Answer:
There are 795 combinations.
Step-by-step explanation:
The number of ways or combinations in which we can select k element from a group of n elements is given by:
So, if Miriam want to choose 3 movies with at least two comedies, she have two options: Choose 2 comedies and 1 foreign film or choose 3 comedies.
Then, the number of combinations for every case are:
1. Choose 2 Comedies from the 10 and choose 1 foreign film from 15. This is calculated as:
2. Choose 3 Comedies from the 10. This is calculated as:
Therefore, there are 795 combinations and it is calculated as:
675 + 120 = 795
If the intersection of two sets is a null set or an empty set, then two sets A and B are disjoint sets. The intersection of a set is therefore empty.
<h3>Explain about the disjoined set?</h3>
Disjoint sets are a pair of sets that do not share any elements. For instance, the sets A=2,3 and B=4,5 are not connected sets. However, set C=3,4,5 and set C=3,6,7 are not disjoint since 3 is a common element in both sets C and D.
Now that we are clear on the disjoint set's definition, let's go on to talking about some more important topics, such the notation and Venn diagram related to it. A B = is the notation used for this particular set. As an illustration, suppose A = 1, 2, 3, and B = 4, 5, 6, 7. A + B = then.
To learn more about disjoined set refer to:
brainly.com/question/28165517
#SPJ1
1. AD/DB=CE/EB
given
2. AD/DB+1=CE/EB+1
Addition Property of Equality
3. AD+DB/DB=CE+EB/EB
using common denominators
4. AB = AD + DB
CB = CE + EB
segment addition
5. AB/DB=CB/EB
Substitution Property of Equality
6.ABC DBE
Reflexive Property of Congruence
7. ABC ~ DBE
SAS similarity criterion
<span>8. </span>
Corresponding angles of similar triangles are congruent.
9. DE|| AC
<span>If the corresponding angles formed by </span>
630 sterling * 1 euro / 0.84 sterling
630 sterling divided by 0.84 sterling = 750 euros
Answer:
√3 is irrational
Step-by-step explanation:
The location of the third point of a triangle can be found using a rotation matrix to transform the coordinates of the given points.
<h3 /><h3>Location of point C</h3>
With reference to the attached figure, the slope of line AC is √3, an irrational number. This means the line AC <em>never passes through a point with integer coordinates</em>. (Any point with integer coordinates would be on a line with rational slope.)
<h3>Equilateral triangle</h3>
The line segments making up an equilateral triangle are separated by an angle of 60°. If two vertices are on grid squares, the third must be a rotation of one of them about the other through an angle of 60°. The rotation matrix is irrational, so the rotated point must have irrational coordinates.
The math of it is this. For rotation of (x, y) counterclockwise 60° about the origin, the transformation matrix is ...
![\left[\begin{array}{cc}\cos(60^\circ)&\sin(60^\circ)\\-\sin(60^\circ)&\cos(60^\circ)\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}x'\\y'\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Ccos%2860%5E%5Ccirc%29%26%5Csin%2860%5E%5Ccirc%29%5C%5C-%5Csin%2860%5E%5Ccirc%29%26%5Ccos%2860%5E%5Ccirc%29%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%27%5C%5Cy%27%5Cend%7Barray%7D%5Cright%5D)
Cos(60°) is rational, but sin(60°) is not. For any non-zero rational values of x and y, the sum ...
cos(60°)·x + sin(60°)·y
will be irrational.
As in the attached diagram, if one of the coordinates of the rotated point (B) is zero, then one of the coordinates of its image (C) will be rational. The other image point coordinate cannot be rational.
