The base of a cube is horizontal. A plane cuts through the cube, creating a pentagon-shaped cross section. The plane is _1_ and
may pass through a pair of adjacent _2_ of the base. Options for 1: a.vertical b.slanting Options for 2: a.vertices b.sides
1 answer:
For this problem, imagine a cube laying flat on the floor. If you zoom in on this, it would show a full square. The cutting plane should be able to form a cross-sectional shape of a pentagon. This is a closed figure comprising of 5 sides. The cutting plane should not be vertical. If it was, then it would only for a linear cross section. If it is horizontal, it would superimpose on the square base. So, if the cutting plane is slanting, it would form a pentagon cross section as shown in the right side of the picture attached. Then, it would pass between two adjacent vertices, and three adjacent sides. So, the complete statement would be:
<span>The base of a cube is horizontal. A plane cuts through the cube, creating a pentagon-shaped cross section. The plane is slanting and may pass through a pair of adjacent vertices of the base.</span>
<span>The base of a cube is horizontal. A plane cuts through the cube, creating a pentagon-shaped cross section. The plane is slanting and may pass through a pair of adjacent vertices of the base.</span>
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In the class, there is a total of 42 students.
25 take biology.
15 take history.
18 take biology but not history.
There are four situations that you have to include in the Venn diagram:
"The students take only biology"
"The students take only history"
"The students take biology and history"
"The students take neither classes"
To draw the Venn diagram, you have to make one circle for each subject, i.e. one circle for biology and one for history, and label them.
Then you have to enter the similarities between both subjects, this means, where the circles overlap, you will find the students that take both subjects.
Finally, outside the circles, you will find the students that take neither subject:
Now, you have to determine how many students are included in each part of the Venn Diagram.
1) You know that 25 students take biology and that 18 take biology but not history, to determine the number of students that take both subjects, you have to calculate the difference between both values:
7 students take biology and history.
2) 15 students take history out of these you know that 7 take also biology. To determine the number of students that take only history, you have to calculate the difference between both values:
8 students take history but not biology.
3) To determine the number of students that take neither class, you have to subtract to the total number of students, those who take only biology plus those who take only history plus those who take both classes:
9 Students of the class take neither class.
Finally, you can write each value in the corresponding part of the Venn diagram:
• Inside the green circle, you have to include the 18 students that take only biology.
,• Inside the blue circle, you have to include the 8 students that take only history.
,• Where both circles overlap, you have to include the 7 students that take both classes.
,• Outside the circles, you have to include the students that take neither.
