<span>The probability that a house in an urban area will develop a leak is 55%. if 20 houses are randomly selected, what is the probability that none of the houses will develop a leak? round to the nearest thousandth.
Use binomial distribution, since probability of developing a leak, p=0.55 is assumed constant, and
n=20, x=0
and assuming leaks are developed independently between houses,
P(X=x)
=C(n,0)p^x* (1-p)^(n-x)
=C(20,0)0.55^0 * (0.45^20)
=1*1*0.45^20
=1.159*10^(-7)
=0.000
</span>
Answer:
791.68 cm/s
Step-by-step explanation:
The volume flow rate can be interpreted as the integral of fluid velocity over area
![\dot{V} = \int\limits^6_0 {v(r) 2\pi r} \, dr\\\dot{V} = 2\pi\int\limits^6_0 {(25-r^2)r} \, dr\\\dot{V} = 2\pi\int\limits^6_0 {25r-r^3} \, dr\\\\\dot{V} = 2\pi[12.5r^2 - r^4/4]_0^6\\\dot{V} = 2\pi(12.5*6^2 - 6^4/4 - 12.5*0 - 0)\\\dot{V} = 2\pi*126 = 791.68 cm/s](https://tex.z-dn.net/?f=%5Cdot%7BV%7D%20%3D%20%5Cint%5Climits%5E6_0%20%7Bv%28r%29%202%5Cpi%20r%7D%20%5C%2C%20dr%5C%5C%5Cdot%7BV%7D%20%3D%202%5Cpi%5Cint%5Climits%5E6_0%20%7B%2825-r%5E2%29r%7D%20%5C%2C%20dr%5C%5C%5Cdot%7BV%7D%20%3D%202%5Cpi%5Cint%5Climits%5E6_0%20%7B25r-r%5E3%7D%20%5C%2C%20dr%5C%5C%5C%5C%5Cdot%7BV%7D%20%3D%202%5Cpi%5B12.5r%5E2%20-%20r%5E4%2F4%5D_0%5E6%5C%5C%5Cdot%7BV%7D%20%3D%202%5Cpi%2812.5%2A6%5E2%20-%206%5E4%2F4%20-%2012.5%2A0%20-%200%29%5C%5C%5Cdot%7BV%7D%20%3D%202%5Cpi%2A126%20%3D%20791.68%20cm%2Fs)
I agree with him that’s the answer
The reflection will be on the other side of the y-axis.
Its coordinates will be (3, 7).
Answer:
Surface area of cylinder= 211.5π
Step-by-step explanation:
Given,
Height of cylinder = 19cm
Diameter of cylinder = 9cm
i.e Radius of cylinder = diameter/2 = 9/2 = 4.5cm
Surface area of cylinder = 2πrh + 2πr²
Plug corresponding values of r and h in surface are formula.
Surface area of cylinder = 2πrh + 2πr² = 2π*4.5*19 + 2π*4.5²
Surface area of cylinder = 171π+40.5π = 211.5π
Hence we get surface area of cylinder= 211.5π
