In a coffee shop “Scratch and Win" contest, one out of three cards is a winner. What is the probability that Shenice would first win on her third try? a. 4 C. 4 27 b. 1 d. 27 81

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A: We have to prove that 0<ak≤1 for all k using the proof by induction.

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A: Given in box all are green tick are correct .

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Q: the initial value problem (y2 – 1)y' – a² – 1 = 0 with an initial condition of y(0) = y0 in the…

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Q: Consider the following weighted voting system [13: 7, 4, 3, 3, 2, 1], what is the weight of P3?

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Q: B. Find the area of the region bounded by the following: r=8sin² ¹0 16.

A: Here we can use the following formula for the area of the polar curve  A=∫∫A r drdθ

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Q: 4-2. (a). What is the coefficient of x’ in (1–x)º (b).What is the coefficient of x7 in (1–x)-9 i AL…

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Q: 29-35 REAL INTEGRALS Evaluate by the methods of this chapter (showing the details): de 29. 25 - 24…

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Q: s of the quadrilateral are parallel. of the quadrilateral are congruent of the quadrilateral are…

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Q: How many different initials can someone have if a per son has at least two, but no more than five,…

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Q: Use Gram Shmidt Algorithm to build an orthonormal basis beginning from the given basis in R: (1, 1,…

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Q: Evaluate the triple integral 1 V1-y V4-z? y? COS cos (z? + y? + z?) dzdzdy. V12 + y? + z2

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Q: 1 2 3 4 6 7 8. 9 10 ATA 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

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Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (y²…

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Q: H.W: Use the root test to determine the following series converge or diverge: 2. a-c*y 1. 5" n=1 n=1

A: 1. Given series is ∑n=1∞n5n Here an = n5n So limn→∞an1n = limn→∞n5n1n = 15 < 1 Hence by Root test…

Q: H.W: Which of the sequences {a,} converge and which diverge: 2. an 1+- 1. a, = 2+(0.1)"

A: 1. Given sequence is  an = 2 + (0.1)n Here limn→∞an = limn→∞2+(0.1)n = 2 + 0 = 2 Which is unique and…

Q: (0 1 1 A=|1 0 1 1 1 0,

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Q: 11. Which system of linear equations has the solution (2, 3)? A. 2x - 5y = 9 x-y = 4 C. 9x - 8y = 19…

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Q: Find the matrix of the quadratic form. Assume x is in R?. a. 3x - 8x,x2 + 2x3 b. 5x, + 18x,x2

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