9 Kitchen staff at a college prepare soup in 10 litre containers to serve to students at lunch time. The grouped frequency table shows the number of complete containers consumed each day last term. 3-5 PS No. complete containers No. days (f) 6-8 9-10 11-15 2 5 49 14 M 10 a Find the mean of the two solutions to the equation ax² + bx + c = 0, where a ≈ 0. b Give a graphical interpretation of the value found in part a. PS 11 Muneeza has 12 different-sized boxes that are all rectangular prisms. Each box has a capacity of 72 millilitres, and the sides of the boxes all measure an integer number of centimetres. One box, for example, measures 2 by 3 by 12 cm and another measures 1 by 8 by 9 cm. Calculate the mean of: a the surface areas of all the boxes b the longest diagonals of all the boxes. 12 The lengths, I cm, of 200 objects are summarised in the following grouped frequency table. Length (1 cm) 9.0110.2 10.2 <1 < 11.4 11.4 < 1< 15.0 15.0 < 1< 16.4 Frequency 30 44 56 70 a Calculate an estimate of the mean length. b The boundary value of 11.4 cm is increased to 12.0 cm. A consequence of this is that the calculated estimate of the mean decreases. Find the least possible number of objects with lengths in the range 11.4 < 1< 12.0 cm. PS 13 An ordinary fair die was rolled 100 times. The results were summarised in a frequency table and the mean score was calculated to be 3.46. It was later discovered that the frequencies, 15 and 20, of two consecutive scores had been swapped. Find the least and greatest possible value of the true mean score.
9 Kitchen staff at a college prepare soup in 10 litre containers to serve to students at lunch time. The grouped frequency table shows the number of complete containers consumed each day last term. 3-5 PS No. complete containers No. days (f) 6-8 9-10 11-15 2 5 49 14 M 10 a Find the mean of the two solutions to the equation ax² + bx + c = 0, where a ≈ 0. b Give a graphical interpretation of the value found in part a. PS 11 Muneeza has 12 different-sized boxes that are all rectangular prisms. Each box has a capacity of 72 millilitres, and the sides of the boxes all measure an integer number of centimetres. One box, for example, measures 2 by 3 by 12 cm and another measures 1 by 8 by 9 cm. Calculate the mean of: a the surface areas of all the boxes b the longest diagonals of all the boxes. 12 The lengths, I cm, of 200 objects are summarised in the following grouped frequency table. Length (1 cm) 9.0110.2 10.2 <1 < 11.4 11.4 < 1< 15.0 15.0 < 1< 16.4 Frequency 30 44 56 70 a Calculate an estimate of the mean length. b The boundary value of 11.4 cm is increased to 12.0 cm. A consequence of this is that the calculated estimate of the mean decreases. Find the least possible number of objects with lengths in the range 11.4 < 1< 12.0 cm. PS 13 An ordinary fair die was rolled 100 times. The results were summarised in a frequency table and the mean score was calculated to be 3.46. It was later discovered that the frequencies, 15 and 20, of two consecutive scores had been swapped. Find the least and greatest possible value of the true mean score.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Answer only 11 and 13
Transcribed Image Text:Kitchen staff at a college prepare soup in 10 litre containers to serve to students at
lunch time. The grouped frequency table shows the number of complete containers
consumed each day last term.
No. complete
containers
No. days (f)
2
5
49
14
M 10 a Find the mean of the two solutions to the equation ax² + bx + c = 0, where a ≈ 0.
b
Give a graphical interpretation of the value found in part a.
PS 11 Muneeza has 12 different-sized boxes that are all rectangular prisms. Each box has a
capacity of 72 millilitres, and the sides of the boxes all measure an integer number of
centimetres. One box, for example, measures 2 by 3 by 12 cm and another measures 1
by 8 by 9 cm.
Calculate the mean of:
PS
9
3-5
6-8
9-10
11-15
a
the surface areas of all the boxes
b the longest diagonals of all the boxes.
12 The lengths, I cm, of 200 objects are summarised in the following grouped freque
table.
Length (1 cm) 9.01 10.2 10.2 <1 < 11.4 11.4 < 1< 15.0 15.0 < 1< 16.4
Frequency
44
56
70
30
a Calculate an estimate of the mean length.
b The boundary value of 11.4 cm is increased to 12.0 cm. A consequence of this is that
the calculated estimate of the mean decreases. Find the least possible number of
objects with lengths in the range 11.4 < 1< 12.0 cm.
PS 13 An ordinary fair die was rolled 100 times. The results were summarised in a frequency
table and the mean score was calculated to be 3.46. It was later discovered that the
frequencies, 15 and 20, of two consecutive scores had been swapped.
Find the least and greatest possible value of the true mean score.
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