We can calculate (62 + 90) / 2 = 76. it's <span>known that 95% lies between the mean and twice the standard deviation. </span><span>if the mean is "μ" and the standard deviation is "σ": </span><span>μ-2σ and μ+2σ. i</span><span>f μ=76, then </span><span>76+2σ = 90, so 2σ = 14, so σ = 7.
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<span>the mean is 76 and the standard deviation 7. </span>
For the given function f(t) = (2t + 1) using definition of Laplace transform the required solution is L(f(t))s = [ ( 2/s²) + ( 1/s) ].
As given in the question,
Given function is equal to :
f(t) = 2t + 1
Simplify the given function using definition of Laplace transform we have,
L(f(t))s = 
= ![\int\limits^\infty_0[2t +1] e^{-st} dt](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%5Cinfty_0%5B2t%20%2B1%5D%20e%5E%7B-st%7D%20dt)
= 
= 2 L(t) + L(1)
L(1) = 
= (-1/s) ( 0 -1 )
= 1/s , ( s > 0)
2L ( t ) = 
= ![2[t\int\limits^\infty_0 e^{-st} - \int\limits^\infty_0 ({(d/dt)(t) \int\limits^\infty_0e^{-st} \, dt )dt]](https://tex.z-dn.net/?f=2%5Bt%5Cint%5Climits%5E%5Cinfty_0%20e%5E%7B-st%7D%20-%20%5Cint%5Climits%5E%5Cinfty_0%20%28%7B%28d%2Fdt%29%28t%29%20%5Cint%5Climits%5E%5Cinfty_0e%5E%7B-st%7D%20%5C%2C%20dt%20%29dt%5D)
= 2/ s²
Now ,
L(f(t))s = 2 L(t) + L(1)
= 2/ s² + 1/s
Therefore, the solution of the given function using Laplace transform the required solution is L(f(t))s = [ ( 2/s²) + ( 1/s) ].
Learn more about Laplace transform here
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Answer:
18/21 = 30/35
Step-by-step explanation:
so the problem says 18/21 so if that's the correct ratio to proportion to the answer would be. 30/35. the reason is that you can divide 18 and 21 by 3 to get 6/7 then if you multiply by 5 you get 30/35. Dividing and multiplying both the denominator and numerator keeps the ratio proportional.
Answer:
BD = 16
Step-by-step explanation:
32/BD = BD/8
BD² = 256
BD = 16
Are you trying to write an equation?
y-8=2(x-3)
y=2x-6+8
y=2x+2
