a. the probability of finding exactly 6 defects in a carpet roll is approximately 0.0403.
b. the probability of finding 3 or fewer defects in a carpet roll is approximately 0.135.
A) The probability of finding exactly 6 defects in a carpet roll can be calculated using the Poisson probability formula:
P(X = 6) = (e^-λ) * (λ^6) / 6!
where λ = 2.0 (the average number of defects per roll), and e is the mathematical constant approximately equal to 2.71828.
Plugging in the values, we get:
P(X = 6) = (e^-2) * (2^6) / 6! = 0.0403
So the probability of finding exactly 6 defects in a carpet roll is approximately 0.0403.
B) To find the probability of finding 3 or fewer defects in a carpet roll, we need to calculate the cumulative probability:
P(X ≤ 3) = Σ_{i=0}^3 P(X = i) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
where P(X = i) is the probability of finding exactly i defects, which can be calculated using the Poisson probability formula.
Plugging in the values and adding the probabilities, we get:
P(X ≤ 3) = (e^-2) + (e^-2) * (2^1) / 1! + (e^-2) * (2^2) / 2! + (e^-2) * (2^3) / 3!
P(X ≤ 3) = 0.135
So the probability of finding 3 or fewer defects in a carpet roll is approximately 0.135.
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Complete question:
The World Carpet and Rug Company buys medium grade carpet in 100-foot rolls. The average number of defects per roll is 2.0. Assuming that these data follow a Poisson distribution,
A) What is the probability of finding exactly 6 defects in a carpet roll chosen at random?
b) What is the probability of finding 3 or fewer defects in a carpet roll?
A rug is 6 7/8
feet long and w feet wide. Which expression does NOT represent the perimeter of the rug in feet?
An expression which does not represent the perimeter of the rug in feet include the following: C. 2(6 7/8) + w.
How to calculate the perimeter of a rectangle?Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;
P = 2(L + W) or P = 2L + 2W
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.Substituting the given parameters into the perimeter of a rectangle formula, we have the following expressions;
P = 2(6 7/8 + W)
P = 2(6 7/8) + 2W = 2W + 13 6/8
P = 6 7/8 + W + 6 7/8 + W
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Catori categorized her spending for this month into four categories: Rent, Food, Fun, and Other. The percents she spent in each category are pictured here.
If Catori spent a total of $2400 this month, how much did she spend on Food? ROUND TO THE NEAREST WHOLE NUMBER
The required amount did she spend on Food is $528.
What is Percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
According to question:We have given;
100% = $2400 which is monthly spend.
Then,
there is 22% spending in food
So,
100% = $2400
1% = $24
22% = $528
Thus, Required spend on Food is $528.
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PLEASE ANSWER QUICKLY!!!!
My parents ordered some books.
My mom ordered 8 books for $19.85.
My dad ordered 6 books for $15.00.
Who had the better/lower unit price?
Your mom had the better/lower unit price.
What is a unit price?A unit price is the cost of a single unit of a product or item, usually expressed per unit of weight, volume, or length. It represents the cost per unit of measurement and allows for comparison of the cost of different products on an equal basis.
For example, the unit price of a bag of apples could be given as the cost per pound, so that a consumer can compare the cost of a 5-pound bag of apples at different stores.
The unit price for your mom's books is $19.85/8 books = $2.48 per book.
The unit price for your dad's books is $15.00/6 books = $2.50 per book.
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The solution to a system of equations for this situation is (2,5). Explain what the solution says about the trees.
In any case, the solution (2,5) is a specific point that satisfies both equations in the system. It tells us that at this particular point, whatever the equations are describing about trees is true.
A location in the coordinate plane that satisfies both equations is typically what a solution to a system of equations in two variables refers to.
If the set of equations in this case has anything to do with trees, we could interpret the answer (2,5) as indicating that there are two different types of trees and five of each type. As an alternative, the equations can reflect the development or health of trees, and the answer (2,5) might point to a certain period of time or place when both varieties of trees are at a given stage of development or health.
In any case, the system's solution (2,5) is a particular location that satisfies both of the system's equations. It indicates that whatever the equations' descriptions of trees are at this specific time are accurate. The answer can shed light on how the system of equations behaves and how it connects to trees, but it does not always reveal information about other locations or circumstances.
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Simplify the expression. the linear expression quantity negative 1 over 7 times r minus 9 minus 2 over 3 times r end quantity minus the linear expression quantity negative 5 over 7 times r plus 10 end quantity
i grow 2 cupcakes every 8 hours for 24 hours
how many cupcakes grow?
