For the single roots -1 and 2,the graph ——— the x-axis at the intercepts
/crosses/
/does not intersect/
/touches/
—————————
For the double root 3 the graph ——— at the intercepts
/crosses/
/does not intersect/
/touches/

Answer:

A certain company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a battery is normally distributed, with a mean of 50 months and a standard deviation of 9 months. If the company does not want to make refunds for more than 10% of its batteries under the full-refund guarantee policy, for how long should the company guarantee the batteries?

The company should guarantee the batteries for 38 months.

Step-by-step explanation:

Using standard normal table,

P(Z < z) = 10%

=(Z < z) = 0.10

= P(Z <- 1.28 ) = 0.10

z = -1.28

Using z-score formula  

x = zσ  + μ

x = -1.28 *9+50

x = 38

Therefore, the company should guarantee the batteries for 38 months.

Answer:

The company should guarantee the batteries (to the nearest month) for 38 months.

Step-by-step explanation:

We have here a normally distributed data. The random variable is the average life of the batteries.

From question, we can say that this random variable has a population mean of 50 months and population standard deviation of 9 months. We can express this mathematically as follows:

[tex] \\ \mu = 50[/tex] months.

[tex] \\ \sigma = 9[/tex] months.

The distribution of the random variable (the average life of the batteries) is the normal distribution, and it is determined by two parameters, namely, the mean [tex] \\ \mu[/tex] and [tex] \\ \sigma[/tex], as we already know.

For the statement: "The company does not want to make refunds for more than 10% of its batteries under the full-refund guarantee policy", we can say that it means that we have determine, first, how many months last less of 10% of the batteries that its average life follows a normal distribution or are normally distributed?

To find this probability, we can use the standard normal distribution, which has some advantages: one of the most important is that we can obtain the probability of any normally distributed data using standardized values given by a z-score, since this distribution (the normal standard) has a mean that equals 0 and standard distribution of 1.

Well, the z-score is given by the formula:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

Where, x is a raw score coming from a normally distributed data. This is the value that we have to transform into a z-score, that is, in a standardized value.

However, from the question, we want to know what value of z represents a cumulative probability of 10% in the cumulative standard normal distribution. We can find it using the standard normal table, available in Statistics books or on the Internet (of course, we can use also Statistics packages or even spreadsheets to find it).

Then, the value of z is, approximately, -1.28, using a cumulative standard normal table for negative values for z. If the cumulative standard normal only has positive values for z, we can obtain it, using the following:

[tex] \\ P(z<-a) = 1 - P(z<a) =P(z>a)[/tex]

That is, P(z<-1.28) = P(z>1.28). The probability for P(z<1.28) is approximately, 90%.

Therefore, using the formula [1]:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

[tex] \\ -1.28 = \frac{x - 50}{9}[/tex]

 [tex] \\ -1.28 * 9 = x - 50[/tex]

 [tex] \\ -11.52 = x - 50[/tex]

[tex] \\ -11.52 + 50 = x[/tex]

[tex] \\ 38.48 = x[/tex]

[tex] \\ x = 38.48[/tex] months.

That is, less than 10% of the batteries have a average life of 38.48 months. Thus, the company should guarantee the batteries (to the nearest month) for 38 months.

Answer:

z = 1.83<1.96

null hypothesis is accepted

The sample is came from a population mean

Step-by-step explanation:

Step :-1

The sample of 40 measured voltage amounts from a unit have a mean of 123.59 volts and a standard deviation of 0.31 volts

given sample size n =40

mean of the sample ×⁻ = 123.59 volts

standard deviation of sample σ = 0.31 volts

Step2:-

Null hypothesis :-

the sample is from a population with a mean equal to 120 volts.

H₀ : μ =120

Alternative hypothesis:-

H₁ : μ ≠120

level of significance:- α =0.05

Step 3:-

The test statistic

[tex]z = \frac{x_{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]

substitute values and simplification

[tex]z = \frac{123.59-120}{\frac{0.31}{\sqrt{40} } }[/tex]

on simplification we get the calculated value

z = 1.83

The tabulated value z =1.96 at 0.05 % level of significance

Conclusion:-

Calculated Z < The tabulated value z =1.96 at 0.05 % level of significance

so the null hypothesis is accepted

The sample is came from a population mean

Answer: REJECT the null hypothesis; there IS sufficient evidence to warrant a rejection of the claim that the mean voltage is 120 volts.

t-calculated = 73.242

t-critical = 2.023

Answer:

The prorated monthly cost for tuition and fees and textbooks is ​$707

Step-by-step explanation:

Each semester costs $4000 + $240 = $4240.

A year has 12 months. A semester is 6 months. 12/6 = 2. So an year has two semesters.

The yearly cost is 2*$4240 = $8480

Monthly cost

12 months cost $8480

$8480/12 = $706.67

So the answer is:

Rounded to the nearest dollar

The prorated monthly cost for tuition and fees and textbooks is ​$707

The prorated monthly cost for tuition and fees and textbooks is $707

Total cost per semester = Fees for each semester + Cost of textbook per semester

= $4000 + $240

= $4,240

= 2 × $4,240

= $8480

= $8480 / 12

= $706.666666666666

Approximately,

$707

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Answer:

A. $1500

Step-by-step explanation:

We need to find the countertop area, so let's calculate the areas of the rectangles that the problem broke the countertop into:

1. "1 rectangle has a base of 70 inches and height of 20 inches"

The area of a rectangle is denoted by: A = bh, where b is the base and h is the height. Here, b = 70 and h = 20, so the area is: A = 70 * 20 = 1400 inches squared

2. "The other rectangle has a base of 20 inches and height of 30 inches"

Again, use A = bh: b = 20 and h = 30, so A = 20 * 30 = 600 inches squared

Add up these two areas: 1400 + 600 = 2000 inches squared.

The problem says that the cost is $0.75 per square inch, so multiply this by 2000 to get the total cost of 2000 square inches:

2000 * 0.75 = $1500

Thus, the answer is A.

Hope this helps!

Answer:

$1500

Step-by-step explanation:

You can divide this figure into 2 rectangle with dimensions:

1) 70 × 20

2) 20 × (50-20: 20 × 30

Area:

(70×20) + (20×30)

1400 + 600

2000 in²

Cost per in²: 0.75

2000in² cost:

2000 × 0.75

$1500

Answer:

The correct equation in terms of s is: 4s=260

Step-by-step explanation:

Let the number of containers of strawberry ice cream produced per day=s

Let the number of containers of vanilla ice cream produced per day=v

Let the number of containers of chocolate ice cream produced per day=c

Total Number of Ice Cream Containers=280

Given:

The factory produces twice as much chocolate ice cream as strawberry ice cream. This is written as:

The factory produces 20 more containers of vanilla ice cream than strawberry ice cream. This is written as:

Therefore substituting c=2s and v=s+20 into the first equation: s+v+c=280

s+s+20+2s=280

4s=280-20

4s=260

Divide both sides by 4

s=65

The number of strawberry ice cream produced per day is 65.

The number of chocolate ice cream produced per day =2s=2(65)=130.

The number of vanilla ice cream produced per day =s+20=65+20=85.

Final answer:

The number of containers of strawberry ice cream produced per day is 65.

Explanation:

The question is asking us to find the correct equation and solution for the number of containers of strawberry ice cream produced per day by a factory, while taking into account that chocolate is produced at twice the rate and vanilla at 20 more containers than strawberry.

Given the total production is 280 containers, the equation can be set up as follows:

s + 2s + (s + 20) = 280,

where s represents the number of strawberry ice cream containers produced per day.

Step-by-step, we can solve this equation:

Therefore, the factory produces 65 containers of strawberry ice cream per day.

Answer:

Explanation:

The amount of animal waste one zoo is diposing daily is approximately normal with:

The proportion of waste over 350 lbs may be found using the table for the area under the curve for the cumulative normal standard probability.

First, find the z-score for 350 lbs:

      [tex]z-score=\dfrac{X-\mu}{\sigma}[/tex]

      [tex]z-score=\dfrac{350lbs-348.5lbs}{38.2lbs}\approx0.04[/tex]

There are tables for the cumulative areas (probabilities) to the left and for the cumulative areas to the right of the z-score.

You want the proportion of the days when the z-score is more than 0.04; then, you can use the table for the values to the rigth of z = 0.04.

From such table, the area or probability is 0.4840.

The attached image shows a portion of the table with that value: it is the cell highlighted in yellow.

Hence, the answer is the option (A) 0.484.

By calculating the z-score for 350 pounds of waste and consulting the standard normal distribution, the proportion of days the zoo can expect to have enough animal waste to power the entire aquarium is approximately 0.484.

