Graphing - Pre-Algebra

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Question

Four candidates ran for mayor of Jackson City; the above circle graph shows the share of the vote that each won.

According to a city ordinance, a candidate must win more than 50% of the vote to win the election; if this does not happen, the two candidates who win the most votes will face each other in a runoff election. Based on the above graph, which of the following is the outcome of the vote?

Answer

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.

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Question

Five candidates ran for mayor of Madison City; the above circle graph shows the share of the vote that each won. Which of the following would be the most reasonable estimate of the percent of the vote Lyle won?

Answer

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.

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Question

Four candidates ran for mayor of Monroe City. The results are below.

$\begin{matrix} \textrm{\underline{Candidate}} & \textrm{\underline{Votes}} \ \textrm{Boatwright} & 8,542 \ \textrm{Delmar} & 3,176 \ \textrm{Stephens} & 1,753 \ \textrm{Van Owen} & 2,578 \end{matrix}$

According to a city ordinance, a candidate must win more than 50% of the vote to win the election; if this does not happen, the two candidates who win the most votes will face each other in a runoff election. Based on the above graph, which of the following is the outcome of the vote?

Answer

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

Boatwright won 8,542 votes. Since , Boatwright won a majority, and thus won the election outright.

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Question

Four candidates ran for mayor of Johnston City. The results are below.

$\begin{matrix} \textrm{\underline{Candidate}} & \textrm{\underline{Votes}} \ \textrm{Allen } & 4,128 \ \textrm{Carter } & 2,177 \ \textrm{Johnson } & 5,813 \ \textrm{Wayne } & 1,578 \end{matrix}$

According to a city ordinance, a candidate must win more than 50% of the vote to win the election; if this does not happen, the two candidates who win the most votes will face each other in a runoff election. Based on the above table, which of the following is the outcome of the vote?

Answer

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:

Johnson won 5,813 votes. Since , he did not win a majority, and he will face the second highest vote-getter, Allen, in a runoff.

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Question

Four candidates ran for mayor of Johnston City. The results are below.

$\begin{matrix} \textrm{\underline{Candidate}} & \textrm{\underline{Votes}} \ \textrm{Allen } & 4,128 \ \textrm{Carter } & 2,177 \ \textrm{Johnson } & 5,813 \ \textrm{Wayne } & 1,578 \end{matrix}$

Which of the following is the best estimate of the percent of the vote won by Johnson?

Answer

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:

$\approx 4,000 + 2,000 + 6,000 + 2,000 = 14,000$

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

As a percent, $\frac{3}{7}$ is equal to:

$\frac{3}{7} \cdot 100 = \frac{300}{7}$

$300 \div 7 \approx 43$

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

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Question

Below is the list of candidates for Student Council president, along with the number of votes each won:

$\begin{matrix} \textrm{\underline{Student}} &\textrm{\underline{Votes}} \ \textrm{Phillips}; & 105\ \textrm{Young}; ; ;& 83\ \textrm{Harris}; ; ; &64 \ \textrm{McCain};& 45\ \textrm{Zimmer}; ; & 39 \end{matrix}$

What percent of the students voted for neither Phillips nor Young (nearest tenth)?

Answer

students voted; of those students, voted for a candidate other than Phillip or Young. To convert this to a percent, use this proportion and solve for :

$\frac{p }{100}= \frac{148}{336}$

$\frac{p }{100} \cdot 100 = \frac{148}{336} \cdot 100$

$p = \frac{14,800}{336} \approx 44.0 %$

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Question

What is the slope of the line that contains the points

?

Answer

Using the equation:

$\frac{y_{1}-y_{2}}{x_{1}-x_{2}}$

you plug in your points (2,4) and (3,4)

$\frac{4-4}{3-2}$ $\frac{0}{1}$

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Question

What is the slope of the line:

$\small \small y=90x+1$

Answer

Using the equation: you know that the slope is m.

When you look at the equation:

$\small y=90x+1$ you see that the value of $\small m$ is $\small 90$ .

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Question

Refer to the above graph. Clark, a sixth grader at Polk, outscored 100 of the students who took the test. What could his score have been?

Answer

students achieved scores between 200 and 600, and Clark outscored all of them.

students achieved scores between 200 and 700; Clark did not outscore all of them.

