Using and Managing Data and Information Assignment 2 - BA3020QA

This assignment solution addresses various tasks related to using and managing data and information. It begins with calculator-based calculations, including exponents, square roots, and fractions. The assignment then moves on to practical problems involving time and cost calculations, such as phone call charges. Further tasks involve calculating the time taken for a task with varying numbers of people, and paint mixtures. The solution includes calculations for face value, VAT, and cost per unit. It also covers probability, correlation analysis, and the equation of a line. The assignment concludes with algebraic equations, simultaneous equations, and an analysis of supply and demand, and profit maximization. The solution provides step-by-step explanations and answers to each task, demonstrating the student's understanding of the concepts.

USING & MANAGING DATA
AND INFORMATION

TABLE OF CONTENTS
TABLE OF CONTENTS................................................................................................................2
TASK 1............................................................................................................................................1
TASK 2............................................................................................................................................2
TASK 3............................................................................................................................................3
TASK 4............................................................................................................................................4
TASK 5............................................................................................................................................4
TASK 6............................................................................................................................................5
TASK 7............................................................................................................................................6
TASK 8............................................................................................................................................7
TASK 9............................................................................................................................................8
TASK 10..........................................................................................................................................8
TASK 11..........................................................................................................................................9
TASK 12..........................................................................................................................................9

TASK 1
a) 2.9  First type 2.9
 press multiply button 2 times
 press equals sign for 5 times
 >answer 594.82
b) 5 √32 –  Type 32
 press square root 5 times
 answer 1.12.
c) 1/(1+0.02)^4 –  Press 1
 press divide
 type 1.02
 press equal sign four times
 it will give 0.9238 answer.
d) 500 * 5^-2 –  First type 5
 press multiply two time
 press equal sign
 it will give 25
 press subtract sign
 press multiply
 type 500
 -12500 as answer.
e) 23.15+√50/(0.9875−3.25) –  Subtract denominator
 Type 0.9875
 press minus button
 press equal it will give -2.2625
 press memory (M+).
 Type 50 and press square root button
 gives 7.072 and
1

 Press + and type 23.15
 gives 30.22.
 Press divide button while 30.22 is on screen and
 press MRC button
 press equals
 gives 13.35 as answer.
TASK 2
5 minutes = 2.2
7 minutes = (7 * 2.2) /5
Cost of 7 minute call £3.08
b)
2.20 = 5 minutes
5.28 = (5.28 * 5) / 2.2
Time of call 12 minutes
TASK 3
a)
4 people = 3 hours
1 person takes = 0.75 hours
Extra people time taken = 0.75*2 = 1.5
Time reduced due to additional 2 people 1.5 hours
Time taken by 6 people = 3- 1.5 = 1.5 hours
6 people has been involved in taking 1.5 hours to paint wall.
b)
12 men takes 5 days to complete 200 m
20 men to complete 400 m
12 men in 1 day complete = 40 m
20 men in 1 day will complete =
(20 men*40m )/12
men
66.66667 m
days to complete 400 m 400m /66.66667
6 days
2

6 days will be taken by 20 men for completing the road of
400m
c)
72 litres 07:02
Yellow 72 *(7/9)
56
Blue 72*(2/9)
16
35 ltrs of yellow paint is been used
Total paint 35 *(9*7)
45
Blue paint 45 – 35
Mixture of blue paint 10 litre
TASK 4
a)
Face Value PV * (1+R)^n
9500 * (1 + 0.0235)^6
9500 * 1.1495
Face Value = £ 10920
b)
i) VAT = 90 * 20%
18
ii) Total cost 90 + 18
108
c)
Cost per unit 6.85 pence
Units used = 56.84 / 0.00685
817 units
3

TASK 5
10 groups consists of t 2 items
{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2,
5}, {3, 4}, {3, 5}, {4, 5}
The Probability of winning lottery
is equal to 1 / (59 :6)
6! 53! / 59!
6!
59* 58* 57 *56* 55*54
1 / 32441381280
TASK 6
Height x Weight y x *y ∑ 𝑥 2
1.65 86 141.9 2.7225
1.43 68 97.24 2.0449
1.56 74 115.44 2.4336
1.74 92 160.08 3.0276
1.55 71 110.05 2.4025
1.67 80 133.6 2.7889
1.58 76 120.08 2.4964
1.47 70 102.9 2.1609
1.51 75 113.25 2.2801
1.61 81 130.41 2.5921
∑ x = 15.77 ∑ 𝑦 = 773 ∑ 𝑥𝑦 = 1224.95 ∑ 𝑥 2 = 24.9495
Average height = 1.577 Average weight = 77.3
n x ( ∑𝑥𝑦) - (∑ 𝑥) x (∑ 𝑦) 10*(1224.95) - (15.77)*(773)
4

