The points with coordinates (4, 8), (2, 10), and (5, 7) all lie on the line 2x+2y=24 . a. Which graph correctly shows these points graphed on the line? What is the slope of the line? Write your answer in simplest form. c. Complete the statement about what the slope tells you about the relationship between lengths and widths of rectangles with perimeter 24. A slope of means that for rectangles of perimeter 24, every extra unit of length put into the width is less unit of length that can be put into the length.

As we have proved that the Fourier transform F(ω), with the only difference being the sign of ω

Firstly, let us recall what the Fourier transform is. It is a mathematical technique that decomposes a function into its frequency components. The Fourier transform is defined as:

F(ω) = ∫ f(t) [tex]e^{(-iwt)}[/tex]dt

where f(t) is the function being transformed, ω is the frequency, i is the imaginary unit, and e^(-iωt) is a complex exponential function. The inverse Fourier transform is defined as:

f(t) = (1/2π) ∫ F(ω) [tex]e^{(iwt)}[/tex] dω

where F(ω) is the Fourier transform of f(t).

Now, let's move on to the symmetry properties of the Fourier transform.

If f(t) is an even function, meaning f(-t) = f(t), then F(ω) is also even, meaning F(-ω) = F(ω).

To prove this, we start with the definition of the Fourier transform and substitute -t for t:

F(-ω) = ∫ f(-t)[tex]e^{(iwt)}[/tex] dt

Then, using the even symmetry of f(t), we can replace f(-t) with f(t):

F(-ω) = ∫ f(t) [tex]e^{(iwt)}[/tex] dt

Therefore, F(-ω) = F(ω) if f(t) is even.

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The estimated simple linear regression equation comes down when the sum of the squared deviations for each y value from the line.

The above statement is false.

Simple linear regression is a linear regression model with a single variable. That is, it takes two-dimensional sample points with one independent variable and one dependent variable, and finds a linear function (a non-vertical straight line) that predicts the value of the dependent variable as the independent variable as accurately as possible.

Simple linear regression is used for estimating the relationship between two quantitative variables. The Simple linear regression is used for:

(1) How strong is the relationship between two variables (such as the relationship between rainfall and soil erosion).

(2) The value of the dependent variable is relative to a value of the independent variable (For example, the amount of soil erosion under a certain amount of precipitation).

Regression models describe the relationship between variables by fitting a line to observed data. Linear regression models use straight lines, while logistic and nonlinear regression models use curved lines. Regression allows you to estimate how the dependent variable changes when the independent variable changes.

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The equation of the plane that contains the line v = (-1, 1, 2) t(6, 4, 3) and is perpendicular to the plane 8x - 5y - 3z - 6 = 0 can be found using the cross product of the direction vector of the line and the normal vector of the plane. The cross product of these two vectors results in the normal vector (3, 42, -62) of the plane.

This vector can be used in the equation 3(x - x0) + 42(y - y0) - 62(z - z0) = 0, with a point on the line, such as (-1, 1, 2), as the point (x0, y0, z0). This results in the equation 3x + 42y - 62z + 85 = 0.

To find an equation for the plane that contains the line v = (-1, 1, 2) t(6, 4, 3) and is perpendicular to the plane 8x - 5y - 3z - 6 = 0, we can use the cross product of the direction vector of the line and the normal vector of the plane.

The direction vector of the line is (6, 4, 3) and the normal vector of the plane is (8, -5, -3).

The cross product of these two vectors is:

| i  j  k  |

| 6  4  3  |

| 8 -5 -3  |

= i(-12 - (-15)) - j(-18 - 24) + k(-30 - 32)

= i(3) - j(-42) + k(-62)

= (3, 42, -62)

This vector is perpendicular to both the direction vector of the line and the normal vector of the plane, so it is the normal vector of the plane we are looking for.

The equation of the plane can be written as:

3(x - x0) + 42(y - y0) - 62(z - z0) = 0

We can use a point on the line, such as (-1, 1, 2), as the point (x0, y0, z0) in the equation:

3(x - (-1)) + 42(y - 1) - 62(z - 2) = 0

3x + 3 + 42y - 42 - 62z + 124 = 0

3x + 42y - 62z + 85 = 0

Therefore, the equation of the plane that contains the line v = (-1, 1, 2) t(6, 4, 3) and is perpendicular to the plane 8x - 5y - 3z - 6 = 0 is 3x + 42y - 62z + 85 = 0.

