6 is the greatest common factor of 30 and 66, because 6(5+11)
Answer:
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Step-by-step explanation:
Answer:
The lower bound of a 99% C.I for the proportion of defectives = 0.422
Step-by-step explanation:
From the given information:
The point estimate = sample proportion ![\hat p](https://tex.z-dn.net/?f=%5Chat%20p)
![\hat p = \dfrac{x}{n}](https://tex.z-dn.net/?f=%5Chat%20p%20%3D%20%5Cdfrac%7Bx%7D%7Bn%7D)
![\hat p = \dfrac{55}{100}](https://tex.z-dn.net/?f=%5Chat%20p%20%3D%20%5Cdfrac%7B55%7D%7B100%7D)
= 0.55
At Confidence interval of 99%, the level of significance = 1 - 0.99
= 0.01
![Z_{\alpha/2} =Z_{0.01/2} \\ \\ = Z_{0.005} = 2.576](https://tex.z-dn.net/?f=Z_%7B%5Calpha%2F2%7D%20%3DZ_%7B0.01%2F2%7D%20%5C%5C%20%5C%5C%20%3D%20Z_%7B0.005%7D%20%3D%202.576)
Then the margin of error ![E = Z_{\alpha/2} \times \sqrt{\dfrac{\hat p(1-\hat p)}{n}}](https://tex.z-dn.net/?f=E%20%3D%20Z_%7B%5Calpha%2F2%7D%20%5Ctimes%20%5Csqrt%7B%5Cdfrac%7B%5Chat%20p%281-%5Chat%20p%29%7D%7Bn%7D%7D)
![E = 2.576 \times \sqrt{\dfrac{0.55(1-0.55)}{100}}](https://tex.z-dn.net/?f=E%20%3D%202.576%20%5Ctimes%20%5Csqrt%7B%5Cdfrac%7B0.55%281-0.55%29%7D%7B100%7D%7D)
![E = 2.576 \times \sqrt{\dfrac{0.2475}{100}}](https://tex.z-dn.net/?f=E%20%3D%202.576%20%5Ctimes%20%5Csqrt%7B%5Cdfrac%7B0.2475%7D%7B100%7D%7D)
![E = 2.576 \times0.04975](https://tex.z-dn.net/?f=E%20%3D%202.576%20%5Ctimes0.04975)
E = 0.128156
E ≅ 0.128
At 99% C.I for the population proportion p is: ![\hat p - E](https://tex.z-dn.net/?f=%5Chat%20p%20-%20E)
= 0.55 - 0.128
= 0.422
Thus, the lower bound of a 99% C.I for the proportion of defectives = 0.422
Angle A = 3x - 10
Angle B = x
Their angle sum = 90° ( complementary angles form 90° )
This can be written in an equation as =
= 3x - 10 + x = 90
= 3x + × + ( -10 ) = 90
= 4x + (-10) = 90
= 4x = 90 + 10 ( transposing-10 from LHS to RHS changes-10 to +10 )
= 4x = 100
= x = 100 ÷ 4 ( transposing ×4 from LHS to RHS changes ×4 to ÷4 )
= x = 25
Angle A = 3x - 10
= 3 × 25 - 10
= 75 - 10
= Angle A = 65°
Angle B = x = 25°
Their sum = 65 + 25 = 90°
Therefore , the complementary angles , Angle A = 65° and Angle B = 25° .