12249.5 - 12190.2
59.3
TASK 7
a)
Equation of line mx +b
It could be seen in the given equation 23.12 is y intercept and 5.34 is the slope
of line
b)
i) Gradient of line
m = y2- y1 / x2 – x1
= 3- 0 / 0 – 2
= 3/2 = 1.5
ii) Equation of line
y = mx + c
y = 1.5 x + 3
iii) Exact value of y
y = 1.5 * 1.5 +3
y = 2.25 + 3
y = 5.25
5

TASK 8
1 meter cotton = a = 2.5
1 meter silk = b = 3.5
Total = c = 6
Total sales = £ 780
Silk Sales 45 metres
a) Equation = a = c – b
b) Cotton sales
Total sales = £780
Silk sales = 45 * £3.5
£157.5
Cotton sales = £780 - £157.5
£622.5
Sales of cotton = 622.5 / 2.5
249 metres
c)
One third of cotton sales = 622.5 / 3
£207.5
Three times amount of silk sales = £157.5 *3
£472.5
Total silk and cotton sales = £472.5 + £207.5
£680
The claims of Jill for higher sales are incorrect
6

TASK 9
a) 5 + 𝑎 /5 = 12
(5*5) + a /5 = (12*5)
25 + a = 60
a = 60 – 25
a = 35
b) 3 (5a – 2) = 37.5
15a – 6 = 37.5
15a = 37.5 – 6
a = 31.5 / 15
a = 2.1
c) 4(x + 3) + 6(2x - 1) = 6x + 36
4x +12 +12x – 6 = 6x + 36
16x + 6 = 6x + 36
16x – 6x = 36 – 6
10x = 30
x = 30 /10 = 3
d) 𝑎 /5 + 5(𝑎 - 4) = 6 - 2(𝑎 +3)
a + (5*5)*(a-4) = 5*(6 – 2 (a+3))
a + 25(a – 4 ) = 30 – 10 (a + 3)
a + 25 a – 100 = 30 – 10a + 30
26a – 100 = 60 – 10a
26a + 10a = 100 + 60
36a = 160
a = 160 /36 = 4.44
7

TASK 10
a)
5x + 30 y = 41.40
5x + 27 y = 37.80
b)
5x + 30 y = 41.40
5x + 27 y = 37.80
0 + 3 y = 3.6
y = 3.6 / 3 = 1.2
5x + 30 y = 41.4
5x + 30*1.2 = 41.4
5x + 36 = 41.4
5x = 41.4 – 36
x = 5.4/5 = 1.08
The rate of 1 kg apple = 1.08
1 kg orange = 1.2
TASK 11
a) Description of Relationship between P & Q for supply and demand lines
It has been analysed that there is inverse relationship between the demand and supply
lines. It is evaluated that the price of products decreases when the supply of products increases in
the market. As per the current case if one unit is purchased it will be priced 300 while if 5 units
are purchased it will be priced 100 per unit. it could be analysed that the price of the product falls
with the increase in demand of product. The inverse relations means if quantity rises price of the
product will fall.
b) It has been said equilibrium point which is the point where the supply and demand are equal.
TASK 12
2 types of units produced
8

1. Base unit (B)
2. Cabinet unit (C)
Base unit (B) Cabinet unit (C) Carpenter each day
spends
Production
department
50 minutes 20 minutes 15 hours
Assembly
department
40 minutes 35 minutes 10 hours
Profit contribution
Base Units = £15
Cabinet Units = £32
Answer
 x be number of base units produced in 1 day
 y by number of cabinet units produced in 1 day
50x +20y < = 15(60)
40x + 35y < = 10(60)
Objective is: maximise ( x+15) + (y+32) = (x + y - 47)
 The main objective is to maximise the profit margins of the units.
9