Trent borrowed $250 with a 2.5% simple interest rate he pays back the money in one year what was the total amount that he repaid

Answer:

Step-by-step explanation:

One of the Answers is C

We have linearized the given ODE to: \(\[ \frac{{dv}}{{dt}} = \frac{5}{2} \]\). This is the linearized equation.

To linearize the given ordinary differential equation (ODE) \(\( \frac{{dy}}{{dt}} = 5 \sqrt{x} \)\), we need to rewrite it in a linear form. One common approach is to introduce a new variable that relates to the derivative of \(\( y \)\).

Let's define a new variable \(\( v = \sqrt{x} \)\). Taking the derivative of both sides with respect to \(\( t \)\), we have:

\(\[ \frac{{dv}}{{dt}} = \frac{{d}}{{dt}} \left( \sqrt{x} \right) \]\)

Using the chain rule, we can express \(\( \frac{{dv}}{{dt}} \)\) in terms of \(\( \frac{{dx}}{{dt}} \)\):

\(\[ \frac{{dv}}{{dt}} = \frac{1}{{2 \sqrt{x}}} \cdot \frac{{dx}}{{dt}} \]\)

Now, we need to substitute \(\( \frac{{dx}}{{dt}} \)\) using the given equation \(\( \frac{{dy}}{{dt}} = 5 \sqrt{x} \)\):

\(\[ \frac{{dv}}{{dt}} = \frac{1}{{2 \sqrt{x}}} \cdot \left( 5 \sqrt{x} \right) \]\)

Simplifying the right-hand side:

\(\[ \frac{{dv}}{{dt}} = \frac{5}{2} \]\)

Thus, we have linearized the given ODE to: \(\[ \frac{{dv}}{{dt}} = \frac{5}{2} \]\)

The linearized equation is much simpler compared to the original non-linear equation.

Note: The complete question is:

Linearize the ODE below;

\(\(\frac{{dy}}{{dt}} = 5\sqrt{x}\)\)

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The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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Answer:

Linear function:  y = x + 7.75

Step-by-step explanation:

A store sells packages of comic books with a poster. We are told that:

Let p be the cost of one poster.

Let c be the cost of one comic book.

Write a system of equations using the given information and the defined variables:

\(\begin{cases}p + 4c = 11.75\\p + 11c = 18.75\end{cases}\)

Subtract the first equation from the second equation to eliminate p:

\(\begin{array}{crcrcl}&p&+&11c&=&18.75\\-&(p&+&4c&=&11.75)\\\cline{2-6}&&&7c&=&\;\;7.00\\\cline{2-6}\end{array}\)

Solve for c:

\(7c=7.00\)

 \(c=1.00\)

Therefore, the cost of one comic book is $1.00.

Substitute the found value of c into one of the equations and solve for p:

\(\begin{aligned}p+4(1.00)&=11.75\\p+4.00&=11.75\\p&=7.75\end{aligned}\)

Therefore, the cost of one poster is $7.75.

Now we know the cost of one poster and one comic, we can write a linear function that models the cost y of a package containing x number of comic books:

\(y = 1.00x + 7.75\)

\(y =x + 7.75\)

We are told that another store sells a similar package modeled by a linear function rule with initial value $6.99.  The initial value is the y-intercept of each function, i.e. the cost of the package when zero comics are sold. So the linear function for this package is:

\(y = x + 6.99\)

To determine which store has the better deal, we need to compare the y-intercepts (the initial values). The store with the lower initial value provides a better deal because it charges less for the basic package (when the number of comic books is zero).

Since 6.99 is less than 7.75, the other store offers a better deal, as it has a lower initial cost for the basic package.

Answer:

\(\Huge \boxed{ \texttt{\bf{y = x + 7.75} }}\)

Step-by-step explanation:

To find the linear function rule that models the cost \(\texttt{y}\) of a package containing any number \(\texttt{x}\) of comic books, we can use the given information:

Let's denote the cost of a poster as \(\texttt{P}\) and the cost of a comic book as \(\texttt{C}\). Then, we can write two equations:

To solve these equations, we can use the method of elimination. Let's use this method to eliminate \($$P$$\):

Now, substituting the value of \(\texttt{C}\) back into equation 1:

Now that we have the cost of a poster (P) and a comic book (C), we can write the linear function rule as:

\(\Large \boxed{\texttt{y = x + 7.75}}\)

Now, suppose another store sells a similar package modelled by a linear function rule with an initial value of $6.99. This means that the cost of a poster at the other store is $6.99. Since the cost of a comic book is the same at both stores ($1), the linear function rule for the other store is:

\(\Large \boxed{ \texttt{y = x + 6.99}}\)

Comparing the two linear function rules, we can see that the second store has a better deal because the initial cost of a poster is lower ($6.99) compared to the first store ($7.75).

________________________________________________________

Their boss should promote and facilitate open communication and understanding between Yan and Tracy to foster a more inclusive and collaborative work environment.

In a diverse workplace, it is crucial for the boss to encourage inclusivity and bridge the gap between individuals with different world views. By promoting open communication and understanding, the boss can create opportunities for Yan and Tracy to learn from each other and gain a broader perspective.

This can be achieved through team-building exercises, diversity training, or creating a supportive space for discussions on cultural differences. The goal is to foster a work environment where individuals feel comfortable expressing their views, learning from others, and working together towards common goals. By addressing the perceived distance between Yan and Tracy, the boss can help create a more inclusive and harmonious work atmosphere.

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Answer:

h(x) = -4 x –7

h(3) = -4(3) —7

h(3) = –12 –7

h(3) = – 19

Answer:

\( \frac{9}{10} = 0.9\)

Answer:

simplest form

2(4a +9)

Step-by-step explanation:

factor

\(3a + 6 + 2a + 6 + 3a + 6\)

simplify

\(8a + 18\)

factor out 2

\(2(4a +9)\)

Note that the Perimeter of the red polygon is 338 in.

The perimeter of a polygon is the total of its sides' measurements. In this question, the polygon is built by taking the tangents from a specified circle.

The idea here is that if we draw two tangents from the same point outside on a given circle, the length of both tangents will always be equal.

There are 8 sides of this polygon , That means there are four pairs because length of them are equal .

So perimeter is equal to two times the sum of four sides given to us .

Perimeter = 2( 22+27+22+98)

Perimeter = 2(169)

Perimeter = 338 in

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Answer:

x \(\geq\) 5 ( the last one)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The inequality of C says the amount of hours of tv that kenny can watch (x) can be exactly or anything below 5 hours

The particular solution is y = (-9/8) * (9x + 81) e^(-x/9) + 85.125.

To solve this differential equation, we can use separation of variables.

dy/dx = -9x/8 e^(-x/9)

dy = (-9/8)x e^(-x/9) dx

Integrating both sides, we get:

y = (-9/8) * (9x + 81) e^(-x/9) + C

where C is the constant of integration.

To find the particular solution, we need to use the initial condition. Let's say that y(0) = 4.

Then, when x = 0, we have:

4 = (-9/8) * (0 + 81) e^(0) + C

C = 4 + (9/8) * 81

C = 85.125

Therefore, the particular solution is:

y = (-9/8) * (9x + 81) e^(-x/9) + 85.125

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Answer:4

Step-by-step explanation:

diagonals of a rectangle are equal therefore QS=RT, 14x+10=11x+22, and solve for x to get 3x=12, so x equals 4

Answer:

I can't see all the pics properly but the graph looks like this:

Step-by-step explanation:

Answer:

69.08

Step-by-step explanation:

Formula: C=Pi(d)

c=22 x 3.14 = 69.08

Answer:

Obtuse Angle

Step-by-step explanation:

Here are the definitions of each type of angle listed!

Acute: Less than 90 degrees

Right: Exactly 90 degrees

Obtuse: More than 90 but less than 180

Reflex: Greater than 180

The angle degree that is shown is (estimate) 112 degrees

That number is more than 90, but less than 180!

Hope this helps!

The diameter of a hemisphere with a volume of 863 in^3 is 40.596 in.

In the given question we have to find the diameter of a hemisphere with a volume of 863 in^3.

As we know that the volume of hemisphere is (2/3)πr^3 cubic unit.

The given volume of hemisphere is 863 in^3.

Now we firstly finding the radius of hemisphere then we find the diameter of hemisphere

The volume of hemisphere = 863 in^3

(2/3)πr^3 = 863

We know that; π = 22/7

(2/3) * (22/7) *r^3 = 863

44/21 * r^3 = 863

Multiply by 21/44 on both side, we get

r^3 = 863*21/44

r^3 = 411.89

r^3 = 412 (approx)

Taking cube root on both side, we get

r = 20.298

Now finding the diameter,

Diameter = 2*radius

Diameter = 2*20.298

Diameter = 40.596 in

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Answer:

h(4)= -2 is the answer

If you travel 2640 feet in 30 seconds in a 65 mi/h zone then the average speed is (b) less than speed limit .

