Answer :
Let's solve each of the mathematical expressions step by step:
### Expression [tex]\((y)\)[/tex]
[tex]\[ 8 \times 4^2 - 8^2 - 2 \times 13 \][/tex]
1. Compute [tex]\( 4^2 \)[/tex]:
[tex]\[ 4^2 = 16 \][/tex]
2. Multiply [tex]\( 8 \)[/tex] by [tex]\( 16 \)[/tex]:
[tex]\[ 8 \times 16 = 128 \][/tex]
3. Compute [tex]\( 8^2 \)[/tex]:
[tex]\[ 8^2 = 64 \][/tex]
4. Multiply [tex]\( 2 \)[/tex] by [tex]\( 13 \)[/tex]:
[tex]\[ 2 \times 13 = 26 \][/tex]
5. Subtract [tex]\( 64 \)[/tex] and [tex]\( 26 \)[/tex] from [tex]\( 128 \)[/tex]:
[tex]\[ 128 - 64 - 26 = 38 \][/tex]
So, the result is:
[tex]\[ y = 38 \][/tex]
### Expression [tex]\((w)\)[/tex]
[tex]\[ 4 \times 6 \div 6 \times 6 \div 2 \][/tex]
1. Multiply [tex]\( 4 \)[/tex] by [tex]\( 6 \)[/tex]:
[tex]\[ 4 \times 6 = 24 \][/tex]
2. Divide [tex]\( 24 \)[/tex] by [tex]\( 6 \)[/tex]:
[tex]\[ 24 \div 6 = 4 \][/tex]
3. Multiply [tex]\( 4 \)[/tex] by [tex]\( 6 \)[/tex]:
[tex]\[ 4 \times 6 = 24 \][/tex]
4. Divide [tex]\( 24 \)[/tex] by [tex]\( 2 \)[/tex]:
[tex]\[ 24 \div 2 = 12 \][/tex]
So, the result is:
[tex]\[ w = 12 \][/tex]
### Expression [tex]\((i)\)[/tex]
[tex]\[ (14 + 3^2) - 2 \times 4 \][/tex]
1. Compute [tex]\( 3^2 \)[/tex]:
[tex]\[ 3^2 = 9 \][/tex]
2. Add [tex]\( 14 \)[/tex] and [tex]\( 9 \)[/tex]:
[tex]\[ 14 + 9 = 23 \][/tex]
3. Multiply [tex]\( 2 \)[/tex] by [tex]\( 4 \)[/tex]:
[tex]\[ 2 \times 4 = 8 \][/tex]
4. Subtract [tex]\( 8 \)[/tex] from [tex]\( 23 \)[/tex]:
[tex]\[ 23 - 8 = 15 \][/tex]
So, the result is:
[tex]\[ i = 15 \][/tex]
### Expression [tex]\((4)\)[/tex]
[tex]\[ 2^2 (126 \div 9) - 5 \times 10 - 1 \][/tex]
1. Compute [tex]\( 2^2 \)[/tex]:
[tex]\[ 2^2 = 4 \][/tex]
2. Divide [tex]\( 126 \)[/tex] by [tex]\( 9 \)[/tex]:
[tex]\[ 126 \div 9 = 14 \][/tex]
3. Multiply [tex]\( 4 \)[/tex] by [tex]\( 14 \)[/tex]:
[tex]\[ 4 \times 14 = 56 \][/tex]
4. Multiply [tex]\( 5 \)[/tex] by [tex]\( 10 \)[/tex]:
[tex]\[ 5 \times 10 = 50 \][/tex]
5. Subtract [tex]\( 50 \)[/tex] and [tex]\( 1 \)[/tex] from [tex]\( 56 \)[/tex]:
[tex]\[ 56 - 50 - 1 = 5 \][/tex]
So, the result is:
[tex]\[ 4 = 5 \][/tex]