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The measure of the angle HCW inscribed in the circle is equals to 161 degrees.

HRWC is inscribed in the circle E,

The angles of the quadrilateral must add up to 360 degrees.

Measure of angle HCW

= ( 360 degrees ) - ( sum of the measures of the other three angles )

⇒ m(HCW) = 360 - (m(RHC) + m(HRW) + m(HWC))

⇒ m(HCW) = 360 - [(6x + 41) + (8x + 51) + (5x + 12)]

⇒ m(HCW) = 360 - (19x + 104)

⇒ m(HCW) =  256 - 19x

Round to the nearest hundredth by plugging in an approximate value of x.

For example, let x = 5, we get,

m(HCW) = 256 - 19(5)

⇒  m(HCW) = 256 - 95

⇒ m(HCW) = 161

Therefore, the measure of angle HCW is approximately 161 degrees.

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Trapezoid ABCD was dilated to create trapezoid A'B'C'D'. Each of the options listed above is true. These statements are true because of the properties of dilation.

There are three possible options when it comes to the question of which statements are true about trapezoids ABCD and A'B'C'D'.

Option 1: Trapezoids ABCD and A'B'C'D' have the same shape but differ in size.

Option 2: All angles and parallel sides of trapezoids ABCD and A'B'C'D' are congruent.

Option 3: The dilated trapezoid is an exact copy of the original, scaled up or down.

The word "dilate" means to enlarge, reduce or distort the original shape, as the question implies. Hence, the basic shape remains the same in all cases, but it gets bigger or smaller.

Option 1 is correct because the original shape of trapezoid ABCD is kept the same and the same shape is enlarged or shrunk.

Option 2 is true because dilation retains angle measurements and preserves parallelism, making it true that all angles and parallel sides of trapezoids ABCD and A'B'C'D' are congruent.

Option 3 is correct since the dilation takes the original and scales it up or down precisely. In other words, it is an exact copy of the original but just a different size.

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It's true that step functions only take on integer values at the steps, but including decimals in your table of values can be helpful in a few ways:

Accuracy: In some cases, the output of the function may be between two integers. For example, if you have a step function that takes on the value 5 between x=1 and x=2, but you need to evaluate the function at x=1.5, including decimals in your table of values will give you a more accurate result.

Visualization: Including decimals in your table of values can help you visualize the shape of the function more clearly. For example, if you're graphing a step function, you can use the decimal values to create a smoother, more continuous graph.

Consistency: Including decimals in your table of values can help ensure consistency and avoid errors. For example, if you only include integer values in your table of values, you may accidentally skip a step or misinterpret the output of the function at a certain point.

Overall, including decimals in your table of values for step functions may not always be necessary, but it can be a helpful tool for accuracy, visualization, and consistency.

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In the limit, the deck of cards will be perfectly shuffled, in the sense that any of the n! possible orderings are equally likely.

The question is asking to show that, in the limit, a deck of n cards will be perfectly shuffled if each number from 1 to n is randomly chosen and the chosen card is placed in position 1. This can be shown as follows:

Let us denote the initial ordering of the deck of cards by P1, P2, ..., Pn. Suppose the first card chosen is Pi, and thus it is put in position 1. Now the ordering is Pi, P1, ..., Pn.

Suppose the next card chosen is Pj. Thus the ordering is now Pj, Pi, P1, ..., Pn. By repeating this process, the ordering of the deck is changing.

As each of the numbers 1, 2, ..., n is equally likely to be chosen, the probability of any particular ordering is the same. This means that, in the limit, the deck of cards will be perfectly shuffled, in the sense that any of the n! possible orderings are equally likely.

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46,536 is the possible number of codes if repeats are not allowed and the second letter must be 'g' and the first digit must be '3'.

If repeats are not allowed, and the second letter must be 'g', and the first digit must be '3', then we have to find the number of codes that can be possible.

Solution: Here we have to calculate the total number of possible codes if repeats are not allowed and the second letter must be 'g' and the first digit must be '3'.

The given conditions:

First digit = 3

Second letter = g

We know that a code is usually formed by combining letters, numbers or both.

Thus, for the formation of the code, the remaining 4 digits are free to choose any digit or alphabet, except the two already selected ones.

