Determine whether each of the following counting problems can be solved by using permutations or combinations, and answer each question. Find the number of ways in which 8 members of a space shuttle crew can be selected from 20 available astronauts.

Q: y² 4. Find an equation of the tangent line to the ellipse += point (2,,-V3) 1 at the 16 4 Select the...

A: We have given the ellipse -                              x216 + y24 = 1 We have to find the equation...

Q: Evaluate the integral. w2 In(w) dw

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Q: Let f (x) = ex - e2x. Find all extreme values (if any) of f on the interval [0, 1]. Determine at whi...

A: We have to find the maximum and minimum value of given function

Q: (a) For g(x, y) = Vg(4,3) = x2 +5y+18, (b) Find the best linear approximation of g(x, y) for (x, y) ...

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Q: A single infected individual enters a community of n susceptible individuals. Let x be the number of...

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Q: 50. Find the vector from the origin to the point of intersection of the medians of the triangle whos...

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Q: A 5-m ladder leans against a wall. Assume the bottom slides away from the wall at a rate of 0.6 m/s....

A: Given that, A 5-m ladder leans against a wall. And Bottom Slides Away from the wall at a rate of 0.6...

Q: - 15x + 14x +2 dy DA. dx - 30 – 2x = dy O B. dx 15x + 14 +2 - dy D C. = - 30x - 2x2

A: we have to find the derivative of y=-15x3+14x+2x

Q: (c) For what values of a and b does the function (ах- 3, x< 4 f(x) = } (-x? + 10x - b, x24 satisfies...

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Q: The Taylor series for f(x) = In(sec(x)) at a = 0 is > Cn(æ)". n=0 Find the first few coefficients. c...

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Q: Write the equation of the circle of radius 5 and center (3, 4) in the form r = a cos θ + b sin θ.

A: Given: Center =(3,4) Radius = acosθ+bsinθ  

Q: Find all solutions of the equation in the interval [0, 2x). (Enter your answers as a comma-separated...

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Q: Factor the expression. Use the fundamental identities to simplify, if necessary. (There is more than...

A: We have to factor

Q: In Problems 27–38, determine whether the equation defines y as a function of x. 27. y = x? 28. y = x...

A: Given, a). y=x2b). y=x3c). y=1x To determine that function exists for the given equations.  

Q: help

A: We find polynomial with given zeros

Q: In Problems 39-46, find the following for each function: (a) f(0) (b) f(1) (c) f(-1) (d) f(-x) (e) -...

A: (39)    f(x) = 3x2 + 2x - 4       (a) f(0) = ? (b) f(1) = ? (c) f(-1) = ?

Q: Determine absolute convergence, conditional convergence, or divergence

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Q: The solution of the following differential equation yfv – 9y" + 20y = 0 , is y(x) = ce2x + Cze¯2x +c...

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Q: If someone could please help me find the derivative, I'd greatly appreciate it

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Q: The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a...

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Q: Explain why the inequality x2 - x + 1 &lt; 0 has the empty set as the solution set

A: Given inequality: x2-x+1&lt;0    

Q: Find the Limit of a Quotient:

A: Given, limx→2x2-4x+13x-5

Q: 1 Determine whether the integral #(lnr)3/2 da converges or diverges. If it converges, give its value...

A: I have used limit method  to evaluate

Q: Find y" if y = 8x sin x. O A. y" = - 16 cos x+ 8x sin x O B. y" = - 8x sin x OC. y" = 16 cos x- 8x s...

A: If y= 8xsinx then find y''

Q: Let R be the region bounded by the following curve. Use the shell method to find the volume of the s...

A: Please see the explanation below

Q: Find the x- and y- intercepts (a,b) of the line L: x- 2y = -4

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Q: Please answer quick! Show all work!

A: All option correct

Q: Find the orthogonal trajectory. y = ke-Sx

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Q: Show that the inequality (x - 2) 2 &gt; 0 has one real number that is not a solution.

A: x-22&gt;0

Q: Use the Newton-Raphson method to find the roots of equation cos x = x correct to 4 decimal places.

A: Please see the explanation below

Q: Please answer quick! Show all work!

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Q: Q3/Discuss the behavior of the following function as x 0: f) = sinx

A: Please rate and feel free to ask any query about any part of the question 

Q: C1. A rectangular room was designed to be built for a length of 15 m and a breadth of 20m. Find the ...

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Q: Discrete Math: Prove for all sets A,B,C if A⊆B, then C−B⊆C−A.

A: Three sets A, B, C are given such that- A⊂B To show- C-B⊂C-A

Q: n exponential function

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Q: In Problems 1–3:(a) Determine the slope and y-intercept of each linear function.(b) Find the average...

A: Given That, 1. f(x)=2x-5 2. h(x)=45x-6 3. G(x)=4   We have to find the Slope and Y-intercept of each...

Q: (2) Find dt2 if y = x2 + 3x -7 and x 2t + 1 | 2

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

Q: 1) 2xỳỳ = (ỳ)² + 1 %3D

A: As you have posted multiple questions so according to our guidelines we will solve only first questi...

Q: (c) Consider the following graph of a function y = f (x): -6 -3 -2 -1 -2 Sketch the absolute value I...

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Q: Determine whether the function is even, odd, or neither. g(x) = x−1

A: gx=x-1⇒gx=1x A function f is said to be even function if f-x=fx and odd function if f-x=-fx.

Q: Find the area of the region that lies beneath the given curve.

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Q: Please help solve all parts. Thanks

A: “Since you have posted a question with multiple sub-parts,  according to our guidelines we will solv...

Q: Find all the roots for the polynomial. For each root, state it's multiplicity. f(x) 36x – 37x³ + ² %...

A: f(x)=x^2(36x^2-37x+1) f(x)=x^2(36x^2-36x-x  +1)            factories f(x)=×^2(36x-1)(x-1)  

Q: We're solving using FTC

A: We have to solve this

Q: 2) Graph a typical solution curve. dy ye' – 9y - dx e

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Q: Use similar triangles to find the coordinates of the point Q that di- vides the segment from P1(x1, ...

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Q: Can you please solve this question step by step?

A: In the question it is asked to calculate order of differential equation. also it is asked to show wh...

Q: Find the product. Leave the result in trigonometric form. (Let 0 s0 < 2x). Зл |클(cos() + / sin( cos ...

A: Answer

Q: Consider the following vector field.F(x, y, z)  =  9yz ln x i  +  (4x − 7yz) j  +  xy8z3 k (a)...

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Q: Please answer quick! Show all work!

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Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.