Horizontal stretch by a factor of 1/3
of the class consists of freshmen.
Step-by-step explanation:
Given,
Total number of students = 40
Number of freshmen = 18
Number of sophomores = 19
Number of juniors = 3
Fraction of freshmen = ![\frac{Number\ of\ freshmen}{Total\ number\ of students}](https://tex.z-dn.net/?f=%5Cfrac%7BNumber%5C%20of%5C%20freshmen%7D%7BTotal%5C%20number%5C%20of%20students%7D)
Fraction of freshmen = ![\frac{18}{40}](https://tex.z-dn.net/?f=%5Cfrac%7B18%7D%7B40%7D)
Fraction of freshmen = ![\frac{9}{20}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B20%7D)
of the class consists of freshmen.
Keywords: fraction, division
Learn more about fractions at:
#LearnwithBrainly
If the diameter is at (9,4) and (-3,-2), then the center of the circle is the midpoint of that segment.
and since we know that the radius of a circle is half of the diameter, whatever long that diameter segment is, the radius is half that.
![\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 9 &,& 4~) % (c,d) &&(~ -3 &,& -2~) \end{array}\qquad % coordinates of midpoint \left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{-3+9}{2}~~,~~\cfrac{-2+4}{2} \right)\implies \stackrel{center}{(3~,~1)}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bmiddle%20point%20of%202%20points%20%7D%0A%5C%5C%5C%5C%0A%5Cbegin%7Barray%7D%7Bccccccccc%7D%0A%26%26x_1%26%26y_1%26%26x_2%26%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0A%26%26%28~%209%20%26%2C%26%204~%29%20%0A%25%20%20%28c%2Cd%29%0A%26%26%28~%20-3%20%26%2C%26%20-2~%29%0A%5Cend%7Barray%7D%5Cqquad%0A%25%20%20%20coordinates%20of%20midpoint%20%0A%5Cleft%28%5Ccfrac%7B%20x_2%20%2B%20%20x_1%7D%7B2%7D%5Cquad%20%2C%5Cquad%20%5Ccfrac%7B%20y_2%20%2B%20%20y_1%7D%7B2%7D%20%5Cright%29%0A%5C%5C%5C%5C%5C%5C%0A%5Cleft%28%20%5Ccfrac%7B-3%2B9%7D%7B2%7D~~%2C~~%5Ccfrac%7B-2%2B4%7D%7B2%7D%20%5Cright%29%5Cimplies%20%5Cstackrel%7Bcenter%7D%7B%283~%2C~1%29%7D)
![\bf -------------------------------\\\\ ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 9 &,& 4~) % (c,d) &&(~ -3 &,& -2~) \end{array} \\\\\\ d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(-3-9)^2+(-2-4)^2}\implies d=\sqrt{(-12)^2+(-6)^2} \\\\\\ d=\sqrt{180}\qquad \qquad \qquad radius=\cfrac{\sqrt{180}}{2}](https://tex.z-dn.net/?f=%5Cbf%20-------------------------------%5C%5C%5C%5C%0A~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%0A%5C%5C%5C%5C%0A%5Cbegin%7Barray%7D%7Bccccccccc%7D%0A%26%26x_1%26%26y_1%26%26x_2%26%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0A%26%26%28~%209%20%26%2C%26%204~%29%20%0A%25%20%20%28c%2Cd%29%0A%26%26%28~%20-3%20%26%2C%26%20-2~%29%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5C%5C%0Ad%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ad%3D%5Csqrt%7B%28-3-9%29%5E2%2B%28-2-4%29%5E2%7D%5Cimplies%20d%3D%5Csqrt%7B%28-12%29%5E2%2B%28-6%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ad%3D%5Csqrt%7B180%7D%5Cqquad%20%5Cqquad%20%5Cqquad%20radius%3D%5Ccfrac%7B%5Csqrt%7B180%7D%7D%7B2%7D)
Answer:
top left corner
Step-by-step explanation: