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3 years ago

you pick a number between 1,000 and 5,000 then you flip a coin identify if the two events are independent or dependent explain

Mathematics

2 answers:

Lelu [443]3 years ago

7 0

Independent one has nothing to with the other

Mariana [72]3 years ago

6 0

Answer with Step-by-step explanation:

Events A and B are said to be independent if:

P(A∩B)=P(A)×P(B)

A:Picking a number between 1000 and 5000

B:flipping a coin

P(A)=1/4001

P(B)=1

P(A∩B)=1/4001

=P(A)×P(B)

Hence, the two events are independent

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Consider the differential equation:

Wewaii [24]

(a) Take the Laplace transform of both sides:

$2y''(t)+ty'(t)-2y(t)=14$

$\implies 2(s^2Y(s)-sy(0)-y'(0))-(Y(s)+sY'(s))-2Y(s)=\dfrac{14}s$

where the transform of $ty'(t)$ comes from

$L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)$

This yields the linear ODE,

$-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s$

Divides both sides by $-s$ :

$Y'(s)+\dfrac{3-2s^2}sY(s)=-\dfrac{14}{s^2}$

Find the integrating factor:

$\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C$

Multiply both sides of the ODE by $e^{3\ln|s|-s^2}=s^3e^{-s^2}$ :

$s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}$

The left side condenses into the derivative of a product:

$\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}$

Integrate both sides and solve for $Y(s)$ :

$s^3e^{-s^2}Y(s)=7e^{-s^2}+C$

$Y(s)=\dfrac{7+Ce^{s^2}}{s^3}$

(b) Taking the inverse transform of both sides gives

$y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]$

I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that $\frac{7t^2}2$ is one solution to the original ODE.

$y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7$

Substitute these into the ODE to see everything checks out:

$2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14$

5 0

3 years ago

The measure of an angle is 60° less than nineteen times the measure of its supplement. what is the measure of the angle?

DerKrebs [107]

Two angles are supplementary when they add up to 180 degrees.

x = angle
19x-60 = supplement angle

x + 19x - 60 = 180
20x = 180 + 60
20x = 240
x = 240/20
x = 12° ← answer

3 0

3 years ago

Plsssss help before it gets locked

ddd [48]

A. Is answer F

B. Could be E or F

5 0

2 years ago

Read 2 more answers

Find the domain of the function. (enter your answer using interval notation.) f(x) = x + 3 if x < −1 −2x if |x| ≤ 1 −2 if x &

Ivenika [448]

The domain of the function is the union of all of the "if" parts of the function definition:

... (-∞, -1) ∪ [-1, 1] ∪ (1, ∞) = (-∞, ∞)