The perimeter of a rectangle is 40 cm. The length is 14 cm.
Let x = width of the rectangle.

Ravi says he can find the width using the equation 2(x + 14) = 40.
Fran says she can find the width using the equation 2x + 28 = 40.

Answer the questions to solve the equations and to compare the steps and solutions.

1. Which of these is the most helpful first step for solving Ravi's equation, 2(x + 14) = 40? (1 point)

Circle the best answer.

Add 14 to both sides
Subtract 14 from both sides
Divide both sides by 2
Multiply both sides by 2

2. What would your next step be? (1 point)

3. Solve Ravi's equation, 2(x + 14) = 40, to find the width of the rectangle. Show your work. (1 point)

4. Which of these is the most helpful first step for solving Fran's equation, 2x + 28 = 40? (1 point)

Circle the best answer.

Multiply both sides by 2
Subtract 28 from both sides
Divide both sides by 2
Add 28 to both sides

5. What would your next step be? (2 points)

6. Solve Fran's equation, 2x + 28 = 40, to find the width of the rectangle. Show your work. (2 points)

7. The two equations have different solution steps. Do they have the same solution? Use the distributive property to show why this answer makes sense. (2 points)

The number of ways to choose only republicans is 330.                               The number of ways to choose the committee consisting of 1 republican and 6 democrats is 5005.                                                                                       The number of ways to choose the committee consisting of 1 republican and 6 democrats is 55055.                                  

The formula for this is ⁿCm is n!/((n-m)!*m!).

The number of ways to choose only republicans  = ¹¹C₇ = 330

The number of ways to choose one republicans = ¹¹C₁ = 11!/((11–1)!*1!) = 11

The number of ways to choose six democrats is ¹⁵C₆ = 15!/((15–6)!*6!) = 5005.

The number of ways to choose the committee consisting of 1 republican and 6 democrats from 15 Democrats and 11 Republican is :

¹¹C₁ * ¹⁵C₆ = 11!/((11–1)!*1!) * 15!/((15–6)!*6!) = 11 * 5005 = 55055

There are 55055 possible committees consisting of 1 republican and 6 democrats.

The number of ways to choose four republicans = ¹¹C₄ = 11!/((11–4)!*4!) = 330

The number of ways to choose three democrats is ¹⁵C₃ = 15!/((15–3)!*3!) = 455

The number ow ways to choose the committee consisting of 4 republican and 3 democrats from 15 Democrats and 11 Republican is : ¹¹C₄ * ¹⁵C₃ = 330 * 455 = 150150

There are 150150 possible committees consisting of 4 republican and 3 democrats.

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The graph created to represent this scenario is a histogram.

Graph is a data structure composed of nodes (vertices) connected by edges, which represent a relationship between the two nodes. Graphs are used to represent networks of communication, data organization, and even abstract concepts like thoughts or ideas. The nodes in a graph are often represented by circles and the edges by lines, but other shapes and symbols are also used. Graphs are a powerful tool for organizing and understanding data, and can be used to solve complex problems.

The x-axis represents the ages of the grandparents and the y-axis represents the number of people who fall into those age categories. The data is plotted in a bar graph format with the bars extending upward to represent the number of individuals in each age group. The highest bar is for those aged 83-84, with four people in this age range. The next highest bar is for those aged 85-86, with four people in this age range as well. The bars continue to descend in height as the age categories increase, with the lowest bar representing those aged 99-100, with four people in this age range as well.

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The next number in this sequence of cube numbers is 125

From the question, we have the following parameters that can be used in our computation:

1,8,27,64......

Each term of teh sequence is the cube of its position

So, we have:

Next term = 5^3

Evaluate

Next term = 125

Hence, the next term is 125

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Answer:

yes, Send me your questions

The sum of the infinite geometric series is 64/7.

Geometric progression is a sequence of numbers such that the ratio of two consecutive numbers is the same for whole sequence.

This ratio is common ratio.

Geometric series is the sum of the numbers in the geometric progression.

Sum of an infinite geometric series can be found by the formula,

S = a / (1 - r)

where a is the first term and r is the common ratio.

Given series is 16 - 12 + 9 - 27/4 + ...

a = 16

r = -12 / 16 = -3/4

S = 16 / (1 - -3/4)

  = 16 / (1 + 3/4)

  = 16 / (7/4)

  = 64/7

Hence the required sum is 64/7.

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The shear force diagram of a simply supported beam is parabolic when it is a linearly varying distributed load.

What is a shear force diagram?

A shear force diagram depicts the shear force's variation throughout the length of the beam.

Examples of internal forces that are produced in a structure when loads are applied include shear force and bending moment. Failures often result from loading in one of two ways:

A beam can be damaged either a) by being sheared across its cross section or b) by being bent excessively.

It is possible to define shear force as the algebraic sum of the loads to the left or right of a point, provided that doing so restores vertical equilibrium.

For the shear force diagram of a simply supported beam to be parabolic, then the load on the beam should be linearly varying distributed load.

The slope or load will vary linearly if the shear force diagram is parabolic.

Therefore the shear force diagram of a simply supported beam is parabolic when it is linearly varying distributed load.

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The derivatives of h(x) is h'(x) = √2 csc ([tex]x^4[/tex] + 1).

We have,

To find h'(x), we need to take the derivative of h(x) with respect to x using the Fundamental Theorem of Calculus.

Given that h(x) = ∫sin(2x - π/4) csc([tex]x^4[/tex] + 1) dt, we can rewrite it as:

h(x) = ∫[a, x] sin(2t - π/4) csc([tex]t^4[/tex] + 1) dt

Now, we'll apply the Fundamental Theorem of Calculus:

h'(x) = d/dx [∫[a, x] sin(2t - π/4) csc([tex]t^4[/tex] + 1) dt]

Using the Leibniz integral rule, we have:

h'(x) = sin(2x - π/4) csc([tex]x^4[/tex] + 1) - sin(2a - π/4) csc([tex]a^4[/tex] + 1)

However, we need to evaluate this derivative at x = π/4 and x = -π/4, so we substitute these values in:

h'(π/4) = sin(2(π/4) - π/4) csc((π/4)^4 + 1) - sin(2a - π/4) csc([tex]a^4[/tex] + 1)

h'(-π/4) = sin(2(-π/4) - π/4) csc((-π/4)^4 + 1) - sin(2a - π/4) csc(a^4 + 1)

Since the derivative is evaluated at the endpoints, the term with sin(2a - π/4) cancels out in both expressions.

Therefore, the derivative simplifies to:

h'(x) = sin(π/4) csc([tex]x^4[/tex] + 1) - sin(-π/4) csc([tex]x^4[/tex] + 1)

simplifying further:

h'(x) = (√2/2) csc([tex]x^4[/tex] + 1) + (√2/2) csc([tex]x^4[/tex] + 1)

Combining like terms, we have:

h'(x) = (√2/2) (csc([tex]x^4[/tex] + 1) + csc([tex]x^4[/tex] + 1))

h'(x) = (√2/2) (2csc([tex]x^4[/tex] + 1))

Finally, simplifying:

h'(x) = √2 csc([tex]x^4[/tex] + 1)

Therefore,

The derivatives of h(x) is h'(x) = √2 csc([tex]x^4[/tex] + 1).

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The complete question:

If h(x) = ∫sin 2x − π/4 csc (x^4 - 1) dt  for −π/4 ≤ x ≤ π/4, then h′(x)?

So, if the curve has a horizontal tangent, the values are = k, where k is an integer, and where the curve has a vertical tangent, the values are = (2k + 1)/2, where k is an integer.

A cardiod is a curve defined by the equation r = 1 + cos(θ), where r is the radial coordinate and θ is the angular coordinate. The equation can be re-written as r = 1 + cos(θ) = 1 + 2cos^2(θ/2) for 0 <= θ <= 2π. A curve has a horizontal tangent when its derivative with respect to θ is equal to zero, which means the slope of the tangent line is 0. The derivative of r with respect to θ is dr/dθ = -sin(θ). Thus, the curve has a horizontal tangent when -sin(θ) = 0, or θ = kπ, where k is an integer.

