Answer:
The common ratio is 1.2.
After 12 weeks the plant will be 4.46 meters long.
After one year the plant will be 6,552.32 meters long.
Step-by-step explanation:
Given that a marrow plants 0.5 m long and every week it grows by 20%, to find the value of the common ratio, calculate how long the plant is after 12 weeks and comment on the predicted length of the marrow after one year must be performed the following calculations:
0.50 x 1.2 ^ X = Y
Therefore, the common ratio is 1.2.
0.50 x 1.2 ^ 12 = Y
0.50 x 8.916 = Y
4.4580 = Y
Therefore, after 12 weeks the plant will be 4.46 meters long.
0.50 x 1.2 ^ 52 = Y
0.50 x 13,104.63 = Y
6,552.32 = Y
Therefore, after one year the plant will be 6,552.32 meters long.
THIS CANNOT BE ANSWERED .......................................................................
Answer:
predictive value of a positive test = 18.18%
predictive value of a negative test = 94.03%
Step-by-step explanation:
Sensitivity = 60% = 0.6
Specificity = 70% = 0.7
Let True Positive = TP
True Negative = TN
False Negative = FN
![Sensitivity = \frac{TP}{TP + FN} \\0.6 = \frac{TP}{TP + FN} \\0.6TP + 0.6FN = TP\\0.4TP = 0.6FN\\TP = 1.5 FN](https://tex.z-dn.net/?f=Sensitivity%20%3D%20%5Cfrac%7BTP%7D%7BTP%20%2B%20FN%7D%20%5C%5C0.6%20%3D%20%5Cfrac%7BTP%7D%7BTP%20%2B%20FN%7D%20%5C%5C0.6TP%20%2B%200.6FN%20%3D%20TP%5C%5C0.4TP%20%3D%200.6FN%5C%5CTP%20%3D%201.5%20FN)
![Specificity = \frac{TN}{TN + FP} \\0.7 = \frac{TN}{TN + FP} \\0.7TN + 0.7FP = TN\\0.7FP = 0.3 TN\\TN = 7/3 FP](https://tex.z-dn.net/?f=Specificity%20%3D%20%5Cfrac%7BTN%7D%7BTN%20%2B%20FP%7D%20%5C%5C0.7%20%3D%20%5Cfrac%7BTN%7D%7BTN%20%2B%20FP%7D%20%5C%5C0.7TN%20%2B%200.7FP%20%3D%20TN%5C%5C0.7FP%20%3D%200.3%20TN%5C%5CTN%20%20%3D%207%2F3%20FP)
Prevalence = 10% = 0.1
Three hundred people are screened, ![T_{total} = 300](https://tex.z-dn.net/?f=T_%7Btotal%7D%20%3D%20300)
Total number of people having the disease, ![T_{disease} = ?](https://tex.z-dn.net/?f=T_%7Bdisease%7D%20%3D%20%3F)
![Prevalence = \frac{T_{disease} }{T_{total} } \\0.1 = \frac{T_{disease} }{300 }\\T_{disease} = 30](https://tex.z-dn.net/?f=Prevalence%20%3D%20%5Cfrac%7BT_%7Bdisease%7D%20%7D%7BT_%7Btotal%7D%20%7D%20%5C%5C0.1%20%3D%20%20%5Cfrac%7BT_%7Bdisease%7D%20%7D%7B300%20%7D%5C%5CT_%7Bdisease%7D%20%3D%2030)
![T_{disease} = TP + FN\\30 = TP + FN](https://tex.z-dn.net/?f=T_%7Bdisease%7D%20%3D%20TP%20%2B%20FN%5C%5C30%20%3D%20TP%20%2B%20FN)
But TP = 1.5 FN
30 = 1.5 FN + FN
30 = 2.5 FN
FN = 30/2.5
FN = 12
TP = 1.5 FN = 1.5 * 12
TP = 18
![FP + TN = T_{total} - T_{disease} \\FP + TN = 300 - 30\\FP + TN = 270\\FP + \frac{7}{3} FP = 270\\\frac{10}{3} FP = 270\\FP = 27 * 3\\FP = 81](https://tex.z-dn.net/?f=FP%20%2B%20TN%20%3D%20T_%7Btotal%7D%20-%20T_%7Bdisease%7D%20%5C%5CFP%20%2B%20TN%20%3D%20300%20-%2030%5C%5CFP%20%2B%20TN%20%3D%20270%5C%5CFP%20%2B%20%5Cfrac%7B7%7D%7B3%7D%20FP%20%3D%20270%5C%5C%5Cfrac%7B10%7D%7B3%7D%20FP%20%3D%20270%5C%5CFP%20%3D%2027%20%2A%203%5C%5CFP%20%3D%2081)
81 + TN = 270
TN = 189
To calculate the Predictive value of positive test (PPT)
![PPT = \frac{TP}{TP + FP} * 100\\PPT = \frac{18}{18+81} * 100\\PPT = \frac{18}{99} * 100\\PPT = 18.18 \%](https://tex.z-dn.net/?f=PPT%20%3D%20%5Cfrac%7BTP%7D%7BTP%20%2B%20FP%7D%20%2A%20100%5C%5CPPT%20%3D%20%5Cfrac%7B18%7D%7B18%2B81%7D%20%2A%20100%5C%5CPPT%20%3D%20%5Cfrac%7B18%7D%7B99%7D%20%2A%20100%5C%5CPPT%20%3D%2018.18%20%5C%25)
To calculate the Predictive value of negative test (PNT)
![PPT = \frac{TN}{FN + TN} * 100\\PPT = \frac{189}{189+12} * 100\\PPT = \frac{189}{201} * 100\\PPT = 94.03 \%](https://tex.z-dn.net/?f=PPT%20%3D%20%5Cfrac%7BTN%7D%7BFN%20%2B%20TN%7D%20%2A%20100%5C%5CPPT%20%3D%20%5Cfrac%7B189%7D%7B189%2B12%7D%20%2A%20100%5C%5CPPT%20%3D%20%5Cfrac%7B189%7D%7B201%7D%20%2A%20100%5C%5CPPT%20%3D%2094.03%20%5C%25)
Answer:
Step-by-step explanation:
if A=1/2 bh
to solve for b
2A=bh
b=2A/h