Help I only have 15 minutes -2 = 12x + 22
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Answer:
The z score for bolt of diameter 18.12 mm is 1.20.
Step-by-step explanation:
Let <em>X</em> = diameter of bolts.
It is provided that the random variable <em>X</em> follows a Normal distribution with mean, <em>μ</em> = 18 mm and standard deviation, <em>σ</em> = 0.10 mm.
A <em>z</em>-score is a standardized score, a numerical, that defines how far a data value from the mean.
The distribution of <em>z</em>-scores is defined by the Standard Normal distribution.
The formula to compute the <em>z</em>-score is:
The value of the diameter of a bolt is, <em>x</em> = 18.12 mm.
Compute the <em>z</em>-score for this value as follows:
Thus, the z score for bolt of diameter 18.12 mm is 1.20.
Answers
b = 2.77 m
A = 43.0°
C = 111.1°
cosine law to find b
b = 2.7708\ m
Find angle A with sine law
![\displaystyle \frac{\sin A}{a} = \frac{\sin B}{b} \\ \\ \sin A = \frac{a \sin B}{b} \\ \\ A = \sin^{-1} \left[ \frac{a \sin B}{b} \right] \\ \\ A = \sin^{-1} \left[ \frac{4.33 \sin 25.9}{2.7708} \right] \\ \\ A = 43.0467020](https://tex.z-dn.net/?f=%5Cdisplaystyle%0A%5Cfrac%7B%5Csin%20A%7D%7Ba%7D%20%3D%20%5Cfrac%7B%5Csin%20B%7D%7Bb%7D%20%5C%5C%20%5C%5C%0A%5Csin%20A%20%3D%20%5Cfrac%7Ba%20%5Csin%20B%7D%7Bb%7D%20%5C%5C%20%5C%5C%0AA%20%3D%20%5Csin%5E%7B-1%7D%20%5Cleft%5B%20%5Cfrac%7Ba%20%5Csin%20B%7D%7Bb%7D%20%20%5Cright%5D%20%5C%5C%20%5C%5C%0AA%20%3D%20%5Csin%5E%7B-1%7D%20%5Cleft%5B%20%5Cfrac%7B4.33%20%5Csin%2025.9%7D%7B2.7708%7D%20%20%5Cright%5D%20%20%5C%5C%20%5C%5C%0AA%20%3D%2043.0467020)
Find C with angles in triangle sum to 180
A + B + C = 180
C = 180 - A - B
C = 180 - 43.0467020 - 25.9
C = 111.1
b = 2.77 m
A = 43.0°
C = 111.1°
cosine law to find b
b = 2.7708\ m
Find angle A with sine law
Find C with angles in triangle sum to 180
A + B + C = 180
C = 180 - A - B
C = 180 - 43.0467020 - 25.9
C = 111.1