Answer:
The Laplace transform of f(t) = 1 is given by
F(s) = (1/s) for all s>0
Step-by-step explanation:
Laplace transform of a function f(t) is given as
F(s) = ∫∞₀ f(t) e⁻ˢᵗ dt
Find the Laplace transform for when f(t) = 1
F(s) = ∫∞₀ 1.e⁻ˢᵗ dt
F(s) = ∫∞₀ e⁻ˢᵗ dt = (1/s) [-e⁻ˢᵗ]∞₀
= -(1/s) [1/eˢᵗ]∞₀
Note that e^(∞) = ∞
F(s) = -(1/s) [(1/∞) - (1/e⁰)]
Note that (1/∞) = 0
F(s) = -(1/s) [0 - 1] = -(1/s) (-1) = (1/s)
Hope this Helps!!!
These are the events in the question above:
<span>D - has disease
</span>
<span>H - healthy (does not have disease)
</span>
<span>P - tests positive </span>
<span>It is the probability that a person has the disease AND tests positive divided by the probability that the person tests positive.
</span>
Sick, + [.04*.91] = .0364
<span>Sick, - [.04*.09] = .0036 </span>
Healthy, + [.96*.04] = 0.0384
<span>Healthy, - [.96*.96] = .9216
</span>
.0364 / (.0364 + .0.0384) = 0.487
Answer:
The correct option is C.
Step-by-step explanation:
The quadratic parent function is
The translation is defined as
.... (1)
Where, k is vertical stretch, a is horizontal shift and b is vertical shift.
If |k|>1, then graph of parent function stretch vertically by factor |k| and if 0<|k|<1, then parent function compressed vertically by factor |k|. Negative k represents the reflection across x axis.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
The graph shift 1 unit right,vertically stretch by a factor of 5 , reflect over the x-axis. So, a=-1, |k|=5 and k=-5
Substitute a=-1 and k=5 in equation (1).
Therefore the correct option is C.
Perimeter of a rectangle:
P = 2(l + w)
Plug in what we know:
P = 2(16 + 7)
Add:
P = 2(23)
Multiply:
P = 46
Now find the perimeter of the semi-circle.
Perimeter of a circle:
P = pi * d
Plug in what we know:
P = 3.14 * 16
Multiply:
P = 50.24
Divide by 2 since it's a semi-circle:
50.24 / 2 = 25.12
Add the two perimeters:
46 + 25.12 = 71.12