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To find the cross product \(\vec{a} \times \vec{b}\), we use the determinant method: Given vectors: \[ \vec{a} = 2\hat{i} + 3\hat{j} + 4\hat{k} \] \[ \vec{b} = 3\hat{i} + 5\hat{j} + 2\hat{k} \] ### Step 1: Write the determinant formula \[ \vec{a} \times \vec{b} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & 3 & 4 \\ 3 & 5 & 2 _________ __________ ___ _________ ____ _______ ____.
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Solve the following system of equations using Cramer's rule.
x + 3y + 2z = 6, -x + 4y + 5z = 8, 2x + 5y + 3z = 10
In a factory there are three machines A, B, C which produce 10%, 40% and 50% items respectively. Past experience shows that percentage of defective items produced by machines A, B, C are 5%, 4%, 2% respectively. An item from the production of these machines is selected at random and it is found defective. What is the probability that it is produced by machine A?
A hospital specialising in heart surgery. In 2023 total of 1000 patients were admitted for treatment. The average payment made by a patient was Rs 1,00,000 with a standard deviation of Rs 20000. Under the assumption that payments follow a normal distribution, find the number of patients who paid between Rs 90,000 and Rs 1,10,000.
If the first term of an AP is 5 and 101 term of the AP is 1005 then
common difference
of the AP will be 105.
Evaluate .
In an iron determination (taking 1 g sample every time) the following four replicate results were obtained: 24.8, 25.2, 23.6 and 24.7 mg iron. Calculate the coefficient of variation and relative standard deviation in ppm of the given data.
Assume that in a population each person is equally likely to have a particular disease and disease status of each individual is independent of each other, then find the probability that out of the 5 randomly selected individuals who are tested for this particular disease exactly 3 have this disease.