Answer:
Therefore the Last option is correct
![\textrm{Area of Sector ACD}=\pi (8\ in)^{2}\times (\frac{42}{360})](https://tex.z-dn.net/?f=%5Ctextrm%7BArea%20of%20Sector%20ACD%7D%3D%5Cpi%20%288%5C%20in%29%5E%7B2%7D%5Ctimes%20%28%5Cfrac%7B42%7D%7B360%7D%29)
Step-by-step explanation:
Given:
Radius = r = 8 in
θ = 42°
To Find:
Area of Sector = ?
Solution:
We know that
![\textrm{Area of Sector}=\pi (Radius)^{2}\times \frac{\theta}{360}](https://tex.z-dn.net/?f=%5Ctextrm%7BArea%20of%20Sector%7D%3D%5Cpi%20%28Radius%29%5E%7B2%7D%5Ctimes%20%5Cfrac%7B%5Ctheta%7D%7B360%7D)
Substituting the given values in the formula we get
![\textrm{Area of Sector ACD}=\pi (8\ in)^{2}\times (\frac{42}{360})](https://tex.z-dn.net/?f=%5Ctextrm%7BArea%20of%20Sector%20ACD%7D%3D%5Cpi%20%288%5C%20in%29%5E%7B2%7D%5Ctimes%20%28%5Cfrac%7B42%7D%7B360%7D%29)
Which is the required Answer.
Therefore the Last option is correct
![\textrm{Area of Sector ACD}=\pi (8\ in)^{2}\times (\frac{42}{360})](https://tex.z-dn.net/?f=%5Ctextrm%7BArea%20of%20Sector%20ACD%7D%3D%5Cpi%20%288%5C%20in%29%5E%7B2%7D%5Ctimes%20%28%5Cfrac%7B42%7D%7B360%7D%29)
Answer:
6e+7
Step-by-step explanation:
divide the volume value by 1e+6
Answer:
0.6173 = 61.73% probability that the product operates.
Step-by-step explanation:
For each integrated circuit, there are only two possible outcomes. Either they are defective, or they are not. The integrated circuits are independent. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
And p is the probability of X happening.
An electronic product contains 48 integrated circuits.
This means that ![n = 48](https://tex.z-dn.net/?f=n%20%3D%2048)
The probability that any integrated circuit is defective is 0.01.
This means that ![p = 0.01](https://tex.z-dn.net/?f=p%20%3D%200.01)
The product operates only if there are no defective integrated circuits. What is the probability that the product operates?
This is P(X = 0). So
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 0) = C_{48,0}.(0.01)^{0}.(0.99)^{48} = 0.6173](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20C_%7B48%2C0%7D.%280.01%29%5E%7B0%7D.%280.99%29%5E%7B48%7D%20%3D%200.6173)
0.6173 = 61.73% probability that the product operates.
Answer:
She should order 12 pizzas.
Step-by-step explanation:
5 pizza for every 20 students gives us the ratio 5:20.
5/20 = 0.25 = the amount of pizza each student gets.
If there are 48 students, you would just multiply 0.25 * 48 to get your answer.