The Distance travelled in 30 seconds is = 2640 feet ,

Average Speed can be calculated by formula; Speed = Distance / Time ,

So , the speed of the person in feet per second will be = 2640/30 ft/sec .

we know the conversion rate that 1 mile = 5280 feet and 1 hr = 3600 sec ,

So , On converting the speed to mi/hr ,

it can be written as = (2640 × 3600)/(5280 × 30)

= 60 mi/hr .

The Speed Limit is given as 65 mi/hr .

On comparing we get the average speed of the person is less than the speed limit .

Therefore , The Average Speed is Less than the Limit .

The given question is incomplete , the complete question is

You travel 2640 feet in thirty seconds while in a 65 mi/h zone. (There are 5280 ft in one mi). Your average speed is:

(a) exactly the speed limit.

(b) less than the speed limit.

(c) larger than the speed limit.

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Your average speed is 98.667 miles per hour, which is calculated by taking the distance traveled (2640 feet) and dividing it by the time taken (thirty seconds) multiplied by the speed limit (65 mi/h). This is based on the fact that there are 5280 feet in one mile.

Step 1: Convert 2640 feet to miles.

1 mile = 5280 feet

2640 feet / 5280 feet = 0.5 miles

Step 2: Calculate speed.

Speed = Distance / Time

Speed = 0.5 miles / (30 seconds/60 seconds)

Speed = 0.5 miles / 0.5 minutes

Speed = 1 mile / 0.5 minutes

Speed = 2 miles/minute

Speed = 2 miles/minute * 60 minutes/hour

Speed = 120 miles/hour

Speed = 120 miles/hour * 65 mi/h

Speed = 78 miles/hour

Speed = 98.667 miles/hour

The average speed is calculated by dividing the distance traveled (2640 feet) by the time taken (thirty seconds) and then multiplying it by the speed limit (65 mi/h). This is based on the fact that there are 5280 feet in one mile. First, the distance (2640 feet) was converted to miles (0.5 miles). Then, the speed (0.5 miles/30 seconds) was calculated, which was then multiplied by the speed limit (65 mi/h) to get the final result of 98.667 miles/hour.

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Answer:

fourth one

Step-by-step explanation:

To find the rate at which average cost is changing when 176 belts have been produced, we need to first find the rate at which the average cost is changing when x belts have been produced.

We know that C(x) = 720 + 37x - 0.068x²We can find the average cost by dividing the total cost by the number of units produced. Average cost = Total cost / Number of units produced Let's consider that x belts have been produced. Then the total cost of producing these x belts is C(x).

Thus, the average cost per belt can be calculated as follows: Average cost = C(x) / x The rate at which the average cost is changing when x belts have been produced is given by the derivative of the average cost with respect to the number of belts produced (x).So, we need to differentiate the equation for average cost with respect to x to find the rate at which the average cost is changing.

Thus, the derivative is given by average cost'(x) = (C(x) / x)'Now, the derivative of the cost function C(x) is given as follows:

C'(x) = 37 - 0.136xaverage cost'(x) = (C(x) / x)'= (720 + 37x - 0.068x²) / x '= [37x² - 2x(720 + 37x) - x²(0.068)] / x²= (37x - 1440 - 0.068x²) / x²Putting x = 176, we get: average cost'(176) = (37(176) - 1440 - 0.068(176²)) / 176²= 13.064

Therefore, when 176 belts have been produced, the average cost is changing at 13.064 dollars per belt for each additional belt.

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Answer:

Explanation:

According to the factor theorem, if we set x+1 to zero, the substitute the x value into the polynomial, if we get a value of zero, then x+1 is a factor of the polynomial, otherwise, it is not

We start by setting x+1 to zero:

Substitute -1 into the polynomial:

This shows that (x+1) is a factor of the polynomial

The correct answer choices for Z and X are $25.08 and $3.72, respectively.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

How to solve for this

To solve for Z and X simultaneously, you can use the following equation: Z + X = 59.5

You can then compare the four given answer choices for Z and X to determine which ones satisfy the equation.

For example, $1.51 + $22.35 = $23.86, which is not equal to 59.5, so neither of these answer choices is correct.

However, $25.08 + $3.72 = $28.80 which is equal to 59.5, so the correct answer choices for Z and X are $25.08 and $3.72, respectively.

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Let A(t) denote the amount of salt (in ounces, oz) in the tank at time t (in minutes, min).

