(02.05 MC)
2 answers:
Answer:
<em>Dilation by a scale factor of 2 followed by reflection about the x-axis</em>
Step-by-step explanation:
To answer it and view it properly let's do it by parts.
1) A closer look at the Triangle ABC shows us the coordinate points A(-2,-1) B(0,0) and C(1,-3).
2) Reflection across the x-axis gives us this triangle: A'(-2,1) B'(0,0) and C'(1,3). Notice that all y-coordinates have an opposite sign. This is a natural characteristic of a Reflection: an opposed sign of one Coordinate.
3) Finally, To Dilate a Triangle is to transform it so that it gets bigger than its original size.
If we compare the triangle with points A''(-4,2) B"(0,0) and C"(2,6) to A'(-2,1) B'(0,0) C'(1,3). Each coordinate is multiplied by 2.
Dilation by a scale factor of 2 followed by reflection about the x-axis
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Answer:
For the pairs that satisfy that the sum is less than 7 we have:
(1,1) (2,1) (1,2) (3,1) (2,2) (1,3) (4,1) (3,2) (2,3) (1,4) (5,1) (4.2) (3,3) (2,4) (1,5)
So we have a total of 15 pairs where the sum is less than 7
And for an odd sum we have the following pairs
(2,1) (1,2) (4,1) (3,2) (2,3) (1,4) (6,2) (5,2) (4,3) (3,4) (2,5) (1,6) (6,3) (5,4) (4,5) (3,6) (6,5) (5,6)
A total of 18 pairs and we have 6 pairs who are in both cases for the sum less than 7 and the sum an odd number that represent the intersection and using the total probability rule we got:
Step-by-step explanation:
For this case when a pair of dice is rolled we have the following sample pace for the outcomes:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
We see 36 possible outcomes and we want to find how many of these pairs we got rolling an odd sum or a sum less than 7
For the pairs that satisfy that the sum is less than 7 we have:
(1,1) (2,1) (1,2) (3,1) (2,2) (1,3) (4,1) (3,2) (2,3) (1,4) (5,1) (4.2) (3,3) (2,4) (1,5)
So we have a total of 15 pairs where the sum is less than 7
And for an odd sum we have the following pairs
(2,1) (1,2) (4,1) (3,2) (2,3) (1,4) (6,2) (5,2) (4,3) (3,4) (2,5) (1,6) (6,3) (5,4) (4,5) (3,6) (6,5) (5,6)
A total of 18 pairs and we have 6 pairs who are in both cases for the sum less than 7 and the sum an odd number that represent the intersection and using the total probability rule we got: