So you have 9x-10 and x= -5
9(-5)-10
-45-10= -55
Your answer would be -55
45n+15
Factor out 15 from the expression
15(3n+1)
Use Square of Sum: (a + b)^2 = a^2 + 2ab + b^2
b^2 + 2b * 12 + 12^2
Simplify 12^2 to 144
b^2 + 2b * 12 + 144
Simplify 2b * 12 to 24b
b^2 + 24b + 144
Answer:
A. 1/4,389
B. 728/4,389
Step-by-step explanation:
Total number of flanges = 22
Defective flanges = 6
Non-defective flanges = 16
A. The probability that all in the sample are defective is given by:
![P(d=5)=\frac{6}{22}*\frac{5}{21}*\frac{4}{20}*\frac{3}{19} *\frac{2}{18}\\P(d=5)=\frac{1}{11}*\frac{1}{7}*\frac{1}{1}*\frac{1}{19} *\frac{1}{3}\\P(d=5)=\frac{1}{4,389}](https://tex.z-dn.net/?f=P%28d%3D5%29%3D%5Cfrac%7B6%7D%7B22%7D%2A%5Cfrac%7B5%7D%7B21%7D%2A%5Cfrac%7B4%7D%7B20%7D%2A%5Cfrac%7B3%7D%7B19%7D%20%2A%5Cfrac%7B2%7D%7B18%7D%5C%5CP%28d%3D5%29%3D%5Cfrac%7B1%7D%7B11%7D%2A%5Cfrac%7B1%7D%7B7%7D%2A%5Cfrac%7B1%7D%7B1%7D%2A%5Cfrac%7B1%7D%7B19%7D%20%2A%5Cfrac%7B1%7D%7B3%7D%5C%5CP%28d%3D5%29%3D%5Cfrac%7B1%7D%7B4%2C389%7D)
The probability is 1/4,389.
B. The probability that none in the sample are defective is given by:
![P(d=0)=\frac{16}{22}*\frac{15}{21}*\frac{14}{20}*\frac{13}{19} *\frac{12}{18}\\P(d=0)=\frac{4}{11}*\frac{1}{7}*\frac{7}{1}*\frac{13}{19} *\frac{2}{3}\\P(d=0)=\frac{728}{4,389}](https://tex.z-dn.net/?f=P%28d%3D0%29%3D%5Cfrac%7B16%7D%7B22%7D%2A%5Cfrac%7B15%7D%7B21%7D%2A%5Cfrac%7B14%7D%7B20%7D%2A%5Cfrac%7B13%7D%7B19%7D%20%2A%5Cfrac%7B12%7D%7B18%7D%5C%5CP%28d%3D0%29%3D%5Cfrac%7B4%7D%7B11%7D%2A%5Cfrac%7B1%7D%7B7%7D%2A%5Cfrac%7B7%7D%7B1%7D%2A%5Cfrac%7B13%7D%7B19%7D%20%2A%5Cfrac%7B2%7D%7B3%7D%5C%5CP%28d%3D0%29%3D%5Cfrac%7B728%7D%7B4%2C389%7D)
The probability is 728/4,389.