Salt flows in at a rate of

\(\dfrac{dA}{dt}_{\rm in} = \left(17 (1 + 15 \sin(t)) \dfrac{\rm oz}{\rm gal}\right) \left(8\dfrac{\rm gal}{\rm min}\right) = 136 (1 + 15 \sin(t)) \dfrac{\rm oz}{\min}\)

and flows out at a rate of

\(\dfrac{dA}{dt}_{\rm out} = \left(\dfrac{A(t) \, \mathrm{oz}}{180 \,\mathrm{gal} + \left(8\frac{\rm gal}{\rm min} - 8\frac{\rm gal}{\rm min}\right) (t \, \mathrm{min})}\right) \left(8 \dfrac{\rm gal}{\rm min}\right) = \dfrac{A(t)}{180} \dfrac{\rm oz}{\rm min}\)

so that the net rate of change in the amount of salt in the tank is given by the linear differential equation

\(\dfrac{dA}{dt} = \dfrac{dA}{dt}_{\rm in} - \dfrac{dA}{dt}_{\rm out} \iff \dfrac{dA}{dt} + \dfrac{A(t)}{180} = 136 (1 + 15 \sin(t))\)

Multiply both sides by the integrating factor, \(e^{t/180}\), and rewrite the left side as the derivative of a product.

\(e^{t/180} \dfrac{dA}{dt} + e^{t/180} \dfrac{A(t)}{180} = 136 e^{t/180} (1 + 15 \sin(t))\)

\(\dfrac d{dt}\left[e^{t/180} A(t)\right] = 136 e^{t/180} (1 + 15 \sin(t))\)

Integrate both sides with respect to t (integrate the right side by parts):

\(\displaystyle \int \frac d{dt}\left[e^{t/180} A(t)\right] \, dt = 136 \int e^{t/180} (1 + 15 \sin(t)) \, dt\)

\(\displaystyle e^{t/180} A(t) = \left(24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t)\right) e^{t/180} + C\)

Solve for A(t) :

\(\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) + C e^{-t/180}\)

The tank starts with A(0) = 15 oz of salt; use this to solve for the constant C.

\(\displaystyle 15 = 24,480 - \frac{66,096,000}{32,401} + C \implies C = -\dfrac{726,594,465}{32,401}\)

So,

\(\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) - \frac{726,594,465}{32,401} e^{-t/180}\)

Recall the angle-sum identity for cosine:

\(R \cos(x-\theta) = R \cos(\theta) \cos(x) + R \sin(\theta) \sin(x)\)

so that we can condense the trigonometric terms in A(t). Solve for R and θ :

\(R \cos(\theta) = -\dfrac{66,096,000}{32,401}\)

\(R \sin(\theta) = \dfrac{367,200}{32,401}\)

Recall the Pythagorean identity and definition of tangent,

\(\cos^2(x) + \sin^2(x) = 1\)

\(\tan(x) = \dfrac{\sin(x)}{\cos(x)}\)

Then

\(R^2 \cos^2(\theta) + R^2 \sin^2(\theta) = R^2 = \dfrac{134,835,840,000}{32,401} \implies R = \dfrac{367,200}{\sqrt{32,401}}\)

and

\(\dfrac{R \sin(\theta)}{R \cos(\theta)} = \tan(\theta) = -\dfrac{367,200}{66,096,000} = -\dfrac1{180} \\\\ \implies \theta = -\tan^{-1}\left(\dfrac1{180}\right) = -\cot^{-1}(180)\)

so we can rewrite A(t) as

\(\displaystyle A(t) = 24,480 + \frac{367,200}{\sqrt{32,401}} \cos\left(t + \cot^{-1}(180)\right) - \frac{726,594,465}{32,401} e^{-t/180}\)

As t goes to infinity, the exponential term will converge to zero. Meanwhile the cosine term will oscillate between -1 and 1, so that A(t) will oscillate about the constant level of 24,480 oz between the extreme values of

\(24,480 - \dfrac{267,200}{\sqrt{32,401}} \approx 22,995.6 \,\mathrm{oz}\)

and

\(24,480 + \dfrac{267,200}{\sqrt{32,401}} \approx 25,964.4 \,\mathrm{oz}\)

which is to say, with amplitude

\(2 \times \dfrac{267,200}{\sqrt{32,401}} \approx \mathbf{2,968.84 \,oz}\)

Answer: 3/5

Step-by-step explanation:

Answer:

\( 1 \frac{1}{6} \)

Step-by-step explanation:

\(\huge \frac{7}{6} = 1 \frac{1}{6} \)

Hope it helps you in your learning process.

In order to advise the tire manufacturer on their advertising effectiveness and allocation, we need to calculate the marginal return to sales for each region, assess the impact of additional advertising expenditure, determine where the additional money should be spent, and consider the reallocation of current advertising expenditures.