### Expression [tex]\((s)\)[/tex]
[tex]\[ (1.95 + 0.05)(4.7 - 2.7) \][/tex]
1. Add [tex]\( 1.95 \)[/tex] and [tex]\( 0.05 \)[/tex]:
[tex]\[ 1.95 + 0.05 = 2.00 \][/tex]
2. Subtract [tex]\( 2.7 \)[/tex] from [tex]\( 4.7 \)[/tex]:
[tex]\[ 4.7 - 2.7 = 2.0 \][/tex]
3. Multiply [tex]\( 2.0 \)[/tex] by [tex]\( 2.0 \)[/tex]:
[tex]\[ 2.0 \times 2.0 = 4.0 \][/tex]
So, the result is:
[tex]\[ s = 4.0 \][/tex]
### Expression [tex]\((n)\)[/tex]
[tex]\[ (3 \times 2)^2 + 7 - 10 \div 5 \][/tex]
1. Multiply [tex]\( 3 \)[/tex] by [tex]\( 2 \)[/tex]:
[tex]\[ 3 \times 2 = 6 \][/tex]
2. Compute [tex]\( 6^2 \)[/tex]:
[tex]\[ 6^2 = 36 \][/tex]
3. Divide [tex]\( 10 \)[/tex] by [tex]\( 5 \)[/tex]:
[tex]\[ 10 \div 5 = 2 \][/tex]
4. Add [tex]\( 36 \)[/tex] and [tex]\( 7 \)[/tex]:
[tex]\[ 36 + 7 = 43 \][/tex]
5. Subtract [tex]\( 2 \)[/tex] from [tex]\( 43 \)[/tex]:
[tex]\[ 43 - 2 = 41 \][/tex]
So, the result is:
[tex]\[ n = 41 \][/tex]
In conclusion, the answers to the problems are:
[tex]\[ \begin{aligned} y & = 38, \\ w & = 12, \\ i & = 15, \\ 4 & = 5, \\ s & = 4.0, \\ n & = 41. \end{aligned} \][/tex]
### Expression [tex]\((y)\)[/tex]
[tex]\[ 8 \times 4^2 - 8^2 - 2 \times 13 \][/tex]
1. Compute [tex]\( 4^2 \)[/tex]:
[tex]\[ 4^2 = 16 \][/tex]
2. Multiply [tex]\( 8 \)[/tex] by [tex]\( 16 \)[/tex]:
[tex]\[ 8 \times 16 = 128 \][/tex]
3. Compute [tex]\( 8^2 \)[/tex]:
[tex]\[ 8^2 = 64 \][/tex]
4. Multiply [tex]\( 2 \)[/tex] by [tex]\( 13 \)[/tex]:
[tex]\[ 2 \times 13 = 26 \][/tex]
5. Subtract [tex]\( 64 \)[/tex] and [tex]\( 26 \)[/tex] from [tex]\( 128 \)[/tex]:
[tex]\[ 128 - 64 - 26 = 38 \][/tex]
So, the result is:
[tex]\[ y = 38 \][/tex]
### Expression [tex]\((w)\)[/tex]
[tex]\[ 4 \times 6 \div 6 \times 6 \div 2 \][/tex]
1. Multiply [tex]\( 4 \)[/tex] by [tex]\( 6 \)[/tex]:
[tex]\[ 4 \times 6 = 24 \][/tex]
2. Divide [tex]\( 24 \)[/tex] by [tex]\( 6 \)[/tex]:
[tex]\[ 24 \div 6 = 4 \][/tex]
3. Multiply [tex]\( 4 \)[/tex] by [tex]\( 6 \)[/tex]:
[tex]\[ 4 \times 6 = 24 \][/tex]
4. Divide [tex]\( 24 \)[/tex] by [tex]\( 2 \)[/tex]:
[tex]\[ 24 \div 2 = 12 \][/tex]
So, the result is:
[tex]\[ w = 12 \][/tex]
