Triangle ABC is congruent to triangle XYZ. In ΔABC, AB = 12 cm and AC = 14 cm. In △XYZ, YZ = 10 cm and XZ = 14 cm. What is the p
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Answer:
(a) 16 students failed for exactly two of the three reasons.
(b) 7 students failed because of poor attendance and not studying but not because of not turning in assignments.
(c) 14 students failed because of exactly one of the three reasons.
(d) 3 students failed because of poor attendance and not turning in assignments but not because of not studying.
Step-by-step explanation:
We are given that one semester in a chemistry class, 14 students failed due to poor attendance, 23 failed due to not studying, 15 failed because they did not turn in assignments, 9 failed because of poor attendance and not studying, 8 failed because of not studying and not turning in assignments, 5 failed because of poor attendance and not turning in assignments, and 2 failed because of all three of these reasons.
As shown in the diagram attached below, a Venn diagram represents the situation given in the question;
In the diagram below, 2 in represents purple color represents the number of students failed because of all three of these reasons.
7 represents the number of students who failed because of poor attendance and not studying but not due to not turning in assignments.
6 represents the number of students who failed because of not studying and not turning in assignments but not due to poor attendance.
3 represents the number of students who failed because of poor attendance and not turning in assignments but not due to not studying.
2 in red color represents the number of students who failed only due to poor attendance.
8 in red color represents the number of students who failed only due to not studying.
4 in red color represents the number of students who failed only due to not turning in assignments.
(a) The number of students who failed because of exactly two of the three reasons = 7 + 6 + 3 = 16 students.
(b) The number of students who failed because of poor attendance and not studying but not because of not turning in assignments = 9 - 2 = 7 students.
(c) The number of students who failed because of exactly one of the three reasons = 2 + 8 + 4 = 14 students.
(d) The number of students who failed because of poor attendance and not turning in assignments but not because of not studying = 5 - 2 = 3 students.
Answer:
m∠2 = 78°
Step-by-step explanation:
From the given picture,
lines 'm' and 'n' are the parallel lines and line 't' is the transverse line.
∠1 and angle with the measure of 78° are corresponding angles.
Therefore, m∠1 = 78°
m∠1 = m∠2 [Vertical angles are equal]
m∠2 = 78°
This is a geometric series with first term 2 and common ratio -4. The general term of such a series (an) in terms of the first term (a1) and common rato (r) is written as
an = a1*r^(n-1)
The sum is the sum of such terms.
an = a1*r^(n-1)
The sum is the sum of such terms.