Assignment Solution: Using & Managing Data and Information - Math

This document presents a comprehensive solution to a math assignment focused on using and managing data and information. The assignment covers a wide range of mathematical concepts, including basic arithmetic calculations involving exponents and square roots, and solving real-world problems using percentages and ratios. It addresses probability calculations, statistical analysis involving height and weight data, linear equations, and calculating gradients and intercepts. The solution also explores algebraic equations, simultaneous equations, and optimization problems related to production and profit maximization. Each task is thoroughly explained, providing step-by-step solutions and calculations to facilitate understanding. The assignment demonstrates a solid understanding of mathematical principles and their practical applications in data analysis and information management.

USING & MANAGING DATA
AND INFORMATION

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

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
 > Press + and type 23.15
 > gives 30.22.
 >Press divide button while 30.22 is on screen and
 > press MRC button
1

 > 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
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 will take 1.5 hours to paint
wall.
b)
12 men = 5 days 200 m
20 men = ? 400 m
In 1 day 12 men completes = 40 m
In 1 day 20 men will complete =
(20 men*40m )/12
men
66.66667 m
days to complete 400 m 400m /66.66667
6 days
20 men will complete 400 m road in 6
days
c)
72 litres 07:02
Yellow 72 *(7/9)
2

56
Blue 72*(2/9)
16
35 litres of yellow is used
Total paint 35 *(9*7)
45
Blue paint 45 – 35
10 litre
TASK 4
a)
FV = PV * (1+R)^n
9500 * (1 +
0.0235)^6
9500 * 1.1495
FV £ 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
TASK 5
10 groups of 2 items
{1, 2}, {1, 3}, {1, 4},
{1, 5}, {2, 3}, {2, 4},
{2, 5}, {3, 4}, {3, 5},
{4, 5}
Probability of winning lottery = 1 / (59 :6)
6! 53! / 59!
3

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)
12249.5 - 12190.2
4

59.3
TASK 7
a)
Equation of line mx +b
In the given equation 5.34 is the slope of line and
23.12 is y intercept
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
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
5

Cotton sales = £780 - £157.5
£622.5
Cotton sales in metres = 622.5 / 2.5
249 metres
c)
1/3 of cotton sold last year = 622.5 / 3
£207.5
3 times amount of silk sold = £157.5 *3
£472.5
Total sales of cotton and silk = £472.5 + £207.5
£680
Claims of Jill are not right
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
6

36a = 160
a = 160 /36 = 4.44
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
1 kg apple = 1.08
1 kg orange = 1.2
TASK 11
a) Relationship between P & Q for supply and demand lines
There is inverse relationship between the demand and supply lines. It could be seen that
the price of the products falls when the supply of products is higher in the market. as per the case
if one unit is purchased it will be costing 300 while if 5 units are purchased it will cost 100 per
unit. From this it could be evaluated that the price of the product falls with the increase in
demand. There is inverse relations means if quantity rises price of the product will fall.
b) It is known as equilibrium point it is the point where the demand and supply are equal.
TASK 12
Given
Two types of units are produced
7

1. Base unit (B)
2. Cabinet unit (C)
Production department Assembly department
Base unit (B) 50 minutes 40 minutes
Cabinet unit (C) 20 minutes 35 minutes
Carpenter each day spends 15 hours 10 hours
Profit contribution
Base Units = £15
Cabinet Units = £32
Solution
Let,
 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)
To maximise the profit margins of the units.
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