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.
Answer:
Option B 
Step-by-step explanation:
we know that
The area of the rectangle room, is equal to
where
L is the length
W is the width
we have
Remember that
1 yard= 3 feet
Convert yards to feet
The area is equal to
Answer:
We have to determine the graph of the given inequality as:
on solving this equation we get:
Since we know that:
Now we know that when 
the value of:
Also for the value other than -1 the function being a quadratic function will always give a non-zero positive value.
Hence, range of the function in intervals could be written as:
(-∞,-1)∪(-1,∞).
Hence, the graph of the function will be the whole of the number line with a open circle on -1.
84 increased by 12% of 84 = (1)84 + (0.12)84, or (1.12)84 = $94.08
