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[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9, which are divisible by 10 and no digit is repeated?, think step by step [/INST] , The answer is The number of 6-digit numbers that can be formed is 120.

[INST] help me answer this question Let us make the table of the given data and append other columns after calculations., think step by step [/INST] Here, the user is required to make a table of given data and add other columns after performing some calculations. , The answer is In this question, the user is being asked to create a table of the given data and append other columns after calculations.

[INST] help me answer this question Write the first five terms of the sequence whose nth term is an = (2n – 3)/6, think step by step [/INST] , The answer is -1/6, 1/6, 1/2, 5/6, 7/6

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question State whether each of the following statements is true or false. If the statement is false, rewrite the given statement correctly., think step by step [/INST] N/A , The answer is N/A

[INST] help me answer this question Given x2/16 + y2/9 = 1, what is the length of the minor axis?, think step by step [/INST] , The answer is Length of minor axis = 2b = 2 (3) = 6

[INST] help me answer this question Find the value of sin 765°., think step by step [/INST] We know that the values of sin x repeat after an interval of 2π or 360°. Therefore, sin 765° = sin (45° + 720°) = sin 45°. Hence, sin 765° = 1/√2. , The answer is The value of sin 765° is 1/√2.

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question x + y ≤ 3, , think step by step [/INST] , The answer is N/A

[INST] help me answer this question 2 (2x + 3) – 10 < 6 (x – 2), think step by step [/INST] The solutions of the given inequality are defined by all the real numbers greater than 4. Hence, the required solution set is (4, ∞). , The answer is x > 4

[INST] help me answer this question Given, y < – 2, think step by step [/INST] , The answer is The solution region of the given inequality is below the line y < – 2. (That is, away from the origin.)

[INST] help me answer this question Question: P (k + 1) is true whenever P (k) is true., think step by step [/INST] Explaination: N/A , The answer is Answer: Therefore, by the principle of mathematical induction, statement P (n) is true for all natural numbers, i.e., n.

[INST] help me answer this question The dimensions of the circle are Diameter = 40 cm, find the Radius., think step by step [/INST] , The answer is Radius = Diameter / 2 = 40 / 2 = 20 cm

[INST] help me answer this question Evaluate<br>(i) 8!<br>(ii) 4! – 3!, think step by step [/INST] {'part1': '8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320', 'part2': '4! - 3! = (4 × 3!) - 3! = 3! (4-1) = 3 × 2 × 1 × 3 = 18'} , The answer is {'part1': '8! = 40320', 'part2': '4! - 3! = 18'}

[INST] help me answer this question Question: The sum of two numbers is 6 times their geometric mean; show that numbers are in the ratio (a/b)^3 : (b/a)^3., think step by step [/INST] Explanation: Upon solving the expression and using the definition of a geometric mean, one can prove that the numbers are indeed in the given ratio. , The answer is Answer: The numbers are in the ratio (a/b)^3 : (b/a)^3.

[INST] help me answer this question A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is (i) 3. (ii) 12., think step by step [/INST] , The answer is The sample space S = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)} n(S) = 12 (i) Let 'P' be the event having the sum of numbers as 3. n(P) = 1 P(P) = n(P)/n(S) = 1/12 (ii) Let 'Q' be the event having the sum of the number as 12. n(Q) = 1 P(Q) = n(Q)/n(S) = 1/12

[INST] help me answer this question Question : 3x + 2y ≤ 12, x ≥ 1, y ≥ 2, think step by step [/INST] The required area to be included would be on the left of the graph x ≥1 and below the graph y ≥2. , The answer is The solution for 3x + 2y ≤ 12 is the area below the line 3x + 2y = 12. The solution for x ≥ 1 is the area on the right side of the line x = 1 and for y ≥ 2 is the area below the line y = 2.

[INST] help me answer this question Are the events A and BI mutually exclusive?, think step by step [/INST] A ∩ BI = A ∩ A = A , The answer is No, they are not mutually exclusive.

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.