Answer:
c
Step-by-step explanation:
Hi, thank you for posting your question here at Brainly.
Since the hedge is surrounding the square base, the area of the base can be determined by subtracting the area of the base from the hedge.
A = pi*r^2 - (4x)^2
A = pi*(6x)^2 - (4x)^2
A = 2x^2*(3pi - 2)
I hope I was able to answer your question. Have a good day.
Answer:
a. P(X = 0) = 0.02586
b. 
c. 
Step-by-step explanation:
From the given information:
a. If the manufacturer stocks 120 components, what is the probability that the 120 orders can be filled without reordering components?


P(X = 0) = 1 × 1 ( 0.97)¹²⁰ ⁻ ⁰
P(X = 0) = 0.02586
b. ) If the manufacturer stocks 122 components, what is the probability that the 120 orders can be filled without reordering components?
![P(X \leq 2 ) = [ P(X=0) + P(X =1) + P(X = 2) ]](https://tex.z-dn.net/?f=P%28X%20%5Cleq%202%20%29%20%3D%20%5B%20P%28X%3D0%29%20%2B%20P%28X%20%3D1%29%20%2B%20P%28X%20%3D%202%29%20%5D)
![P(X \leq 2 ) = [(^{122}_{0})(0.03)^0 (0.97)^{122-0}+(^{122}_{1})(0.03)^1 (0.97)^{122-1}+(^{122}_{2})(0.03)^2 (0.97)^{122-2}]](https://tex.z-dn.net/?f=P%28X%20%5Cleq%202%20%29%20%3D%20%5B%28%5E%7B122%7D_%7B0%7D%29%280.03%29%5E0%20%280.97%29%5E%7B122-0%7D%2B%28%5E%7B122%7D_%7B1%7D%29%280.03%29%5E1%20%20%280.97%29%5E%7B122-1%7D%2B%28%5E%7B122%7D_%7B2%7D%29%280.03%29%5E2%20%280.97%29%5E%7B122-2%7D%5D)
![P(X \leq 2 ) = [\dfrac{122!}{0!(122-0)! } \times 1 \times (0.97)^{122}+\dfrac{122!}{1!(122-1)! } \times (0.03) (0.97)^{121}+\dfrac{122!}{2!(122-2)! } \times 9 \times 10^{-4} \times (0.97)^{120}]](https://tex.z-dn.net/?f=P%28X%20%5Cleq%202%20%29%20%3D%20%5B%5Cdfrac%7B122%21%7D%7B0%21%28122-0%29%21%20%7D%20%5Ctimes%201%20%5Ctimes%20%20%280.97%29%5E%7B122%7D%2B%5Cdfrac%7B122%21%7D%7B1%21%28122-1%29%21%20%7D%20%5Ctimes%20%280.03%29%20%20%280.97%29%5E%7B121%7D%2B%5Cdfrac%7B122%21%7D%7B2%21%28122-2%29%21%20%7D%20%5Ctimes%209%20%5Ctimes%2010%5E%7B-4%7D%20%5Ctimes%20%280.97%29%5E%7B120%7D%5D)
![P(X \leq 2 ) = [(1 \times 1 \times 0.02433 )+(122 \times (0.03) \times 0.025083)+(7381 \times 9 \times 10^{-4} \times 0.02586)]](https://tex.z-dn.net/?f=P%28X%20%5Cleq%202%20%29%20%3D%20%5B%281%20%5Ctimes%20%201%20%5Ctimes%20%200.02433%20%29%2B%28122%20%5Ctimes%20%280.03%29%20%20%5Ctimes%200.025083%29%2B%287381%20%5Ctimes%209%20%5Ctimes%2010%5E%7B-4%7D%20%5Ctimes%200.02586%29%5D)

