Find a positive number for which the sum of its reciprocal and four times its square is the smallest possible.

Q: A cat is falling from a branch. Its height t seconds after it fell is given by the function h(t) =…

A: We have given height  ht=-16t2+5 To get for what height cat was falling  Put t=0 h0=0+5 h0=5 height…

Q: The quadratic function that has the same shape as y=x^2 but is shifted to the right 3 units and up 2…

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Q: Graph f(x) = 5x^3 +17x^2 – 14x – 8  Identify the variables, domain and range. Determine the data…

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Q: State the domain and range of each function a.4x-6y+12=0 b. y=4x^2+12x+9

A: Given :  a. 4x-6y+12=0 b. y=4x^2+12x+9

Q: Where is optimization often applied and what is its importance?

A: Solution:Optimization:Optimization methods are used in many areas of study to find solutions that…

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Q: (0, 3) 2 1- (2.0)

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Q: Eliminate the parameter tbut do not graph. x = cos 2t, y = cos t

A: Given : x = cos2ty = cost

Q: Sketch y= x^3-3x^2-105x Find minumum and max points and point of inflection  please show all steps

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Q: 4- 3- 2- 4 - -31/4-T/2\-T/4 -D1 TU2 3T/4 T/4 -2 -3 -4 -5- -6+ dentify the function whose graph…

A: The graph is a cotangent function because y(0)=∞and y(π)=∞. The general function of the graph is…

Q: Identify all solutions of the function: H(m)=12m^3(m-18)(m+63)(m^2+25)

A: Given:

Q: 65. lim x→0 sinx(1 - cos x) x²

A: Limit

Q: - Define a recursive function f(h) for the sequence in terms of f(h – 1). f(h) = I Define an…

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Q: Problem 5. Suppose a large tank contains 20L of pure water, into which 10 grams of lactose is…

A: (a)Given that the tank has a total capacity of 100L. Initially, 10g of lactose is added in 20L of…

Q: The circle x^2+y^2-6x-10y+k=0 does not touch or intersect the coordinate axes,and the point (1,4) is…

A: The equation of the circle is                  x2+y2-6x-10y+k=0    ...(1)whose center is C(3,5) and…

Q: State the domain and range for the function f(x)=2x^2 - 7.

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Q: Write an equation for the function graphed below. f (x) = ±Gfunction (x – H) + K 土 [ Select ] G = […

A: NOTE: Refresh your page if you can't see any equations. . as we can see, the given graph represents…

Q: Fix this equation please, it should be a peicewise function/step function.

A: According to the given information, the price for a child's pass is $38.99; the price for an adult's…

Q: Create a graph that best represents f(x)=6x^2-5. Then identify the vertex and find the axis symmetry

A: This question is based on graphing a parabola.

Q: y=x^2 + 6x+ 3 function in vertex form, the graph to represent the function

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Q: Graph A Graph B Graph C Graph D

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Q: In (x³ – 2x² - 5x+6) -

A: The given function

Q: Write a function that reflects f（x）= 2x^3 + 1 across the x-axis and shifts it 3 units down.

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.