Here,

A curve has a vertical tangent when its second derivative with respect to θ is equal to zero, which means the rate of change of the slope is 0. The second derivative of r with respect to θ is d^2r/dθ^2 = -cos(θ). Thus, the curve has a vertical tangent when -cos(θ) = 0, or θ = (2k + 1)π/2, where k is an integer.

So, the values of θ where the curve has a horizontal tangent are θ = kπ, where k is an integer, and the values of θ where the curve has a vertical tangent are θ = (2k + 1)π/2, where k is an integer.

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9 feet is equivalent to 3 total yards since 3 feet is 1 yard. 3 feet wide is equivalent to 1 yard.

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The equation of plane will be x+y-2z=4.

A plane in geometry can go on forever in two dimensions. The absence of width. An illustration of coordinate geometry is a plane. The coordinates of a point in a plane determine its position.

In mathematics, a plane is a two-dimensional, flat surface that never ends. A plane is a two-dimensional equivalent that includes three spatial dimensions, a line, and a point. In some higher-dimensional environments, planes can resemble subspaces, as though the room's walls had been greatly extended. These walls possess a distinct existence all their own, just as in the framework of Euclidean geometry.

The equation of plane can be used to represent a plane surface in three dimensions. There are numerous methods that can be used to find the equation for a plane depending on the input values given. The equation for the plane can be expressed in either cartesian form or vector form.

Hence, the general form of the equation is A(x−x1)+B(y−y1)+C(z−z1)=0

Now,

The solution is provided in image.

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The rhombus have the meeting of the side length CD to be equal to 15.

A rhombus is a two-dimensional geometric shape with four equal sides and four equal angles, but the angles are not necessarily 90 degrees. It is a type of parallelogram.

Since all the sides of the rhombus are equal, then;

AD = AB = CD

4x - 9 = 2x + 3 = CD

we can solve for x as follows:

4x - 9 = 2x + 3

4x - 2x = 9 + 3 {collect like terms}

2x = 12

x = 12/2 {divide through by 2}

x = 6

so;

AD = 4(6) - 9

AD = 15.

Therefore, the rhombus have the meeting of the side length CD to be equal to 15.

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The set of all objects of interest is called population.

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a) z ⊂ r - True

b) z ⊆ r - True

c) z ⊆ r - True

d) n ⊂ r - True

e) z ⊂ n - False

What is the subset?

A subset is a set of elements that are contained within another set. The elements of the subset are referred to as its members or elements, and the set that contains the subset is called the superset.

In mathematical notation, if A is a subset of B, it is written as A ⊆ B. If A is not a subset of B, it is written as A ⊈ B.

Given the definitions:

z = {...-3,-2,-1,0,1,2,3,...} - The set of all integers.

n = {1,2,3,4, ...} - The set of all positive integers.

r = set of real numbers - The set of all real numbers (positive, negative, and zero).

(a) z ⊂ r - True. The set of integers is a subset of the set of real numbers.

(b) z ⊆ r - True. The set of integers is a subset of the set of real numbers.

(c) z ⊆ r - True. This is the same statement as in (b).

(d) n ⊂ r - True. The set of positive integers is a proper subset of the set of real numbers.

(e) z ⊂ n - False. The set of integers is not a subset of the set of positive integers.

Hence,

a) z ⊂ r - True

b) z ⊆ r - True

c) z ⊆ r - True

d) n ⊂ r - True

e) z ⊂ n - False

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The object is moving in a straight line from location d to location f. The velocity of the object at each location is indicated by the arrows and is increasing from location d to location e, then decreasing from location e to location f.

The object is moving in a straight line from location d to location f, indicated by the dotted line. The velocity of the object at each location is indicated by the arrows. At location d, the arrow is pointing in the direction of the movement and has a smaller magnitude than the arrows at locations e and f. This indicates that the velocity of the object is increasing from location d to location e. At location e, the arrow has the largest magnitude and is pointing in the same direction as the dotted line. This indicates that the velocity of the object is at a peak at location e. From location e to location f, the arrow is pointing in the opposite direction of the dotted line and has a magnitude that is smaller than the arrow at location e. This indicates that the velocity of the object is decreasing from location e to location f.

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An expression for the total number of coins Nancy and Bill have is

5x - 2 coins.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Nancy has x coins. Bill has 2 coins fewer than four times the number of coins Nancy has.

The numerical form of the statement will be for the total number of coins they both have is,

= x + (4x - 2).

= 5x - 2 coins.

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The given expression (5x² + 25x + 20) / 7x is equivalent to the expression [(x² + 2x + 1) / (x - 1)] × [(5x² + 15x - 20) / (7x² + 7x)].

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is - (5x² + 25x + 20) / 7x

The other two expression are -

(x² + 2x + 1) / (7x² + 7x)

Let the unknown expression be x.

So according to the question -

(x² + 2x + 1) / (7x² + 7x) × x = (5x² + 25x + 20) / 7x

Cross multiply the polynomials -

x = [(5x² + 25x + 20) / 7x] × [(7x² + 7x) / (x² + 2x + 1)]

Here, it can be seen that (x² + 2x + 1) is the expansion of (x + 1)² and (7x² + 7x) = 7x (x + 1).

Substitute these values into the equation -

x = [(5x² + 25x + 20) / 7x] × [7x (x + 1) / (x + 1)²]

Simplify the equation -

x = (5x² + 25x + 20) / (x + 1)

Here, it can be seen that (5x² + 25x + 20) is the expansion of 5 (x + 4) (x + 1).

Substitute these value into the equation -

x = 5 (x + 4) (x + 1) / (x + 1)

Simplify the equation -

x = 5 (x + 4)

Multiply the numerator and denominator by (x - 1) -

x = 5 (x + 4) (x - 1) / (x - 1)

x = 5x + 20 (x - 1) / (x - 1)

x = 5x² - 5x + 20x - 20 / (x - 1)

x = 5x² + 15x - 20 / (x - 1)

So the unknown expression is 5x² + 15x - 20 / (x - 1).

Verify by substituting -

[(x² + 2x + 1) / (x - 1)] × [(5x² + 15x - 20) / (7x² + 7x)]

Here, it can be seen that (x² + 2x + 1) is the expansion of (x + 1)² and (7x² + 7x) = 7x (x + 1).

Substitute these values into the equation -

[(x + 1)² / (x - 1)] × [5 (x + 4) (x - 1) / 7x (x + 1)]

5 (x + 4) (x + 1) / 7x

Simplify the equation -

5x + 20 (x + 1) / 7x

5x² + 5x + 20x + 20 / 7x

5x² + 25x + 20 / 7x

This expression is equivalent to the original expression.

Therefore, the unknown expressions are (5x² + 15x - 20) and (x - 1).

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They should use 1/45 of a gallon of soap out of 1/9 each day, so it lasts six days.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

They have 1/9 of a gallon of soap.

To find the amount of soap so that it can last six days:

Divide the total amount of soap by the total number of days.

That means,

= 1/9 ÷ 6

= 1/9 x 1/6

= 1/ 45

Therefore, 1/45 is the required value.

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When using chi2, the expected cell count in a table should be larger than 10.

Chi2 analysis is a statistical function used to compare the observed frequency of an event to the expected frequency.

The ideal minimum value for the expected cell count is 10, although a value of 15 is even better. This is because the chi2 function assumes that the data is normally distributed and has a minimum number of expected occurrences.

The lower the expected cell count, the less reliable the results of the chi2 analysis will be. In fact, if the expected cell count is below 5, the results should not be considered trustworthy at all.

