Question

1) a) From the set {-8, -2/3, 5i, √(-9), √2, 0, 3+3i, -2.35, 7}

i) List the set of Natural Numbers

ii) List the set of Integers

iii) List of the set of Rational Numbers

vi) List the set of Real Numbers

2)Solve the following pairs of simultaneous equations 3x + y = 7 and 2x - 2y = 2

b) i) -30 ÷ -6 - (-12 + 8) – 4 x 3 =

c)Calculate the simple interest earned if a deposit of $ 900,000 is left for 12 years at an interest rate of 3% .

ii) Calculate the interest rate for a 12 years investment of $600,000 to gained $180,000 interest.

Answer #1

4. a) i) If 4
individuals are selected from a group of 7 people,
how many possible selection option could be
made?
ii) In a competition prizes are given to 6 of the 10
participants.
How many possible prize lists could be made if they are given
different prizes?
b) In how many ways can the letters of the word
SEMESTER be rearranged?
5) If the fifth term of a AP
is...

i) Simplify the following equations 3(2x – 5) – 2(5x - 7) + 9 =
ii) Solve 3x – 2 divided by 2= 4x - 5 divided by 4 (5marks)
c) Solve the following pairs of simultaneous equations 2x + y =
7 and x - 2y = -1

3) If A = 3
1 and B
= 1 7
0
-2
5 -1
Find
a) BA
b) determinant
B
c) Adjoint A
d)
A-1
4) Using matrix method solve the following simultaneous
equations
5x – 3y = 1
2x – 2y = -2
5) Given that f(x) = 6x - 5 g(x) = 3x +
4 and h(x) = 4x – 6
2
Find:-
i)...

4. Let set U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
14, 15, 16, 17, 18, 19, 20}
set A = numbers in U that divide into 12 with no remainder,
set B = numbers in U that divide into 16 with no remainder, and set
C = the numbers in U that divide into 20 with no remainder.
a. Made a Venn diagram showing the elements of the sets U, A,...

Let A = {0, 3, 6, 9, 12}, B = {−2, 0, 2, 4, 6, 8, 10, 12}, and C
= {4, 5, 6, 7, 8, 9, 10}.
Determine the following sets:
i. (A ∩ B) − C
ii. (A − B) ⋃ (B − C)

let the universal set be U = {1, 2, 3, 4, 5, 6, 7, 8, 9} with A
= {1, 2, 3, 5, 7} and B = {3, 4, 6, 7, 8, 9}
a.)Find (A ∩ B) C ∪ B
b.) Find Ac ∪ B.

Suppose, I = {set of locations for establishing a hospital} =
{1, 2, 3, 4, 5, 6, 7}
xi is a decision variable which equals 1 if a
hospital is set up at location i; otherwise, xi = 0.
The following are a list of constraints. I'd like to know how to
formulate them in terms of x.
Constraint 1: If locations 6 and 7 are selected, then location 3
is also selected
Constraint 2: If 6 or 7 are...

Consider the matrix list x = [[1, 2, 3], [4, 5, 6], [7, 8, 9]].
Write a list comprehension to extract the first column of the
matrix [1, 4, 7]. Write another list comprehension to create a
vector of twice the square of the middle column.

Consider the following two sample data sets.
Set 1: 4 5
7 6 8
Set 2: 7 19 12
4 2
a. Calculate the coefficient of variation for each data set.
b. Which data set has more variability?

=Using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 only once,
find all the possible 3 digit number plus another 3 digit number to
equal a 4 digit number. (No repetition of numbers is allowed.) One
example is 589+437=1026.
We are asked to find ALL the possibilities. I know it has to do
with combinations, but I'm not quite sure if I'm using it the
proper way.

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