A pair of fair cubic dice are rolled until the sum of their outcomes is 12. What is the expected number of times the dice are rolled?

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Q: What congruence do all integers of the form 6k+ 1 satisfy?

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Q: 15. For all integers a, b, and c, if a b and a c then a(b+c).

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Q: 5. Bernoulli's Equations b. 2x³y' = y(y² + 3x²)

A: Explanation of the answer is as follows

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Q: Problem 4. Find the total derivative of the following function: df dr. af of dy + dr Dy dr F(x,y) =…

A: Sol:-

Q: The solution to the differential equation: [y² (x + sin²5x) - 3y|dx + (yx² − 3x + 2xy −5+ 6yysin10x)…

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Q: A Holstein calf weighed 93-pounds when born. The calf was sold 250 days later weighing 583 pounds.…

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Q: 2. cos xdy = -(sin x) ydx + dx

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Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 OA. 4 O B.…

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Q: 24. For all integers a, b, and c, if a b and a c then a (2b-3c). 25. For all integers a, b, and c,…

A: Explanation of the answer is as follows

Q: 11. If A¹ = [1 27 4 6 12. If A¹ = -1 solve AX = 1 2 0] 3 1 2 4 1 [3] for X. -2 solve AX = 1 for X. 4

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Q: a) If p(x) = x² + x² + s ²+x+1, and g(x) = x² + : b) If p(x) = x² + x³ + x² + x + 1, and g(x) = x² +…

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Q: (a) Use the Midpoint Rule, with n=4, to approximate the integral fo Tedz. (Round your answers to six…

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Q: Derive the statements in 24-26 as corollaries of Theorems 4.3.1, 4.3.2, and the results of exercises…

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Q: Let n be a positive integer and p a prime that divides n. Prove that pis prime in Zn.

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Q: The characteristic polynomial of the matrix A = is p(A) = (A - 3)²1² The matrix has two real…

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Q: completely inhomogeneous diffusion problem on the half-line for 0 < x <∞, 0<t<∞ Vt V₁ - kvxx = f(x,…

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Q: Suppose E and F are two events in the same sample space S with probabilities p(E) = 0.81 and p(F) =…

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Q: Find all the Sylow 3-subgroups of S4.

A: We have to find all the Sylow 3-subgroups of S4.

Q: Let p, q and r be the propositions: p: Wild foxes have been seen in the area. q: Hiking is safe on…

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Q: Question 31 Solve for the IF of the equation y(x + y + 1)dx + x(x + 3y + 2)dy = 0 O A. O B. O C. ev…

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Q: If 3x^2+3x+xy=5 and y(5)=−17y(5)=-17, find y'(5)y′(5) by implicit differentiation

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Q: D. The computation from part C above shows that between any two unequal real numbers is another real…

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Q: How many packages should you purchase from each pub- lisher to get exactly 4,500 horror novels and…

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Q: company makes whoke wheat crackers and sesame crackers. The crackers are sold by the box. Each box…

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Q: let p be a prime and f(x) = (x-1(x-2)-₁ (2- (P-1)) - (2₁²-11) them all the co-efficient of this…

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Q: Premise 1: Some real numbers are integers. Premise 2: All integers are rational numbers. Conclusion:…

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Q: If y=f(x)=7e^x + 3x^4 - 20x - 5, use the tangent line to approximate f(0.2)

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Q: 1. Determine for each of the following differential equations whether it is linear, separable, both,…

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Q: 2x₁ + 4x₂x3 = 15 7x₁3x₂ + 3x3 = -4 4x13x28x3 = 19

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Q: What are the possibilities for the number of elements of order 5 in agroup of order 100?

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Q: Classify the given Differential Equation according to (1) ORDER; (2) DEGREE; (3) TYPE; (4) LINEARIT…

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Q: 5. Find the Fourier cosine series and the Fourier sine series of f(x). Draw f(x) 0 if 0<x<1 and its…

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Q: Exercise 3.2 Provide an upper bound of the Lagrange interpolation error for the following functions:…

A: Given:  f1(x)=cosh(x), xk=-1+0.5k, k=0,.....,4. f2(x)=sinh(x), xk=-1+0.5k, k=0,.....,4. f3(x)=…

Q: 12 Prove that if (a, 91) = 1 and (b, 91) = 1, then 91 | a¹² – 6¹²

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Q: An archery game is played by shooting arrows at a target. Each person can choose to have two or…

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