Here is a graph that shows some values for the number of cups of flour \(f\), required to make \(x\) batches of modeling clay.

Eight points plotted on the coordinate plane with the origin labeled “O”. The x axis is labeled “batches of clay” and the numbers 0 through 8 are indicated. The y axis is labeled “cups of flour” and the numbers 0 through 6 are indicated. There are horizontal gridlines halfway between each integer. The data are as follows: 1 comma one half. 2 comma 1. 3 comma one and one half. 4 comma 2. 5 comma 2 and one half. 6 comma 3. 7 comma 3 and one half. 8 comma 4.

1. Complete the table so that the pair of numbers in each column represents the coordinates of a point on the graph.

   \(x\)	1	2	3	4	5	6	7
   \(f\)

2. What does the point \((8,4)\) mean in terms of the amount of flour and number of batches of modeling clay?

3. Write an equation that shows the amount of flour in terms of the number of batches.

Every day a factory produces 90 cars.

1. A worker at the factory wants to know how many cars are produced  for different numbers of days. Write an equation that shows the number of cars, \(c\), depends on the number of days, \(n\). 
2. A manager wants to know how many days it will take to produce a certain number of cars. Write an equation that shows the number of days, \(n\), depends on the number of cars, \(c\).

Kiran shops for books during a sale. All books are sold at 80% of their original price.

1. Complete the table to show how much Kiran would pay for differently priced books during the sale.
2. Write an equation that relates the sale price, \(s\), to the original price \(p\).
3. Complete the graph showing the relationship between the sale price and the original price by plotting the points from the table.

original price in dollars \((p)\)	sale price in dollars \((s)\)
1
2
3
4
5
6
7
8
9
10

Coordinate grid with the origin labeled “O”. The x axis is labeled “original price in dollars” and the numbers 0 through 10 are indicated. The y axis is labeled “sale price in dollars” and the numbers 0 through 10 are indicated. There are horizontal gridlines halfway between each integer.

Find the value of each expression when \(x\) is 4.

1. \((6-x)^3+6\)
2. \(2 + x^3\)
3. \(2^x-12\)
4. \(\left(\frac{1}{2}\right)^x\)
5. \(1^x + 2^x\)
6. \(\frac{2^x}{x^2}\)

Find \((12.34) \boldcdot (0.7)\). Show your reasoning.

For each expression, write another division expression that has the same value and that can be used to help find the quotient. Then, find each quotient.

1. \(302.1 \div 0.5\)

2. \(12.15 \div 0.02\)

3. \(1.375 \div 0.11\)