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3 years ago

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

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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<h2>a) Select all that apply</h2>

$\overline{LL'}, \ \overline{MM'} \ and \ \overline{NN'}$ are each perpendicular to the line of reflection

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 $\overline{LL'}, \ \overline{MM'} \ and \ \overline{NN'}$ 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>

The line of reflection is the perpendicular bisector of each segment joining a point and its image. 

A bisector is the line dividing something into two equal parts. In this case, the line of reflection divides each segment into two equal parts and is perpendicular because this line form a right angle with each segment. As we demonstrated in a) each segment is perpendicular to the line of reflection, so the first statement is false. On the other hand, each side of the original triangle is not perpendicular to its image and this is obvious when taking a look at the figure. Finally, as we said the line of reflection is perpendicular to each of the mentioned segments, so they can't be parallel as established in the last statement.

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3 years ago