Answer: a.) 40320
b.) 336
Step-by-step explanation:
since we have 8 possible positions, with 8 different candidates, then there are 8 possible ways of arranging the first position, 7 possible ways of arranging the Second position, 6 ways of arranging the 3rd position, 5 possible ways od arranging the 4th position, 4 possible ways of arranging the 5th position, 3 possible ways of arranging the 6th position, 2 possible ways of arranging the 7th position and just one way of arranging the 8th position since we have only one person left.
Hence, the Number of possible sample space for different 8 positions is by multiplying all the number of ways we have in our sample space which becomes:
8*7*6*5*4*3*2*1 = 40320.
b.) By the sample space we have, since we've been asked ti arrange for only the firat 3 positions, then we multiply just for the first 3ways of choosing the positions, this becomes:
8*7*6 = 336
I think it’s 700, but I’m not positive
Answer:
55
Step-by-step explanation:
plug in the numbers to the equation
7(5)+5(4)=55
<h3>
Answer: C. (x+6) is a factor of p</h3>
Explanation:
p(-6) = 0 means that plugging x = -6 into p(x) leads to p(x) = 0.
If (x+6) was a factor of p(x), then we can say
p(x) = (x+6)q(x)
where q(x) is some other polynomial. Now let's replace x with -6
p(x) = (x+6)q(x)
p(-6) = (-6+6)q(-6)
p(-6) = 0*q(-6)
p(-6) = 0
The value of q(-6) doesn't matter as multiplying 0 with any number leads to 0.
This is all based on the special case of the remainder theorem that says "if p(k) = 0, then (x-k) is a factor of p(x)".
First we rewrite the expression correctly:
tn = ((-1) ^ n) * (n)
We now look for each of the terms:
t1 = ((-1) ^ 1) * (1) = - 1
t2 = ((-1) ^ 2) * (2) = 2
t3 = ((-1) ^ 3) * (3) = - 3
t4 = ((-1) ^ 4) * (4) = 4
The first four terms of the sequence are then:
-1, 2, -3, 4
Answer:
B.
-1, 2, -3, 4