We know that the number of codes that can be formed by n objects taken k at a time, without repetition is given by:P(n, k) =n!/(n−k)!

Here, n = 25, as we have to select 25 letters, starting from A to Y.

We exclude G from these, as it has already been selected as the second letter.

k = 4 as we need to select 4 remaining characters.

We have to find the number of possible codes that can be formed without repetition, and with the conditions specified.

Here, we have 1 fixed number (3) and one fixed alphabet (g) and four spaces for the remaining digits:

Thus, the number of ways of selecting the remaining four characters = 24 × 23 × 22 × 21

Total number of codes possible = 1 × 1 × 24 × 23 × 22 × 21 = 46,536, which is our answer.

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The probability of an element being selected is 0.1

The probability of an element being selected on the first selection from a simple random sample of 40 elements from a population of 400 is 0.1

Explanation: Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

Probability is used in statistical analysis to make predictions and draw conclusions about data.

In this question, the population consists of 400 elements, and a simple random sample of 40 elements is to be drawn from it.

The probability of an element being selected on the first selection is the same as the probability of any one of the 400 elements being selected, which is 1/400 or 0.0025.

Therefore, the correct answer is option (d) 0.1

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Answer:

tan 45° = 1

Step-by-step explanation:

45° is a Special angle,so tan 45° = 1

or it's like the identity of tan

tan 45= sin45° ÷ cos45°

=√2/2 ÷ √2/2

=1

Answer:

Let's let t be the time in minutes that both machines have been working. Then, the number of boxes packed by Machine A in t minutes is 8t, and the number of boxes packed by Machine B in t minutes is 11t.

The difference between the number of boxes packed by Machine B and Machine A is less than 200, so we can write the following inequality:

11t - 8t < 200

Simplifying, we get:

3t < 200

Dividing both sides by 3, we get:

t < 200/3

To the nearest second, this is approximately 66.67 seconds.

Therefore, the possible lengths of time that the machines have been working is t < 66.67 seconds.

Note that this inequality only gives us an upper bound on the time that the machines have been working, since we know that the difference between the number of boxes packed by Machine B and Machine A is less than 200. We do not have any information on the minimum time that the machines have been working, so there are infinitely many possible solutions that satisfy the given conditions.

Step-by-step explanation:

If we have 3/5 bran muffins and Andrea has 10 muffins, she purchased 6.

Purchased in the past tense and past participle. In a sale, the transaction is finished when the buyer pays the seller. In a transaction, the buyer has two options: they either pay the seller in full or they can arrange financing with a third party, like a bank or leasing firm. The amount an investor pays for an investment is referred to as the purchase price, and when the investment is sold, that figure becomes the investor's cost basis for calculating gain or loss. Shoes Unlimited places an order with a foreign supplier for 10,000 pairs of sneakers. This entails the issuance of a purchase order, which is a formal declaration by the business that it will buy the specified kind and number of shoes.

Based on the given condition,

Formulate:

10*3/5

Calculate.

10*3/5

Simplify.

2*3

Calculate.

6

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Answer:

Step-by-step explanation:

This word problem involves solving a set of two equations for two unknowns: M (cost of 1 thin mint), and T (cost of 1 trefoil).

First customer: 3*M + 2*T = 1.35

Second customer: 5*M + 1*T = 1.55

Solving the second equation for T:     T = 1.55 - 5*M

Then, we can plug this into the first equation:

3*M + 2*(1.55 - 5*M) = 1.35

3*M + 3.1 - 10*M = 1.35

-7*M = 1.35 - 3.1

-7*M = -1.75

M = -1.75/-7

M = 0.25 --> one thin mint costs $0.25

Now that we have one price, we can solve for the other one.

T = 1.55 - 5*M = 1.55 - 5*(0.25)

T = 1.55 - 1.25 = 0.30 --> one trefoil costs $0.30

The birthplace of humans is believed to be in Africa, specifically in the eastern and southern regions of the continent. This is based on evidence from archaeological and genetic studies.

According to the theory of evolution, humans evolved from earlier primates over millions of years through a process of natural selection. The earliest human ancestors were likely small, tree-dwelling primates that lived in Africa about 6-7 million years ago.

Over time, some of these primates evolved into bipedal creatures that walked upright on two legs. One of the most well-known early human ancestors is Australopithecus, which lived about 4-2 million years ago and is known for its distinctive skull shape.

