a student found the slope of a line that passes through the points (1,14) and (3,4) to be 5. what mistake did she make?
1 answer:
M = (y2-y1)/(x2-x1)
= (4-14)/3-1
= -10/2
= -5
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Follows are the solution to the given points:
Step-by-step explanation:
Given values:
![P(\frac{D}{A})=0.02 \\\\P(\frac{D}{B})=0.01\\\\P(A)=\frac{10,000}{10,000+2000} =\frac{10}{12} =\frac{5}{6} \\\\P(B)=\frac{1}{6}\\\\](https://tex.z-dn.net/?f=P%28%5Cfrac%7BD%7D%7BA%7D%29%3D0.02%20%5C%5C%5C%5CP%28%5Cfrac%7BD%7D%7BB%7D%29%3D0.01%5C%5C%5C%5CP%28A%29%3D%5Cfrac%7B10%2C000%7D%7B10%2C000%2B2000%7D%20%3D%5Cfrac%7B10%7D%7B12%7D%20%3D%5Cfrac%7B5%7D%7B6%7D%20%5C%5C%5C%5CP%28B%29%3D%5Cfrac%7B1%7D%7B6%7D%5C%5C%5C%5C)
For point a:
![P(D) =p(D\cap A) +P(D \cap B)\\\\](https://tex.z-dn.net/?f=P%28D%29%20%3Dp%28D%5Ccap%20A%29%20%2BP%28D%20%5Ccap%20B%29%5C%5C%5C%5C)
![=P(\frac{D}{A}) \times P(A) + P(\frac{D}{B}) \times P(B)\\\\=0.02 \times \frac{5}{6} + 0.01 \times \frac{1}{6}\\\\=\frac{0.1}{6} + \frac{0.01}{6}\\\\=\frac{0.1+0.01}{6} \\\\=\frac{0.11}{6} \\\\=\frac{11}{600} \\\\=0.0183](https://tex.z-dn.net/?f=%3DP%28%5Cfrac%7BD%7D%7BA%7D%29%20%5Ctimes%20P%28A%29%20%2B%20P%28%5Cfrac%7BD%7D%7BB%7D%29%20%5Ctimes%20P%28B%29%5C%5C%5C%5C%3D0.02%20%5Ctimes%20%5Cfrac%7B5%7D%7B6%7D%20%2B%200.01%20%5Ctimes%20%5Cfrac%7B1%7D%7B6%7D%5C%5C%5C%5C%3D%5Cfrac%7B0.1%7D%7B6%7D%20%2B%20%5Cfrac%7B0.01%7D%7B6%7D%5C%5C%5C%5C%3D%5Cfrac%7B0.1%2B0.01%7D%7B6%7D%20%5C%5C%5C%5C%3D%5Cfrac%7B0.11%7D%7B6%7D%20%5C%5C%5C%5C%3D%5Cfrac%7B11%7D%7B600%7D%20%5C%5C%5C%5C%3D0.0183)
For point b:
![P(\frac{A}{D})= \frac{P(\frac{D}{A}) \times P(A)}{P(D)}\\\\](https://tex.z-dn.net/?f=P%28%5Cfrac%7BA%7D%7BD%7D%29%3D%20%5Cfrac%7BP%28%5Cfrac%7BD%7D%7BA%7D%29%20%5Ctimes%20P%28A%29%7D%7BP%28D%29%7D%5C%5C%5C%5C)
![= \frac{0.02 \times \frac{5}{6}}{\frac{11}{600}}\\\\= \frac{0.02 \times \frac{5}{6}}{0.0183333333}\\\\= \frac{0.02 \times 0.833333333}{0.0183333333}\\\\= \frac{0.0166666667}{0.018}\\\\=0.9090 \approx 0.0991](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B0.02%20%5Ctimes%20%5Cfrac%7B5%7D%7B6%7D%7D%7B%5Cfrac%7B11%7D%7B600%7D%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B0.02%20%5Ctimes%20%5Cfrac%7B5%7D%7B6%7D%7D%7B0.0183333333%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B0.02%20%5Ctimes%200.833333333%7D%7B0.0183333333%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B0.0166666667%7D%7B0.018%7D%5C%5C%5C%5C%3D0.9090%20%5Capprox%200.0991)
For point c:
![P(\frac{A}{D^C})=\frac{P(\frac{D^c}{A}) \times P(A)}{P(D^c)}\\\\](https://tex.z-dn.net/?f=P%28%5Cfrac%7BA%7D%7BD%5EC%7D%29%3D%5Cfrac%7BP%28%5Cfrac%7BD%5Ec%7D%7BA%7D%29%20%5Ctimes%20P%28A%29%7D%7BP%28D%5Ec%29%7D%5C%5C%5C%5C)
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Step-by-step explanation:
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