Question

1. a company makes sheets of plywood. a sheet made up of 8 layers is $\frac{3}{4}$ inches thick. how thick is a sheet of plywood made up of 6 layers?

1. leslie evaluated $-2.2 + 4.6 \times (-0.5)$ as $-1.2$. zack evaluated the same expression as $-4.5$. who is correct? explain your answer.

extend

1. some artists panels are laminated, 7-layer boards. many have a centre core made of five layers of material and two thin wood veneer outer panels.

design a 7-layer board that is a total of $\frac{7}{8}$-inch thick and has a $\frac{1}{2}$-inch centre core. make a sketch and include the thickness of all layers.

1. in her last basketball game, jacqui made $\frac{3}{7}$ of her free throws. in the game before that, she made $\frac{5}{8}$ of her free throws. jacqui believes that she made $\frac{8}{15}$ of her total free throws. is jacqui right or wrong? explain your reasoning.
2. simplify $sqrt{14.58 - 3.5(1.14 + 2.69) + (-9.44)}$. explain why it is not possible to find a final answer.

Explanation:

Problem 6

Step1: Find thickness per layer

$\text{Thickness per layer} = \frac{\frac{3}{4}}{8} = \frac{3}{4} \times \frac{1}{8} = \frac{3}{32}$ inches

Step2: Calculate 6-layer thickness

$\text{Total thickness} = 6 \times \frac{3}{32} = \frac{18}{32} = \frac{9}{16}$ inches

Step1: Do multiplication first

$4.6 \times (-0.5) = -2.3$

Step2: Add to the remaining term

$-2.2 + (-2.3) = -4.5$

Step1: Find total outer thickness

$\text{Total outer thickness} = \frac{7}{8} - \frac{1}{2} = \frac{7}{8} - \frac{4}{8} = \frac{3}{8}$ inches

Step2: Find single outer panel thickness

$\text{One outer panel} = \frac{\frac{3}{8}}{2} = \frac{3}{16}$ inches

Step3: Split core into 5 equal layers

$\text{One core layer} = \frac{\frac{1}{2}}{5} = \frac{1}{10}$ inches

Answer:

$\frac{9}{16}$ inches

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Problem 7