Later, other species of human ancestors, such as Homo erectus and Homo neanderthalensis, appeared and spread to different parts of the world. Modern humans, Homo sapiens, emerged about 300,000 years ago in Africa, and eventually migrated to other parts of the world.

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The value of A4 hex in TINFO 320 floating point format is C3800000 hex.

To convert A4 hex to TINFO 320 floating point format, we need to first convert the hex value to binary, then separate the binary value into the sign, exponent, and mantissa parts, and finally convert those parts into their respective TINFO 320 floating point format values.

Convert A4 hex to binary:
A4 hex = 1010 0100 binary

Separate the binary value into the sign, exponent, and mantissa parts:
Sign: 1
Exponent: 0100 1
Mantissa: 000 0000 0000 0000 0000 0000

Convert the sign, exponent, and mantissa parts into their respective TINFO 320 floating point format values:
Sign: 1 (negative)
Exponent: 4 + 127 = 131 (biased exponent)
Mantissa: 0 (normalized mantissa)

Combine the TINFO 320 floating point format values to get the final value:
TINFO 320 floating point format value = 1 1000 0011 0000 0000 0000 0000 0000 0000
= C3800000 hex

Therefore, the value of A4 hex in TINFO 320 floating point format is C3800000 hex.

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Answer:

130 years exact

Step-by-step explanation:

The progress reports may be given verbally to immediate supervisors, management, and users.

The above statement is False.

Progress reports are reports in which you update project information. Progress reports allow management and clients to stay informed of project status and to modify or adjust tasks, schedules and budgets.

Progress reports are important beyond simply tracking and managing various projects happening at the same time. Progress reports also provide valuable insight into how your team can complete projects more efficiently.

In addition to providing an overview of ongoing projects, well-structured progress report templates allow project managers to identify critical issues affecting team productivity and project progress.

Although progress reports may be given orally to immediate supervisors, they are usually communicated in writing to management and users.

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The particle is moving to the left on the intervals (0, 5) and (10, 12).

We  need to find when its velocity is negative, in order to determine when the particle is moving to the left.

Where the  velocity function, v(t), is described as the derivative of the position function, s(t), and is given by:

v(t) = s'(t) = t^2 - 15t + 50

We find  the roots of the quadratic equation v(t) = 0, in order to  find the intervals where the particle is moving to the left.

t^2 - 15t + 50 = 0

Applying the quadratic formula, we can determine the roots:

t = (15 ± sqrt(15^2 - 4150)) / (2*1) = (15 ± 5) / 2

The  roots are t = 5 and t = 10.

We then can conclude that the particle is moving to the left on the intervals (0, 5) and (10, 12).

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Answer: The answer would be A

Step-by-step explanation:

The perimeter of the sector is 16 + π cm (or approximately 22.28 cm if we use 3.14 as an approximation for π).

To find the perimeter of the sector, we need to add the lengths of the two radii and the arc length of the sector.

If the sector has an angle of 45 degrees and a radius of 8 cm, then the arc length of the sector can be calculated as:

Arc Length = (angle/360) x 2πr

Arc Length = (45/360) x 2π(8)

Arc Length = π

The perimeter of the sector is then:

Perimeter = 2r + Arc Length

Perimeter = 2(8) + π

Perimeter = 16 + π

A sector of a circle is a region bounded by two radii and an arc, where the arc is a portion of the circle. The sector is determined by the central angle that subtends the arc.

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The line l = ⟨1, 2, -(18/5)⟩ + t⟨4, 0, 24/5⟩ intersects the plane x - y + 2z = -9 at the point (-5, -1, -3) when x = -3.

We know that the line is given as: l = ⟨1 2,5 2,-(18/5)⟩And we have the following equation of a plane: x - y + 2z = -9

The point of intersection of the line and the plane is ( -5 , -1 , -3)

when x = -3 The equation of the line can be written in the following vector form:l = a + t(b - a)where a and b are the vectors such that they lie on the line, and t is the parameter.

The point of intersection of the line and the plane lies on both the line and the plane. Hence, it satisfies the equation of both the line and the plane.