Therefore, his score fell in the range from 601 to 700, making 635 the only plausible choice of the five.

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Question

Find the slope of the line between the points and .

Answer

Recall the slope formula:

$\small \small m=\frac{rise}{run}=\frac{y2-y1}{x2-x1}$

Plug in the two given points:

$\small m = \frac{y2-y1}{x2-x1}= \frac{7-4}{4-2}$

$\small m = \frac{7-4}{4-2} = \frac{3}{2}$

The slope of the line is $\small \frac{3}{2}$ .

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Question

Refer to the above bar graph.

What percent of the students achieved a score above 400?

Answer

30 students achieved a score of 401-500; 40 students achieved a score of 501-600; 16 achieved a score of 601-700; 10 achieved a score of 701-800. Add these:

The number of students who took the test is the sum of the students who finished in the six ranges:

The question is now to find out what percent 96 is of 120, which can be calculated as follows:

$\frac{96}{120} \times 100 % = 80 %$

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Question

Refer to the above bar graph.

How many students at Polk Middle School scored from 301 to 700 on the math portion of the SCAT?

Answer

students scored in the 301-400 range.

students scored in the 401-500 range.

students scored in the 501-600 range.

$\underline{+16}$ students scored in the 601-700 range. Add these:

students in all scored anywhere from 301-700.

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Question

If a line crosses through the points and , where does it cross the -axis?

Answer

Don't forget, when graphing points on a graph go left or right first then go up or down.

(2,8) and (3,9) has a slope of 1.

The slope is found using the formula,

$m=\frac{y_2-y_1}{x_2-x_1}$

where

and

$m=\frac{9-8}{3-2}=1$

Rise of 1 and a Run of 1.

Other coordinates are

The line will cross the y-axis at .

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Question

Find the mean and median of the following set of numbers.

Answer

Average or Mean is the total divided by the number of items.

Total equals 66, divided by the 11 numbers equals 6.

$Mean=\frac{2+ 2+ 2+ 3+ 3+ 6+ 7+ 8+ 10+ 11+ 12}{11}=\frac{66}{11}=6$

The Median is the middle number when put in order from least to greatest.

Five numbers on the left of 6 and five numbers on the right of 6. Six is in the middle when in order from least to greatest.

Answer is 6.

Mean = 6

Median = 6

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Question

What is the midpoint of the following sets of coordinates.

Answer

The midpoint formula is:

$\frac{(x_1 + x_2)} { 2}, \frac{(y_1 + y_2)} { 2}$

Given our points are we can plug them into the midpoint formula and get the following.

$\frac{(2 + 4)} { 2}, \frac{(8 + 4)} { 2}$

Simplifing the we find the coordinate of the midpoint.

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Question

What is the slope of a line that is horizontal like the following? $\leftrightarrow$

Answer

The slope of a horizontal line is zero.

The slope of a vertical line is undefined.

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Question

Using the following bar graph, what is the total number of books borrowed by Jessica and Emma?

Answer

When reading a bar graph, each bar contains different information. Look at the following bar graph.

The names of each student are displayed at the bottom. The number of books borrowed is displayed at the left. Each bar represents the number of books borrowed by a specific student.

We are asked to find the total number of books borrowed by Jessica and Emma. If we locate Jessica's name on the bottom, we can see the value of the bar is 5. This means Jessica borrowed 5 books. If we locate Emma's name on the bottom, we can see the value of the bar is 4. Now, finding the total number of books borrowed by Jessica and Emma, we simply add.

So the total number of books borrowed by Jessica and Emma is 9.

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Question

What percentage of books are NOT science fiction?

Answer

A pie chart contains portions that total to 100%. To find the percentage of books that are NOTscience fiction, we subtract the percentage of science fiction from 100%.

The percentage of books that are sicence fiction is 17%. So,

Therefore, 83% of the books are NOTscience fiction.

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Question

A line graphed on the coordinate plane below.

Give the equation of the line in slope intercept form.

Answer

The slope of the line is $\dpi{100} \small -2$ and the y-intercept is $\dpi{100} \small 4$ .

The equation of the line is $\dpi{100} \small y=-2x+4$ .

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Question

The equation of a line is .

What are the slope and the y-intercept?

Answer

The equation of the line is written in slope-intercept form, , where is the slope and is the y-intercept. In this example, the y-intercept is a negative number.

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