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### Instruction: help me answer this question `f(x) = sqrt(x - 1)`, think step by step
### Assistant: , The answer is The domain of the function is `x ≥ 1`.
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### Instruction: help me answer this question Find the mean, variance and standard deviation using short-cut method, think step by step
### Assistant: To find the mean, variance, and standard deviation, the reader must first calculate Yi, Yi2, fiyi, and fiyi2, then use those values to find the mean, variance, and standard deviation using the formulae provided in the question. , The answer is The mean is 93, variance is 105.583, and standard deviation is 10.275.
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### Instruction: help me answer this question Given x2/49 + y2/36 = 1, what is the length of the minor axis?, think step by step
### Assistant: , The answer is Length of minor axis = 2b = 2 (6) = 12
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### Instruction: help me answer this question What is the formula used to calculate the mean (x̅)?, think step by step
### Assistant: , The answer is x̅ = A + (h/N) * i
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### Instruction: help me answer this question Describe two events which are mutually exclusive but not exhaustive., think step by step
### Assistant: , The answer is Let A be the event of getting at least two heads. So, A = (HHH, HHT, THH, HTH). Let B be the event of getting only head. So, B= (HHH). Therefore, A ∩ B = (HHH), and A and B are mutually exclusive but not exhaustive.
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### Instruction: help me answer this question (i) {3, 4} ⊂ A is incorrect, think step by step
### Assistant: , The answer is Here 3 ∈ {3, 4}; where, 3∉A.
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### Instruction: help me answer this question Find the standard deviation for X., think step by step
### Assistant: , The answer is The standard deviation for X is √35, which is approximately 5.91.
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### Instruction: help me answer this question What is the perimeter of the triangle?, think step by step
### Assistant: , The answer is x + (x + 3) + 2x ≤ 91 cm
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### Instruction: help me answer this question If the sum of n terms of an A.P. is (pn + qn2), where p and q are constants, find the common difference., think step by step
### Assistant: Using the sum formula and coefficients of n and n^2, we solved for the common difference. , The answer is The common difference is 2q.
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### Instruction: help me answer this question (i) Number of places is as 1 2 3 4 5 6 7 8 9 10 11 12, (ii) There should always be 4 letters between P and S. Possible places of P and S are 1 and 6, 2 and 7, 3 and 8, 4 and 9, 5 and 10, 6 and 11, 7 and 12, Find the number of permutations., think step by step
### Assistant: , The answer is Possible ways =7, No. of permutations =2 × 7 =14
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### Instruction: help me answer this question Given that P (3, 2, – 4), Q (5, 4, – 6) and R (9, 8, –10) are collinear. Find the ratio in which Q divides PR., think step by step
### Assistant: , The answer is Hence, the ratio in which Q divides PR is 1: 2.
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### Instruction: help me answer this question True., think step by step
### Assistant: , The answer is Each element of {a} is also an element of {a, b, c}.
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### Instruction: help me answer this question If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram., think step by step
### Assistant: This is the contrapositive of the statement in (b). , The answer is
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### Instruction: help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step
### Assistant: , The answer is The domain of the function is all real numbers except `x = 4`.
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### Instruction: help me answer this question What is the coefficient of variation (C.V) for group B?, think step by step
### Assistant: , The answer is The coefficient of variation (C.V) for group B is 35.
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### Instruction: help me answer this question What is the converse of the given statement: "If a number x is odd, then it is a prime number.", think step by step
### Assistant: The converse statement is created by interchanging the hypothesis and conclusion of the original statement. , The answer is If a number is not odd, then it is not a prime number.
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### Instruction: help me answer this question Hence, the solution to the inequalities is given by the shaded region in the graph.
, think step by step
### Assistant: , The answer is N/A
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### Instruction: help me answer this question Find the derivative of the following functions.
(ii) sec x, think step by step
### Assistant: , The answer is The derivative of sec x is not provided.
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### Instruction: help me answer this question Vertices (±7, 0), e = 4/3, think step by step
### Assistant: , The answer is The vertices of the hyperbola are (±7, 0) and the eccentricity is e = 4/3.
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### Instruction: help me answer this question Vertices (± 6, 0), foci (± 4, 0), think step by step
### Assistant: The vertices and foci given are on the x-axis, so the equation will be of the form x2/a2 + y2/b2 = 1. Here, a = 6, c = 4. Using a2 = b2 + c2, b2 = 36 – 16 = 20. So, the equation of the ellipse is x2/36 + y2/20 = 1. , The answer is The equation of the ellipse is x2/36 + y2/20 = 1
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### Instruction: help me answer this question Write the general term in the expansion of
<br>- (x² – y)⁶, think step by step
### Assistant: The general term Tr+1 in the binomial expansion is given by Tr+1 = n C r an-r br. Here, a = x² , n = 6 and b = -y. Putting values in (i), we get Tr+1 = 6Cr x 2(6-r) (-1)r yr = -1^r 6cr .x12 – 2r. yr , The answer is The general term is -1^r 6cr .x12 – 2r. yr
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