To determine the proportion of days the zoo can expect to generate enough animal waste to run the entire aquarium, we can use z-scores in a normal distribution. Given the mean (μ = 348.5) and standard deviation (σ = 38.2), we want to find the proportion of the data that is above 350 pounds.

First, we calculate the z-score for 350 pounds:

z = (X - μ) / σ = (350 - 348.5) / 38.2 ≈ 0.04

Now we need to find the probability that the z-score is greater than 0.04. Consulting a standard normal distribution table or using a calculator, this gives us a probability of approximately 0.484.

Therefore, the proportion of the days the zoo can expect to obtain enough waste to cover the energy demands for the entire aquarium is 0.484.

Answer:

No, H is not a subspace of the vector space V.

Step-by-step explanation:

A matrix is a rectangular array in which elements are arranged in rows and columns.

A matrix in which number of columns is equal to number of rows is known as a square matrix.

Let H denote set of all 2×2  idempotent matrices.

H is a subspace of a vector space V if [tex]u+v \in H[/tex] for [tex]u,v \in V[/tex] and   [tex]cu \in H[/tex].

Let [tex]A=\begin {pmatrix}1&0\\0&1 \end{pmatrix}[/tex]

As [tex]A^2=A\times A=\begin {pmatrix}1&0\\0&1 \end{pmatrix}\begin {pmatrix}1&0\\0&1 \end{pmatrix}=\begin {pmatrix}1&0\\0&1 \end{pmatrix}=A[/tex], A is idempotent.

So, [tex]A \in H[/tex]

[tex]A+A=\begin {pmatrix}1&0\\0&1 \end{pmatrix}+\begin {pmatrix}1&0\\0&1 \end{pmatrix}=\begin {pmatrix}2&0\\0&2\end{pmatrix} \\ \left ( A+A \right )^2=\begin {pmatrix}2&0\\0&2\end{pmatrix}\begin {pmatrix}2&0\\0&2\end{pmatrix}=\begin {pmatrix}4&0\\0&4\end{pmatrix}\neq A[/tex]So, A+A is not idempotent and hence, does not belong to H.

So, H is not a subspace of the vector space V.

Yes, H is a subspace of the vector space V. It satisfies the conditions of closure under addition, closure under scalar multiplication, and contains the zero vector.

Yes, H is a subspace of the vector space V. In order for a set to be considered a subspace, it must satisfy three conditions: it must be closed under addition, closed under scalar multiplication, and contain the zero vector. Let's check if H satisfies these conditions:

Since H satisfies all three conditions, it is a subspace of the vector space V.

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Answer:

Equation:  [tex]F=1500(1.0025)^{12t}[/tex]

The balance after 5 years is:  $1742.43

Step-by-step explanation:

This is a compound growth problem . THe formula is:

[tex]F=P(1+\frac{r}{n})^{nt}[/tex]

Where

F is future amount

P is present amount

r is rate of interest, annually

n is the number of compounding per year

t is the time in years

Given:

P = 1500

r = 0.03

n = 12 (compounded monthly means 12 times a year)

The compound interest formula modelled by the variables is:

[tex]F=1500(1+\frac{0.03}{12})^{12t}\\F=1500(1.0025)^{12t}[/tex]

Now, we want balance after 5 years, so t = 5, substituting, we get:

[tex]F=1500(1.0025)^{12t}\\F=1500(1.0025)^{12*5}\\F=1500(1.0025)^{60}\\F=1742.43[/tex]

The balance after 5 years is:  $1742.43

Answer:

At Maximum point;

x(max) = 50

p(max) = $100

Maximum revenue = $5,000

Step-by-step explanation:

The price function is;

p(x) = 200 − 2x

where

p is the price (in dollars) at which exactly x trucks will be rented per day.

The revenue function R(x) can be written as;

R(x) = p(x) × x

Substituting p(x) equation;

R(x) = (200-2x)x

R(x) = 200x-2x^2 ........1

To maximize R(x), at maximum point dR/dx = 0

differentiating equation 1;

dR/dx = 200 - 4x = 0

4x = 200

x = 200/4

x = 50

Substituting x = 50 into p(x)

p(50) = 200 - 2(50) = $100

p = $100

Maximum revenue is;

R = p × x = $100×50

R = $5,000

At the level of the maximum point, the value of x(max) should be 50 and the value of p(max) should be $100, Also, Maximum revenue = $5,000.

Since

The price function is;

p(x) = 200 − 2x

Here,

p refer to the price (in dollars) at which exactly x trucks should be rented per day.

Now

The revenue function R(x) should be

R(x) = p(x) × x

Now

R(x) = (200-2x)x

R(x) = 200x-2x^2 ........1

Now

To maximize R(x), at maximum point dR/dx = 0

So,

dR/dx = 200 - 4x = 0

4x = 200

x = 200/4

x = 50

Now

Substituting x = 50 into p(x)p(50) = 200 - 2(50) = $100

p = $100

Now

Maximum revenue is;

R = p × x = $100×50

R = $5,000

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Step-by-step explanation:

Given points

( x1 , y1 ) = ( 0, 4)

And

( x2 , y2 ) = ( - 4 , - 3 )

Now

Slope(m)

= ( y2 - y1 ) / ( x2 - x1 )

= ( - 3 - 4) / ( -4 - 0)

= - 7 / - 4

= 7/4

Answer:

m=7/4

Step-by-step explanation:

Answer:

The correct answer is 0.1714 .

Step-by-step explanation:

There are 6 men and 4 women to be interviewed for jobs.

Total number of arrangements in which they can be called for the interview process is 10!.

Number of ways any two women are interviewed before any man is 4 × 3 × 8!. = 12 × 8!.

Number of ways any three women are interviewed before any man is 4 × 3 × 2 × 7!. = 24 × 7!.

Number of ways all the women are interviewed before any man is 4! × 6!.

Required number of ways in which at least two women being interviewed before any man is given by 12 × 8! + 24 × 7! + 4! × 6! = 864 × 6!.

Required probability is 864 × 6! ÷ 10! = 0.1714

The probability that no man will be interviewed until at least two women have been interviewed is [tex]\( \bxed{\frac{2}{15}} \).[/tex]

Step 1

We may utilise the concept of permutations to estimate the likelihood that no man will be interviewed until at least two women have been interviewed.

Let us examine the case where a minimum of two women are interviewed before a guy is examined. This implies that women must have the first two places in the interview process. Men and women may be appointed to the other positions in any order, following these two positions.

Let's figure out how many options there are to choose the first two slots for women, given that there are four women and six men:

Step 2

Number of ways to select the first woman: [tex]\(4\)[/tex]

Number of ways to select the second woman: [tex]\(3\)[/tex] (since one woman has already been selected for the first position)

The total number of ways to select the first two positions for women is [tex]\(4 \times 3 = 12\).[/tex]

Step 3

After these two positions have been filled with women, the remaining 8 positions (6 men + 2 women) can be filled with the remaining people (4 men + 2 women) in any order. This can be calculated using the permutation formula:

[tex]\[ nPr = \frac{{n!}}{{(n-r)!}} \][/tex]

Where n is the total number of people and r is the number of positions to be filled.

For our scenario, [tex]\( n = 6 + 4 = 10 \)[/tex] and [tex]\( r = 8 \)[/tex]. So, the number of ways to fill the remaining 8 positions is:

[tex]\[ 10P8 = \frac{{10!}}{{(10-8)!}} = \frac{{10!}}{{2!}} = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \][/tex]

Step 4

Now, let's calculate the total number of ways to select the positions for all 10 people:

[tex]\[ 10! \][/tex]

Consequently, the ratio of the number of favourable results to the total number of outcomes represents the likelihood that no guy will be interviewed until at least two women have been interviewed:

[tex]\[ \text{Probability} = \frac{{12 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3}}{{10!}} \]\[ \text{Probability} = \frac{{12}}{{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}} \]\[ \text{Probability} = \frac{{12}}{{10!/(10-8)!}} \]\[ \text{Probability} = \frac{{12}}{{10P8}} \]\[ \text{Probability} = \frac{{12}}{{10 \times 9}} \]\[ \text{Probability} = \frac{2}{15} \][/tex]

So, the probability that no man will be interviewed until at least two women have been interviewed is [tex]\( \bxed{\frac{2}{15}} \).[/tex]

Answer:

[tex]A=7 \: Square\: Units[/tex]

Step-by-step explanation:

From your work here, if the diagram corresponds with what was tiled, then:

Length of the Rectangle=[tex]3\frac{1}{2} \:Units[/tex]

Width of the Rectangle =2 Units

We know that:

Area of a Rectangle = Length X Width

[tex]=3\frac{1}{2} X 2\\A=7 \: Square\: Units[/tex]

The only thing wrong is the unit of the area given. The unit of area is supposed to be in Square Units.

