Answer:
i think it is AAAAA
Step-by-step explanation:
Case 1: Probabilities cannot add up to a number greater (or less) than 1. This would mean there is greater than a 100% chance of something happening which just doesn't make sense. 0.4 + 0.4 + 0.3 = 1,1
Case 2: You cannot have a negative probability. That is claiming that there is a -10% chance of an event happening, there is at the very least a 0%. Despite them "adding" up to 1, the negative probability makes no sense.
Hope I helped!
Your answer is B F(x) * (0.5)^x
(d) The particle moves in the positive direction when its velocity has a positive sign. You know the particle is at rest when
and
, and because the velocity function is continuous, you need only check the sign of
for values on the intervals (0, 3) and (3, 6).
We have, for instance
and
, which means the particle is moving the positive direction for
, or the interval (3, 6).
(e) The total distance traveled is obtained by integrating the absolute value of the velocity function over the given interval:
![\displaystyle\int_0^6|v(t)|\,\mathrm dt=\int_0^3-v(t)\,\mathrm dt+\int_3^6v(t)\,\mathrm dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_0%5E6%7Cv%28t%29%7C%5C%2C%5Cmathrm%20dt%3D%5Cint_0%5E3-v%28t%29%5C%2C%5Cmathrm%20dt%2B%5Cint_3%5E6v%28t%29%5C%2C%5Cmathrm%20dt)
which follows from the definition of absolute value. In particular, if
is negative, then
.
The total distance traveled is then 4 ft.
(g) Acceleration is the rate of change of velocity, so
is the derivative of
:
![a(t)=v'(t)=-\dfrac{\pi^2}9\cos\left(\dfrac{\pi t}3\right)](https://tex.z-dn.net/?f=a%28t%29%3Dv%27%28t%29%3D-%5Cdfrac%7B%5Cpi%5E2%7D9%5Ccos%5Cleft%28%5Cdfrac%7B%5Cpi%20t%7D3%5Cright%29)
Compute the acceleration at
seconds:
![a(t)=\dfrac{\pi^2}{18}\dfrac{\rm ft}{\mathrm s^2}](https://tex.z-dn.net/?f=a%28t%29%3D%5Cdfrac%7B%5Cpi%5E2%7D%7B18%7D%5Cdfrac%7B%5Crm%20ft%7D%7B%5Cmathrm%20s%5E2%7D)
(In case you need to know, for part (i), the particle is speeding up when the acceleration is positive. So this is done the same way as part (d).)