The volume if a cylindrical can is 15.7 in. The diameter is 2 in. Find the height. Use =3.14
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(1)
we are given
we can use quadratic formula
now, we can compare and find a , b and c
we get
now, we can plug these values into quadratic formula
we can simplify it
so, we will get solution
{−3+i, −3−i}.........Answer
(2)
we are given equation as
Since, Jamal solve this equation by completing square
so, firstly we will move constant term on right side
so, subtract both sides by 14
we can write
so, we will add both sides by 4^2
we get
..............Answer
An actual two-by-two table is a tabular representation containing two rows and two columns.
- The columns consist of the tested True positive for prostate cancer and tested True Negative for prostate cancer
- The rows consist of the predicted positive screening and predicted negative values
Mathematically, the set-up of the two-by-two table for this data can be computed as:
Tested True Positive for cancer True Negative Total
Predicted Positive 800 3200 4000
Predicted Negative 100 95900 96000
Total 900 99100 100000
<h3>b)</h3>The prevalence rate of prostate cancer in this population is:
= 9 per thousand.
<h3>c)</h3>
The calculation of the sensitivity of this screening is as follows:
where;
- TP = True positive for cancer
- PN₁ = Predicted Negative for true positive cancer
∴
= 0.889
= 88.9%
The interpretation shows that 88.9% are correctly identified to be actual positive for prostate cancer.
<h3>d)</h3>The calculation of the specificity of this screening is as follows:
where;
- TN = True positive for cancer
- PN₂ = Predicted Negative for true negative cancer
∴
= 0.9677
= 96.77%
The interpretation shows that 96.7% of an actual negative is correctly identified as such.
<h3>e)</h3>
The positive predicted value of the screening test is computed as:
= 0.2
= 20%
The interpretation of the positive predicted value of this screening shows that 20% that are subjected to the diagnosis of positive prostate cancer truly have the disease.
Learn more about tabular representation here: