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Q: 1. Prove by Mathematical Induction that 1³ +2³+...+n³ = ‘n(n+1) 2 2 for all integers n ≥ 1 3

A: According to the new guideline if there are more than 1 question then we have to solve only 1…

Q: Write the quadratic function in standard form. f(x) = x² + 18x + 78 f(x) = =

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Q: Factor the following polynomial. If the polynomial cannot be factored, write prime. 6x³48x² 120x

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Q: Suppose a principal P is invested at an annual rate r compounded m times per year. The amount after…

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Q: to $11,500 in 2 years and the interest amount earned was $950,

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Q: Henry plans to purchase a new sports car. The dealer requires a  5%  down payment on the  $33,000…

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Q: Match each variable with its meaning in the following simple terest formulas. = Prt = P +Prt: =…

A: We have to find out solution

Q: implies Lemuel Score: 17, 20, 18, 12, 11, 9, 11, 12, 13, 16, 25, 18, 1 1. What is the mean of the…

A: We have to find the mean,range, percentile 78 according to given condition.

Q: Minimize and maximize P=20x+10y Subject to 5x +9y2 78 5x + 2y ≤ 64 -x+y ≤ 4 x, y ≥ 0 at is the…

A: To find the minimum value of the LPP.

Q: Tabular representations for the functions f, g, and h are given below. Write g(x) and h(r) as…

A: Let's find function from the given table.

Q: Let T : R2[x] → R2[x] be given by T(a+bx+cx2 ) = a + b(x+ 1) + b(x + 1)2 . Let v = x + 1. Find a…

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Q: 14. The general solution of y' - 4y = 2e²√√y is:

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Q: f(x) = +2 29 Enter the intercepts as points, (a, b). The x-intercept is The y-intercept is The field…

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Q: h(x)={3x+2 for x>0} h(x)={5x-1for x<0} h(8)=?

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Q: The table to the right shows the number of internet hosts from 1994 to 2012. (A) Let x represent the…

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Q: 13 01 5. Find a basis for the column space of the matrix 0 0 0 0 A 0 0 0 0 0 1 3 B {3 1 C { D { E {…

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Q: Consider the given matrix. Determine det(A) and the inverse matrix of A.

A: Here we have to find the determinant and inverse of a matrix.

Q: The graph of a square root function has a domain of (0,∞) and range of [1,∞). In two or more…

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Q: A rectangular field is  0.35  kilometers long and  0.3  kilometers wide. What is the area of the…

A: Area of the rectangular field

Q: When Sam had  2  years left in college, he took out a student loan for  $15,175 . The loan has an…

A: We have to find the monthly payment.

Q: Find the domain of the rational function. Enter your answer in interval notation. To enter ∞, type…

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Q: Write a scalar equation of each plane, Given its vector equation [x, y, z] = [7, -3, 4]+s [1, -2,…

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Q: Rewrite the quadratic function in vertex form (which our OpenStax textbook also calls the standard…

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Q: The path of a punted football is modeled by 16 f(x): == -x² + 7 5 -X + 1.5 1225 where f(x) is the…

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Q: Prove by contrapositive: if x is odd then x²+3x+5 is odd

A: Concept: Contrapositive method: A conditional statement's contrapositive is built through negating…

Q: How can all real zeroes be found for f(x) = x^4 - x^3 - 20x^2?

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Q: Solve for u. 4 7 3 5 Simplify your answer as much as possible 0 1

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Q: 14. The general solution of y'- 4y = 2e²√y is: (a) y = √Ce² - e² (b) y¹/2 = Ce²+eª (c) y = Ce²+ e*…

A: Given problem:- The general solution of y' -4y=2ex√y

Q: Rationalize the denominator and simplify. 2 13

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Q: Find the optimum solution for the-3 following modal using the graphical method. Max Z =4X1+3X2…

A: Above question is solved.

Q: 9. Consider the orthonormal basis S for R³ S = (v₁,v₂,v,} where v₁ = (0,1,0) and v₁ = Let u = V₂ = =…

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Q: Q1) Determine the halve range odd expansion of the function whose definition is: 0≤x≤1 f(x) = - {...…

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Q: Solve the given equation for x. 32x-x²-3-8 (Use a comma to separate answers.) X=

A: Given query is to find the values of x

Q: 1 The expression divided by 2x - 1. Find the values of the constants a and b. 2x³ + ax² + bx-30 is…

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Q: Gertrude accepted a job as a fashion model after being offered a $375 signing bonus. If she makes…

A: This question can be solved using the concept of linear equation in two variables.

Q: *Consider the following matrices /1 ^ - (-:2 -2) - - († ;) -- (1 5² : :;) -- () -- (9) 1 1/2 3 0 A B…

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Q: 7:³ 5x² Consider the function f(x) = - + 3 +2x10. 3 The tangent line through the point (3, 2) is…

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Q: Write interval notation 3z + 4 > -11

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Q: Use the Jacobi method and Gauss-Seidel method to solve the following system until L²-norm of Ax is…

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Q: A psychologist uses two types of boxes with mice and rats. The amount of time (in minutes) that each…

A: let number of Mice = x  and number of Rats = y   Box A Box B

Q: Solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions. (Enter…

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Q: Find a unit vector in the direction of u and in the direction opposite that of u. u = (-15, -8) (a)…

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Q: Find (A, B), ||A||, ||B||, and d(A, B) for the matrices in M2,2 using the inner product (A, B) =…

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Q: 1: Which of the following vectors are linearly dependent? 21 1 [11 2 A: and 3 C: B: 2 and 4 [3] d 7…

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Q: State the value of k in the equation of a sinusoidal function, if it's period is 100. 18 5 36000 1…

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Q: 2: The function f(x) = x² + 2x² + 3x² + 4x₁x₂ + 5x₂x3 + 6x₁x3 can be written in the form f(X) = XTQX…

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Q: Solve the linear programming problem. Maximize and minimize z = 3x + 4y Subject to 2x+y ≥ 30 x+2y 2…

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Q: Is there a better example of this... it's hard to follow

A: Let's solve.

Q: 8.1

A: We will solve the problem.

Q: 4 Given that log m2 ≈ 0.59, log m4≈ 1.18, and log m6~1.525, find log m 4 log m (Type an integer or a…

A: Explanation of the answer is as follows