Answer:
11,800 different four letter permutations can be formed using four letters out of the first 12 in the alphabet
Step-by-step explanation:
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
In this question:
Permutations of four letters from a set of 12 letters. So
11,800 different four letter permutations can be formed using four letters out of the first 12 in the alphabet
The distacne between the points (x1,y1) and (x2,y2) is
so the distance between (4,5) and (10,13) is
well, first
x1=4
y1=5
x2=10
y2=13
so
D=√100
D=10
the distance is 10 units
7x + 17 = 7x - 17
7x + 17 - 7x = 7x - 17 - 7x
17 = -17
Inconsistent: for no value of x is the above equation true. 17 ≠ -17.
Hope this helps! :)
Answer:
Note that orthogonal to the plane means perpendicular to the plane.
Step-by-step explanation:
-1x+3y-3z=1 can also be written as -1x+3y-3z=0
The direction vector of the plane -1x+3y-3z-1=0 is (-1,3,-3).
Let us find a point on this line for which the vector from this point to (0,0,5) is perpendicular to the given line. The point is x-0,y-0 and z-0 respectively
Therefore, the vector equation is given as:
-1(x-0) + 3(y-0) + -3(z-5) = 0
-x + 3y + (-3z+15) = 0
-x + 3y -3z + 15 = 0
Multiply through by - to get a positive x coordinate to give
x - 3y + 3z - 15 = 0
Answer:
210
Step-by-step explanation:
Here comes the problem from Combination.
We are being asked to find the number of ways out in which 3 students may sit on 7 seats in a row. Please see that in this case the even can not be repeated.
Let us start with the student one. For him all the 7 seats are available to sit. Hence number of ways for him to sit = 7
Let us see the student second. For him there are only 6 seats available to sit as one seat has already been occupied. Hence number of ways for him to sit = 6
Let us see the student third. For him there are only 5 seats available to sit as two seat has already been occupied. Hence number of ways for him to sit = 5
Hence the total number of ways for three students to be seated will be
7 x 6 x 5
=210