Therefore, we have:(-5, -1, -3) = ⟨1, 2, -(18/5)⟩ + t⟨4, 0, 24/5⟩and x = -3t = (x1 - a1) / (b1 - a1)t = (-3 - 1) / (5 - 1)t = -1We now have the point of intersection of the line and the plane,

which can be determined as follows:(-5, -1, -3) = ⟨1, 2, -(18/5)⟩ + t⟨4, 0, 24/5⟩⟹ (-5, -1, -3) = ⟨1, 2, -(18/5)⟩ - ⟨4, 0, 24/5⟩⟹ (-5, -1, -3) = ⟨-3, 2, -78/5⟩Thus, the line l = ⟨1, 2, -(18/5)⟩ + t⟨4, 0, 24/5⟩ intersects the plane x - y + 2z = -9 at the point (-5, -1, -3) when x = -3.

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For part a, the vector x can be expressed as a linear combination of a1 and a2 as x = -a1 - 2a2. For parts b, c, d, no linear combination of the given vectors can express x. For part e, x = a1 - 2a2 + 2a3 with constants k1=1, k2=-2, and k3=2.

To express x=(-3,-6) as a linear combination of a1=[1,4] and a2=[-2,3], we need to find constants k1 and k2 such that x = k1 * a1 + k2 * a2. Solving for k1 and k2, we get:

-3 = k1 * 1 + k2 * (-2)

-6 = k1 * 4 + k2 * 3

Solving this system of equations, we get k1=-6 and k2=1. Therefore, x can be expressed as:

x = -6 * [1,4] + [ -2,3] = [-8, 9]

x = -a1 - 2a2

To express x=[5,9,5) as a linear combination of a1=[2,1,4), a2=[1,-1,3), and a3=[3,2,5), we need to find constants k1, k2, and k3 such that x = k1 * a1 + k2 * a2 + k3 * a3. Solving for k1, k2, and k3, we get:

5 = k1 * 2 + k2 * 1 + k3 * 3

9 = k1 * 1 - k2 * 1 + k3 * 2

5 = k1 * 4 + k2 * 3 + k3 * 5

Solving this system of equations, we get k1=1, k2=0, and k3=1. Therefore, x can be expressed as:

x = 1 * [2,1,4] + 0 * [1,-1,3] + 1 * [3,2,5] = [5,3,9]

To express x=[2,-1,4) as a linear combination of a1=[3,6,2] and a2=[2,10,-4], we need to find constants k1 and k2 such that x = k1 * a1 + k2 * a2. Solving for k1 and k2, we get:

2 = k1 * 3 + k2 * 2

-1 = k1 * 6 + k2 * 10

4 = k1 * 2 + k2 * (-4)

This system of equations has no solution, since the second equation implies that k2 is negative, but the third equation implies that k2 is positive. Therefore, x cannot be expressed as a linear combination of a1 and a2.

To express x=(2,2,3] as a linear combination of a1=[6,-2,3), a2=[0,-5,-1), and a3=[-2,1,2], we need to find constants k1, k2, and k3 such that x = k1 * a1 + k2 * a2 + k3 * a3. Solving for k1, k2, and k3, we get:

2 = k1 * 6 + k2 * 0 + k3 * (-2)

2 = k1 * (-2) + k2 * (-5) + k3 * 1

3 = k1 * 3 + k2 * (-1) + k3 * 2

Solving this system of equations, we get k1=1, k2=1, and k3=1. Therefore, x can be expressed as:

x = 1 * [6,-2,3] + 1 * [0,-5,-1] + 1 *[-2,1,2]

To express x = [17,2,3], as linear combination of a1 = [1, -2,3), a2 = [5, -2,6], a3 = [4,0,3], We need to find constants k1, k2, and k3 such that:

x = k1a1 + k2a2 + k3*a3

Substituting the given values:

[17, 2, 3] = k1[1, -2, 3] + k2[5, -2, 6] + k3[4, 0, 3]

This gives us the following system of linear equations:

k1 + 5k2 + 4k3 = 17

-2k1 - 2k2 = 2

3k1 + 6k2 + 3k3 = 3

Solving for k1, k2, and k3, we get:

k1 = 1, k2 = -2, k3 = 2

Therefore, we can express x as a linear combination of a1, a2, and a3 as:

x = a1 - 2a2 + 2a3

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The mass of one worker bee is \,1\cdot{ 10^{-4}}1⋅10 −4 kg, and there are 4\cdot{ 10^4}4⋅10 4 worker bees in the hive.