At the end of 24 hours, 48 cupcakes will have grown. Every 8 hours, two cupcakes are grown, so after 24 hours, 24 sets of two cupcakes have been grown. Therefore, 48 cupcakes have grown.
At the end of 24 hours, 48 cupcakes will have grown. This is because every 8 hours, two cupcakes are grown. After 24 hours, 24 sets of two cupcakes have been grown. This means that in the 24 hours, two cupcakes were grown a total of 24 times. When this total is multiplied by two, it results in 48 cupcakes being grown. Therefore, after 24 hours, 48 cupcakes have grown. It is important to note that this is only the number of cupcakes that have grown in the 24 hour period, and not the total number of cupcakes. This number includes any cupcakes that were already present at the beginning of the 24 hour period, so the total number of cupcakes at the end of the 24 hour period could be higher than 48.
1. Calculate the number of sets of cupcakes grown in 24 hours: 24 hours divided by 8 hours = 3 sets
2. Calculate the number of cupcakes grown in 24 hours: 3 sets multiplied by 2 cupcakes = 6 cupcakes
3. Calculate the total number of cupcakes grown in 24 hours: 6 cupcakes multiplied by 4 sets = 24 cupcakes
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are these shapes similar
B: no, bc the side lengths ans angles arent similar
Find the length side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.
Answer:
50.1
Step-by-step explanation:
let the height = h
so because that angle is 62 so it's supplemental angle in left triangle is 28°
in any triangle, the tangent of an angle is opposite/adjacent
so height/28 = tan28° =0.53
so height = 14.8
in any triangle, the sine of an angle is opposite/hypotenuse
so height / x = sin 38°
so x = 14.8 / sin 38° = 14.8/0.296 =50.1
please answer b i need help
Answer: don't no
Step-by-step explanation:
Ayuda:
La capacidad de una memoria USB es de 49\8 GB. Cuantos GB enteros contiene?
The USB stick contains 6 whole GB
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that the capacity of a USB stick is 49/8 GB.
Given is the expression as -
49/8
Dividing, we get -
6.125
6 + 0.125
where 6 is a whole number while 0.125 is a decimal.
Therefore, the USB stick contains 6 whole GB.
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{Question in english -
Aid:
The capacity of a USB stick is 49\8 GB. How many whole GB does it contain?}
two furniture stores sell a recliner that has a price of $360. Store A discounts the recliner by $150 and then adds 7.5% sales tax. Store B adds the tax first then takes the discount. Are the Selling Prices the same? Justify your answer
Answer:
no
Step-by-step explanation:
A: 360 -150 = 210 * (1+7%) = 224.7
B: 360 * 1.07 -150 =385.2 -150 =235.2
given z is a standard normal random variable. what is pr(z < 2.3)? use excel and carry your answer to at least five decimal places.
pr(z < 2.3) is =NORMSDIST(2.3) which equals 0.9893 or a probability of 0.9893 that a standard normal random variable is less than 2.3.
The probability that a standard normal random variable is less than 2.3 can be calculated using the cumulative distribution function (CDF) of the standard normal distribution. This function gives us the probability that a standard normal random variable is less than or equal to a given value.
In Excel, you can use the NORMSDIST function to calculate the CDF of the standard normal distribution. The syntax for this function is:
=NORMSDIST(x)
where x is the value for which you want to calculate the CDF.
In this case, to calculate the probability that a standard normal random variable is less than 2.3, we would use the following formula in Excel:
=NORMSDIST(2.3)
This gives us the result of 0.9893 or a probability of 0.9893 that a standard normal random variable is less than 2.3.
Note: The cumulative distribution function can also be approximated using tables or calculators that have the function built in. The result obtained using these methods may have some slight differences compared to the result obtained using Excel.
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Isaac has a total of 90 pennies, nickels, and quarters. He has 3 1/2 times as many quarters as nickels and 1/2 as many pennies as nickels. How many of each coin does he have?
Answer:
see below
Step-by-step explanation:
90 x, y, z
x pennies =1/2y
y nickels
z quarters = 3 1/2 y
so 1/2y+y+3 1/2 y =90
total 5y =90
y =18
x=9
z = 63
Two radio towers have been positioned 8 miles apart at points A and B. Point D is located exactly 4 miles from point A. The third tower will be placed at point C so that all three towers are equidistant from each other.