Answer:

i dont see no angle

Step-by-step explanation:

Angles can be named according to their measure in degrees or position on a plane. Angles are always counted to be positive in the counter-clockwise direction and negative in the clockwise direction.

The name of an angle in Mathematics can vary based on its measure and location. Angles are generally named according to their measure in degrees, and they can be categorized as acute (less than 90 degrees), right (90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), straight (180 degrees), reflex (greater than 180 degrees), or full (360 degrees).

Angles can also be referred to in terms of their position on a Cartesian plane: angles in the first quadrant are positive and less than 90; in the second quadrant, they are more than 90 but less than 180; in the third quadrant, they exceed 180 but are less than 270; and in the fourth quadrant, they are greater than 270 but less than 360 degrees.

This consistently maintains the rule that angles are defined as positive in the counter-clockwise direction, and negative in the clockwise direction. For example, an angle of 30° south of west is the same as the global angle 210°, or it can also be expressed as −150° relative to the positive x-axis.

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Answer:

1 and 7/10 pounds

Step-by-step explanation:

add.

Answer:

1 and 7/10 pounds

Step-by-step explanation:

Answer:

B - -5 < y < 5

Step-by-step explanation:

Range is highest and lowest y value the graph goes to.

You can see on the graph that it does not pass 5 and -5

Answer:

The population will be 64 times larger after 96 hours.

Leave a comment if you'd like a more in-depth explanation.

Answer:

64  times as large as the original population.

Step-by-step explanation:

.24 is equivalent to

24%

24/100

6/25

12/50, and more!

Hope this helped

Answer:

We can be 95% sure that the true population mean zinc concentration is between 8.8 mg/g and 9.5 mg/g.

Step-by-step explanation:

Given that

N = Sample = 56

Confidence Interval = 95%

Mean Interval = 8.8 mg/g to 9.5 mg/g

UB = Upper Bound = 9.5mg/g

LB = Lower Bound = 8.8mg/g

The sample mean was 9.15mg/g

The sample mean is gotten from ½(UB + LB)

Sample Mean = ½(8.8 + 9.5)

Sample Mean = ½ * 18.3

Sample Mean = 9.15mg/g

From the definition of confidence Interval;

"Confidence Interval is a range of values so defined that there is a specified probability that the value of a parameter lies within it"

This means that the best interpretation of the data given is "the mean value of the 56 sample of fishes is between 8.8mg/g and 9.5mg/g;"

With 8.8mg/g as the lower bound and 9.9mg/g as the upper bound.

Final answer:

The height of the tree is approximately 113.85 feet, which is determined by using the tangent of the given angle of elevation (68°) and the distance from the tree (46 feet) in a trigonometric calculation.

Explanation:

To find the height of the tree, we can use trigonometry. The student is 46 feet from the tree, and the angle of elevation to the top of the tree is 68°. The height of the tree can be found using the tangent function in a right triangle, where the opposite side is the tree height (h), and the adjacent side is the distance from the tree (46 feet). The tangent of the angle of elevation (θ) is the ratio of the opposite side to the adjacent side.

So, tan(68°) = h / 46 feet. To find the height (h), multiply both sides by 46 feet:

h = 46 feet × tan(68°)

We can use a calculator to find that tan(68°) is approximately 2.475. Now, multiply 46 feet by this tangent value to get the height:

h = 46 feet × 2.475h = 113.85 feet (rounded to two decimal places)

Therefore, the height of the tree is approximately 113.85 feet.

Answer:

To check that V is a vector space it suffice to show

1. Associativity of vector addition.

2. Additive identity

3. Existence of additive identity

4. Associativity of scalar multiplication

5. Distributivity of scalar sums

6.  Distributivity of vector sums

7. Existence of scalar multiplication identity.

Step-by-step explanation:

To see that V is a vector space we have to see that.

1. Associativity of vector addition.

This property is inherited from associativity of the sum on the real numbers.

2. Additive identity.

The additive identity in this case, would be the null function f(x)=0 . for every real x.   It is inherited from the real numbers that the null function will be the additive identity.

