Answer:
i) There are 40320 possible orders
ii) There are 336 possible orders for the first 3 positions.
Step-by-step explanation:
Given: The number of finalists = 8
The number of boys = 3
The number of girls = 5
To find the number of sample point the sample space S for the number of possible orders, we need to find factorial of 8!
The number of possible orders = 8!
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8
= 40320
ii) From all 8 finalist, we need to choose first 3 position. Here the order is important. So we use permutation.
nPr =
Here n = 8 and r = 3
Plug in n =8 and r = 3 in the above formula, we get
8P3 = 
= 
= 6.7.8
= 336
So there are 336 possible orders for the first 3 positions.
Not sure about the first part but X is 11 because if 14 is congruent to x + 3 then you just do 14-3 which is 11 and then since you figured out x is 11 you just plug that into 11-y and so if it needs to equal 3 then 11-3 = 8. So basically x=11 y=8
C. 3:00 p.m.
Low tide occurred at 5:00 a.m. (t=5) and the graph shows that high tide occurred at both 12:00 a.m. (t=0) and 10:00 a.m. (t=10).
That means that between high tide and low tide, 5 hours pass (5-0=5 and 10-5=5).
So if the last high tide was at 10:00 a.m., the next low tide will happen another 5 hours later. 5 hours after 10:00 a.m. is 3:00 p.m.
Answer: C= (3,2) and D=(2.2, 2.8)
Step-by-step explanation:
The coordinates of point P(x,y) divides a line segment having end points M
and N
in m:n will be :-

Given : The endpoints of AB are A(1,4) and B(6,-1).
If point C divides AB in the ratio 2 : 3, the coordinates of point C will be :-

Simplify,

Thus , coordinate of C= (3,2)
If point D divides AC in the ratio 3 : 2, the coordinates of point D will be :-

Simplify,

Thus , coordinate of D= (2.2,2.8)