### Expression [tex]\((i)\)[/tex]
[tex]\[ (14 + 3^2) - 2 \times 4 \][/tex]
1. Compute [tex]\( 3^2 \)[/tex]:
[tex]\[ 3^2 = 9 \][/tex]
2. Add [tex]\( 14 \)[/tex] and [tex]\( 9 \)[/tex]:
[tex]\[ 14 + 9 = 23 \][/tex]
3. Multiply [tex]\( 2 \)[/tex] by [tex]\( 4 \)[/tex]:
[tex]\[ 2 \times 4 = 8 \][/tex]
4. Subtract [tex]\( 8 \)[/tex] from [tex]\( 23 \)[/tex]:
[tex]\[ 23 - 8 = 15 \][/tex]
So, the result is:
[tex]\[ i = 15 \][/tex]
### Expression [tex]\((4)\)[/tex]
[tex]\[ 2^2 (126 \div 9) - 5 \times 10 - 1 \][/tex]
1. Compute [tex]\( 2^2 \)[/tex]:
[tex]\[ 2^2 = 4 \][/tex]
2. Divide [tex]\( 126 \)[/tex] by [tex]\( 9 \)[/tex]:
[tex]\[ 126 \div 9 = 14 \][/tex]
3. Multiply [tex]\( 4 \)[/tex] by [tex]\( 14 \)[/tex]:
[tex]\[ 4 \times 14 = 56 \][/tex]
4. Multiply [tex]\( 5 \)[/tex] by [tex]\( 10 \)[/tex]:
[tex]\[ 5 \times 10 = 50 \][/tex]
5. Subtract [tex]\( 50 \)[/tex] and [tex]\( 1 \)[/tex] from [tex]\( 56 \)[/tex]:
[tex]\[ 56 - 50 - 1 = 5 \][/tex]
So, the result is:
[tex]\[ 4 = 5 \][/tex]
### Expression [tex]\((s)\)[/tex]
[tex]\[ (1.95 + 0.05)(4.7 - 2.7) \][/tex]
1. Add [tex]\( 1.95 \)[/tex] and [tex]\( 0.05 \)[/tex]:
[tex]\[ 1.95 + 0.05 = 2.00 \][/tex]
2. Subtract [tex]\( 2.7 \)[/tex] from [tex]\( 4.7 \)[/tex]:
[tex]\[ 4.7 - 2.7 = 2.0 \][/tex]
3. Multiply [tex]\( 2.0 \)[/tex] by [tex]\( 2.0 \)[/tex]:
[tex]\[ 2.0 \times 2.0 = 4.0 \][/tex]
So, the result is:
[tex]\[ s = 4.0 \][/tex]
### Expression [tex]\((n)\)[/tex]
[tex]\[ (3 \times 2)^2 + 7 - 10 \div 5 \][/tex]
1. Multiply [tex]\( 3 \)[/tex] by [tex]\( 2 \)[/tex]:
[tex]\[ 3 \times 2 = 6 \][/tex]
2. Compute [tex]\( 6^2 \)[/tex]:
[tex]\[ 6^2 = 36 \][/tex]
3. Divide [tex]\( 10 \)[/tex] by [tex]\( 5 \)[/tex]:
[tex]\[ 10 \div 5 = 2 \][/tex]
4. Add [tex]\( 36 \)[/tex] and [tex]\( 7 \)[/tex]:
[tex]\[ 36 + 7 = 43 \][/tex]
5. Subtract [tex]\( 2 \)[/tex] from [tex]\( 43 \)[/tex]:
[tex]\[ 43 - 2 = 41 \][/tex]
So, the result is:
[tex]\[ n = 41 \][/tex]
In conclusion, the answers to the problems are:
[tex]\[ \begin{aligned} y & = 38, \\ w & = 12, \\ i & = 15, \\ 4 & = 5, \\ s & = 4.0, \\ n & = 41. \end{aligned} \][/tex]
