- The Charleston Recycling Company collects 50,000 tons of recyclable material every month. The chart below shows the kinds of materials that are collected by the company’s five trucks. What is the second most common material that is recycled?
- Cardboard
- Glass
- Paper
- Plastic
- Other
In the pie chart, the larger the amount of the variable, the larger the slice. In this chart, paper is the most common recycled material, or the largest variable, representing 40% of the total.
- Given that the Charleston Recycling Company collects 50,000 tons of recyclable material every month, approximately how much paper is recycled every month?
- 40,000 tons
- 50,000 tons
- 60,000 tons
- 15,000 tons
- 20,000 tons
The chart indicates that 40% of the total recycled material is paper. Since 50,000 tons of material are recycled every month, the total amount of paper will be 40% of 50,000 tons.
\(\tfrac{40}{100}\times 50,000=20,000 \text{ tons}\)
- Forty students in a class take a test that is graded on a scale of 1 to 10. The histogram in the figure below shows the grade distribution, with the \(x\)-axis representing the grades and the \(y\)-axis representing the number of students obtaining each grade. If the mean, median, and modal values are represented by \(n\), \(p\), and \(q\), respectively, which of the following is true?
- \(n \gt p \gt q\)
- \(n \gt q \gt p\)
- \(q \gt p \gt n\)
- \(p \gt q \gt n\)
- \(q \gt n \gt p\)
The mean of the distribution can be computed by multiplying each grade by the number of students obtaining it, summing, and then dividing by the total number of students. Here, \(n = 4.2\).
The median is the value \(p\) for which an equal number of students have received grades that are higher or lower than \(p\). Here, \(p = 4\).
The mode is the most frequently obtained grade, and here, \(q = 3\).
Thus, \(n \gt p \gt q\).
- The graph below shows a straight line passing through the origin. Point P1 has the coordinates \((-5,-3)\). What is the \(x\)-coordinate of point P2 if its \(y\)-coordinate is 3?
- 0.8
- 1
- 5
- 3
- 8
Slope is defined to be \(\dfrac{\text{change in } y}{\text{change in } x}\).
As the line goes from the point \((-5,-3)\) to \((0,0)\), \(y\) increases by 3 and \(x\) increases by 5. Thus, the slope is \(\tfrac{3}{5}\).
Since the line is straight, the slope is the same throughout. In other words, each time \(y\) increases by 3 units, \(x\) will increase by 5 units. It is given in the problem that the \(y\)-coordinate of P2 is 3. So, as we move along the line from the origin \((0,0)\) to P2, \(y\) has increased by 3 units. Therefore, \(x\) will increase by 5 and so the \(x\)-coordinate of P2 is 5.
- Examine the graph below and determine which of the following is true.
- \(y-x=x-z\)
- \(w+z=y\)
- \(y-z=w\)
- \(w+x=y+z\)
Read the values of each bar from the vertical axis:
- \(w = 3\)
- \(x = 4\)
- \(y = 6\)
- \(z = 2\)
Since \(y – x=6 – 4=2\) and \(x–z=4–2=2\), Choice A is correct.
- The chart below represents the average amount of rain falling each month in the town of Tegulpa. During which month of the year does the most rainfall?
- January
- April
- August
- December
The graph is at its highest point for the first data point, which corresponds to 12 inches of rain during the month of January.
- Which month shows the greatest increase in rainfall compared to the preceding month?
- January
- March
- August
- October
Rainfall in October increases to six inches from one inch in September. This represents an increase of five inches. None of the other month-to-month differences are as great.
- A circle graph is used to show the percent of patient types that a hospital sees. How many degrees of the circle should the graph show to represent pediatric if \(\tfrac{1}{3}\) of the patients are pediatric patients?
- 90°
- 120°
- 220°
- 360°
- 180°
Since pediatric patients are one-third of the total, we need to determine one-third of 360°.
\(\dfrac{1}{3}\times 360°=120°\)
Another way you could come to this conclusion is by dividing the circle into three equal parts.
\(360° \div 3=120°\)
- Prizes are to be awarded to the best pupils in each class of an elementary school. The number of students in each grade is shown in the table below, and the school principal wants the number of prizes awarded in each grade to be proportional to the number of students. If there are 20 prizes, how many should go to fifth grade students?
- 5
- 4
- 7
- 3
- 2
First, determine the proportion of students in fifth grade. Since the total number of students is 180, this proportion is \(\tfrac{36}{180}=0.2=20%\).
Then, determine the same proportion of the total prizes, which is 20% of 20, or 4.