Answer:
{ (HHHH) (HHHT) (HHTH) (HTHH) (THHH) (HHTT) (HTTH) (TTHH) (HTHT) (THTH) (THHT) (TTTH) (TTHT) (THTT) (HTTT) (TTTT) }
P(first and last head) = 4/16 = 1/4
Answer:
$13.79
Step-by-step explanation:
13.13x0.05=0.6565
Tax=0.66
13.13+0.66=13.79
Answer:
The minimum cost is $17.30c
Step-by-step explanation:
Given
--- Volume
--- cost of wall paint
---cost of ceiling paint
Required
Minimum cost of paint
The volume is calculated as:
![V =xyz](https://tex.z-dn.net/?f=V%20%3Dxyz)
Substitute 288 for V
![288 =xyz](https://tex.z-dn.net/?f=288%20%3Dxyz)
Make z the subject
![z = \frac{288}{xy}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B288%7D%7Bxy%7D)
The surface area is calculated as:
![Area = 2(yz + xz) + xy](https://tex.z-dn.net/?f=Area%20%3D%202%28yz%20%2B%20xz%29%20%2B%20xy)
Because xy represent the dimension of the ceiling and the opposite of the ceiling (the floor) will not be painted. Hence, it does not require a coefficient of 2
The cost is:
![C = 0.06 * 2(yz + xz) + 0.16 * xy](https://tex.z-dn.net/?f=C%20%3D%200.06%20%2A%202%28yz%20%2B%20xz%29%20%2B%200.16%20%2A%20xy)
Substitute ![z = \frac{288}{xy}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B288%7D%7Bxy%7D)
![C = 0.06 * 2(y*\frac{288}{xy} + x*\frac{288}{xy}) + 0.16 * xy](https://tex.z-dn.net/?f=C%20%3D%200.06%20%2A%202%28y%2A%5Cfrac%7B288%7D%7Bxy%7D%20%2B%20x%2A%5Cfrac%7B288%7D%7Bxy%7D%29%20%2B%200.16%20%2A%20xy)
![C = 0.06 * 2(\frac{288}{x} + \frac{288}{y}) + 0.16 * xy](https://tex.z-dn.net/?f=C%20%3D%200.06%20%2A%202%28%5Cfrac%7B288%7D%7Bx%7D%20%2B%20%5Cfrac%7B288%7D%7By%7D%29%20%2B%200.16%20%2A%20xy)
![C = 0.12(\frac{288}{x} + \frac{288}{y}) + 0.16 * xy](https://tex.z-dn.net/?f=C%20%3D%200.12%28%5Cfrac%7B288%7D%7Bx%7D%20%2B%20%5Cfrac%7B288%7D%7By%7D%29%20%2B%200.16%20%2A%20xy)
![C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 * xy](https://tex.z-dn.net/?f=C%20%3D%20%28%5Cfrac%7B34.56%7D%7Bx%7D%20%2B%20%5Cfrac%7B34.56%7D%7By%7D%29%20%2B%200.16%20%2A%20xy)
![C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 xy](https://tex.z-dn.net/?f=C%20%3D%20%28%5Cfrac%7B34.56%7D%7Bx%7D%20%2B%20%5Cfrac%7B34.56%7D%7By%7D%29%20%2B%200.16%20xy)
Differentiate w.r.t x and y
![C_x = -\frac{34.56}{x^2} + 0.16y](https://tex.z-dn.net/?f=C_x%20%3D%20-%5Cfrac%7B34.56%7D%7Bx%5E2%7D%20%2B%200.16y)
![C_y = -\frac{34.56}{y^2} + 0.16x](https://tex.z-dn.net/?f=C_y%20%3D%20-%5Cfrac%7B34.56%7D%7By%5E2%7D%20%2B%200.16x)
By comparison: ![x = y](https://tex.z-dn.net/?f=x%20%3D%20y)
Set them equal to 0
![C_y = -\frac{34.56}{y^2} + 0.16x=0](https://tex.z-dn.net/?f=C_y%20%3D%20-%5Cfrac%7B34.56%7D%7By%5E2%7D%20%2B%200.16x%3D0)
![-\frac{34.56}{y^2} + 0.16x=0\\](https://tex.z-dn.net/?f=-%5Cfrac%7B34.56%7D%7By%5E2%7D%20%2B%200.16x%3D0%5C%5C)
Substitute x for y
![-\frac{34.56}{x^2} + 0.16x=0](https://tex.z-dn.net/?f=-%5Cfrac%7B34.56%7D%7Bx%5E2%7D%20%2B%200.16x%3D0)
![0.16x=\frac{34.56}{x^2}](https://tex.z-dn.net/?f=0.16x%3D%5Cfrac%7B34.56%7D%7Bx%5E2%7D)
Cross multiply
![0.16x^3 = 34.56](https://tex.z-dn.net/?f=0.16x%5E3%20%3D%2034.56)
![x^3 = \frac{34.56}{0.16}](https://tex.z-dn.net/?f=x%5E3%20%3D%20%5Cfrac%7B34.56%7D%7B0.16%7D)
![x^3 = 216](https://tex.z-dn.net/?f=x%5E3%20%3D%20216)
Take the cube root of both sides
![x = \sqrt[3]{216}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%5B3%5D%7B216%7D)
![x = 6](https://tex.z-dn.net/?f=x%20%3D%206)
![x=y= 6](https://tex.z-dn.net/?f=x%3Dy%3D%206)
Substitute 6 for x and for y in ![C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 xy](https://tex.z-dn.net/?f=C%20%3D%20%28%5Cfrac%7B34.56%7D%7Bx%7D%20%2B%20%5Cfrac%7B34.56%7D%7By%7D%29%20%2B%200.16%20xy)
![C = (\frac{34.56}{6} + \frac{34.56}{6}) + 0.16 * 6* 6](https://tex.z-dn.net/?f=C%20%3D%20%28%5Cfrac%7B34.56%7D%7B6%7D%20%2B%20%5Cfrac%7B34.56%7D%7B6%7D%29%20%2B%200.16%20%2A%206%2A%206)
![C = (\frac{2*34.56}{6}) + 5.76](https://tex.z-dn.net/?f=C%20%3D%20%28%5Cfrac%7B2%2A34.56%7D%7B6%7D%29%20%2B%205.76)
![C = 11.52 + 5.76](https://tex.z-dn.net/?f=C%20%3D%2011.52%20%2B%205.76)
![C = 17.28](https://tex.z-dn.net/?f=C%20%3D%2017.28)
--- approximated
In order to find a percentage of a number, you must first put the percentage into decimal form.
5% = 0.05
Then, you can multiply this decimal by the number
30*0.05=1.5
Answer:
20%
Step-by-step explanation:
If we think of the circle as 1, and each piece 1/5, and since we know that 1/5 = 20%, we can conclude that each piece takes up 20% of the circle.