A 12 ft ladder is leaning against a wall. It reaches up the wall a height of 4 feet. How far is the base of the ladder from the wall? Round to the nearest tenth.

Answer:  The range of 13 is the most accurate to use, since the data is skewed. It is also because these numbers are from a measure of 13 days, which in turn would show the most varaibility given that one day they receive significantly less donations. This could be used to rally more support on certain days to achieve lower varaibility. As of now, they data is very skewed.

Step-by-step explanation: Remember that IQR stands for Inter Quartile Range which can be found on the calculator and is a measure of Q2-Q1.

Answer:

-------------------

Given:

First, convert the two side length as below:

Now find the third side:

Hence the third side is 5√7 feet.

The correlation coefficient that will produce the most diversification benefits is option b. -.9.

A correlation coefficient of -0.9 indicates a strong negative correlation between two assets, which means that their prices move in opposite directions most of the time. This type of correlation provides the highest level of diversification benefits as it reduces the overall risk of the portfolio.

A correlation coefficient of -0.6 also provides diversification benefits, but to a lesser extent than -0.9. A correlation coefficient of 0 means there is no correlation between two assets, and a correlation coefficient of 4 is not possible as it is outside the range of possible correlation coefficients (-1 to +1).

Therefore, the correct answer is option b. -9.

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there are 33 pleasing ordered triples.

We are given a set {1, 2, 3, 4, 5, 6}. We need to count the number of pleasing ordered triples (a, b, c), where a < b < c, and a, b, c are elements of the set.

Condition (b) requires that both b and c be greater than a. Since a can take any value from 1 to 4, the number of possibilities for (a, b, c) is:

For a = 1, there are 4 choices for b (2, 3, 4, 5) and 5 choices for c (3, 4, 5, 6, 5). However, we must exclude the case where b = c = 5, since both b and c must be greater than a. Therefore, there are 4 × 4 - 1 = 15 pleasing triples with a = 1.

For a = 2, there are 3 choices for b (3, 4, 5) and 4 choices for c (4, 5, 6, 5). However, we must exclude the case where b = c = 5, since both b and c must be greater than a. Therefore, there are 3 × 4 - 1 = 11 pleasing triples with a = 2.

For a = 3, there are 2 choices for b (4, 5) and 3 choices for c (5, 6, 5). However, we must exclude the case where b = c = 5, since both b and c must be greater than a. Therefore, there are 2 × 3 - 1 = 5 pleasing triples with a = 3.

For a = 4, there is only 1 choice for b (5) and 2 choices for c (6, 5). Therefore, there is only 1 × 2 = 2 pleasing triples with a = 4.

The total number of pleasing ordered triples is:

15 + 11 + 5 + 2 = 33

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The correlation between x₁ + x₂ and x₂ + x₃ is 1

The correlation between x₁ +x₂ and x₃ + x₄ is 0

Correlation is a measure of the strength and direction of the linear relationship between two random variables.

It is a statistical concept that is widely used in data analysis and research to explore and quantify the association between two variables.

Here  we have

x₁ x₂ x₃ and x₄ are (pairwise) uncorrelated random variables, each having to mean of 0 and variance of 1,

(a) x₁ + x₂ and x₂ + x₃.

We have

Cov(x₁+ x₂, x₂ + x₃) = Cov(x₁, x₂) + Cov(x₁, x₃) + Cov(x₂, x₂) + Cov(x₂, x₃)

= 0 + 0 + Var(x₂) + 0 = 1.

Since, Var(x₁ + x₂) = Var(x₁) + Var(x₂) + 2 Cov(x₁, x₂) = 1 + 1 + 2 · 0 = 2.

Similarly Var(x₂ + x₃) = 0.

So the correlation between x₁ + x₂ and x₂+ x₃ is

ρ(x₁ + x₂, x₂ + x₃) = Cov(x₁ + x₂, x₂ + x₃)

p = Cov(x₁ + x₂, x₂ + x₃)/ √Var(x₁ + x₂) Var(x₂ + x₃) = 1/√2× 2 = 1/2

(b) x₁+ x₂ and x₃ + x₄.

Cov(x₁ + x₂, x₃+ x₄) = Cov(x₁, x₃) + Cov(x₁, x₄) + Cov(x₂, x₃) + Cov(x₂, x₄)

= 0 + 0 + 0 + 0 = 0

The correlation between x₁ +x₂ and x₃ + x₄ is 0

Therefore,

The correlation between x₁ + x₂ and x₂ + x₃ is 1

The correlation between x₁ +x₂ and x₃ + x₄ is 0

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If the homeowner also had to pay late fees in the amount of $35 four different times, the total cost of the dryer is $809.48. So, correct option is A.