What should be the distance from the third tower to point D? Round the answer to the nearest tenth of a mile.
Answer:
7 miles
Step-by-step explanation:
Let's call the distance from point C to point D as "x".
We know that the distance from A to B is 8 miles, and the distance from A to D is 4 miles. To ensure that all three towers are equidistant from each other, the distance from C to B must be equal to 8 miles.
Using the Pythagorean Theorem, we can find the distance from C to D:
(x)^2 + (4)^2 = (8)^2
Expanding and simplifying the equation:
x^2 + 16 = 64
x^2 = 48
x = sqrt(48) = 6.928
So the distance from the third tower to point D is approximately 6.9 miles (rounded to the nearest tenth of a mile).
Answer:
6.9 miles
Step-by-step explanation:
Since the distance between points A and B is 8 miles, and point C is equidistant from points A and B, triangle ABC is an equilateral triangle with side lengths of 8 miles.
As point D is 4 miles from point A, point D is the midpoint of AB.
Therefore, the distance between point C and point D is the altitude of the triangle.
The formula for the altitude of an equilateral triangle is:
[tex]h=\dfrac{\sqrt{3}}{2}s[/tex]
where s is the the side length.
Therefore, the altitude of an equilateral triangle with side length 8 miles is:
[tex]\implies h=\dfrac{\sqrt{3}}{2} \cdot 8[/tex]
[tex]\implies h=4\sqrt{3}[/tex]
[tex]\implies h=6.9\; \sf miles\;(nearest\;tenth)[/tex]
Therefore, the distance from the third tower C to point D is 6.9 miles to the nearest tenth of a mile.
Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional questions.
Site 1: "Quadrilaterals"
Site 2: Hierarchy of Figures
Explain why a square must be a rectangle, but a rectangle does not have to be a square. (Site 1)
A square must be a rectangle because it's a four-sided geometric shape with four right angles and congruent sides, but a rectangle doesn't always have congruent sides.
What is a square?In Mathematics and Geometry, a square can be defined as a type of quadrilateral in which the length of all its four (4) sides are equal in magnitude (congruent) and the sum of all its interior angles is equal to 360 degrees (360°) and it forms a right angle.
What is a rectangle?In Mathematics and Geometry, a rectangle can be defined as a type of quadrilateral in which its opposite sides are equal and all the angles that are formed are right angles.
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At 10:00 a.m., two boys start out on their bikes to meet each other from towns located
68 miles apart. They meet at 1:00 p.m. If one boy traveled 3 miles per hour faster than
the other, what was the speed of each boy?
Answer:
Below
Step-by-step explanation:
From 10 am to 1 pm is three hours
the boys covered distance = 68 miles in 3 hours
x = rate1
x+3 = rate2
rate X time = distance
(x + x+3) X 3 = 68
6x+9 = 68
6x = 59
x = 9 5/6 mph then the other rate is x+3 = 12 5/6 mph
Answer: 9.833...
Step-by-step explanation:
The boys traveled a combined 68 miles in 3 hours (difference between 10am and 1pm). This makes their combined speed equal to 68/3.
We can make this equation to model how that combined speed breaks down between them:
68 miles/3 hours = (3 + x) miles/1 hour + x miles/1 hour
To solve:
68/3 = (3 + x) + x
68 = (3 + 2x) * 3
68 = 9 + 6x
59/6 = x
9.833... = x
There are 45 students in a speech contest yesterday 2/3 of them gave their speeches today 1/5 of the remaining students gather speeches how many students still haven't got their speeches
Answer:
12
Step-by-step explanation:
45 total
2/3 * 45 = 30 gave speeches
so 15 remaining
1/5 *15 = 3 gave speeches
remaining 12 didn't
-. How many yards are there in 12.5 miles?
How much would Brielle's family spend on gas each year if they dive about 15,000 miles a year?
If the Car drive 15, 000 miles then gas used is 315 galloons.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
for example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
In 16.8 galloons of gas the Car can travel 400 miles.
So, if they dive about 15,000 miles then the gas in galloons used
= 16.8/400 x 15000
= 2.1 x 150
= 315 galloons.
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in 1996, consumer spending per person per year or the internet was $13.24. the spending increased by about 36% per person per year from 1996 to 2002. predict the spending per person per year on the internet in 2007
$615.9 is the spending per person per year on the internet in 2007.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Consumer spending per person per year or the internet was $13.24. t
The spending increased by about 36% per person per year from 1996 to 2002.
