In a random check on an assembly line, the probability of finding a defective item is 0.005. Determine the following probabilities: a. P(exactly 5 defectives out of 15 items inspected) b. P(5 or less defectives out of 15 items inspected) c. P(at least 3 defectives out of 15 items inspected)

Q: Evaluate the integral: LIVE 1 I√9r²+25 dr.

A: We will solve the given question using simple Integration rules.

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A: To show that , tan2x+1+tanx.secx=1+sinxcos2x

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A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Evaluate the following integral by using Odd and Even Powers Method: y = [₁ cos5 (1x) dx

A: We will evaluate the given integral by using odd and even power method in the following step.

Q: if Find: A = sin(u)i + was (u)j + (u)k B = cos(u) i - sin (u) j C = 2 i + 3j -K - 3K du [ A x (B x…

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Q: 3)Evaluate the following integral by using Trigonometric Substitutions Method. dx √√9x² +9

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Q: . For what values of a are the points (6, 2, 3) and (a, 2, 5) and the line = (2,-1,-2) + t(3,1,-2)…

A: I have appended the formula used in the solution part of the question

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Q: (x² - 12x + 9) dx (x²-3x + 2)²

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Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = 7 sin(x) + 7 cos(x),…

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Q: 2. Find y' if y = 7* (log4 x)⁹.

A: The given function y=7xlog4x9

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Q: 1. Find the area of the region that lies inside the cardioid T-1+ sin 0 and outside the circle r -…

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: Solve 5^(x-3)=2^(6x-8)

A: Topic = Algebra

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A: This is a problem related to graph function. Based on the general formula and concept we will answer…

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Q: Use the table of integrals to evaluate the integral. (Use C for the constant of integration.) 9 sec²…

A: This question can be solved using the concept of integration by substitution.

Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A:

Q: Q6) Find the Area bounded by the curves y = √√x and x = 2y-y² ,with sketch.

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Q: 2. Find y' if y = 7* (log4 x)⁹.

A:

Q: Find a point on y = x closest to (18,0) For what x is the slope of the tangent line at x to the…

A: Given

Q: Graph the parabola y=(x^2-100x)/50

A: Graph the parabola y=(x^2-100x)/50

Q: Ive the given differential equation using two (2) methods. (x² + 6y2) dx - 4xydy = 0; if x = 1, y =…

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Q: Verify Property 2 of the definition of a probability density function over the given interval. f(x)…

A: Given problem:- Verify Property 2 of the definition of a probability density function over the given…

Q: Q5) Evaluate the following integral by using Partial Fractions Method 2x²-3x+2 y = dx -

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Q: Q2. Find the angle between the vectors and .

A:

Q: Use the midpoint sum formula to calculate the area under the curve f(x) = x³ from x=0 to x-12 using…

A: Given: f(x)=x3 from x=0 to x=12 using 4 rectangles with width h=3

Q: 4) Find the intervals where the following function is concave down: ππι y = 2sin² (2x) - 4x, x € -

A:

Q: (x² - 12x + 9) dx (x²-3x + 2)²

A:

Q: 6. If q p² p³ - 1 9² p2 µ³ – 1 1 = 0, show that pqr = 1. - 22

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Q: = 8* can be obtained from the graph of g(x) = 8 by one of the following The graph of the function…

A: We have f(x)=-8x and g(x)=8x So, f(x)=-g(x)

Q: Rewrite the expression without the log of a product, power or root. 108₁ (2¹3√10)-[ log3 =

A:

Q: The doubling period of a bacterial population is 10 minutes. At time t = 80 minutes, the bacterial…

A: Given: The doubling period of a bacterial population is 10 minutes. At time t =80 minutes, the…

Q: 2 /// }} لال ملاملا

A: The given equation is;  y'''-y''-6y'=ex.

Q: 3 -6 -4 -3 4 Let y = V1 = 1 5 -1 Compute the distance d from y to the subspace of R4 spanned by v₁…

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Q: The value of the following limit Lim (cos(x))ou(x) IS:

A:

Q: 1. For the vectors v = and u = a. Find v-u b. Find ||v|| and ||u|| c. Find the angle between v and…

A:

Q: A rope is attached to a boat at water level, and a personon a dock is pulling the rope at the rate…

A: Let's find speed of boat.

Q: 2) Find the length of the shortest ladder that can pass over a fence 1.8 m high and reach a wall 3 m…

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Q: Find the limit, if it exists. (If an answer does not exist, 3 - xy ху lim (x, y) → (2, 1) x² +2 +9y²

A: We will apply the limits.

Q: Provide your answer below: Domain in interval notation is Range in interval notation is

A: This is a problem related to domain and range of the function. Based on the general formula and…

Q: You want to purchase a building to open your restaurant and you are given 3 different payment…

A: Here, the total amounts of the payment schedules are to be compared. i. The upfront cash payment is…