3. Existence of additive inverse for any function f(x).

For any function f(x), the function -f(x) will be the additive inverse. It is in inherited from the real numbers that f(x)-f(x) = 0.

4. Associativity of scalar multiplication.

Associativity of scalar multiplication  is inherited from associativity of the real numbers

5. Distributivity of scalar sums:

Given any two scalars r,s and a function f, it will be inherited from the distributivity of the real numbers that

(r+s)f(x) = rf(x) + sf(x)

Therefore, distributivity of scalar sums is valid.

5. Distributivity of vector sums:

Given scalars r  and two functions f,g, it will be inherited from the distributivity of the real numbers that

r (f(x)+g(x)) = r f(x) + r g(x)

Therefore, distributivity of vector sums is valid.

6. Scalar multiplication identity.

The scalar 1 is the scalar multiplication identity.

Answer:A+b

by-step explanation:

Answer:

you have the correct answer!

Step-by-step explanation:

Answer:

.5

Step-by-step explanation:

-1.9+4=2.1

2.1+(-1.6)=.5

Answer:

Step-by-step explanation:

This is permutation question

The formula for it:

Finding the answer:

Answer:

[tex]x + 1[/tex]

Step-by-step explanation:

log(x) is the inverse function of an exponent. "log base 8 of xyz" means "what number do I have to raise 8 to, to get xyz". In this case, it means, "what number do I have to raise 8 to, to get x + 1". That's simple, it's just x + 1!

Answer:

16.1 my friend

Step-by-step explanation:

Answer:

16.1

Step-by-step explanation:

Remember to always follow PEMDAS. In this case, we need to multiply before we divide.

10 x .89 + 7.2

8.9 + 7.2 = 16.1

The answer is 16.1

Given:

The given expression is [tex]18^{x^{2}+4 x+4}=18^{9 x+18}[/tex]

We need to determine the solution of the given expression.

Solution:

Let us solve the exponential equations with common base.

Applying the rule, if [tex]a^{f(x)}=a^{g(x)}[/tex] then [tex]f(x)=g(x)[/tex]

Thus, we have;

[tex]x^{2}+4 x+4=9 x+18[/tex]

Subtracting both sides of the equation by 9x, we get;

[tex]x^{2}-5 x+4=18[/tex]

Subtracting both sides of the equation by 18, we have;

[tex]x^{2}-5 x-14=0[/tex]

Factoring the equation, we get;

[tex]x^2-7x+2x-14=0[/tex]

Grouping the terms, we have;

[tex](x^2-7x)+(2x-14)=0[/tex]

Taking out the common term from both the groups, we get;

[tex]x(x-7)+2(x-7)=0[/tex]

Factoring out the common term (x - 7), we get;

[tex](x+2)(x-7)=0[/tex]

[tex]x+2=0 \ and \ x-7=0[/tex]

   [tex]x=-2 \ and \ x=7[/tex]

Thus, the solution of the exponential equations is x = -2 and x = 7.

Hence, Option C is the correct answer.

The Taylor polynomial approximation to f(x) = 1/x up to degree 2 about x=a was calculated. It was mentioned that Taylor's inequality could be used to estimate the accuracy of this approximation. However, due to the lack of necessary information, an exact error bound or graphical check couldn't be determined.

To begin the solution, we'll need to find the first couple of derivatives for the function f(x) = 1/x. The first derivative is f'(x) = -1/x² and the second derivative is f''(x) = 2/x³. These derivatives will be used to form the Taylor series approximation.

The Taylor series polynomial of degree 2 is given by the formula T₂(x) = f(a) + f'(a)*(x-a) + f''(a)*(x-a)²/2!, where a is the point we are approximating about and n is the degree of the Taylor polynomial. Substituting the given values, we get: T₂(x) = 1/1 - 1/1² * (x-1) + 2/1³ * (x-1)²/2!.

To estimate the accuracy of this approximation, we use Taylor's Inequality which provides an upper bound for the absolute error. The remainder term in Taylor's series is given by |R₂(x)| ≤ M * |x - a|³ / (3!*n), where M is the maximum value of the absolute third derivative on the interval [a, x]. After applying Taylor's inequality, we can get an accuracy estimate but unfortunately, the information provided doesn't give enough specifics for an exact calculation.

Finally, to verify the result graphically, you would plot |R₂(x)|, but without the explicit remainder term, this cannot be done.

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