At a homeowners' association meeting, a board member can vote yes, vote no, or abstain on a motion, There are thres motions on which each board member must vote, Complete parts (a) through (e) below. a) Determine the number of points in the sample space, , a

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To determine the number of points in the sample space for the voting scenario described, we need to consider the following:

1. Each board member has 3 options for each motion: vote yes, vote no, or abstain.
2. There are 3 motions.

To find the total number of points in the sample space, we can use the formula for the total outcomes, which is given by:

$$
\text{Total Outcomes} = (\text{Number of options per motion})^{\text{Number of motions}}
$$

In this case, the number of options per motion is 3 (yes, no, abstain), and the number of motions is 3.

Now, let's calculate the total outcomes:

$$
\text{Total Outcomes} = 3^3
$$

Now, I will calculate $$3^3$$.
Calculate the value by following steps:
- step0: Calculate:
  $$3^{3}$$
- step1: Evaluate the power:
  $$27$$
The total number of points in the sample space is $$ 27 $$.
There are 27 possible ways for the board members to vote on the three motions.

At a homeowners' association meeting, a board member can vote yes, vote no, or abstain on a motion, There are thres motions on which each board member must vote, Complete parts (a) through (e) below. a) Determine the number of points in the sample space, , a

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