36% of 13.24
36/100×13.24
0.36×13.24
4.7664
[tex]A=Pe^{rt}[/tex]
[tex]A=13.24e^{0.34(6)}[/tex]
[tex]A=13.24e^{2.04}[/tex]
A=101.82
Now the total amount is 101.82
From 2002 to 2007, the number of years are 5.
[tex]A=101.82e^{0.36(5)}[/tex]
[tex]A=101.82e^{1.8}[/tex]
A=101.82×6.049
A=615.9
Hence, $615.9 is the spending per person per year on the internet in 2007.
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Charlie has a utility function U(A, B) = AB, the price of apples is $1, and the price of bananas is $2. If Charlie’s income were $120, how many units of bananas would he consume if he chose the bundle that maximized his utility subject to his budget constraint? * 1 point a. 30 b. 15 c. 60 d. 6 e. 90
Charlie would consume 30 units of bananas if he chose the bundle that maximized his utility function subject to his budget constraint There for the answer is option A
Charlie's utility function is given by U(A, B) = AB, where A is the number of apples he consumes and B is the number of bananas he consumes. The price of apples is $1, and the price of bananas is $2.
If Charlie's income is $120, he has a budget constraint given by:
1A + 2B = 120
To maximize his utility subject to this budget constraint, Charlie must use his income to purchase the combination of apples and bananas that gives him the greatest value of U(A, B).
The solution to this problem can be found by using the method of Lagrange multipliers. From the budget constraint, we can solve for A in terms of B:
A = 120 - 2B
Substituting this into the utility function, we have:
U(B) = (120 - 2B)B = 120B - 2B^2
To maximize U(B), we must find the value of B that maximizes this expression. Taking the derivative of U(B) with respect to B and setting it equal to zero, we find that:
dU/dB = 120 - 4B = 0
Solving for B, we find that:
B = 30
Thus, if Charlie chose the bundle that maximizes his utility subject to his budget constraint, he would consume 30 units of bananas. The answer is therefore a. 30.
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8x+y=-16 - -3x+ y= 5
Jayden folded a 66 \text{ cm}66 cm66, start text, space, c, m, end text strip of paper into 666 equal parts to model a honeycomb cell. Each part was one side of the model.
What is the length of one side of the model?
Jayden is folding a paper strip of 66 cm into a 6 sided honeycomb. So the length of each side will be 11cm.
Jayden has a paper strip of length 66 cm. He had to make a honeycomb with it. It will have six equal sides. To calculate the length we have to formulate the equation.
Total length = number of sides × length of one side
66 = 6 × x
Dividing by 6 on both sides,
66÷6 = 6x ÷ 6
11 = x
So the length of the side of honeycomb will be of 11 cm.
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The complete question is as below
Jayden folded a 66cm strip of paper into 6 equal parts to model a honeycomb cell's. Each part was one side of the model. What is the length of one side of the model?
A part-time receptionist made $9101.99 last year. If he claimed himself as an
exemption for $3650 and had a $5700 standard deduction, what was his
taxable income last year?
O A. $5451.99
OB. $0
OC. $248.01
OD. $3401.99
He had a taxable income of $-748.01 last year, which means he did not owe any federal income tax for the period.
What is simple interest?
The simple interest method, which always adds interest to the starting principal amount at the same rate for each time cycle, is a quick and easy way to calculate interest on money. Any bank where we deposit money will return our investment with interest. Simple interest is one of the several forms of interest that banks charge. Now, before going into any detail on the concept of fundamental curiosity,
The formula for simple interest is:
S = p*t*r/100
The part-time receptionist's taxable income would be calculated by deducting their exemptions and standard deduction from their gross income. The person's gross income was $9101.99. A $3650 exemption was requested by the person. They also qualified for a $5700 standard deduction.
We can figure out their taxable income by deducting the exemption and standard deduction from their gross income. $9101.99 - $3650 - $5700 = $-748.01 would be used to compute the taxable income.
Hence He had a taxable income of $-748.01 last year, which means he did not owe any federal income tax for the period.
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What is the area of the painting shown?
x+4
X
x+6
x+2
Answer: Area = 4x^2 + 24x + 32
Step-by-step explanation:
Area = length x width
Length = x + 6 + x + 2 = 2x + 8
Width = x + 4 + x = 2x + 4
area = 2x + 8 * 2x + 4
multiply each term by each term
Area = 4x^2 + 24x + 32
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-2
X
Which statement is true about the graphed function?
O F(x) <0 over the interval (-∞, -4)
O F(x) <0 over the interval (-∞, -3)
O F(x) > 0 over the interval (-∞, -3)
F(x) > 0 over the interval (-∞, -4)
O
The statement "F(x) > 0 over the interval (-∞, -4)" is true.
What is function?A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. The addition, subtraction, multiplication, and division of functions are discussed in function algebra. We just perform the same operation for individual functions at the same input for every arithmetic operation of two functions at an input.
Here,
For any value of x less than -4, substituting it into the expression f(x) = x² + 4 will result in a positive value since x² is always positive. For example, if x = -5, then f(x) = (-5)² + 4 = 9 + 4 = 13, which is positive.
So, for all values of x that are less than -4, the function f(x) will have a positive value, making the statement "F(x) > 0 over the interval (-∞, -4)" true.
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What integer values satisfy both inequalities?
Please Keep in mind I need 3
Hi there, here's your answer:
We have -1 < x ≤ 2 and -2 ≤ x < 3
Let's first solve both the inequalities one at a time.
Case 1:
-1 < x ≤ 2
The solution set for this inequality is (-1 , 2]
Case 2:
-2 ≤ x < 3
The solution set for this inequality is [-2 , 3)
Now, the values that satisfy both these inequalities can be taken from the solution set of case 1.
Thus, we get a new solution set for the satisfactory values.
New solution set = (0,2]
The required integer values are:
0, 1 and 2.
Hope this helps!
Answer: 0, 1, 2
Step-by-step explanation:
0 is less then 2 and 3 and greater than -1 and -2
Same for 1 and 2, but for 2 in the first equation it is equal but look at these signs [tex]\leq \geq[/tex]
It means equal or less/greater than.
2 is = 2 so it satsifys the first equation.
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which expression is equivalent to 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a
The equivalent expression to 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a is 6/5a + 2/3b - 7/6b + 1/8.
Expression is a mathematical phrase that can contain numbers, variables, and operators.
An equivalent expression is a different expression that has the same value as the original expression. In this question, we need to find an equivalent expression to 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a.
Let's start by simplifying the fractions in the expression. We can see that 4/5a and 2/5a have a common denominator of 5a. We can add these two fractions by finding a common denominator and then adding the numerators. The equivalent fraction to 4/5a + 2/5a is 6/5a.
Next, we can simplify the expression by combining like terms, which are terms that have the same variable and coefficient.
The equivalent expression to
=> 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a = 6/5a + 2/3b - 7/6b - 3/4 + 1/8.
Finally, we can simplify the expression by combining the constants, which are terms without variables. The equivalent expression to
=> 6/5a + 2/3b - 7/6b - 3/4 + 1/8
after combining constants is
=> 6/5a + 2/3b - 7/6b + 1/8.
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How much of the circle is shaded? Write your answer as a fraction in simplest form.
Answer:
13/24
Step-by-step explanation:
First we create a common denominator by multiplying the denominators of 8 and 3 to get 24. Now we convert the two given fractions
[tex] \frac{1}{8} = \frac{3}{24} [/tex]
[tex] \frac{1}{3} = \frac{8}{24} [/tex]
A full circle is 24/24. Now all we do is subtract
[tex] \frac{24}{24} - \frac{8}{24} - \frac{3}{24} = \frac{13}{24} [/tex]
Answer:
13/24
Step-by-step explanation:
1-11/24
=
13/24
Please help me understand this problem
The perimeter of this 19-sided regular polygon is equal to 152 cm.
The side length of this 19-sided regular polygon is equal to 8 cm.
How to calculate the side length of a regular polygon?Mathematically, the area of a regular polygon can be calculated by using this formula:
Area = (n × s × a)/2
Where:
n is the number of sides.s is the side length.a is the apothem.Substituting the parameters into the area of a regular polygon formula, we have;
1,816.4 = (19 × s × 23.9)/2
3632.8 = 454.1s
Side length, s = 3632.8/454.1
Side length, s = 8 cm.
In Mathematics, perimeter of a regular polygon can be calculated by using this formula:
Perimeter of regular polygon = number of sides × side length
Perimeter of regular polygon = 19 × 8
Perimeter of regular polygon = 152 cm.
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Complete Question:
Find the perimeter and side length of a 19-sided regular polygon with an apothem of 23.9 cm and an area of 1,816.4 cm.