namely, how many times does 1/4 go into 3/8?
![\bf \cfrac{3}{8}\div \cfrac{1}{4}\implies \cfrac{3}{\underset{2}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot \cfrac{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{1}\implies \cfrac{3}{2}\implies 1\frac{1}{2}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B3%7D%7B8%7D%5Cdiv%20%5Ccfrac%7B1%7D%7B4%7D%5Cimplies%20%5Ccfrac%7B3%7D%7B%5Cunderset%7B2%7D%7B~~%5Cbegin%7Bmatrix%7D%208%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%7D%7D%5Ccdot%20%5Ccfrac%7B~~%5Cbegin%7Bmatrix%7D%204%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%7D%7B1%7D%5Cimplies%20%5Ccfrac%7B3%7D%7B2%7D%5Cimplies%201%5Cfrac%7B1%7D%7B2%7D)
Answer:
Part A:

Part B:

Step-by-step explanation:
Part A:
The number of rivets=22 rivets
Probability that no rivet is defective= (1-p)^22
The probability that at least one rivet is defective=1-(1-p)^22
For 19% of all seams need reworking, probability that a rivet is defective is given by:

![(1-p)^{22}=0.81\\p=1-\sqrt[22]{0.81} \\p=0.0095](https://tex.z-dn.net/?f=%281-p%29%5E%7B22%7D%3D0.81%5C%5Cp%3D1-%5Csqrt%5B22%5D%7B0.81%7D%20%5C%5Cp%3D0.0095)
Part B:
For 9% of all seams need reworking, probability of a defective rivet is:
![1-(1-p)^{22}=0.09\\p=1-\sqrt[22]{0.91} \\p=0.0043](https://tex.z-dn.net/?f=1-%281-p%29%5E%7B22%7D%3D0.09%5C%5Cp%3D1-%5Csqrt%5B22%5D%7B0.91%7D%20%5C%5Cp%3D0.0043)
Answer:
0.42
Step-by-step explanation:
<3
Using the De Moivre's Theorem, let us work out for the fourth roots of 81(cos 320° + i sin 320° ).
zⁿ = rⁿ (cos nθ + i sin nθ)
z⁴ = 81(cos 320° + i sin 320° )
z = ∜[81(cos 320° + i sin 320° )]
= ∜[3^4 (cos 4*80° + i sin 4*80°)]
= 3(cos 80° + i sin 80°)
<span> </span>
Step-by-step explanation:
