In order to solve this question, we need to use both the equation and the table. We are looking for the corresponding \(\displaystyle y\) value for \(\displaystyle x=6\). We can plug \(\displaystyle 6\) into the \(\displaystyle x\)  in our equation to solve for \(\displaystyle y\).

\(\displaystyle y=7(6)+3\)

\(\displaystyle y=42+3\)

\(\displaystyle y=45\)

The pattern for the set is all even numbers up until \(\displaystyle 20\).  The missing even number between \(\displaystyle 10\) and \(\displaystyle 14\) would be \(\displaystyle 12\) and the missing number between \(\displaystyle 14\) and \(\displaystyle 18\) would be \(\displaystyle 16\).

Add 23 to the first element to get the second element. The increment decreases by two with each successive entry. The pattern can be seen below:

\(\displaystyle 8 \bold {+23} = 31\)

\(\displaystyle 31 \bold {+21} = 52\)

\(\displaystyle 52 \mathbf{+ 19} = 71\)

\(\displaystyle 71 \mathbf{+ 17} = 88\)

To get the element in the circle, add 15:

\(\displaystyle 88\mathbf{ + 15}= 103\), the correct response.

This is confirmed by adding 13;

\(\displaystyle 103 \mathbf{+ 1 3 } = 116\), the next number in the sequence.

The figures alternate between lines with squares and lines with circles, so the next figure must be a line with a square. This eliminates Figures (c) and (d) and leaves Figures (a) and (b).

If we only look at every other figure - the ones with the squares - we note that each figure is the previous one rotated one quarter turn clockwise. The next figure in the sequence is therefore the figure resulting from a one-quarter turn of the fifth figure - this is Figure (b).

The way to get from one entry of the sequence to the next alternates between multiplying by four and subtracting one, as follows:

\(\displaystyle 2 \mathbf{ \times 4} = 8\)

\(\displaystyle 8 \mathbf{ -1} = 7\)

\(\displaystyle 7 \mathbf{ \times 4} = 28\)

\(\displaystyle 28 \mathbf{ -1} = 27\)

\(\displaystyle 27 \mathbf{ \times 4} = 108\)

\(\displaystyle 108\mathbf{ -1} = 107\)

Continuing the pattern:

\(\displaystyle 107 \mathbf{ \times 4} = 428\)

\(\displaystyle 428\mathbf{ -1} = 427\), the correct choice.

Each figure is obtained by rotating the previous figure one-eighth of a turn clockwise, with the position of the letter and the number also so changed. Also, the number increases by two, and the letter, which is always in the opposite corner, is the letter corresponding to the number (A = 1, C = 3, etc...).

The next number in the pattern is 13; the thirteenth letter in the alphabet is "M"; and, to continue the pattern of rotating one-eighth of a turn clockwise each time, the "M" must be at the very bottom, with the "13" being at the top. This means that Figure 3 is the next figure in the sequence.

By comparing the sizes of the sectors, it can be seen that Mills won the largest share of the vote - but not at least one half of it - and Jones won the second-largest share. Therefore, they will face each other in a runoff.

Since we are asking for an estimate, one way to work this problem is to round each candidate's vote tally to the nearest thousand, then adding the rounded numbers:

\(\displaystyle 4,178 + 2,177 + 5,813 + 1,578\)

\(\displaystyle \approx 4,000 + 2,000 + 6,000 + 2,000 = 14,000\)

Johnson's share of the vote is about 6,000 of those approximately 14,000 votes, or \(\displaystyle \frac{6,000}{14,000} = \frac{6}{14} = \frac{3}{7}\)

As a percent, \(\displaystyle \frac{3}{7}\) is equal to:

\(\displaystyle \frac{3}{7} \cdot 100 = \frac{300}{7}\)

\(\displaystyle 300 \div 7 \approx 43\)

Therefore, 40% is the best estimate of the choices we are given.

The sector representing Lyle is roughly one-tenth to one-eighth of the circle - in other words, 10-12 % of it. This is the approximate percent of the vote won by Lyle.

We can determine whether the highest vote-getter, Johnson, won the election outright by comparing Johnson's votes to the sum of the votes of his opponents. The votes won by his opponents sum up to:

\(\displaystyle 4,128 + 2,177 + 1,578 = 7,883\)

Johnson won 5,813 votes. Since \(\displaystyle 5,813 < 7,883\),  he did not win a majority, and he will face the second highest vote-getter, Allen, in a runoff.