The degree of freedom determines the level of significance in the results, which is an important factor in interpreting the results of a chi2 analysis. In general, the larger the expected cell count, the more reliable the results will be.

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The x-intercepts are approximately x = 1.305, 5.695. These are the x-coordinates where the parabolic function crosses the x-axis.

What is parabola?

A parabolic function is a type of mathematical function that describes a parabolic curve or parabola. A parabola is a U-shaped curve that is symmetrical about its axis of symmetry.

The equation y = x^2 - 3x - 7 represents a parabolic function with its vertex located at (-3/2, -7). To find the x-coordinates of the x-intercepts (also known as the roots or zeros), we need to solve the equation x^2 - 3x - 7 = 0. This can be done using various methods, such as the quadratic formula or factoring.

Using the quadratic formula, the x-intercepts can be found as follows:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 1, b = -3, c = -7, and √ represents the square root symbol.

So,

x = (-(-3) ± √((-3)^2 - 4(1)(-7))) / 2(1)

x = (3 ± √(9 + 28)) / 2

x = (3 ± √37) / 2

Hence, the x-intercepts are approximately x = 1.305, 5.695. These are the x-coordinates where the parabolic function crosses the x-axis.

So the answer to the question is:

1.305, 5.695

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The number of students in a class of 360 students who would be expected to choose pizza or a sandwich as their favorite type of lunch will be 280. Then the correct option is C.

In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

The probability who choose pizza or a sandwich as their favorite type of lunch will be given as,

p = (30 + 40) / (30 + 20 + 40)

p = 70 / 90

p = 7 / 9

Then the expected value is given as,

E(x) = 360 x (7/9)

E(x) = 280

The number of students in a class of 360 students who would be expected to choose pizza or a sandwich as their favorite type of lunch will be 280. Then the correct option is C.

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Answer: 266.666667%

Step-by-step explanation:

I got that after i worked it out

Answer:

Step-by-step explanation:

Total atomic events or count = 2598960

Now, According to the question:

A joint probability distribution represents a probability distribution for two or more random variables. Instead of events being labelled A and B, the condition is to use X and Y as given below. f(x, y) = P(X = x, Y = y) The main purpose of this is to look for a relationship between two variables.

In a deck of cards there are 52 cards having 4 different suits each having 13 different ranks.

In a joint probability distribution of 5 cards hand from a 52 deck of cards is calculated as shown below:

Total atomic events or count = ⁵²C₅

= 52!/5! * (52-5)!

= 52!/5! * 47!

= (48 x 49 x 50 x 51 x 52)/5!

= 311875200/120

= 2598960

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The dot product of two vectors u and v can be represented using index notation as u_i v_i.

A mathematical language called index notation is used to describe the components of a vector or tensor. It consists of an element's position in the vector or tensor and a symbol, typically a Latin or Greek letter.

A mathematical language called index notation is used to describe the components of a vector or tensor. The element's position in the vector or tensor is indicated by a symbol (often a Latin or Greek letter) with an integer subscript. How to utilise index notation is as follows:

Vectors can be represented by a single letter with a subscript, such as v i, where I stands for the element's position in the vector.

Tensors are multidimensional arrays that can be described using an index notation for each element. For instance, T i,j can be used to represent the element in a matrix's ith row and jth column.

Executing operations: Index notation can be used to express operations like matrix multiplication and the vector dot product. For instance, u_i v_i can be used to denote the dot product of the two vectors u and v.

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The collection of short line segments with a slope that should satisfy the specified differential equation at each point is referred to as the direction field.

The stated differential equation is :

y' = 2y – 3 => dy/dx = 2y – 3

Find equilibrium solution, at dy/dx = 0.

2y – 3  = 0

y = 3/2

At y = 3/2, the intervals are: ]3/2, ∞[

Put any value of y in this differential equation,

2y – 3  at y = 2

2*2 – 3 = 1 > 0

Thus, slope becomes positive for y > 3/2 .

As, the relation between t and the obtained solution y are increases.

