Question

review
determine each unit rate and graph each rate on the coordinate plane.

1. \\(\frac{3}{4}\\) cup of punch to \\(\frac{1}{8}\\) cup of lemon - lime
2. 1 cup of lemon - lime : \\(1\frac{1}{2}\\) cups of punch

(then there are two coordinate plane graphs, the left one has y - axis labeled cups of lemon - lime and x - axis labeled cups of punch, the right one has y - axis labeled cups of lemon - lime and x - axis labeled cups of punch)
answer each question. use 3.14 for \\(\pi\\). round to the nearest hundredth.

1. the diameter of a circle is 4 cm. determine the area of the circle.
2. the radius of a circle is 5.24 ft. determine the circumference of the circle.

determine each sum or product.

1. \\(71.05 + 0.54\\)
2. \\(89.2\times5.3\\)

Explanation:

Problem 1: Unit Rate and Graphing

Step 1: Find the unit rate (punch per lemon - lime)

The ratio is $\frac{3}{4}$ cup of punch to $\frac{1}{8}$ cup of lemon - lime. To find the unit rate (punch per 1 cup of lemon - lime), we divide the amount of punch by the amount of lemon - lime. So, $\frac{\frac{3}{4}}{\frac{1}{8}}=\frac{3}{4}\times8 = 6$. The unit rate is 6 cups of punch per cup of lemon - lime.

Step 2: Graphing

• The x - axis is cups of punch and the y - axis is cups of lemon - lime.
• The relationship is linear. We can use the point $(\frac{3}{4},\frac{1}{8})$ and the slope (unit rate reciprocal for lemon - lime per punch, $\frac{1}{6}$). But a simpler way is to use the unit rate. When $y = 1$ (1 cup of lemon - lime), $x = 6$ (6 cups of punch). We can also use the given ratio: when lemon - lime is $\frac{1}{8}$ cup, punch is $\frac{3}{4}$ cup. We can plot points like $(6,1),(3,0.5),(\frac{3}{4},\frac{1}{8})$ etc. and draw a straight line through them.

Problem 2: Unit Rate and Graphing

Step 1: Find the unit rate (punch per lemon - lime)

The ratio is 1 cup of lemon - lime to $1\frac{1}{2}=\frac{3}{2}$ cups of punch. The unit rate of punch per lemon - lime is $\frac{3}{2}=1.5$ cups of punch per cup of lemon - lime.

Step 2: Graphing

• The x - axis is cups of punch and the y - axis is cups of lemon - lime.
• The relationship is linear. When $y = 1$ (1 cup of lemon - lime), $x=\frac{3}{2}=1.5$ (1.5 cups of punch). We can plot points like $(1.5,1),(3,2),( \frac{3}{2},1)$ etc. and draw a straight line through them.

Problem 3: Area of a Circle

Step 1: Find the radius

The diameter $d = 4$ cm, so the radius $r=\frac{d}{2}=\frac{4}{2}=2$ cm.

Step 2: Use the area formula

The formula for the area of a circle is $A=\pi r^{2}$. Using $\pi = 3.14$ and $r = 2$, we get $A=3.14\times2^{2}=3.14\times4 = 12.56$ $cm^{2}$.

Answer:

(for area of circle): $12.56$ $cm^{2}$

Problem 4: Circumference of a Circle

Step 1: Use the circumference formula

The formula for the circumference of a circle is $C = 2\pi r$. Given $r = 5.24$ ft and $\pi=3.14$.

Step 2: Calculate the circumference

$C=2\times3.14\times5.24=6.28\times5.24 = 32.9072\approx32.91$ ft.