A car runs over a nail and the nail gets caught in the tire tread. The tire has a diameter of 40 cm and rotates at a rate of 10 revolutions per minute. The function, h(t), represents the height of the nail in cm, and t represents time in seconds. • State the amplitude, • the equation of the midline, the maximum and minimum values, and

Q: Find the point on the graph of f (x) = (9x + 8)/æ + 5x (x > 0) at which the tangent line is…

A:

Q: A batter hits a baseball at a point 3 feet above ground at a velocity of 100 feet per second and an…

A: Given: f(x)=-0.0032x2+x+3 Determine the height of base ball at a distance of 300 feet.

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A: f(x) = 4πx33 Volume of sphere , f(x) = 4πx33 where,  x is the radius of sphere in inches.…

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Q: A parking lot charges $2 per hour for the first 4 hours, then $3 per hour after that. Which…

A: Given, a parking lot charges $2 per hour for the first 4 hours, then $3 per hour after that. Let the…

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A:

Q: (c) F{-h(x+ 1) + 2h(x) – h(x – 1)}, where h(x) is the unit step function defined on page 235 of the…

A:

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A: (b)

Q: Find the point P on the graph of the function y=sqrtx closest to the point (9,0) The x coordinate of…

A: We have to find the point P on the graph of the function y=x closest to the point (9,0). Also, find…

Q: Find f′(x) and find the equation of the line tangent to the graph of f at x=3.   f(x)=7x/2x

A: Given query is to find the equation of tangent line to f(x) ate x=3.

Q: A ball is projected off of a 400-ft-tall building at a velocity of 45 ft/sec. The function f (x) =…

A:

Q: Find the slope m and the equation of the tangent line to the graph of the function f at the point…

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Q: Solve f(x) = (1/5)x where f(x) = 0 ( do not convert it to decimal form)

A:

Q: The function f(x) = (4/3) πx3 describes the volume, f(x), of a sphere of radius x inches. If the…

A: fx=43πx3 Differentiating with respect to x, we get f'x=ddx43πx3=43π·3x2            ∵dxndx=nxn-1=4πx2

Q: If an object is projected upward from ground level with an initial velocity of 96 ft per sec, then…

A: The function for height of the object is given as: S(t) = -16t2+96t We have to find: (a) Time taken…

Q: The acceleration of a moving body is given by the function a = 6t +4. If the velocity after 4…

A: Given, Acceleration of the body  a=6t+4 Velocity after 4 seconds = 70m/s Displacement in that time =…

Q: The amount A (in g) remaining of a radioactive substance after time t (in years) is found by solving…

A: We have to solve the differential equation as a function of t.

Q: Juanita wishes to have a rectangular garden in her backyard with an area of 64 ft2. Letting x denote…

A: we know that area of rectangle =  length × width

Q: Find an equation for the line tangent to the graph of f(x)=−7xe^x at the point (a,f(a)) for a=2.

A: Given:

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A: Given function fx=x2 To find rate of change of area.

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Q: Suppose that a particle has been shot into the air in such a way that the rate at which its height…

A: v = 320 - 32tIf h represents the height of the particle at any time t, then:v = dh / dt = 320 - 2t

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A: Given function fx=x2 to find rate of change of area.

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A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: If we put a cool object into a preheated oven, Newton's law of heating tells us that the difference…

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Q: The slope of the line tangent to the graph of f(x) = 19 – 4x² at the point x = -9 18 8 O 152 72 144

A: Given that: f(x)=19-4x2

Q: Find a formula for a cubic function f if f(1) = 6 and f(−1) = f(0) = f(2) = 0.

A:

Q: Find the function f whose graph has slope 2x2 + 4 df dx and which passes through the point (1, 1).

A: Given: The slope of the function is, dfdx=2x2+4x

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Q: The function f(x) = πx2 describes the area of a circle, f(x), in square inches, whose radius…

A: Given,  The area of the circle is described by the function  fx=πx2 in square inches. Where x is the…

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A: The area is found by making a function of area into a variable and finding the values at which…

Q: Find the average rate of change of f(x) = 7x² – 4 on the interval (3, b]. Your answer will be an…

A: Finding the average rate of a function in a given interval

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Q: 8. 4 2

A: In this question we will use basic of calculus i.e use of tangent function. We will write the…

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A: Consider the intercept points, 54,0    and    0,-1

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A: Consider the function that describes the area of a circle  fx=πx2

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Q: The function f(x) = 4ᴫx2 describes the surface area, f(x), of a sphere of radius x inches. If the…

A: Given: The surface area of a sphere is, fx=4πx2 . Radius of the sphere is, x=6 inches. The…

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Q: Find the average rate of change of f(x) = 7x² – 4 on the interval [3, b]. Your answer will be an…

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Q: The amount A (in g) remaining of a radioactive substance after time t (in years) is found by solving…

A:

Q: Find the point P on the graph of the function y= sqrt(x) closest to the point (6,0)The x coordinate…

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Q: Determine the equation of the function whose amplitude is half the original function, the period is…

A: To determine: The equation of the function whose amplitude is half the given function, the period is…

Q: The velocity of Engr. Garcia in meters/sec when he jumped out of the plane given is given by the…

A: Velocity is given by the formula v(h) = (9.8)(2)(h) , where h is the height Here we need to find the…

Q: A batter hits a baseball at a point 3 ft. above ground at a velocity of 100 ft. /sec and an angle of…

A: Function value at any point can be found out by substituting point in function.

Q: A ball is thrown into the air with an initial upward velocity of 48 ft/s. The height () of the ball…

A: Given, initial upward velocity = 48 ft/s h(t)=-16t2+48t+4

Q: According to a mathematical model of coughing, the velocity v, of the airstream is related to the…

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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.