Can someone please help me with this math question
1 answer:
Answer:
Step-by-step explanation:
A). From the table of relative frequencies,
Let the relative frequency of women who prefer mineral water = x
Total of relative frequencies of women preferring purified water and mineral water = 0.59
Since, Total of relative frequencies of women who prefer purified water and mineral water = Relative frequency of women preferring purified water + Relative frequency of women preferring mineral water
0.59 = 0.14 + x
x = 0.59 - 0.14
x = 0.45
B). Relative frequency of men who prefer mineral water = 0.13
Let the frequency of men who prefer mineral water = x
Since, relative frequency =
0.13 =
x = 200 × 0.13
x = 26
Therefore, number of shoppers who are men and prefer mineral water = 26
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Answer:
Step-by-step explanation:
We are given the coordinates of a quadrilateral that is G(1,-1), H(5,1), I(4,3) and J(0,1).
Now, before proving that this quadrilateral is a rectangle, we will prove that it is a parallelogram. For this, we will prove that the mid points of the diagonals of the quadrilateral are equal, thus
Join JH and GI such that they form the diagonals of the quadrilateral.Now,
JH= and
GI=
Now, mid point of JH=
=
Mid point of GI=
Since, mid point point of JH and GI are equal, thus GHIJ is a parallelogram.
Now, to prove that it is a rectangle, it is sufficient to prove that it has a right angle by using the Pythagoras theorem.
Thus, From ΔGIJ, we have
(1)
Now, JI= and GJ=
Substituting these values in (1), we get
Thus, GIJ is a right angles triangle.
Hence, GHIJ is a rectangle.
Also, The diagonals GI= and HJ=
are equal, thus, GHIJ is a rectangle.