### Let's solve each part of the question step-by-step.
#### Part 1: [tex]\( 10 - 28 \times (-5) \)[/tex]
1. Calculate [tex]\( 28 \times (-5) \)[/tex].
2. Subtract the result from 10.
[tex]\[
10 - [28 \times (-5)] = 10 - (-140) = 10 + 140 = 150
\][/tex]
Result: [tex]\( 150 \)[/tex]
#### Part 2: [tex]\( 117.5 \times 0.3 \)[/tex]
1. Multiply 117.5 by 0.3.
[tex]\[
117.5 \times 0.3 = 35.25
\][/tex]
Result: [tex]\( 35.25 \)[/tex]
#### Part 3: [tex]\( 12 \times 3 \frac{1}{4} \times \left(-2 \frac{2}{3}\right) \)[/tex]
1. Convert the mixed numbers to improper fractions:
[tex]\[
3 \frac{1}{4} = \frac{13}{4}, \quad -2 \frac{2}{3} = -\frac{8}{3}
\][/tex]
2. Multiply the fractions:
[tex]\[
12 \times \frac{13}{4} \times -\frac{8}{3} = \frac{12 \times 13 \times (-8)}{4 \times 3} = 13 \times (-8) = -104
\][/tex]
Result: [tex]\( -104 \)[/tex]
#### Part 4: [tex]\( 13 \frac{3}{5} \times \left(-\frac{7}{8}\right) \)[/tex]
1. Convert the mixed number to an improper fraction:
[tex]\[
13 \frac{3}{5} = \frac{68}{5}
\][/tex]
2. Multiply the fractions:
[tex]\[
\frac{68}{5} \times -\frac{7}{8} = \frac{68 \times (-7)}{5 \times 8} = \frac{-476}{40} = -11.9
\][/tex]
Result: [tex]\( -11.9 \)[/tex]
#### Part 5: [tex]\( 1430 \times (-32) \)[/tex]
1. Multiply 1430 by -32.
[tex]\[
1430 \times (-32) = -45760
\][/tex]
Result: [tex]\( -45760 \)[/tex]
#### Part 6: [tex]\( 15 - 0.7 \times 3.1 \)[/tex]
1. Multiply 0.7 by 3.1.
2. Subtract the result from 15.
[tex]\[
15 - (0.7 \times 3.1) = 15 - 2.17 = 12.83
\][/tex]
Result: [tex]\( 12.83 \)[/tex]
#### Part 7: [tex]\( - \frac{13}{12} \times \frac{2}{3} \times \frac{5}{7} \)[/tex]
1. Multiply the fractions:
[tex]\[
- \frac{13}{12} \times \frac{2}{3} \times \frac{5}{7} = - \frac{13 \times 2 \times 5}{12 \times 3 \times 7} = - \frac{130}{252} = - 0.5158730158730158
\][/tex]
Result: [tex]\( -0.5158730158730158 \)[/tex]
#### Part 8: [tex]\( 17 - 3 \times 3 \times (-5) \times (-9) \)[/tex]
1. Multiply [tex]\( 3 \times 3 \times (-5) \times (-9) \)[/tex].
2. Subtract the result from 17.
[tex]\[
3 \times 3 = 9
\][/tex]
[tex]\[
9 \times (-5) = -45
\][/tex]
[tex]\[
-45 \times (-9) = 405
\][/tex]
[tex]\[
17 - 405 = -388
\][/tex]
Result: [tex]\( -388 \)[/tex]
### Summary of Results:
[tex]\[
\begin{align*}
10 - 28 \times (-5) & = 150 \\
117.5 \times 0.3 & = 35.25 \\
12 \times 3 \frac{1}{4} \times \left(-2 \frac{2}{3}\right) & = -104 \\
13 \frac{3}{5} \times \left(-\frac{7}{8}\right) & = -11.9 \\
1430 \times (-32) & = -45760 \\
15 - 0.7 \times 3.1 & = 12.83 \\
-\frac{13}{12} \times \frac{2}{3} \times \frac{5}{7} & = -0.5158730158730158 \\
17 - 3 \times 3 \times(-5) \times(-9) & = -388 \\
\end{align*}
\][/tex]