Thus, y < 3/2 : intervals are: ]- ∞, 3/2[

Put any value of y in this differential equation,

2y – 3  at y = 1

2*1 – 3 = -1 < 0

Thus, slope becomes negative for y < 3/2 .

As, the relation between t and the obtained solution y in decreases.

Therefore,  the direction field for the stated differential equation is obtained.

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the correct question is-

Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of y as t → 0. If this behavior depends on the initial value of y at t = 0, describe the dependency.

y' = 2y – 3

The wavelength for radio waves with frequency 3 × 10^9 is given as follows:

3 x 10^-1 m.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

y = (3 x 10^8)/x.

The wavelength for radio waves with frequency x = 3 × 10^9 is given as follows:

y = (3 x 10^8)/(3 x 10^9).

y = 3 x 10^(-1).

(keep the base and subtract the exponents).

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The Nitrogen is commonly considered as a Trigonal Pyramidal molecule .

In a Trigonal Pyramidal arrangement, there are three atoms attached to the central atom at the corners of a triangular plane, with the fourth atom attached above or below the plane.

This molecular geometry is commonly observed in compounds where the central atom has five valence electrons, such as nitrogen in its most common oxidation state of +3.

The Nitrogen in this oxidation state forms compounds like nitrogen triiodide (NI₃) and nitrogen trioxide (NO₃), which have a trigonal pyramidal geometry.

Therefore , Yes , Nitrogen is trigonal pyramidal .

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In 300 collisions between a car and a deer,  there are 40 deer fatalities per 100 collisions is = 1.72.

Mean = 3 Standard Deviation = 1.72.

The standard deviation measures the spread of the data about the mean value. It is useful in comparing sets of data which may have the same mean but a different range.

Standard deviation is the measure of dispersion of a set of data from its mean. It measures the absolute variability of a distribution; the higher the dispersion or variability, the greater is the standard deviation and greater will be the magnitude of the deviation of the value from their mean.

In 300 collisions between a car and a deer,  there are 40 deer fatalities per 100 collisions is = 1.72.

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In 300 collisions between a car and a deer,  there are 40 deer fatalities per 100 collisions is = 1.72.

Mean = 3 Standard Deviation = 1.72.

The standard deviation measures the spread of the data about the mean value. It is useful in comparing sets of data that may have the same mean but a different range.

Standard deviation is the measure of the dispersion of a set of data from its mean. It measures the absolute variability of a distribution; the higher the dispersion or variability, the greater the standard deviation and the greater will be the magnitude of the deviation of the value from their mean.

In 300 collisions between a car and a deer,  there are 40 deer fatalities per 100 collisions is = 1.72.

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(a) H'(6) is the rate of change of the height of the tree at time t=6, which is the slope of the line tangent to the graph of H(t) at that point. Using the data in the table, we can estimate H'(6) to be 3.2 meters per year. This means that, at t=6, the height of the tree is increasing at a rate of 3.2 meters per year.

(b) H'(t) is the rate of change of the height of the tree at time t. Since H'(t) is twice-differentiable, it is continuous and can take any value between its minimum and maximum values. Therefore, there must be at least one time t, for 2 < t < 10, such that H'(t) = 2.

(c) To approximate the average height of the tree over the time interval 2 ≤ t ≤ 10, we can use a trapezoidal sum with the four subintervals indicated by the data in the table. We have:

Therefore, the average height of the tree over the time interval 2 ≤ t ≤ 10 can be approximated by the trapezoidal sum:

(10 + 14 + 18 + 22) × (2 + 2 + 3 + 3) / 8 = 196/8 = 24.5 meters.

(d) According to the given model, G(x) = 100x/(1+x), if the tree is 50 meters tall, then the diameter of the base of the tree is x = 2, and the rate of change of the height of the tree with respect to time, in meters per year, is given by G'(2) = 100(1 - 2)/(1 + 2)² = -100/9. Therefore, the rate of change of the height of the tree with respect to time, in meters per year, at the time when the tree is 50 meters tall is -100/9 meters per year.

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