First translate the question into an equation.
"What percent" means x/100, "of 40" means times 40, "is 14" equals 14.
So we have (x)(40) = 14 or 40x = 14.
Dividing both sides by 40, we find that x = 0.35.
Now, we want to write our answer as a percent.
So we move the decimal 2 places to the right and we have 35%.
The answer is B) The transformation rule is (x, y) -> (x + 0, y + 4).
For a regular tessellation, the shapes can be duplicated infinitely to fill a plane such that there is no gap. The only shapes that can form regular tessellations are equilateral traingle(all sides are equal. This means that it can be turned to any side and it would remain the same), square and regular hexagon. Looking at the given options, we have
Shape Tessellate?
Octagon No
Hexagon Yes
Pentagon No
Square Yes
Triangle No(unless it is specified that it is an equilateral triangle)
Given that the cubical piece has side (s) 7 mm, and a cylindrical hole of diameter (d) as 3 mm.
The volume of the piece can be calculated as,
![\begin{gathered} \text{Volume of piece}=\text{ Volume of cube}-\text{ Volume of cylinder} \\ V=s^3-\frac{\pi}{4}d^2s \\ V=7^3-\frac{\pi}{4}(3)^2(7) \\ V=343-\frac{63\pi}{4} \\ V\approx293.52mm^3 \\ V\approx293.52\times10^{-9}\text{ }m^3 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BVolume%20of%20piece%7D%3D%5Ctext%7B%20Volume%20of%20cube%7D-%5Ctext%7B%20Volume%20of%20cylinder%7D%20%5C%5C%20V%3Ds%5E3-%5Cfrac%7B%5Cpi%7D%7B4%7Dd%5E2s%20%5C%5C%20V%3D7%5E3-%5Cfrac%7B%5Cpi%7D%7B4%7D%283%29%5E2%287%29%20%5C%5C%20V%3D343-%5Cfrac%7B63%5Cpi%7D%7B4%7D%20%5C%5C%20V%5Capprox293.52mm%5E3%20%5C%5C%20V%5Capprox293.52%5Ctimes10%5E%7B-9%7D%5Ctext%7B%20%7Dm%5E3%20%5Cend%7Bgathered%7D)
It is mentioned that the material costs $207 per cubic meter, so the cost (c) of 1 piece is calculated as,
![\begin{gathered} \text{Cost of 1 piece}=\text{ Cost per unit volume}\times\text{ Volume of 1 piece} \\ c=207\times293.52\times10^{-9} \\ c\approx60758.64\times10^{-9} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BCost%20of%201%20piece%7D%3D%5Ctext%7B%20Cost%20per%20unit%20volume%7D%5Ctimes%5Ctext%7B%20Volume%20of%201%20piece%7D%20%5C%5C%20c%3D207%5Ctimes293.52%5Ctimes10%5E%7B-9%7D%20%5C%5C%20c%5Capprox60758.64%5Ctimes10%5E%7B-9%7D%20%5Cend%7Bgathered%7D)
This is the cost (in dollars) for 1 piece.
Given that the manufacturer wants to produce 1,000,000 such pieces, so the total cost (TC) is calculated as,
![\begin{gathered} \text{Total Cost}=\text{ Cost per piece}\times\text{ No. of pieces} \\ TC=60758.64\times10^{-9}\times1,000,000 \\ TC=60758.64\times10^{-9}\times10^6 \\ TC=60758.64\times10^{-3} \\ TC=60.75864 \\ TC\approx60.75 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BTotal%20Cost%7D%3D%5Ctext%7B%20Cost%20per%20piece%7D%5Ctimes%5Ctext%7B%20No.%20of%20pieces%7D%20%5C%5C%20TC%3D60758.64%5Ctimes10%5E%7B-9%7D%5Ctimes1%2C000%2C000%20%5C%5C%20TC%3D60758.64%5Ctimes10%5E%7B-9%7D%5Ctimes10%5E6%20%5C%5C%20TC%3D60758.64%5Ctimes10%5E%7B-3%7D%20%5C%5C%20TC%3D60.75864%20%5C%5C%20TC%5Capprox60.75%20%5Cend%7Bgathered%7D)
Thus, the total prototypes will cost around $60.75