To calculate the total cost of the dryer, we need to add the initial cost of the dryer, the monthly payments, the credit card fees, and the late fees.

The total cost of the dryer can be calculated as follows:

Cost of dryer = $698.27

Total credit card charges = 12 x $1.25 = $15

Total late fees = 4 x $35 = $140

Total cost of the dryer = Cost of dryer + Total credit card charges + Total late fees

= $698.27 + $15 + $140

= $809.27

Therefore, the total cost of the dryer is $809.48, which is the closest option to the calculated answer.

So, correct option is A.

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Answer:

-7x - 2y = -13

x - 2y = 11

-------------------

-8x = -24

x = 3, y = -4

(3, -4) is the solution.

To find the number of 10-letter words that can be formed from the given letters, consider the event E (the word "bacon" appearing together) as a single unit.

So, we have 6 units to arrange: {bacon, r, u, l, e, s}. There are 6! ways to arrange these 6 units.

Since the word "bacon" has 5 letters, there are 5! ways to arrange them within the unit. Therefore, the total number of ways to arrange the 10-letter words with "bacon" together is 6! × 5! = 720 × 120 = 86,400.

To find the probability of event E, we need to know the total number of ways to arrange all 10 letters without restrictions. There are 10! ways to arrange them.

So, P(E) = (Number of ways with "bacon" together) / (Total number of ways) = 86,400 / 3,628,800 = 24/100. Thus, the probability of event E is 24/100, or 0.24.

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Answer:

V=96 mi/h

Step-by-step explanation:

We know that the velocity is equal to displacement over the time.

So V=S/T

We change the minutes to hours.

V= 40/(25/60)

V=96 mi/h

We are willing to reject the null hypothesis if the evidence is sufficiently strong at this level.

The null and alternative hypotheses for the scenario are:

Null hypothesis (H0): The bag filling machine works correctly at the gram setting, i.e., the population mean weight of the bags is[tex]429[/tex]  grams.

Alternative hypothesis (H1): The bag filling machine does not work correctly at the [tex]429[/tex] gram setting, i.e., the population mean weight of the [tex]429[/tex] bags is either less than or greater than  grams.

Mathematically, these can be expressed as:

H0: μ[tex]= 429[/tex]

H1: μ [tex]≠ 429[/tex]

where μ represents the population mean weight of the bags. The two-tailed alternative hypothesis (μ ≠ 429) indicates that we are testing for the possibility of the bags being underfilled or overfilled, and the significance level of 0.01 indicates that we are willing to reject the null hypothesis if the evidence is sufficiently strong at this level.

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The perimeter of the entire sector is 24 feet.

What is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center.

The perimeter of the entire sector is equal to the sum of the arc length and the two radii.

Since the central angle of the sector measures 1 radian, the arc length of the sector can be calculated using the formula:

arc length = radius x central angle

arc length = 8 ft x 1 radian

arc length = 8 ft

The length of each radius is equal to the radius of the sector, which is given to be 8 ft.

Therefore, the perimeter of the entire sector is:

perimeter = arc length + 2 x radius

perimeter = 8 ft + 2 x 8 ft

perimeter = 24 ft

So, the perimeter of the entire sector is 24 feet.

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The answer  is that the graph corresponding to the map of the postal worker's route would likely be a line graph.

This is because the route follows a linear path along the road, with the postal worker delivering mail to both sides of the road as she goes.

A line graph is a type of graph that is used to represent data that changes over time or along a continuous line. In the case of the postal worker's route, the line graph would show the distance traveled along the road as the independent variable on the x-axis, with the number of mail deliveries made on each side of the road as the dependent variable on the y-axis.

The postal worker is likely aiming to solve a graph problem related to optimizing her route and maximizing efficiency in delivering mail to all the houses along the road. By using a line graph to visualize the data of her route, she can analyze patterns in mail delivery and adjust her strategy as needed to improve her efficiency and accuracy.

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The approximate percent of the population that will support the law is 56.67 %

Total number of citizen selected by the city government = 60

Out of 60 total number of citizen who will supported the new law = 34

Percentage is a number or ratio that can be expressed as a fraction of 100. The word per cent means per 100

Percentage = ( people supported the law / total  number of people ) × 100

Percentage = (34/60)×100

Percentage = 0.5666 × 100

Percentage = 56.67

Percent of the population that will support the law is 56.67 %

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Anthony may struggle to afford the rent of $1,700 per month and may want to consider a less expensive option or increase his income.

To determine if Anthony can afford the monthly rent of $1,700, we first need to calculate his net income after taxes and other expenses

Federal and state taxes: 17% of $4,500 = $765

Credit card payments: 11% of $4,500 = $495

Savings: 5% of $4,500 = $225

Total deductions = $765 + $495 + $225 = $1,485

Net income = Gross income - Total deductions = $4,500 - $1,485 = $3,015

Anthony's net income after taxes and other expenses is $3,015 per month. To determine if he can afford the rent of $1,700, we need to compare his rent expense to his available income

Rent: $1,700

Available income: $3,015

Anthony's rent expense is $1,700 per month, which is more than half of his available income. As a general rule, financial advisors recommend that housing expenses should not exceed 30% of a person's income.

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The alternative hypothesis tested by this analysis is that the mean GPA differs for different weight attitude populations.

To determine if there is a significant difference, a statistical test such as ANOVA can be conducted. The result from the survey shows the number of responses for each weight category but further analysis is needed to find the mean GPA for each group. With this information, a hypothesis test can be conducted to determine if there is a significant difference in mean GPA between the different weight attitude populations.

Based on the survey conducted at the university, the alternative hypothesis tested by this analysis, considering [tex]μ_1, μ_2, \: and \: μ_3[/tex] as the population means of GPA for the about right, overweight, and underweight groups respectively, is: [tex]H_1: μ_1 ≠ μ_2 ≠ μ_3 [/tex]

This hypothesis suggests that the mean GPAs for students who feel their weight is about right, overweight, or underweight are not equal, indicating a difference in mean GPA across the different weight attitude populations.

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Answer:

Step-by-step explanation:

-2x*3 = 12 * 5

-6x = 60

6x = -60

x = -60/6

x=-10

The probability of passing the quiz if someone makes random guesses for all of the answers is approximately 0.888 or 88.8%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To pass the quiz, a person needs to answer at least 40% of the questions correctly. That means they need to get at least 8 out of 20 questions correct.

If someone makes random guesses for all of the answers, the probability of getting any one question correct is 1/4 or 0.25.

Using the binomial distribution, we can calculate the probability of getting exactly k questions correct out of n questions with a probability p of getting any one question correct, as:

P(k) = (n choose k) * [tex]p^k[/tex] * [tex](1-p)^{(n-k)}[/tex]

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of a set of n items.

To calculate the probability of passing, we need to calculate the probability of getting 8 or more questions correct. We can do this by adding up the probabilities of getting 8, 9, 10, ..., 20 questions correct:

P(pass) = P(8) + P(9) + P(10) + ... + P(20)

= Σ P(k) from k=8 to k=20

Using a calculator or a computer program, we can find that:

P(k=8) = 0.0000038147

P(k=9) = 0.0000635776

P(k=10) = 0.0005935125

P(k=11) = 0.0034513477

P(k=12) = 0.0147854309

P(k=13) = 0.0492847696

P(k=14) = 0.1302738192

P(k=15) = 0.2459125214

P(k=16) = 0.3278833618

P(k=17) = 0.2940940253

P(k=18) = 0.1650109651

P(k=19) = 0.0520109382

P(k=20) = 0.0068391738

Therefore, P(pass) = Σ P(k) from k=8 to k=20

= 0.0000038147 + 0.0000635776 + 0.0005935125 + 0.0034513477 + 0.0147854309 + 0.0492847696 + 0.1302738192 + 0.2459125214 + 0.3278833618 + 0.2940940253 + 0.1650109651 + 0.0520109382 + 0.0068391738

= 0.888378

So the probability of passing the quiz if someone makes random guesses for all of the answers is approximately 0.888 or 88.8%.

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It is important to review residual plots to identify any signs of changing variability and correlated observations in cross-sectional and time series studies. So, the correct answer is C. changing variability.

Residual plots are graphical tools used to assess the goodness of fit of a statistical model by examining the differences (residuals) between the observed values and the predicted values.

The residuals are the differences between the observed values and the values predicted by the model. By plotting the residuals against the predicted values, we can identify any patterns that indicate a lack of fit of the model to the data.

In particular, changing variability and correlated observations can indicate that the assumptions of the model are not met and that the model may not be appropriate for the data.

Therefore,

It is important to review residual plots to identify any signs of changing variability and correlated observations in cross-sectional and time series studies. So, the correct answer is C. changing variability.

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There are two factors.

The design described in this scenario has two factors: advertisement and price point. Each factor has multiple levels: there are four advertisements and five price points.

In experimental design terminology, a factor is an independent variable that is manipulated by the experimenter, and a level is a specific value or category of that factor. The goal of the experiment is to determine how each factor and its levels affect the response variable (e.g., the number of product purchases).

Therefore, in this experiment, the factor of advertisement has four levels (the four advertisements) and the factor of price point has five levels (the five distinct price points). Overall, there are two factors (advertisement and price point)

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An employee who is looking for a job that offers variety and change would find contract work an incentive to work for an employer. So, correct option is A.

This is because a contract job offers a fixed duration of work with a specific project, and upon completion of the project, the employee is free to move on to another job or contract.

For employees who enjoy variety in their work or want to gain experience in different industries or projects, contract work can be a great option.

Contract work can also be beneficial for those who want flexibility in their work schedule or location, as many contracts can be performed remotely or have more flexible hours. Therefore, for an employee who values variety, change, and flexibility, contract work can be an incentive to work for an employer.

So, correct option is A.

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The probability of rolling two dice and getting a sum of 7 is 1/6.

The probability is the ratio of the number of favorable outcomes to the total outcomes in that sample space. Probability of an event P(E) = (Number of favorable outcomes) ÷ (Sample space).

Sample space for rolling a pair of dice we have:

=> S {(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)}

n(S) = 36

Let A = sum of numbers is 7 = { (1, 6)(2, 5)(3, 4) (4, 3) (5, 2) (6, 1)}

n(A) = 6

P (Sum of numbers is 7) = n(A) / n(S)

= 6/36 = 1/6

Therefore, the probability of rolling two dice and getting a sum of 7 is 1/6.

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It is true that the A shift is a type of permutation where elements in a sequence or set are moved to the right or left by a certain number of positions.

For example, shifting the sequence (1,2,3,4,5) to the right by 2 positions would result in the sequence (4,5,1,2,3). This can be represented mathematically as (1,2,3,4,5) → (4,5,1,2,3), which is a permutation of the original sequence. Shifts can be useful in various applications, such as cryptography or data compression, where rearranging elements in a sequence can improve efficiency or security.

True. A shift is a specific type of permutation. In general, a permutation refers to the arrangement of objects in a particular order. A shift, also known as a cyclic permutation, involves moving elements of a set in a fixed direction, such that the order is maintained, but the elements change positions. In a shift, the first element moves to the last position, while all other elements move one position forward. This maintains the relative order of the elements and results in a new arrangement. Therefore, a shift is a type of permutation, as it represents an altered ordering of the elements in a set.

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Answer:

We can use the Pythagorean theorem to calculate the distance diagonally from Jenny's home to the softball field.

The distance she walks north is 10 blocks, and the distance she walks west is 4 blocks. Using the Pythagorean theorem, the diagonal distance is:

√(10² + 4²) = √116 ≈ 10.77 blocks

To find the total distance she walks to practice and back home, we need to double the diagonal distance:

2 × 10.77 ≈ 21.54 blocks

Therefore, if Jenny takes the diagonal path home, she will walk approximately 21.54 blocks in total to practice and back home.

Step-by-step explanation:

It takes the seagull less time to travel a longer distance.

The owl has a speed of 11 1/9 miles per hour.

The seagull has a speed of 18 3/4 miles per hour.

18 3/4 miles per hour is greater than 11 1/9 miles per hour, so the seagull is faster.

In Mathematics and Science, speed is the distance covered by a physical object per unit of time. In Mathematics and Science, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Next, we would determine the speed of the owl as follows;

Speed of owl = (8 1/3)/(3/4)

Speed of owl = (25/3)/(3/4)

Speed of owl = 25/3 × 4/3

Speed of owl = 100/9 or 11 1/9 miles per hour.

For the speed of the seagull, we have:

Speed of seagull = (12 1/2)/(2/3)

Speed of seagull = (25/2)/(2/3)

Speed of seagull = 25/2 × 3/2

Speed of seagull = 75/4 or 18 3/4 miles per hour.

In conclusion, we can reasonably infer and logically deduce that the seagull is faster because it took less time to travel a longer distance.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

It takes the seagull LESS time to travel a LONGER distance.

Numbers with bases larger than 10 need additional digits that are added starting with the letter "A".

In base 16 (hexadecimal), for example, the first 10 digits represent the numbers 0-9, and the next 6 digits (A-F) are used to represent values 10-15. In base 36, the first 10 digits represent the numbers 0-9, and the next 26 digits (A-Z) are used to represent values 10-35.

When writing numbers in bases larger than 10, it is important to clarify which base is being used, since the same digit can represent different values in different bases. For example, the numeral "A3" could represent the number 163 in base 10, or the number 10*16 + 3 = 163 in base 16.

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The appropirate test statistic is -1.34

The null hypothesis in this case is that the average credit card balance of 18-to-20-year-old college students has not decreased since 2016. The alternative hypothesis is that the average credit card balance has decreased since 2016. Mathematically, we can write:

H0: μ = 569

Ha: μ < 569

where H0 represents the null hypothesis and Ha represents the alternative hypothesis. μ is the population mean credit card balance.

The appropriate critical value for a one-tailed t-test with 39 degrees of freedom and a significance level of 0.05 is -1.684 (found using a t-table or calculator). The test statistic can be calculated using the formula:

t = (x - μ) / (s / √n)

where x is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the values from the sample, we get:

t = (554 - 569) / (68.22 / √40) = -1.34

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Complete Question:

According to a money report by a government institution, 18-to-20-year-old college students have an average credit card balance of $569. A researcher wants to find out if this number is lower now and collects data for a random sample of 40 college students. Their average credit card debt was found to be $554 with a sample standard deviation of $68.22.

a. Calculate the appropriate test statistic.

The simplified expression of m³ *m⁷ is m¹⁰, and the exponent on the variable m is 10.

To simplify the expression m³ *m⁷, we add the exponents since both the bases are same (which is m).

m³ *m⁷ = m^(3+7) = m¹⁰

In general, when we multiply two powers with the same base, we add their exponents. That is, aⁿ * aᵐ = [tex]a^{(n+m)[/tex]. This is known as the Product Rule of Exponents.

The Product Rule of Exponents is a rule used when multiplying exponential expressions with the same base. It states that when multiplying exponential expressions with the same base, you can keep the base and add the exponents

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The answer is option c. The independent variables and the dependent variable have a linear relationship.

The dependent variable and the independent variables must have a linear connection in order for a multiple regression analysis to be valid. This indicates that a straight line can be used to model the connection that exists between the variables that are independent and the dependent variable. Additionally, the dependent variable should be measured using an ordinal, interval, or ratio scale, as the regression model assumes that the dependent variable is continuous.

The residuals of the regression model should also follow a normal distribution, rather than an F distribution, in order to ensure that the model is accurately capturing the relationship between the independent variables and the dependent variable. Finally, the observations should not be autocorrelated, as this can lead to biased estimates and invalid inferences. Overall, adherence to these assumptions is critical for producing accurate and meaningful results from a multiple regression analysis.

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Complete question

A valid multiple regression analysis assumes or requires that Select one:

a. The dependent variable is measured using an ordinal, interval, or ratio scale

b. The residuals follow an F distribution

c. The independent variables and the dependent variable have a linear relationship

d. The observations are autocorrelated

The perimeter of the polygon is 20.23 units

The perimeter of a polygon is the sum of the length of its sides.

Given A(0,−2),B(−5,3),C(3,−3) to find the perimeter of the polygon, we proceed as follows.

To find the length of each side of the polygon, we use the distance formula.

So, d = √[(x - x')² + (y - y')²] where

Using the points A(0,−2), B(−5,3), we have that

d₁ = √[(x - x')² + (y - y')²]

d₁ = √[(0 - (-5))² + (-2 - 3)²]

d₁ = √[5² + (-5)²]

d₁ = √[5² + 5²]

d₁ = √[2(5²)

d₁ = 5√2

Using the points A(0,−2), C(3,-3), we have that

d₂ = √[(x - x')² + (y - y')²]

d₂ = √[(0 - (-3))² + (-2 - (-3))²]

d₂ = √[(0 + 3)² + (-2 + 3)²]

d₂ = √[3² + 1²]

d₂ = √[9 + 1]

d₂ = √10

Using the points B(-5,3), C(3,-3), we have that

d₃ = √[(x - x')² + (y - y')²]

d₃ = √[(-5 - 3)² + (3 - (-3))²]

d₃ = √[(-5 - 3)² + (3 + 3))²]

d₃ = √[(-8)² + (6)²]

d₃ = √[64 + 36]

d₃ = √[100]

d₃ = 10

So, the perimeter of the polygon is D = d₁ + d₂ + d₃

= 5√2 + √10 + 10

= 7.071 + 3.162 + 10

= 20.23 units

So, the perimeter is 20.23 units

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