150 students were polled. 75 of them are learning Hindi. 60 of them are learning Italian. 40 of them are learning neither Hindi nor Italian. How many of them are learning both Hindi and Italian?

Q: 0.5 -0.5 1A) Using the direction field graph below, find y(2) if y(0) = 0. (Note the vertical and…

A: In the slope field graph below ,  Blue curve represent the solution when the initial condition is…

Q: n Consider Dn, the dihedral group of order 2n. Let Rn =, which is a cyclic subgroup of order n. Let…

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Q: How are double integrals evaluated as iterated integrals? Does the order of integration matter? How…

A: To Explain: How are double integrals evaluated as iterated integrals? Does the order of integration…

Q: 27 20 Y()=0, YOX=5 Use laplace transform to Solve the initial value problem: y" +9y=68 (+-5) y (0) =…

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Q: (a) Derive a finite difference formula for the first derivative by using three terms plus the…

A: Question number- (2) (a) We need to derive finite difference formula for the first derivative by…

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Q: 7. If y varies directly with the square root of x, and y = 48 when x = 4, (a) Find the variation…

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Q: A tank initially contains 60 gal of pure water. Brine containing 3 lb of salt per gallon enters the…

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Q: Use the laplace transform to solve the initial value Problem y" + ay = cos(4x) y(0) = 0, y₁ (0)=0 Y…

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Q: Let T be a linear transformation between n-dimensional vector spaces V and W, where a = (a₁, a2,…

A: It is given that T:V→W is a linear transformation such that Tαβ=Iαβ, where α=a1,a2,⋯,an and…

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Q: 10. r(t) = F(t) x G(t), where F(t) = t³i – tj + tk, G(t) G(t) = 3√/ti+ 1 t + īj + (t + 2) k -j 1

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Q: (b) A factory has three resources, steel, labour and electricity. The fol- lowing table shows the…

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Q: Wilderness Fanatic, a manufacturer of outdoor goods, is willing to supply 1100 of its Blue Thrash…

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Q: Find an LU factorization of the matrix A (with L unit lower triangular). L = U= A= -50 3 15 2 6 15 8…

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Q: - Show that the equation of the circle passing through (1, 1) and the points of intersection of the…

A: we need to show that equation of circle passing through (1,1) and point of intersection of given two…

Q: If the circle x^2+y^2=1 is completely contained in the circle x^2+y^2+4x+3y+k=0,then find the values…

A: The first equation of circle is x2+y2=1. The second equation of circle is x2+y2+4x+3y+k=0. To find…

Q: graph both the ne screen. Is the .-2 anction k(t). pe of the curve. 0≤t≤8T sa curve y = f(x) tion y…

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Q: Mark each sequence {n} having the property that In In (-1)"n n+1 In |xn = (-1)" In = {cos(nn/3)} 1…

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Q: Jackie and Christine are racing again! We only get some discrete data this time, but we can find the…

A: Sol:- (a) We can plot their movements on the xy-plane as follows:         y-axis         |  C     *…

Q: x 1 Let c ER be the smallest positive root of f(x) = 20 x³-20 x²-25 x+4. Consider, g(x)=x²-x²_ 4 +…

A: As per the question we are given two polynomial functions f(x), g(x) and we have to : Show that…

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Q: You may need to use the appropriate appendix table or technology to answer this question. Ahmadi,…

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Q: For each equation prove if it is convex: (either using linear algebra or prove by points) A. f(x) =…

A: Definition of convex:-  A function f from R to R is said to be convex if it's second derivative is…

Q: Consider the triangle, A ABC, in R³, given that the three vertices are A = (-1,2,0) B = (1,0,1) C =…

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Q: Show that if C₁,C₂: Rd x Rd → Problem 2. (Non-negative definite functions R are non-negative…

A: Non-negative definite functions: A function f(x, y) is said to be non-negative definite if it…

Q: Find the point(s) on the curve of y = = x²+1 where the tangent line is horizontal.

A: Given curve : y=xx2+1

Q: Find the particular solution. 3. (D³ + D² + 4D + 4)y = 0; when x = 0, y = 0, y' = -1,y" = 5 4. (D² -…

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Q: Use the graph to determine a. the function’s domain; b. the function’s range; c. the x-intercepts,…

A: From the given graph, we have to find its domain, range, x-intercepts, y-intercepts, and the…

Q: Consider the graph and determine the open intervals on which the function is increasing and on which…

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Q: Mark all the true statements about sequences of real numbers. If the limit superior of a bounded…

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Q: The natural number a divides the natural number b.

A: We have to translate the following statement into a quantified sentence. "The natural number a…

Q: Find a bijection between the following sets: (a) (8,00) and R. (b) (-8, 8) and R. (c) {-1,1} x N and…

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Q: One method of slowing the growth of an insect population without using pesticides is to introduce…

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Q: 1. Given ARST, R = 66°, S = 72° and t = 6.4. Solve for the missing angle and the two missing sides…

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Q: Give an example of a 2 x 3 matrix A and a vector b so that the system Az = b has special solution 35…

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Q: 3. We consider the following linear system: 1 2 X1 (90-0 4 30 x2 X3 022 1 (a) Solve the following…

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Q: (It may help to draw a picture for this question). Let A, B, C be three points with position vectors…

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Q: Let A be a lower triangular nxn matrix with nonzero entries on the diagonal. Show that A is…

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Q: 8. State whether the following infinite geometric series are convergent or divergent. State the…

A: Given Data: Let us consider the given data, a. t1=144 , r=-112-112b. -5+10-20+40+.....c.…

Q: Let X be a discrete random variable that takes on the values -2, 3, 4, 5, 6, 7 with respective…

A: "Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: Problem 3. How many 7-digit numbers have no two adjacent digits equal.

A: To count the number of 7-digit numbers with no two adjacent digits equal, we can use the following…

Q: Let U and V denote vector spaces over F. Consider o: U →→ V denote a linear transformation where…

A: Null space (σ) is a subspace of the vector space U and its dimension is nullity(σ)=m. Let…

Q: Solve the equation Ax = b by using the LU factorization given for A. Also solve Ax = b by ordinary…

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Q: 5. If A is a set with 5 elements, how many elements are in P(A), the power set of A.

A: The given problem is to find that how many elements are there in power set of A, P(A) Given A is the…

Q: Suppose that a motorboat is moving at 49 ft/s when its motor suddenly quits, and that 9 s later the…

A: Sol:- We can solve this problem by using the differential equation dv/dt = -kv, where v is the…

Q: (a) If supA < supB, show that there exists an elementb ∈ B that is an upper bound for A.(b) Give…

A: (a) Given: supA < supB, To show: that there exists an element b∈B that is an upper bound for A.…

Q: 1. 2. 3. Consider inverse. 0 -27 -1/2 -3 1 4 -3 4 Use the algorithm from Section 2.2 to show that A…

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Q: must give each answer written 9+6log_(4)x=14

A: must give each answer written 9+6log_(4)x=14

Q: We want to train a mouse to follow a particular path in the maze (see image 1). To measure the…

A: The Behavioural Assessment Matrix (BAM): It is a tool used in applied behaviour analysis to identify…