Four students are randomly selected from an algebra class and asked whether they suffer from math anxiety. Find the sample space for the possible outcomes of the survey using a tree diagram.

Q: Prove that the only prime of the form n² - 4 is 5.

A: Suppose p is a prime such that p=n^2-4. Then we have p=n^2-4=(n+2)(n-2). we know that prime number…

Q: Let the vectors (i, j, k) constitute an orthonormal basis. In terms of this basis, a general basis…

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Q: 0 Test for absolute convergence or directe. (-1)^+2 금 61-1-1 Convergence, Condstreral Ininty)

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Q: Which of the following is the domain D of the function f(x, y) = ln(x² + y² − 1) ? Select one…

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Q: BREEUROBTEN 館 R=300,000 (0.0282 127 Rumen non POCEDIC Umag DOFC 1- (1+0.0282) 12/307) 12 PLAFON

A: An expression or mathematical expression is a finite combination of symbols that is well-formed…

Q: 20 This question has two parts - make sure you answer both. A Markov process is given by the rule…

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Q: (a) Write down any 3 by 3 matrix M. Split M into S + A where S = ST is symmetric and A = -AT is…

A: To find :(a) Write down any 3 by 3 matrix M. Split M into S + A where S = ST is symmetric and A =…

Q: (i) Estimate the sum for n = = 10, 100 and 1000 (you may use computational tools to help, make sure…

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Q: (x² + y²)dx − 2xy dy = 0

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Q: Let V be a finitedimensionalvector space and let {v1, v2, . . . , vn} be a linearlyindependentsubset…

A: Given: V is a finite-dimensional vector space and v1, v2, . . . , vn is a linearly independent…

Q: Construct a polynomial function with the following properties: fifth degree, 5 is a zero of…

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Q: A coincidence is defined as a striking occurrence of two or more events at one time apparently by…

A: It is given that neither person is born in a leap year. It is required to find the probability that…

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 250…

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Q: 3. Consider the vectors *-(3) -(5)- *-(-3) (3). = = X₂ (a) Show that x, and x₂ form a basis for R².…

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Q: Consider the differential equation (2x-xy) dx-2dy=0 with the initial condition y = 1 when x = 1.…

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Q: Let a, b, n E Z. Prove: If a|n and b|n with gcd(a, b) = 1, then ab|n. (I

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Q: Find the consumers' surplus and the producers' surplus at the equilibrium price level for the given…

A: At equilibrium point demand and supply will be same

Q: Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to…

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Q: Which of the following is equivalent to: log3 5 - log, 16 + log3 8 Select one alternative: O log, 10…

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Q: What is the output of the following pseudocode? count: 0 For i = 1 to 4 For ji+ 1 to 5 End-for…

A: We have a pseudocode in question which uses a nested for loop. Below are details  It initialize…

Q: You are looking at a balloon that is 300 ft away. If the height of the balloon is increasing at a…

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Q: Find the degree and a basis for Q(√3 + √5) over Q(√15). Findthe degree and a basis for Q(√2, 3√2,…

A: In this question, we have to find the degree and a basis for Q(√3 + √5) over Q(√15) and the degree…

Q: Let à = ( − 1, 3, — 5) and 7 = ( − 3, 2, 3). - Find a unit vector normal to a and b with negative z…

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Q: g(x) = −4(x + 3)(x − 3)(x + 1)

A: A function is defined as a relation between a set of inputs having one output each. A function is a…

Q: Copy the graph paper given below. Given, F(x, y) = -yi+xj, sketch the vector field ♬ by drawing…

A: Given: The vector field F→ is given by:                                             F→x,y=-yi^+xj^

Q: 27 This question has two parts - make sure you answer both. Consider the second order differential…

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Q: QUESTION 9 in = where z = g(u, v) and u(r, s), v(r, s). Find the number of terms in

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Q: Set A = {2,3,4,5,7,8,9} and set B = { 3, 5, 2, 7, 6, 9 y Find the union and intersection of A and B

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Q: 1. A Markov chain has state space {0, 1, 2} and transition probability matrix .1 .5 .4 P = 0 0 1 .2…

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Q: Let f(x)=√x - 2. What is the domain of (f of)(x)? Select one alternative: ○ [6,00) ○ [4,00) [2,00) ○…

A: Answer :- option A is correct

Q: 75-86. Logarithmic differentiation Use logarithmic differentiation to evaluate f'(x). 84.…

A: fx=1+x2sinx Taking ln on both side ⇒logfx=log1+x2sinx Now differentiating with respect to x…

Q: 9. If you have $100,000 today invested at 9% annual interest, how long will you be able to receive a…

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Q: A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12). Find…

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Q: The point x = 0 is a regular singular point of the given differential equation. 3x²y" - xy + (x² +…

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Q: Joe and his partners have contracted to purchase the franchise rights, worth $66,000, to open and…

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Q: D

A: We have to solve given problem:

Q: All row exchange matrices are symmetric: pT= P. Then pT P = I becomes  P2 = I. Other permutation…

A: Let P be a permutation matrix. (a) If P be a permutation matrix which sends row 1 of Identity to Row…

Q: Choose the correct option(s). 1. The two-point forward difference requires two nodes to approximate…

A: TASK: To Select the correct option and explain: (a) The two-point forward difference requires two…

Q: , Examine the tables below and answer the questions that follow. Table A Table B Year 0 1 2 3 4 5 6…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Problem 1. ²+2 (a) Let f: RR be defined by f(x) = Compute f'(x) and determine where f(x) is…

A: The derivative of a function of a real variable measures the sensitivity to change of the function…

Q: Find the points on the cone z2 = x2 + y2 that are closest to the point (6, 2, 0). smaller z-value…

A: Given equation of the cone z2=x2+y2 Let x,y,z be the point on the cone Therefore the distance…

Q: Give an example of a unique factorization domain with a subdomainthat does not have a unique…

A: We know the definition of unique factorization domain UFD, An integral domain D is unique…

Q: 19 Suppose A is a 3 by 3 symmetric matrix with three different eigenvalues, and that two of the…

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Q: 5 A homeowner needing carpeting has calculated that 145 sq yd of carpet must be ordered. However,…

A: Solution:

Q: If f(z)= |z1²., at what points are the Cauchy-Riemann equations satisfied? Justify.

A: Let z=x+iy and f(z)=u(x,y)+iv(x,y) . Then f is said to satisfy the Cauchy-Riemann equations at a…

Q: Using the definition of limit (so, without using Arithmetic of Limits), show that i. limn→∞ 2/n +…

A: We have to find the limit using definition of limit.

Q: k=1 (-1)kke-k²

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Q: Let a, b, n E Z. Prove: If an and bln with gcd(a, b) = 1, then abln.

A: If g(a,b)=d then there exist r and s such that ar+bs=d. If a|c then it means there exists x such…

Q: Let V be the set of all polynomials over Q of degree 2 together withthe zero polynomial. Is V a…

A: The set of all polynomials over Q of degree 2 is given by V=a+bx+cx2  a, b, c∈ℚ, where ℚ is the set…

Q: 22 Consider the linear differential equation Select one alternative: ○ (x³y)' = x² ○ (x³y)' = x³ ○…

A: The given linear differential equation is ,               dydx+3xy = x (.)  Solution of a first…