Complete Solution: Foundations of Mathematics Assignment 02

This document provides a detailed solution to a mathematics assignment, covering a range of topics. The solution begins with numerical comparisons, including percentages and ratios, and proceeds to solve word problems involving ratios of populations. It also includes solutions to algebraic problems, such as solving linear equations, matrix operations (addition, multiplication, determinant, and inverse), and percentage calculations related to survey data on machine preferences. The assignment further explores financial mathematics, including simple interest calculations, and concludes with problems on arithmetic progressions, including finding specific terms and relationships between consecutive terms. The solution provides step-by-step explanations and calculations for each problem, offering a comprehensive guide for students studying foundational mathematics.

Assignment 02
1.1)
= =0.66
68.75%=0.6875
0.673
2:3=0.
Therefore the numbers in descending order is,
0.6875>0.673>0. >0.66
That is,
68.75%>0.673>2:3>
Hence the answer
1.2)given,
men:women:children = 6:7:3
total women = 42000
let the ratio be x
the ratio becomes 6x:7x:3x
7x=42000
x=6000
1.2.1)
total people living together in Outapi is,
6x+7x+3x
=16x
Where x =6000
Total people=16*6000
=96000

Hence the answer.
1.2.2)
Number of children living in outapi=3x
=3*6000=18000
Hence the answer.
1.2.3)
42000=20% increase in 10 years.
That is 120% increase.
42000=120x%
X=42000/1.2
=35000
Number of women lived 10 years ago=35000
Hence the answer.
1.2.4)
Given 12000 attend school and 48% of them are boys.
12000*48%=5760
Therefore number of boys attending the school are=5760
So number of girls attending school are = 12000-5760
=6240
Hence the answer.
2)
Given, -5≤x≤-3 and -1≤y≤2
To find the largest possible value of
2.1) x+y
Largest value of x = -3

Largest value of y= 2
So x+y = -3+2
=-1
Hence the answer.
2.2) xy
Smallest value of x = -5
Smallest value of y = -1
So largest value of xy to be positive= -5*-1
=5
Hence the answer.
2.3)
Smallest value of x=-5
Square of smallest value=
=25
Largest value of y =2
Therefore =50
Hence the answer.
3.1)
Given,
2x-5y=9…………………………..1)
And,
7x-y=15……………………………2)
The solution is x= and y=
Where D is the determinant,

D= =-2+35=33
And =-9+75=66
And =30-63=-33
Therefore x= = =2
And y= = =-1
Hence the answer.
3.2)
Given, A=
B=
C=
D=
E=
3.2.1)
A+B=
=
Hence the answer.
3.2.2)
AC=
=
Hence the answer.
3.2.3)

B=
Determinant
=7
Hence the answer.
3.2.4)
= = * =
Hence the answer
3.2.5)
=
=
adjA= =
determinant A, =10
Therefore =
Hence the answer.
4)
4.1)
T=number of people who like treadmill=935
E= number of people who like elliptical machine. =846
E-T= number of people who only like elliptical machine. =321

4.2)
Number of people who liked both machines, = 525.
%= *100=26.609%
4.3)number of people who only liked treadmill = 935-525=410
4.4)number of people who liked neither of the machine = 2050-(410+525+321)
=1256
%age= *100=61.268%
Hence the answer.
5.1)
Interest= Principal*rate*time(in years)
Here interest=17$
Rate=6%
Time= 4 months=4/12 yrs=1/3 yrs
Substituting in the equation,
I=Prt
17=P*0.06*
17=P*0.02
P=850$
Hence the answer
5.2)
Terms=
=16+25+36+49=126
Hence the answer.

6.1)
given
11, 8, 5, 2……
The given sequence is an arithmetical progression.
Here a=11
Common difference = -3
General term in an A.P is given by,
= =a + (n-1)d
Where n is the number of terms.
To find whether -150 is a term of this progression,
Substitute
That is -150=a + (n-1)d
=-150=11 + (n-1)*-3
=-161 = (n-1)*-3
Which leads to n is a fraction which cannot be true.
So -150 is not a term in the sequence.
6.2)
Given,
A,B,C,D are consecutive terms in an arithmetic progression.
Therefore let A be the first term,
B be the 2nd term,
C be the 3rd term, and
D be the 4th term.
Let the common difference be x.
The relation between A ,B,C,D=

B=A + x
C=A + 2x
D=A + 3x
To find,
Substituting in the above equation…
=
=
=
=
=3
Hence the answer.