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The ages (in years) of 50 individuals on a mailing list, in ascending order are:


10 11 13 14 14 15 15 17 18 20


20 21 22 24 26 26 26 27 29 30


31 31 33 34 36 36 36 37 38 39


40 41 41 43 44 45 45 46 47 48


49 51 53 55 57 58 59 59 60 60


Consider the frequency table for the data:


A B C D


Interval Frequency Frequency Frequency Frequency


0,5 – 15,5 5 7 7 5


15,5 – 30,5 14 13 12 15


30,5 – 45,5 16 17 18 14


45,5 – 60,5 15 13 13 16


The column that represents the correct frequencies for the data is


[1] A


[2] B


[3] C


[4] D

find the general solutions of (x+y+2z) dz/dx+(x+y+2z)dz/dy=3z


A quality-control exercise was carried out by ChocCheer for estimating the percentage of defective chocolate


bars in a large shipment of 1 000 boxes with 100 bars in each box. Twenty boxes were chosen at random,


and every bar in them checked. The number of defective bars in each of the boxes are:


8, 10, 4, 3, 11, 6, 9, 10, 2, 7, 6, 12, 9, 11, 6, 3, 14, 9, 5, 4


Choose the CORRECT statement.


[1] The variable is the 1 000 boxes of chocolate bars.


[2] The sample unit 149.


[3] The sample is the 20 boxes of chocolate bars that were selected.


[4] The population is the 100 chocolate bars per box

To save money for a new house, you want to begin contributing money to a savings account. Your plan



is to make equal contributions to the account for eight years. Each contribution will be R18 490,00. The



contributions will come at the end of every three month period, starting three months from now. The savings



account pays 9% interest per annum, compounded quarterly. How much money do you expect to have in



the account at the end of the eight years

(a)Check whether the set ]-5,7]nl [-7,5[ contains any e -neighbourhood of 3. 2 (b)What are the suficient conditions for a set to have a limit point ? Check whether the set {+-1/n | neN} has any limit point in R.

Using the definition, show' that the sequence [1/√n]neN is Cauchy.

1. Mr. Ronald Aquino is currently working on his thesis on the effectiveness of design

thinking methods in teaching statistics and probability using one-shot pretest-post test

design. Before the implementation of the design thinking methods, he administered a

pretest to 20 randomly selected grade 11 students. The same test was administered at

the end of the experiment to the same group of students. He wants to know whether the

design thinking methods is effective by determining whether a significant difference

exists between the pretest and post test scores of the students using 0.05 level of

significance; that is, Mr. Aquino desires to determine whether the post test scores of the

students are significantly higher than their pretest scores. The table below shows the

scores of the 20 students.


b. Are design thinking methods effective in enhancing the performance of senior high school

students in statistics and probability?


1. Mr. Ronald Aquino is currently working on his thesis on the effectiveness of design

thinking methods in teaching statistics and probability using one-shot pretest-post test

design. Before the implementation of the design thinking methods, he administered a

pretest to 20 randomly selected grade 11 students. The same test was administered at

the end of the experiment to the same group of students. He wants to know whether the

design thinking methods is effective by determining whether a significant difference

exists between the pretest and post test scores of the students using 0.05 level of

significance; that is, Mr. Aquino desires to determine whether the post test scores of the

students are significantly higher than their pretest scores. The table below shows the

scores of the 20 students.


a. Is there a significant difference between the pretest and post test scores of the 20

students?





Determine which of the following biconditional statements are true.

                (a)  if and only if .

                (b)  if and only if .

                (c)  if and only if .

Select one:

a. (a) and (b)

b. (a) and (c)

c. (b)

d. (c)

e. (a)


Find the complete integral of p^2 + q^1/2 -y


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