<em>C </em>∩ <em>J</em>) = 16.
The number of students who like all three, <em>n</em> (<em>R </em>∩ <em>C </em>∩ <em>J</em>) = 5.
Consider the Venn diagram below.
Compute the probability that a randomly selected student likes jazz or country but not rock as follows:
P (J ∪ C ∪ not R) = P (Only J) + P (Only C) + P (Only J ∩ C)
Thus, the probability that a randomly selected student likes jazz or country but not rock is 0.422.