To find the marginal return to sales for each region, we differentiate the sales equation with respect to x. For Region 1, ds_1/dx = 36 - 2.6x, and for Region 2, ds_2/dx = 19 - 1.2x. If $10 million is being spent on TV advertising in each region, we substitute x = 10 into the respective equations to find the marginal return to sales. In Region 1, ds_1/dx = 36 - 2.6(10) = 11, and in Region 2, ds_2/dx = 19 - 1.2(10) = 7. Hence, the marginal return to sales is $11 million in Region 1 and $7 million in Region 2.

To determine which region would benefit more from additional advertising expenditure, we compare the marginal returns. Since the marginal return in Region 1 is higher ($11 million) compared to Region 2 ($7 million), Region 1 would benefit more from additional advertising expenditure.

If additional money is made available for advertising, it should be spent in Region 1 as it has the higher marginal return. Increasing the advertising expenditure in Region 1 would likely result in a greater increase in sales revenue compared to Region 2.

To reallocate money already being spent to produce more sales revenue, we should compare the coefficients of the quadratic term (x^2) in the sales equations. In Region 1, the coefficient is -1.3, and in Region 2, it is -0.6. Since the coefficient in Region 1 is larger in absolute value, reallocating some advertising expenditure from Region 2 to Region 1 would likely lead to a larger increase in sales revenue overall.

Therefore, based on the analysis, the tire manufacturer should focus on increasing advertising expenditure in Region 1, as it has a higher marginal return, and consider reallocating some advertising funds from Region 2 to Region 1 to optimize sales revenue.

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Answer:

Step-by-step explanation:

To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:

a) To find the value of \(\sf 3(x - y) \\\):

\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)

b) To find the value of \(\sf 6x - 6y \\\):

\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)

c) To find the value of \(\sf y - x \\\):

\(\sf y - x = - (x - y) = -4 \\\)

Therefore:

a) The value of \(\sf 3(x - y) \\\) is 12.

b) The value of \(\sf 6x - 6y \\\) is 24.

c) The value of \(\sf y - x \\\) is -4.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The surface area of the given surface between the planes y = 0, y = 2, z = 0, and z = 2 is 4√2. The surface area of the given surface between the planes y = 0, y = 2, z = 0, and z = 2 is found using a double integral of a cross product.

To find the surface area, we'll use the double integral of a cross product formula: Surface Area = ∬√(1 + (fₓ)² + (fᵧ)²) dA

where fₓ and fᵧ are the partial derivatives of the function f(x, y) that defines the surface.

The given surface is defined by x = 2² + y. Let's find the partial derivatives of f(x, y): fₓ = ∂f/∂x = ∂/∂x (2² + y) = 0

fᵧ = ∂f/∂y = ∂/∂y (2² + y) = 1

Now, let's set up the double integral over the region between the planes y = 0, y = 2, z = 0, and z = 2:

Surface Area = ∬√(1 + (fₓ)² + (fᵧ)²) dA

Since fₓ = 0, the square root term becomes 1: Surface Area = ∬√(1 + (fᵧ)²) dA

The region of integration is defined by 0 ≤ y ≤ 2 and 0 ≤ z ≤ 2. We can express the surface area as a double integral:

Surface Area = ∫₀² ∫₀² √(1 + (fᵧ)²) dz dy

Since fᵧ = 1, the square root term simplifies:

Surface Area = ∫₀² ∫₀² √(1 + 1²) dz dy

= ∫₀² ∫₀² √2 dz dy

= √2 ∫₀² ∫₀² dz dy

= √2 ∫₀² [z]₀² dy

= √2 ∫₀² 2 dy

= √2 [2y]₀²

= √2 (2(2) - 2(0))

= 4√2

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The probability that there are less than two errors in a particular chapter and exactly two errors in a particular chapter is 0.1992 and 0.2240 respectively

We can model the number of errors in a chapter as a Poisson distribution with a mean of 3.0, since the occurrence of errors is random and independent, and the average number of errors is known.

Let X be the random variable representing the number of errors in a chapter.

To find the probability of less than two errors in a particular chapter, we need to calculate P(X < 2).

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

= e^(-3.0) × (3.0^0 / 0!) + e^(-3.0) × (3.0^1 / 1!)

= 0.0498 + 0.1494

= 0.1992

Therefore, the probability that there are less than two errors in a particular chapter is 0.1992 or approximately 19.92%.

To find the probability of exactly two errors in a particular chapter, we need to calculate P(X = 2).

P(X = 2) = e^(-3.0) × (3.0^2 / 2!)

= 0.2240

Therefore, the probability that there are exactly two errors in a particular chapter is 0.2240 or approximately 22.40%.

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