Counting technique: Seven children are to be selected from a group of nine children. a) What is the probability that Danylo and Shuying are included? b) What is the probability that Danylo and Shuying are not included?

Q: (d) Find the coordinates of the inflection point. Hence state the intervals for which the curve is c...

A: A graph is given in the questionx-intercepts: -1,0, 1,0, 2,0y-intercept: (0,1)

Q: "sin²(x) + sin(x) os²(x) To evaluate the -dx using basic formula of integration (without using subst...

A: Let's find. 

Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded b...

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Q: 0 -2 0 4 2 0.5 a 2 ,X= Y= 3 7 Let A= b 2 -1c and Z= Given that X + Y = Z, find- if 3 d possible-: (S...

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Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as improper f...

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Q: *(1,). What is the equation of the line that is tangent to the graph of y = at (x³ + 1)?

A: We can find the equation of line as below.

Q: Evaluate the integral. 6 dx 16

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Q: Determine whether the series converges, and if so find its sum. f the series diverges, indicate that...

A: Topic:- sequence and series

Q: y'-2y/x=x^2e^x x=1 and y=0 solve using linear equation (diff eq

A: Given :y'-2xy=x2ex

Q: For the following exercises, draw the region bounded the curves. Then, use the disk method to find t...

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Q: Problem 5 Given the function f(x) = 9 – 2x² a) Calculate the difference quotient at the two points P...

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Q: Given the functionf(x) = x² – 2bx +c, where b and c are constants, determine the values of b, and c ...

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Q: Consider the function f(x, y) = x2 + 2y2 – 4x – 4y, defined on R². Find and classify all the extrema...

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Q: Determine the value of , f(x)dx given that f(x)dx = 3 and f(x)dx = 8.

A: Question no. 2,Given,           ∫52fxdx=3 and ∫59fxdx=8To find : Determine the value of ∫29fxdx.

Q: What is the reference angle for the given angle measure drawn in standard position? Drag an angle me...

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Q: Find the derivative of f(x) = Inx + 1].

A: f(x) = ln [x2x2+1]f'(x) = ddx[ ln [x2x2+1] ]f'(x)= 1 x2x2+1 ddx[x2x2+1]

Q: 6. If f(2) = 3,f'(2) = 5, g(2) = –1, and g'(2) = –4, find (f g)'(2).

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Q: If F is a continuous on the set of real numbers, then SnF(x)dx = rfFlx)dx (A) True B) False

A: topic- indefinite integral

Q: Find one real root of ln(x^4) = 0.70 using five iterations of bisection method on the interval (0.5,...

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Q: The height of the cylinder is 8 inches.   We'll be analyzing the surface area of a round cylinder ...

A: We have to find the domain, inverse function and evaluate r(275).

Q: 1. Sx2 In(x + 1) dx

A: Note: - “Since you have asked multiple questions, we will solve the first question for you. If you w...

Q: Eliminate the arbitrary constants. Show your solution

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Q: 56. Slopes on the graph of the cotangent function Graph y cot x and its derivative together for 0 <x...

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Q: Evaluate the following integrals: dx 1. Vzax-x2

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any ...

Q: Let f(æ) (3- 2æ) 3. 2x)* f(r) has one critical value at A = For a A, fx) is Increasing Decreasing

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Q: Physically, integrating f(x)dx means finding the area under the curve from a to b area to the left o...

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Q: 3e"dx 3x 1. 3x – 16 2. x 10 – 3x°dx 3. / In (cos®) an@ de 3.

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Q: The number of wiretaps authorized each year by U.S. state courts from 1990 to 2015 can be approximat...

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Q: Find the area of the region that lies under the graph of f over the given interval. Please solve usi...

A: Topic:- application of derivatives

Q: If the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the poin...

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Q: 10. Do the required operations and simplify. State any restrictions. (x+1}*x (x-1)? x+2x-3x+4x+3 a)....

A: We can simplify the given questions as below.

Q: In each part, find a formula for the general term of the the sequence, starting with n = 1. 1 1 1 (a...

A: A detailed solution is given below

Q: show complete solutions

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Q: d) f(x) = (2r – 3)*(5x² + 2)'

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Q: The figure shows the median lifetime eamings E in dollars determined by the highest level of educati...

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Q: xy'=y-√(x^2-y^2) solve using homogenous equations (diff eq)

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Q: Suppose that {a, } is a monotone sequence such that a, 10 or increases- in this case we can't say w...

A: We need to choose correct options.

Q: 8. For the quadratic function f(x)=2x² – 24.x+90 (a) Complete the square to put the equation into a(...

A: Given query is to find the the vertex form and the minimum value of f.

Q: F+9 2x-(4+F) 4. Let f(x) = VBx -(F+5) h(x) = Vx + (k + 3+ F) and g(x) = . Answer 8+K the followings:...

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Q: Rewrite the integration in terms of u. 1 x cos 10rx² dx = COs u du Apply the constant multiplication...

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Q: f (2) 2. Find if Ar) -(1-x²)(* -1) =

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Q: (c) Determine with justification whether each of the following functions R → R is one-to-one, onto o...

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Q: A ladder 10 meters long rests on horizontal ground and leans against a vertical wall. The foot of th...

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Q: p) Find f o g oh with its domain of definition: f(x) = |x – 4|, g(x) = 1 ,h(x) = Vx %3D %3D X - 1 c)...

A: We have to find the domain of the function in first problem.  We also have to find the function g(t)...

Q: Find the derivative of: 4√x

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Q: Ans. 15, 22, 30 6. In a triangle, the smallest angle is half of the largest angle and the other angl...

A: In a triangle, the smallest angle is half of the largest angle and the other angle is 8 degrees larg...

Q: A baseball diamond is a square 90 ft on a side. A player runs from first base to second base at 15 f...

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Q: 3. Set-up the definite integral(s) to get the area of the shaded region. y = (x – 1)2 + 3 y = -x2 + ...

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Q: Regian bounded by y-x and y=X+2

A: Since you have posted multiple question in this question which are not interlinked so i have solved ...

Q: Let f(x) = (3 – a) f(1) has one critical value at A = For I < A, f(r) is Select an answer Select an ...

A: We have to find the critical point and monotonic intervals.