A group of randomly selected members of Mothers' Club were asked how many kids they have. The table below shows the results A gr
2 answers:
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Answer: The correct options are
(A) Rotation 90° anticlockwise.
(D) (x, y) → (–y, x).
Step-by-step explanation: Given that ΔXYZ is rotated to create the image triangle ΔX'Y'Z'.
Triangle XYZ and its image triangle X'Y'Z' are shown in the attached figure.
The co-ordinates of the vertices of ΔXYZ are X(0, 0), Y(0, -2) and Z(-2, -2).
And the co-ordinates of the vertices ΔX'Y'Z' are X'(0, 0), Y'(2, 0) and Z'(2, -2).
<u>Option (A) Rotation 90°:</u>
We see from the figure that if we rotate ΔXYZ is rotated 90° anticlockwise, then it will coincide with ΔX'Y'Z'.
So, rotation of 90° anticlockwise is a correct option.
<u>Option (B) Rotation 180°:</u>
If we rotate ΔXYZ is rotated clockwise or anticlockwise 180°, then it will NOT coincide with ΔX'Y'Z'.
So, rotation of 180° is NOT a correct option.
<u>Option (C) Rotation 270°:</u>
If we rotate ΔXYZ is rotated clockwise 270°, then also it will not coincide with ΔX'Y'Z'.
So, rotation of 270° clockwise is also a correct option.
<u>Option (D) (x, y) → (–y, x):</u>
We see that the co-ordinates of both the triangle follow the transformation
X(0, 0) ⇒ X'(0, 0)
Y(0, -2) ⇒ Y'(2, 0)
Z(-2, -2) ⇒ Z'(2, -2).
So, the transformation is (x, y) ⇒ (-y, x).
Therefore, the transformation (x, y) → (–y, x) is a correct option.
<u>Option (E) (x, y) → (y, -x):</u>
We see that the co-ordinates of both the triangle does NOT follow this transformation
For example, suppose this transformation is correct. Then, we have
Y(0, -2) ⇒ (-2, 0), which are not the co-ordinates of Y'.
Therefore, the transformation (x, y) → (–y, x) is NOT a correct option.
Thus, the correct options are:
(A) Rotation 90° anticlockwise.
(D) (x, y) → (–y, x).
Answer:
<u></u>
- <u>a) 3/7</u>
- <u>b) 3/5</u>
Explanation:
The figure attached shows the <em>Venn diagram </em>for the given sets.
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<em><u>a) What is the probability that the number chosen is a multiple of 3 given that it is a factor of 24?</u></em>
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From the whole numbers 1 to 15, the multiples of 3 that are factors of 24 are in the intersection of the two sets: 3, 6, and 12.
There are a total of 7 multiples of 24, from 1 to 15.
Then, there are 3 multiples of 3 out of 7 factors of 24, and the probability that the number chosen is a multiple of 3 given that is a factor of 24 is:
- 3/7
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<em><u>b) What is the probability that the number chosen is a factor of 24 given that it is a multiple of 3?</u></em>
The factors of 24 that are multiples of 3 are, again, 3, 6, and 12. Thus, 3 numbers.
The multiples of 3 are 3, 6, 9, 12, and 15: 5 numbers.
Then, the probability that the number chosen is a factor of 24 given that is a multiple of 3 is:
- 3/5
