William payed $8.55 at the discount price
Answer:
The number of ways are there to paint the four buildings is 48.
Step-by-step explanation:
I) let the first building be any color. Therefore the first building can be painted with any of the 4 colors.
Therefore the first building can be colored in 4 ways.
ii) the second building can be colored in 3 ways since it cannot be colored the
same color as the first building.
iii) the third building can also be colored in 3 ways.
iv) the last building can be colored in 2 ways because it cannot be the same color as the first building or the color of the adjacent building.
Therefore the total number of ways the buildings can be colored = 4 
3 3 2 = 48.
For the transformation
the Jacobian is
with determinant
The vertices of the triangle in the 
-plane are
Then the integral is
When you have ratios, and some unknowns, you can create complex fractions from them. Bring them to the same denominator, and solve for x.
Example - we have this proportion:
2-x
5-45
And we can change it into fraction:
\frac{2}{5}=\frac{x}{45}
\frac{2*9}{5*9}=\frac{x}{45}
\frac{18}{45}=\frac{x}{45}
18=x
In case of more complex fractions it may come in handy.
Answer:
1: Tip, $2.23
2: Tax, $0.74
3: Total, $17.87
4: Split, $5.95
Step-by-step explanation:
To find the tip, you must multiply the tip percentage by the bill, (which has not been taxed yet). The tip is 15%, which is equivalent to 0.15. The tip multiplied by the bill (0.15×14.90) equals $2.23.
To find the tax, you do the same as you did with the tip. The tax is 5%, which equals 0.05. The tax multiplied by the bill, (0.05×14.90) equals $0.74. The total cost is the bill, tip, and tax added together, (14.90+2.23+0.74) equals $17.87. To find out how much each person will pay equally, you must divide the total bill by the amount of people, (17.87÷3) which equals $5.95.
