First, the best advice I can give you is to go to sleep. You pretty much know what you know, and being well-rested will help you think clearly, recall details, and avoid careless mistakes.
1)
[tex]=(5 \times 10^3)+(2 \times 10^2)=(50 \times 10^2)+(2 \times 10^2)\\=10^2(50+2)=52 \times 100 = 5200 = 5.2 \times 10^3[/tex]
2)
[tex]=(5 \times 10^2) \times (5 \times 10^3)=5^2 \times 10^5 \\= 25 \times 100,000 = 2,500,000 = 2.5 \times 10^6[/tex]
3) Yes, dilating with a scale factor that is less than 1 (and greater than 0) corresponds to a decrease.
4) Yes, dilating with a scale factor greater than 1 corresponds to an increase.
5) To find the slope of a scatter plot, you need to make a line of best fit, that is, the line that passes through as many points as possible and has about as many points above it as below it. Then, find two of those points that the line passes through and calculate the slope between those points. For two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], the slope is
[tex]m= \dfrac{y_2-y_1}{x_2-x_1}[/tex].
This is an estimate. To find a better approximation, you can use the least-square method, but I think that probably involves higher-level math that you don't need. If you think you do need to solve it this way, just comment here and I'll explain it. Note that you can also calculate it using Microsoft Excel or a regression plot on a graphing calculator.
