A single, six-sided die is rolled. Find the probability of rolling an even number or a number less than 3. The probability is(Type an integer or a fraction. Simplify your answer.)

Q: Given the differential equation y"+ 4y' + 2y = - 4 sin(4t), y(0) = - 1, y'(0) = 2 Apply the Laplace ...

A: Given - Given the differential equation y'' + 4y' + 2y = -4sin4t,  y0 = -1, y'0 = 2 To find - Apply ...

Q: Find the general solution of the following differential equation. Primes denote derivatives with res...

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Q: how many subsets of {0,1 ....,9} have cardinality 4 or more?

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Q: Assume that it costs a manufacturer approximately C(x) = 800,000 + 340x + 0.0005x2 dollars to manufa...

A: In this question, optimization technique is used. Optimization Technique using maxima and minima The...

Q: 2. The goal is to compute the determinant of the following matrix. Follow the instructions. 2 -3 7 -...

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Q: The marginal cost of the xth box of light bulbs is  10 +  [ln(x + 1)] (x + 1)2,  and the fixed cost ...

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Q: Suppose G is a connected graph with n > 1 vertices and n –1 edges. Prove that G has a vertex of degr...

A: Given G is connected graph with n>1vertices and n-1 edges. Since the graph has n-1 edges and it i...

Q: 2. The temperature T and pressure P of a gas inside a pressure cooker follows the equation T/P = 8. ...

A: Note: Since you have asked multiple question, we will solve the first question for you. If youwant a...

Q: Let p ∈ Z be prime. Prove that pZ is prime.

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Q: A motor scooter you want to purchase costs $2,800, before sales tax. Given a sales tax rate of 4% de...

A: 4% of 2800 is = ( 4 x 2800) /100 = 112  

Q: You want to put a 3 inch thick layer of topsoil for a new 12 ft by 25 ft garden. The dirt store sell...

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Q: Nutrition   Use duality to answer the following application. Oz makes lion food out of giraffe and g...

A: A mathematical statement, which states that two expressions are not equal is called an inequation an...

Q: 15. Is the set of all differentiable real-valued functions defined on Ra sub- space of C(R)? Justify...

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Q: Obtain the general solution to the equation. dr +r tan 0 = 7 tan 0 de The general solution is r(0) =...

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Q: Define the sets A, B, C, D, and E as follows: A = {x € R: x 2} C = {x € R: |x| < 2} D = {x € R: |x|...

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Q: In a triangle, assume a is opposite side a, ß is opposite side b, and y is opposite side c. Three me...

A: A triangle is a plane figure or a polygon with three sides and three vertices. If any one of the ang...

Q: Verify the following trigonometric identity:cos4t−cos2t= sin4t−sin2t

A: The trigonometric identities can be verified by solving the left hand side and right hand side separ...

Q: Determine the power and the rms value for each of the following signals: (a) 5+10cos(100r +x/3) (b) ...

A: Since you have asked for the parts e, c and f we have solved it for you.

Q: A bag of candy was opened and the number of pieces was counted. The results are shown in the table b...

A: The probability of any event A is PA=nFnT Here, nF is the number of favorable outcomes and nT is the...

Q: For every element x in A, there is an element in y is B such that (x,y)∈F. QUESTION: How does this ...

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Q: Solve the system below using augmented matrix methods. Graph each solution set. Discuss the differen...

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Q: Find an equation for the paraboloid z = 5 – (x² + y²) in cylindrical coordinates. (Type theta for 0 ...

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Q: Honda Accord depreciates at 15% per year. Six ars ago it was purchased for $21,000. What is it worth...

A: The exponential function is defined in the form y=abx where a will be the initial value and b will b...

Q: Perform the Indicated operations and designate each answer (a - f) using the listing method Let U = ...

A: Given  U = {a,b,c,d,e,f,g} X = {a,c,e,g} Y = {a,b,c} Z = {b,c,d,e,f}

Q: Exercise 4.11 Suppose m is Lebesgue measure and A is a Borel measurable subset of R with m(A) > 0. P...

