Replace all x's with 4's in the function:
![f(4) = \frac{1}{3} \times {4}^{4}](https://tex.z-dn.net/?f=f%284%29%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%5Ctimes%20%20%7B4%7D%5E%7B4%7D%20)
Simplify/solve.
![= \frac{1}{3} \times 256](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%5Ctimes%20256)
![= \frac{256}{3}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B256%7D%7B3%7D%20)
So, the answer is C.
Answer:
1.26 m^2 / s.
Step-by-step explanation:
The area A of the triangle = 1/2*7*12 sin x = 42 sin x where x is the angle between the lines.
Relation between the rates is
dA/dt + dA/dx * dx/dt
We are given that dx /dt = 0.06 rad/s.
A = 42 sin x
dA/dx = 42 cos x
So dA/dt = 42 cos x * 0.06
When x = π/3 ( I am assuming that π 3 means π divided by 3 ):
dA/dt = 42 cos π/3 * 0.06
= 1.26 m^2/s.
Answer:
The answer is 686 but I coukd be wrong.
Answer:
Time taken for the ball to hit the ground back = 3.08 s
Step-by-step explanation:
h(t)= -16t² + 48t + 4
when will rhe object come back to hit rhe ground?
When the ball is at the level.of the ground, h(t) = 0.
0 = -16t² + 48t + 4
-16t² + 48t + 4 = 0
Solving the quadratic equation
t = 3.08 s or t = -0.08 s
Since the time cannot be negative,
Time taken for the ball to hit the ground back = 3.08 s
Hope this Helps!!!
Step-by-step explanation:
Answer:
<em>P= 0.0606 = 60.6%</em>
Step-by-step explanation:
<u>Binomial Distribution
</u>
The required probability will be calculated by using the Binomial Distribution with n=385 independent events each with a probability of success equal to p=0.0362 with k=8 or fewer successes.
The PMF (Probability Mass Function) for the Binomial Distribution is
![\displaystyle B(k,n,p)=\binom{n}{k}p^kq^{n-k}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20B%28k%2Cn%2Cp%29%3D%5Cbinom%7Bn%7D%7Bk%7Dp%5Ekq%5E%7Bn-k%7D)
Where
![q = 1-p=0.9638](https://tex.z-dn.net/?f=q%20%3D%201-p%3D0.9638)
We need to compute a range of probabilities from k=8 to k=0. We'll show how to compute for k=8
![\displaystyle B(8,385,0.0362)=\binom{385}{8}0.0362^8\ 0.9638^{377}=0.03014](https://tex.z-dn.net/?f=%5Cdisplaystyle%20B%288%2C385%2C0.0362%29%3D%5Cbinom%7B385%7D%7B8%7D0.0362%5E8%5C%200.9638%5E%7B377%7D%3D0.03014)
When the probability is cumulative and a high number of calculations need to be performed, we use automated tools (like Excel, digital calculator, etc) to compute the sum. We used Excel's BINOMDIST(8, 385, 0.0362, 1) function to get the total probability to get
![\boxed{P=0.0606 = 60.6\%}](https://tex.z-dn.net/?f=%5Cboxed%7BP%3D0.0606%20%3D%2060.6%5C%25%7D)