Answer:
y - (-3) = -8/5 (x - 2)
Step-by-step explanation:
-3 -5 = -8
2 - (-3) = 5
slope = -8/5
y - (-3) = -8/5 (x - 2)
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
Answer:
-2
Step-by-step explanation:
use the slope formula which is y2-21/x2-x1
these are what i chose my numbers to be
-4=x1
-1= y1
-2= x2
-5= y2
-5-(-1)/-2-(-4) = -2
thats all
6x²-x-12
Use the foil method to multiply each term and then simplify
Answer: in 95% of races, his finishing time will be between 62 and 64 seconds.
Step-by-step explanation:
The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean . The empirical rule is further illustrated below
68% of data falls within the first standard deviation from the mean.
95% fall within two standard deviations.
99.7% fall within three standard deviations.
From the information given, the mean is 63 seconds and the standard deviation is 5 seconds.
2 standard deviations = 2 × 0.5 = 1
63 - 1 = 62 seconds
63 + 1 = 64 seconds
Therefore, in 95% of races, his finishing time will be between 62 and 64 seconds.