(c) If the manufacturer stocks 125 components, what is the probability that the 120 orders can be filled without reordering components?
![P(X \leq 5 ) = [ P(X=0) + P(X =1) + P(X = 2) +P(X = 3)+P(X = 4)+ P(X = 5) ]](https://tex.z-dn.net/?f=P%28X%20%5Cleq%205%20%29%20%3D%20%5B%20P%28X%3D0%29%20%2B%20P%28X%20%3D1%29%20%2B%20P%28X%20%3D%202%29%20%20%2BP%28X%20%3D%203%29%2BP%28X%20%3D%204%29%2B%20P%28X%20%3D%205%29%20%20%20%20%5D)
![P(X \leq 5 ) = [(^{122}_{0})(0.03)^0 (0.97)^{122-0}+(^{122}_{1})(0.03)^1 (0.97)^{122-1}+(^{122}_{2})(0.03)^2 (0.97)^{122-2} + (^{122}_{3})(0.03)^3 (0.97)^{122-3} + (^{122}_{4})(0.03)^4 (0.97)^{122-4}+ (^{122}_{5})(0.03)^5 (0.97)^{122-5}]](https://tex.z-dn.net/?f=P%28X%20%5Cleq%205%20%29%20%3D%20%5B%28%5E%7B122%7D_%7B0%7D%29%280.03%29%5E0%20%280.97%29%5E%7B122-0%7D%2B%28%5E%7B122%7D_%7B1%7D%29%280.03%29%5E1%20%20%280.97%29%5E%7B122-1%7D%2B%28%5E%7B122%7D_%7B2%7D%29%280.03%29%5E2%20%280.97%29%5E%7B122-2%7D%20%2B%20%28%5E%7B122%7D_%7B3%7D%29%280.03%29%5E3%20%280.97%29%5E%7B122-3%7D%20%2B%20%28%5E%7B122%7D_%7B4%7D%29%280.03%29%5E4%20%280.97%29%5E%7B122-4%7D%2B%20%28%5E%7B122%7D_%7B5%7D%29%280.03%29%5E5%20%280.97%29%5E%7B122-5%7D%5D)
![P(X \leq 5 ) = [\dfrac{122!}{0!(122-0)! } \times 1 \times (0.97)^{122}+\dfrac{122!}{1!(122-1)! } \times (0.03) (0.97)^{121}+\dfrac{122!}{2!(122-2)! } \times 9 \times 10^{-4} \times (0.97)^{120} + \dfrac{122!}{3!(122-3)! }*(0.03)^3(0.97)^{122-3)}+ \dfrac{122!}{4!(122-4)! }*(0.03)^4(0.97)^{122-4)} +\dfrac{122!}{5!(122-5)! } *(0.03)^5(0.97)^{122-5)}]](https://tex.z-dn.net/?f=P%28X%20%5Cleq%205%20%29%20%3D%20%5B%5Cdfrac%7B122%21%7D%7B0%21%28122-0%29%21%20%7D%20%5Ctimes%201%20%5Ctimes%20%20%280.97%29%5E%7B122%7D%2B%5Cdfrac%7B122%21%7D%7B1%21%28122-1%29%21%20%7D%20%5Ctimes%20%280.03%29%20%20%280.97%29%5E%7B121%7D%2B%5Cdfrac%7B122%21%7D%7B2%21%28122-2%29%21%20%7D%20%5Ctimes%209%20%5Ctimes%2010%5E%7B-4%7D%20%5Ctimes%20%280.97%29%5E%7B120%7D%20%2B%20%5Cdfrac%7B122%21%7D%7B3%21%28122-3%29%21%20%7D%2A%280.03%29%5E3%280.97%29%5E%7B122-3%29%7D%2B%20%5Cdfrac%7B122%21%7D%7B4%21%28122-4%29%21%20%7D%2A%280.03%29%5E4%280.97%29%5E%7B122-4%29%7D%20%2B%5Cdfrac%7B122%21%7D%7B5%21%28122-5%29%21%20%7D%20%2A%280.03%29%5E5%280.97%29%5E%7B122-5%29%7D%5D)

Answer:
x=11
Step-by-step explanation: