What value of x is in the solution set of the inequality 8x – 6 > 12 + 2x?
a. –1

b.0

c. 3

d. 5

It would be more efficient to take the new road from Crimson to Sunshine to get home.

To determine the shortest route home, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the two sides are the distances you traveled west (6 miles) and south (8 miles).

Using the Pythagorean theorem, we have:

Hypotenuse² = 6² + 8²
Hypotenuse² = 36 + 64
Hypotenuse² = 100
Hypotenuse = √100 = 10 miles

So, the shortest route home (the new road) is 10 miles. If you go back the way you came, you would travel 6 miles west and then 8 miles north, for a total of 14 miles. The longer route (14 miles) is 4 miles longer than the shorter route (10 miles). Therefore, you should take the new road to get home more quickly.

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The chances of success in cycling across the United States is higher on the central route because more than half of the people who started on this route finished it (52%), while on the other routes the chances of successful completion is lower (route north (0%) south (0.02%).

According to the above, to find the probability of success in crossing the United States from coast to coast, we must divide the number of successful attempts by the total number of attempts as shown below:

North Route

0 ÷ 2 = 0

Center Route

10 ÷ 19 = 0.52

South Route

1 ÷ 39 = 0.025

According to the above, the highest probability of success is found in the central route with 0.52, that is to say that more than half of those who tried this route finished.

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The probability that the students have to wait at most 4 periods for the teacher to trip is approximately 0.8215

The probability of the teacher not tripping during a single period is 1 - 0.35 = 0.65.

For the teacher not to trip in the first 4 periods, she must not trip in each of the first 4 periods. Since the periods are independent, we can multiply the probabilities together:

P(not tripping in first 4 periods) = 0.65 * 0.65 * 0.65 * 0.65 = 0.65^4 ≈ 0.1785

Now, we subtract this probability from 1 to find the probability that the students have to wait at most 4 periods for the teacher to trip:

P(at most 4 periods) = 1 - P(not tripping in first 4 periods) = 1 - 0.1785 ≈ 0.8215

So, the probability that the students have to wait at most 4 periods for the teacher to trip is approximately 0.8215, or 82.15%.

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The value of the expression 65,536 x 4h for h = -4 is 256. The value represents the number of bacteria in the culture 4 hours before 8:00 A.M.

To find the value of the expression for h = -4, we substitute -4 for h in the expression [tex]65536*4^{h}[/tex]. This gives us

65536*4⁻⁴

To simplify this, we need to evaluate the exponent first. Remember that a negative exponent means we take the reciprocal of the base raised to the positive version of the exponent. So 4⁻⁴ is the same as 1/(4⁴), or 1/256.

Substituting that back into the expression, we get

65536*(1/256) = 256

So the value of the expression for h = -4 is 256.

The value of the expression in part (a) represents the number of bacteria in the culture 4 hours before 8:00 A.M. Since h is negative, we are looking at a time before 8:00 A.M. Specifically, h = -4 means we are looking at 4 hours before 8:00 A.M., or 4:00 A.M.

So the expression 65536*4⁻⁴ tells us how many bacteria were in the culture at 4:00 A.M., assuming the bacteria quadrupled every hour from that point until 8:00 A.M.

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The ratios that have a unit rate of 3 include the following:

A. 15/2 cups: 2 1/2 cups

C. 2 cups: 2/3 cups

F. 2 1/2 cups: 5/6 cups

In Mathematics, the unit rate is sometimes referred to as unit ratio and it can be defined as the quantity of material that is equivalent to a single unit of product or quantity.

15/2 cups : 5/2 cups

15/2 ÷ 5/2 : 5/2 ÷ 5/2

15/2 × 2/5  : 1

3 : 1  (True)

1 cup: 1/4 cups

1 × 4 : 1/4 × 1

4 : 1   (False)

2/3 cups: 1 cup

2/3 × 3/2  : 1 × 3/2

1 : 3/2   (False)

3 3/4 cups: 2 cups

(4 × 3 + 3)/4 : 2

15/4 : 2

15/8  : 2/2

15/8 : 1    (False).

2 cups: 2/3 cups

2 × 3/2 : 2/3 × 3/2

3  : 1   (True).

2 1/2 cups: 5/6 cups

(2 × 2 + 1)/2 : 5/6

5/2  : 5/6

5/2 × 6/5 : 5/6 × 6/5

3 : 1  (True).

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Complete Question:

Which ratios have a unit rate of 3? Choose all that apply.

15/2 cups: 2 1/2 cups

1 cup: 1/4 cups

2/3 cups: 1 cup

3 3/4 cups: 2 cups

2 cups: 2/3 cups

2 1/2 cups: 5/6 cups

10³ times 8 bacteria will Harriet have in the dish at the end of 6 hours, if she has 10³ bacteria now and they double every 2 hours, option D.


Starting with the initial number of bacteria: 10³

Since the bacteria double every 2 hours, after 2 hours, there will be 10³ × 2 bacteria.

After another 2 hours (total of 4 hours), the bacteria will double again: (10³ × 2) × 2 = 1³ × 2²

After the final 2 hours (total of 6 hours), the bacteria will double once more: (10³ × 2²) × 2 = 10³ × 2³

So, at the end of 6 hours, Harriet will have 10³ × 2³ bacteria in the dish. The correct answer is D. 10³ times 8.

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Answer:

6w-9

Step-by-step explanation:

2w×3=6w

-3×3=-9

=6w-9

"The median student height in Class A is equal to the median student height in Class B."

Based on the given information, we can conclude that the median student height in Class A is e.

qual to the median student height in Class B. However, we cannot make any definitive conclusions about the range or mean heights of the two classes based on this limited information.

The range is a measure of the spread of the data and is calculated by subtracting the minimum value from the maximum value. Without knowing the actual height values for each student in both classes, we cannot compare the ranges and determine which class has a greater range.

The mean height is a measure of the central tendency of the data and is calculated by adding up all the heights and dividing by the total number of students. Again, without knowing the actual height values, we cannot calculate the mean heights for each class and compare them.

Therefore, the only conclusion that can be made based on the given information is that the median student height in Class A is equal to the median student height in Class B.

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The critical value z a/2 that corresponds to a 97% level of confidence is 1.96, and the critical value z a/2 that corresponds to an 80% level of confidence is 1.28.

In statistical hypothesis testing, the critical value is the point beyond which we reject the null hypothesis. To find the critical values, we need to use the standard normal distribution table or calculator.

For a 97% level of confidence, the significance level (α) is 0.03, and the critical value can be found by dividing α by 2 to get 0.015 (since it's a two-tailed test), and then finding the corresponding z-value using the standard normal distribution table or calculator. The z-value is 1.96.

Similarly, for an 80% level of confidence, the significance level (α) is 0.20, and the critical value can be found by dividing α by 2 to get 0.10 (since it's a two-tailed test), and then finding the corresponding z-value using the standard normal distribution table or calculator. The z-value is 1.28.

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The height of the pile of books in terms of a and b is 4a cm + 2b cm.

To find the height of the pile of books in terms of a and b, we need to multiply the number of books by the thickness of each book. Since there are (2a+b) books in the pile and the thickness of each book is 2cm, the height of the pile can be expressed as:

(2a+b) x 2cm

Expanding this expression, we get:

4a cm + 2b cm

Therefore, the height of the pile of books in terms of a and b is 4a cm + 2b cm. This means that for every additional 'a' book, the height of the pile will increase by 4cm and for every additional 'b' book, the height of the pile will increase by 2cm.

It's important to note that this formula assumes that all the books are the same size and have the same thickness. If there are any variations in size or thickness, the formula may not accurately represent the height of the pile. Additionally, it's important to ensure that all units of measurement are consistent (in this case, cm for both the thickness of the book and the height of the pile).

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Since the limit of the ratio is less than 1 (1/3 < 1), the series is absolutely convergent (Option A). To determine the convergence of the series, we can use the Ratio Test. The series in question is:

Σ (3n² + 3) / (3n³ + 1)
First, we find the ratio between consecutive terms:
R = (a_(n+1)) / a_n = ((3(n+1)² + 3) / (3(n+1)³ + 1)) / ((3n² + 3) / (3n³ + 1))
R = (3(n+1)² + 3)(3n³ + 1) / ((3n² + 3)(3(n+1)³ + 1))
Now, as n goes to infinity:
lim (n -> ∞) R = lim (n -> ∞) (9n² + 6n + 3)(3n³ + 1) / (9n² + 3)(9n³ + 3n² + 3n + 1)
In this case, the highest power of n in the numerator and denominator is n⁵. To simplify, we can divide both the numerator and denominator by n⁵:
lim (n -> ∞) (9 + 6/n + 3/n²)(3 + 1/n²) / (9 + 3/n)(9 + 3/n² + 3/n + 1/n³)
As n approaches infinity, the terms with n in the denominator approaches zero:
lim (n -> ∞) (9)(3) / (9)(9) = 27 / 81 = 1/3
Since the limit of the ratio is less than 1 (1/3 < 1), the series is absolutely convergent (Option A).

To determine whether the series 3n² +  3n³ +1 is absolutely convergent, conditionally convergent, or divergent, we can use the ratio test.
Using the ratio test, we have:
lim n→∞ |(3(n+1)² + 3)/(3n² + 3n³ +1)
= lim n→∞ |(3n² + 6n + 3)/(3n³ + 3n² +1)
= lim n→∞ |(n² + 2n + 1)/(n³ + n²)
= 0
Since the limit is less than 1, the series is absolutely convergent. Therefore, the answer is A. Absolutely convergent.

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We know that when you have this data, you can proceed with calculating the confidence intervals to determine IMM Thai's lead.

Hi there! The survey results seem to indicate that IMM Thai is indeed ahead of the other Thai restaurants among the voters.

To determine a range of likely values for IMM Thai's true lead over Lucky House, Thai Temple, and Thai Basil combined, you would need to calculate confidence intervals.

Unfortunately, I cannot provide specific calculations without the necessary data (sample size, mean, standard deviation, etc.).

Once you have this data, you can proceed with calculating the confidence intervals to determine IMM Thai's lead.

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A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

A probability can be classified as experimental or theoretical, as follows:

The dice has eight sides, hence the theoretical probability of rolling a six is given as follows:

1/8 = 0.125 = 12.5%.

(each of the eight sides is equally as likely, and a six is one of these sides).

The experimental probabilities are obtained considering the trials, hence:

The more trials, the closer the experimental probability should be to the theoretical probability.

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The value of the expression when x=8 is 56/9.

To find the value of an expression, follow these steps:

To find the value of the expression when x=8, we substitute 8 for x in the expression:

(8^2 - 8) / (8+1)

= (64 - 8) / 9

= 56/9

Therefore, the value of the expression when x=8 is 56/9.

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Since it has four sides and four angles, it is also simply called a quadrilateral.

Rick drew a rhombus. Some names that might describe the figure, considering the properties of quadrilaterals, are:
Quadrilateral: A rhombus is a type of quadrilateral, which means it has four sides and four angles.
Parallelogram: A rhombus is also a parallelogram because its opposite sides are parallel to each other.
Square: If the rhombus has four right angles, then it can also be called a square. A square is a specific type of rhombus and a special case of a parallelogram where all angles are right angles.
A rhombus is a type of quadrilateral that has four sides of equal length. It is also classified as a parallelogram because it has two pairs of parallel sides. Additionally, since all angles in a rhombus are equal, it can also be called an equilateral parallelogram. Finally, since it has four sides and four angles, it is also simply called a quadrilateral.
So, Rick's figure can be described as a quadrilateral, parallelogram, and potentially a square depending on its angles.

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The circle has horizontal tangent lines at the points (1, 2 + √(14)) and (1, 2 - √(14)) and the circle has vertical tangent lines at the points (1 + √(8), -2) and (1 - √(8), -2).

To find the points where the circle defined by x^2 + y^2 - 2x - 4y = 11 has horizontal and vertical tangent lines, we need to use implicit differentiation to find the derivatives of x and y with respect to each other.

Taking the derivative of both sides of the equation with respect to x, we get:

2x + 2y(dy/dx) - 2 - 4(dy/dx) = 0

Simplifying, we get:

(dy/dx) = (x-1) / (y+2)

To find the points where the circle has horizontal tangent lines, we need to find where the derivative dy/dx is equal to zero. This occurs when x-1 = 0, or x = 1. Substituting this value of x back into the original equation, we get:

1 + y^2 - 4y = 11

Simplifying, we get:

y^2 - 4y - 10 = 0

Using the quadratic formula, we get:

y = 2 ± √(14)

To find the points where the circle has vertical tangent lines, we need to find where the derivative dy/dx is undefined, which occurs when y+2 = 0, or y = -2. Substituting this value of y back into the original equation, we get:

x^2 - 2x + 4 = 11

Simplifying, we get:

x^2 - 2x - 7 = 0

Using the quadratic formula, we get:

x = 1 ± √(8)

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The algebraic expression is equivalent to the expression is 125/4x + 34. Option B

Algebraic expressions are simply defined as expressions that are composed of terms, variables, constants, coefficients and factors.

These algebraic expressions are also composed of mathematical operations, such as;

From the information given, we have;

25/4(5x-4/5)+29

expand the bracket, we get;

125x - 100/5 + 29

Find the LCM, we get;

125x - 100 + 145/5

Divide the values

125/4x + 34

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Answer:

Step-by-step explanation:

To use a number line to find the number that is 7 more than -9, we start by finding -9 on the number line. Then, we move 7 units to the right (because we want to find a number that is 7 more), staying on the number line.

Starting from -9 on a number line, we can count 7 units to the right, which brings us to:

-9 + 7 = -2

Therefore, the number that is 7 more than -9 is -2.

Paul has 18 interest-free days for the $300 stereo purchase.

He will need to pay the full balance of his June billing statement.

If Paul's credit card closes on the 6th of the month and his payment is due on the 24th, then he has 18 days between the close of the billing cycle and the due date of his payment.

If Paul purchases a stereo for $300 on June 8th, then the transaction will be included in his billing cycle for the month of June. Since his billing cycle closes on the 6th, the $300 charge will appear on his June billing statement.

If Paul pays off his credit card in full each month, then he will need to pay the full balance of his June billing statement by the due date of June 24th to avoid finance charges. This means he will need to pay $300 for the stereo, plus any other charges that may have been included on his billing statement for the month of June.

Therefore, the number of interest-free days that Paul will have for the $300 stereo purchase is 18 days, which is the number of days between the billing cycle close date (June 6th) and the payment due date (June 24th).

To summarize:

Paul has 18 interest-free days for the $300 stereo purchase.

Paul will need to pay the full balance of his June billing statement, including the $300 stereo charge, by June 24th to avoid finance charges.

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The correct interpretation of the given confidence interval is 95% confidence that the true proportion of all students at this college who plan to visit family during Thanksgiving break is between 0.83 and 0.93 .
Then the required answer to the given question is Option D.


Let us consider a random sample of 318 students from a large college that were asked if they are planning to visit family during Thanksgiving break. Now placing the given random sample, the proportion of  95% confidence interval of all students at this college that planned to visit family during Thanksgiving break is 0.78 to 0.98 .


The formula for evaluating the confidence interval is

CI = p ± z × √((p × (1 - p)) / n)

Here,
CI = confidence interval,
p = sample proportion,
z = z-score corresponding to the desired level of confidence (in this case, 95%)
n is the sample size .

Applying  the values

CI = 0.88 ± 1.96 × √((0.88 × (1 - 0.88)) / 318)
CI = 0.88 ± 0.05
CI = (0.83, 0.93)
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The vector s obtained from the top SVD represents the difficulty scores for each item in the dataset, which can be used to rate or rank them accordingly.

Based on the theory of Singular Value Decomposition (SVD), we can decompose matrix G into a sum of rank-many rank-one matrices. If G is approximated by a rank-one matrix sq^T, where s ∈ R^n and q ∈ R^m have non-negative components, we can use this fact to compute a difficulty score or rating.

The vector s can be interpreted as the difficulty score vector for each item, where its components represent the difficulty levels of individual items in the dataset. By using the top singular value decomposition, we can extract the most significant singular values and corresponding singular vectors to approximate G. The higher the value in the s vector, the higher the difficulty level of the corresponding item.

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Answer:

Step-by-step explanation:

Your total spent is $15

Your friend spent $3 more than you, this is represented by 3+x.

You spent an unknown amount of money, this is represented by x.

So, your equation is 15=3+x+x.

This becomes 15=3+2x.

You then subtract 3 to the other side to get.

12=2x

Then divide 12 by 2, in order to leave variable "x" by itself.

6=x is the amount you spent on lunch.

Your friend spent $3 more so add $3 to the amount you spent to get...

$9 spent by your friend.

You=$6

Friend=$9

Total=$15

To prove the solution is correct, plug 6 in for x.

15=3+2(6)

15=3+12

15=15 thus proving the solution is correct.

The measure of the smallest angle is 37.1 degrees

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

The legs of a right triangle measure 11.4 meters and 15.1 meters

So, the measure of one of the acute angles is

tan(x) = 11.4/15.1

Evaluate

tan(x) = 0.7550

Take the arc tan of both sides

So, we have

x = 37.1

This means that the measure of the smallest angle is 37.1 degrees

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The range of the relation is ( 0,2)

The set which contains all the second elements, on the other hand, is known as the range of the relation.

For example, the two terms a and b have the following values

a: 1, 2 ,4, 8, 10

b: 1, 4 , 12, 14.

The range of relation between the two values is ( 1 ,4) because the two values are common to both term.

Similarly, looking at the term x and y , we can see that only 0 and 2 are common to both terms.

Therefore the range of relation is (0,2)

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The pollster should survey 2627 voters in order to be 96 percent confident that the true proportion of U.S. voters opposing capital punishment is estimated to within 0.02.

To determine the sample size needed for estimating a proportion, we can use the formula:

n = (Z^2 * p * q) / E^2

where:

n is the sample size

Z is the z-value corresponding to the desired confidence level (96 percent confidence corresponds to a z-value of approximately 1.75)

p is the estimated proportion (since we don't have an initial estimate, we can assume a conservative estimate of 0.5)

q is 1 - p (complement of the estimated proportion)

E is the desired margin of error (0.02)

Plugging in the values, we have:

n = (1.75^2 * 0.5 * 0.5) / 0.02^2

n ≈ 2627

Therefore, the pollster should survey 2627 voters in order to be 96 percent confident that the true proportion of U.S. voters opposing capital punishment is estimated to within 0.02.

This sample size calculation ensures that the estimate of the true proportion will have a margin of error (E) of 0.02 or less, providing a high level of confidence (96 percent) in the accuracy of the estimate.

In conclusion, by using the formula for sample size estimation, the pollster should survey 2627 voters to achieve a 96 percent confidence level with a margin of error of 0.02 when estimating the true proportion of U.S. voters opposing capital punishment.

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The equation of the straight line connecting these points in the form of y = mx + c is given as y = (1/2)x + 1.

The line in the slope-intercept equation is given as,

y = mx + c

where:

m = the slope of the line

c = the y-intercept

The slope m of the line connecting two points (x1, y1) and (x2, y2) is given by the formula

= (y₂ - y₁) / (x₂ - x₁)

Substituting the coordinates values of P and Q into this formula, we get

[tex]m = (3 - 0) / (4 - (-2))[/tex]

= 3/6

= 1/2

Therefore, the value of the m is 1/2

We can find the value of c by substituting the m and x values in the equation. using the point P and  Substituting x and y values in the equation we get

x = - 2

y = 0  

[tex]0 = (1/2) × (-2) + c[/tex]

c = 1

Therefore, the value of c is 1.

By substuting the m and c values in the standard slope-intercept formula we get y = (1/2)x + 1.

Therefore, the equation of the line connecting points P and Q is y = (1/2)x + 1.

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The expected value of Lucas going fishing is $26.56. This is calculated by multiplying the probability of each outcome (catching 0, 1, 2, or 3 walleye) by its corresponding payoff ($0, $0, $20, or $100) and adding the results.

To calculate the expected value of Lucas going fishing, we need to consider all possible outcomes and their respective probabilities

Lucas catches all 3 walleye Probability = (3/4) * (2/3) * (1/2) = 1/4 (since he has to catch each walleye in succession, with decreasing probabilities)

Value = $100

Lucas catches 2 walleye Probability = (3/4) * (2/3) * (1/2) * (1/4) * 3 = 9/32 (he has to catch 2 walleye in any order and then not catch the catfish in the remaining attempt)

Value = $20

Lucas catches 1 walleye Probability = (3/4) * (2/3) * (1/2) * (1/4) * (1/4) * 3 = 3/32 (he has to catch 1 walleye and then not catch the other two walleye and the catfish)

Value = $0

Lucas catches no walleye and no catfish Probability = (1/4) = 1/4 (since he has to catch the catfish)

Value = $0

Therefore, the expected value of Lucas going fishing is

E(X) = (1/4)$100 + (9/32)$20 + (3/32)$0 + (1/4)$0 = $26.56

So, on average, Lucas can expect to make $26.56 each time he goes fishing.

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Alexi to consider these factors before deciding how many apples to produce depends on the demand for apples in her area, the size of her garden, and her ability to produce apples efficiently.

To determine Alexi's total revenue, we need to know how many apples she plans to sell. Let's assume that Alexi plans to sell X apples.

If Alexi sells each apple for $3, her total revenue will be:

Total revenue = Price per apple x Number of apples sold

Total revenue = $3 X X

Total revenue = $3X

To determine the cost of producing the apples, we need more information about Alexi's production costs. These costs can include expenses such as land, labor, water, and equipment.

Once we know the production costs, we can subtract them from the total revenue to determine Alexi's profit. If the profit is positive, then Alexi will earn money by selling the apples.

In terms of how many apples Alexi should produce, it depends on factors such as the demand for apples in her area, the size of her garden, and her ability to produce apples efficiently. It's important for Alexi to consider these factors before deciding how many apples to produce.

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The lateral surface area of the triangular prism with side lengths of the base of a triangular prism are 5 meters, 8 meters, and 10 meters the height of the prism is 16.5 meters is 379.5 m²

Lateral surface area of prism = (a + b + c )h

a =  base side = 5m

b = base side = 8m

c = base side = 10m

h = height = 16.5 m

Lateral surface area of prism = (5 + 8 + 10)16.5

The lateral surface area of the prism = 379.5m²

The lateral surface area of the triangular prism is 379.5 m²

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