To find the mass of all the worker bees in the hive together, we need to multiply the mass of one worker bee by the number of worker bees in the hive:

\,1\cdot{ 10^{-4}}1⋅10 −4 kg \times 4\cdot{ 10^4}4⋅10 4 = 4\cdot{ 10^{-4}}4⋅10 −4 kg \times 4\cdot{ 10^4}4⋅10 4

Using the rules of exponents, we can simplify this expression:

4\cdot{ 10^{-4}}4⋅10 −4 kg \times 4\cdot{ 10^4}4⋅10 4 = 4 \times 4 \times 10^{-4}10 4 = 16 \times 10^0 = 16

So, the mass of all the worker bees in the hive together is 16 kg. In scientific notation, this is \,1.6\cdot{ 10^1}1.6⋅10 1 kg.

Therefore, the answer is \boxed{1.6\cdot{ 10^1}}1.6⋅10 1 kg.

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The probability of P(X ≤ 2) = 0.85. The probability of P(X > 1) = 0.3. The mean of distribution is µx = 1.1, The standard deviation is σx = 0.93.

To find P(X ≤ 2), we sum the probabilities of all the values of X up to and including 2:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= 0.4 + 0.3 + 0.15

= 0.85

Therefore, P(X ≤ 2) = 0.85.

To find P(X > 1), we need to subtract P(X ≤ 1) from 1:

P(X > 1) = 1 - P(X ≤ 1)

= 1 - [P(X = 0) + P(X = 1)]

= 1 - (0.4 + 0.3)

= 0.3

Therefore, P(X > 1) = 0.3.

To find µx, the mean of the distribution, we use the formula:

µx = Σ(x * p(x))

where the sum is taken over all possible values of X.

µx = (0 * 0.4) + (1 * 0.3) + (2 * 0.15) + (3 * 0.1) + (4 * 0.05)

= 0 + 0.3 + 0.3 + 0.3 + 0.2

= 1.1

Therefore, µx = 1.1.

To find σx, the standard deviation of the distribution, we use the formula:

σx = sqrt[Σ((x - µx)^2 * p(x))]

where the sum is taken over all possible values of X.

σx = sqrt[((0 - 1.1)^2 * 0.4) + ((1 - 1.1)^2 * 0.3) + ((2 - 1.1)^2 * 0.15) + ((3 - 1.1)^2 * 0.1) + ((4 - 1.1)^2 * 0.05)]

= sqrt[(1.21 * 0.4) + (0.01 * 0.3) + (0.49 * 0.15) + (1.21 * 0.1) + (3.61 * 0.05)]

= sqrt[0.484 + 0.003 + 0.0735 + 0.121 + 0.1805]

= sqrt[0.862]

Therefore, σx = sqrt[0.862] ≈ 0.93.

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log 7

log (7x2/3) + log (11/5) - log (11x2/5x3) [ log laws ]

log 7 + log 2 - log 3 + log 11 - log 5 - [ log 11 + log 2 - (log 5 + log 3)]

log 7 + log 2 - log 3 + log 11 - log 5 - [ log 11 + log 2 - log 5 - log 3]

log 7 + log 2 - log 3 + log 11 - log 5 - log 11 - log 2 + log 5 + log 3

{ + log 3 - log 3 gets cancelled + log 2 - log 2 gets cancelled + log 11 - log 11 gets cancelled + log 5 - log 5 gets cancelled }

log 7

Answer:

0.67

Step-by-step explanation:

Jill has a total of 6 cans of food, and she knows that there are 2 cans of fruit, 3 of corn, and 1 of beans. So the total number of cans of food that are not fruits is 3 + 1 = 4.

Therefore, the probability that Jill chooses a can of food that is not a fruit is 4/6 or simplified, 2/3.

So the probability that she chooses a can of food that is not a fruit is 2/3 or approximately 0.67.

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a) The domain of g is U between 0 and n, since the integral is taken over the domain of f(x), which goes from 0 to n. The range of g can be estimated by looking at the area of the region below the graph of f(x) and above the x-axis. It is seen that this area is positive but less than 2; therefore, the range og is (0,2).

b) The maximum of g is achieved when the graph of f(x) is highest, which occurs at x = 3. The minimum of g is achieved when the graph of f(x) is lowest, which occurs at x = 1.

To learn more about range, refer below:

https://brainly.com/question/28135761

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