One semester in a chemistry class, 14 students failed due to poor attendance, 23 failed due to not studying, 15 failed because t
hey 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.
Required:
a. How many failed for exactly two of the three reasons?
b. How many failed because of poor attendance and not studying but not because of not turning in assignments?
c. How many failed because of exactly one of the three reasons?
d. How many failed because of poor attendance and not turning in assignments but not because of not studying?
Required:
a. How many failed for exactly two of the three reasons?
b. How many failed because of poor attendance and not studying but not because of not turning in assignments?
c. How many failed because of exactly one of the three reasons?
d. How many failed because of poor attendance and not turning in assignments but not because of not studying?
1 answer:
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.
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Answer:
a) 61.2, b) 38.4 and c) 4.98
Step-by-step explanation:
Given:
The mean width of 12 I-Pads is 5.1 inches.
The mean width of 8 Kindles is 4.8 inches.
Question asked:
a. What is the total width of the I-Pads?
b. What is the total width of the Kindles?
c. What is the mean width of the 12 I-Pads and 8 Kindles?
Solution:
<u>As we know:</u>
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a) Thus, the total width of the I-Pads are 61.2 inches.
b) Thus, total width of the Kindles are 38.4 inches.
Combined width of both I-pad and Kindles = 61.2 + 38.4 = 99.6 inches
Combined number of observations = 12 + 8 =20
Combined mean of width of the 12 I-Pads and 8 Kindles = Combined width of both I-pad and Kindles Combined number of observations
Combined mean of width of the 12 I-Pads and 8 Kindles =
c) Thus, the mean width of the 12 I-Pads and 8 Kindles is 4.98 inches.
9514 1404 393
Answer:
13 in by 51 in
Step-by-step explanation:
The area is the product of the dimensions, so is ...
663 = x(4x -1)
4x^2 -x -663 = 0 . . . . . . subtract 663 to put in standard form
Using the quadratic formula, we can find the solutions.
x = (-(-1) ±√((-1)^2 -4(4)(-663)))/(2(4))
x = (1 ± √10609)/8 = (1 ±103)/8
Only the positive solution is of any use in this problem, so ...
x = 104/8 = 13
4x-1 = 4(13)-1 = 51
The dimensions of the rectangle are 13 inches by 51 inches.
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I find it easiest to solve these using a graphing calculator.
