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wlad13 [49]
3 years ago
9

What Numbers Go Into The Venn Diagram

Mathematics
1 answer:
antiseptic1488 [7]3 years ago
6 0

Answer:

(a)The total number of outcomes where the sum is 9 or

    greater than 9 is  10

(b)Total number of outcomes where the sum is odd = 18

(c)Total number of outcomes where the  sum greater or equal to 9 and is

     also odd = 6

Step-by-step explanation:

Here, Sample Space = { Sum of the two digits when two dices are thrown together}

or,   S   =   {2,3,4,5,6,7,8,9,10,11,12}

(a)  The number of ordered pairs where sum is  9 or greater than 9

    = { sum is 9  ,  Sum is 10 ,  Sum is 11,   Sum is 12}

    = {(6,3)(3,6),(4,5)(5,4) ,   (5,5), (6,4),(4,6)  , (6,5)(5,6),   (6,6)}

Hence the total number of outcomes where the sum is 9 or

greater than 9 is  10

(b)  The number of ordered pairs where sum is odd.

    = { Sum is 3 ,  Sum is 5,   Sum is 7, Sum is 9, Sum is 11}

    = {(1,2)(2,1),   (4,1)(1,4),(2,3)(3,2) ,   (6,1), (1,6),(5,2),(2,5),(4,3)(3,4)  ,

        (6,3)(3,6), (4,5)(5,4),  (6,5),(5,6)}  = 18

Hence total number of outcomes where the sum is odd = 18

(c) Intersection point refers the outcomes which have sum greater or equal to 9 and is odd

Here, the possible outcomes are  = { Sum is 9 ,  Sum is 11}

                                            ={ (6,3)(3,6), (4,5)(5,4),  (6,5),(5,6)}  = 6

Hence total number of outcomes where the  sum greater or equal to 9 and is also odd = 6

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\overline{LL'}, \ \overline{MM'} \ and \ \overline{NN'}<em> are each perpendicular to the line of reflection</em>

<em></em>

This option is the only one that is correct. The line of reflection is  y=-1. When we talk about reflection, we are talking about reflecting across a line, or axis. Reflecting a shape means looking at the mirror image on the other side of the axis. So in this case, this mirror is the line of reflection.  As you can see, these three segments \overline{LL'}, \ \overline{MM'} \ and \ \overline{NN'}<em> </em>form a right angle at the point each segment intersects the line y=-1.

<h2>b) Find each length</h2>

Since the line y=-1 is an axis that allows to get a mirror image, therefore it is true that:

\overline{LS}=\overline{L'S} \\ \\ \overline{MT}=\overline{M'T} \\ \\ \overline{NU}=\overline{N'U}

To find those values \overline{LS}, count the number of units you get from the point S to L, which is 3 units. Do the same to find \overline{MT} but from the point T to M, which is 6 units and finally, for \overline{NU} but from the point U to N, which is 4 units. Therefore:

\overline{LS}=\overline{L'S}=3 \ units \\ \\ \overline{MT}=\overline{M'T}=6 \ units \\ \\ \overline{NU}=\overline{N'U}=4 \ units

<h2>c) Correct Statement</h2>

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<em />

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