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If the numbers are arranged in increasing order by erasing numbers then the following sub-set will be found.

Subset 1: 9, 12, 20, 27, 28, 29, 39

Subset 2: 9, 32, 34, 35, 37, 39, 55, 66, 72, 73, 77, 83, 84

Subset 3: 44, 55, 66, 72, 73,

Subset 4: 12, 13, 14, 21, 23, 24, 25, 26

Subset 5: 7, 8, 17, 22, 24, 25, 26

Subset 6: 42, 61, 66, 72, 73, 77, 83, 84

Therefore in subset 2, a few numbers are erased to get the increasing order. And in this sub-set, erasing everything except first and third numbers i.e. 9, and 32 then the remaining increasing order will be 9, 32, 34, 35, 37, 39, 55, 66, 72, 73, 77, 83, 84

If the numbers are arranged in decreasing order by erasing numbers then the following sub-set will be found.

Subset 1: 44, 42, 41, 39, 29, 21, 1, 2

… (1)

… (2)

… (3)

… (4)

Eliminate the variable :

(3) – (2)

(A)

3* equation (2) + equation (4)

(B)

Now, equation (1)*2 + (A)

= 4 (C)

5 *(1) – (B)

= -13 (D)

(C) + (D)

= -19/4

Putting the value of in (D), get

= - 25/4

Putting the value of and in (1), get

-25/4 – 19/4 + = 4

Or, = 4 + 25/4 + 19/4

Or, = 50/4

Or, = 50/12

Or, = 25/6

Putting the value of and and in equation (2), get

-25/4 – 19/4 - + 50/12 = 1

Or, = 50/12 -25/4 – 19/4 – 1

Or, = - 47/6

The total cost of smartwatch and mobile phone = £1,250

The price of a mobile is 3 times the price of a smartwatch.

(a)

Let the price of the smartwatch = £x

Therefore, The price of mobile = £3x

As per the question, £x + £3x = £1,250 … (i)

The above equation shows the total cost in terms of the cost of the smart watch.

(b)

£x + £3x = £1,250

Or, 4x = 1,250

Or, x = £1,250/ 4

Or, x = £ 312.50

The cost of the smart watch £ 312.50

The price of mobile = £(3 * 312.50)

= £ 937.50

(c)

The VAT rate = 14%

The VAT on the mobile phone = £ 937.50 * 14%

= £131.25

… (v)

Putting all the values in equation (v), get

2.6 – 0.45 = 2 * 15.6/ ()( -)

Or, 2.15 = 3.12 * 144/ 12.57 (6 - 5)

Or, 2.15 = 35.74 *

Or, 2.15/35.74 =

Or, 0.06 =

Squaring both sides, get

Or, (1 + k)/ 64.4 = 36/10000

Or, 1+k = 0.23

Or, k = 0.23 – 1

Or, k = - 0.77

1.2 v + 0.64u = 0.85

Or, 1.2 v = 0.85 - 0.64u

Or, v = (0.85 - 0.64u)/ 1.2

Table 1: values of v

(Source: Self-created)

Graph 1: Graph of equation 1.2 v + 0.64u = 0.85

(Source: self-created)

2u + 7v = 52

Or, 2u = 52 - 7v

Or, u = (52 - 7v)/ 2

Table 1: values of u

(Source: Self-created)

Graph 2: Graph of equation 2u + 7v = 52

(Source: self-created)

A = Returning Customer

B = Discount Code

Q = Discounted customer

(a)

A = 1, represents Returning customer

A = 0, represents new custome

B = 0, without discounted code

B = 1, With Discount code

Q = 0, Without discounted customer

Q = 1, Discounted customer

**Truth Table**

Table: Truth Table

(Source: Self-created)

(b)

Boolean Expression for Discounted customer of the trading company

Q = (A + B).

(a)

Table: Frequency distribution table

(Source: Self-created)

(b)

The above frequency distribution table is discontinuous. It has to be converted into continuous frequency distribution, then

The adjustment factor = (Lower limit of a class - the upper limit of the previous class)/ 2

= (380 - 375)/ 2

= 5/2

= 2.5

The adjustment factor has to be subtracted from all the lower limit and add to the all upper limit of the classes.

Table: Frequency distribution table for Histogram

(Source: Self-created)

Figure: Histogram

(Source: self-created)

Mean = * /

= 1481/77

= 19.23Total members of the symphony (n) = 77 (odd)

Median = ((n+1)/2)th number of term

= ((77 + 1)/2)th number of term

= 39 th number of term

= 19 year

**Re-arrangement**

g. Start

a. Search for a school

f. Are seats available?

h. Is there an admission test?

b. Prepare for the admission test and write test

c. Did you pass the exam?

e. End

Input integer points and

**Algorithm**

Input: n, , x.

Output:

Step 1: When i = 0, p = 1

Step 2: When i n

Step 3: p = p * ()

Step 4: let i = i+ 1

Step 5: Output p.

**Journals**

Greco, C., Di Carlo, M., Vasile, M. and Epenoy, R., 2018, October. An intrusive polynomial algebra multiple shooting approach to the solution of optimal control problems. In 69th International Astronautical Congress.

Li, G.L., Xu, X., Hao, K., Sun, P., Cao, J., Yang, W.L., Shi, K. and Wang, Y., 2021. Exact solution of the quantum integrable model associated with the twisted $ D^{(2)} _3 $ algebra. arXiv preprint arXiv:2110.02699.

Luo, S., Song, M., Li, X., Zhang, Y., Hong, J., Yang, X., Zou, X., Xu, N. and You, L., 2018. Reconfigurable skyrmion logic gates. Nano letters, 18(2), pp.1180-1184.

Zhang, P., Gao, D., An, K., Shen, Q., Wang, C., Zhang, Y., Pan, X., Chen, X., Lyv, Y., Cui, C. and Liang, T., 2020. A programmable polymer library that enables the construction of stimuli-responsive nanocarriers containing logic gates. Nature Chemistry, 12(4), pp.381-390.

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