A: Given, m is Lebesgue measure and A is a Boral measurable subset ofℝ with m(A)&gt;0.  To prove that i...

Q: 2-Suppose that you have n data points (x1, y1), ..., (xn, yn), with the xi all distinct. Which of th...

A: Question 2 is related to Existence and Uniqueness of interpolating polynomials Question 3 is asking ...

Q: Consider the surface f(x,y.z) = 2x + 3y² +2z? - 7= 0, which may be regarded as a level surface of th...

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Q: Let X and Y be topological spaces and fix some yo E Y. Show that the map f: X → X x Y defined by f (...

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Q: 1. Why is f not a function from R to R if a) f(x) = 1/x? b) f(x) = VT? c) f(x) = ±/(x² + 1)?

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Q: Let U = {a, b, c, d, e, f, g, h, i}. Subsets K, L, M and N are as follows: K = {a, e, i} L = {b, d,...

A: A set is a well-defined collection of objects. The objects, which belong to the set, are called elem...

Q: 10. Given the matrices 1 -1 4 2 -1 1 1 2 A= -1 3 0 B= C= -1 0 3 4 4 4 D= 5 E= [1 2 3] F= G= 8. 8. 6 ...

A: Image is attached with detailed solution.

Q: The function ƒ defined by, 2x, ifx is rational f (x)= -x+ 27, ifx is irrational continuous only at, ...

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Q: Consider the following function: f(x) = 3x? – 2x +1 (1) Evaluate f(x)dr. Answer:

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Q: Find the area of the shaded region of the graph of r=1+sin (0)

A: To find → area of the shaded region of the of the graphπ = 1 + sinθ    

Q: 2. Draw a phase line for the equation y' = y (y – 5). If y(0) 2, what is the lim y(x)?

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Q: In a lengthy ciphertext message, sent using a linear cipher C = a P +b (mod 26), the most frequently...

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Q: Let M be an abelian group and D a subgroup. For any element m of M, where m has order 2, define mD={...

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Q: a. Prove that for any sets A,B⊆X and for any function f:X⟶Y, f(A∩B)⊆f(A)∩f(B).       b. Prove that...

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Q: 3. identify a pattern in the sequence of figures. Then use the pattern to find the next figure in th...

A: In this question, we have to find out next figure in sequence by decoding the pattern.

Q: .. For the following partial differential equations find the ordinary differential quations that are...

A: Since you have asked a question with multiple subparts so as per guidelines will solve the first thr...

Q: Solve the problem: max(min) x^2+y^2 +z subject to x^2+2y^2+4z^2=1  Suppose the constraint is changed...

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Q: Problem 6.4.12: y" + 2y' + 5y = 25t – 1008(t – n), y(0) = -2, y'(0) =5

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Q: Let z = x(1 – i) + 8(-2+ i), where x is a real number. If z? is a negative real %3D number, what is ...

A:  Given, z=x(1-i)+8(-2+i) and z2 is a negative real  number. We have to find the value of x  

Q: Find all complex numbers which make the following equations true 2+1=1 and +1|= 1

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Q: Construct a table that displays the number of directed paths of length 1 or 2 between each pair of v...

A: Fill table by the number of directed path between two vertices . If the number of directed path betw...

Q: Find the eigenvalues of A=[a b a b] for any a,b of R . Determine all the values of the constants a,b...

A: Given matrix is A=abab. First we have to find the eigenvalues of the matrix A. The eigenvalues of A ...

Q: Show that if a,b, and c≠0 are integers, then a∣b if and only if ac∣bc.

A: We have to prove the following statement -  If a,b, and c≠0 are integers, then a∣b if and only if ac...

Q: ^2 be pact sub els of a tnc space A. Show NaEA Ka is closed 4. Let {Ka}aea be a collection of compac...

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Q: Consider a rod of length 28 for which a = 1. Suppose the initial temperature distribution is given b...

A: Define the equation of the temperature of the rod then determine the value of the variable by substi...