Answer:
120 different slates of candidates are possible.
Step-by-step explanation:
The order is important.
For example, a slate of John, Rose and Elisa means that John is the chairperson, Rose is the secretary and Elisa is the treasurer. If two of them are exchanged, their roles will also be changed. So we use the permutations formula to solve this question.
Permutations formula:
The number of permutations of x elements from a set of n elements is given by:

In this problem, we have that:
6 members will be chosen for 3 roles. So

120 different slates of candidates are possible.
Answer:
is the nth term of the given sequence.
Step-by-step explanation:
The sequence given is

We can clearly see that 1st term is
and 2nd term is
2nd term is obtained by multiplying the 1st term by 2.
2nd term is
and 3rd term is 1.
3rd term is obtained by multiplying the 2nd term by 2.
3rd term is 1 and 4th term is 2.
4th term is obtained by multiplying the 3rd term by 2.
Clearly, the given series is a <em>Geometric Progression(GP)</em> with
First term, 
Common Ratio,
We know that
term for a GP is:

Putting values of <em>a</em> and <em>r</em>

Hence,
is the nth term of the given sequence.
Answer:
3 1/8
Step-by-step explanation:
25/9 * 9/8 =
9's cancel out
25/8 =
3 1/8
Answer: Angie = 6, Jemma = 18
<u>Step-by-step explanation:</u>
Let x represent the current age of Angie
Current Age Age 5 years from now
Angie: x x + 5
Jemma: 3x 3x + 5
5 years from now the sum of their ages is 34
(x + 5) + (3x + 5) = 34
4x + 10 = 34
4x = 24
x = 6
Angle's current age is x = 6
Jemma's current age is 3x = 3(6) = 18
Answer:
The Correct option is B: True
Step-by-step explanation:
A condition is a state of something with respect to its quality, working order, or appearance at a particular point in time. Hence, a condition can tell if a hypothesis is true or false at that time, but once the condition changes, it can change the conclusion and hence the hypothesis also.