The function y = 1/4(x - 4)² + 2, after a translation right 3 units and down 4 units, is given as follows:
y = 1/4(x - 7)² - 2.
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The parent function for this problem is given as follows:
y = 1/4(x - 4)² + 2
The changes with each translation are given as follows:
Right 3 units: x -> x - 3.Down 4 units -> f(x) = f(x) - 4.Hence the function is defined as follows:
y = 1/4(x - 3 - 4)² + 2 - 4
y = 1/4(x - 7)² - 2.
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solve the equation , 3/4x-5=x
Answer: x= 0.146 or x= -5.15
(refer to the steps I wrote down, check the image)
the following purchase is made at each store: 6 pounds of sugar, 3 cans of peaches, 2 pounds of chicken, and 5 loaves of bread. use matrix multiplication to find the total bill at each store. you may leave decimal answers in this problem. interpret the solution with context to the application.
The total cost of the items purchased at each store is $68, $52, and $72 respectively.
The total bill at each store can be found by using matrix multiplication. We will create a matrix of the costs of each item, and then multiply it by a matrix of the amounts of each item purchased. The resulting matrix will give us the total cost of the items purchased.
Let x be the matrix of costs per item:
x = [[5, 2.5, 2, 3],
[4, 2.75, 1.5, 2],
[6, 3, 1.75, 3.5]]
Let y be the matrix of amounts of items purchased:
y = [[6, 3, 2, 5]]
We can then find the total cost at each store by multiplying x and y together:
xy = [[68, 36.75, 29, 45.5],
[52, 28.25, 21, 30],
[72, 40, 33.5, 52.5]]
Interpreting the solution with context to the application, we can see that the total cost of the items purchased at each store is $68, $52, and $72 respectively.
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determin the median for each of the following sit of data 11, 12, 14, 16, 20, 13, 18, 15, 11, 16
I am pretty sure the answer is 14.5
Answer:
14.5
Step-by-step explanation:
Arrange the numbers from small to big
11, 11, 12, 13, 14, 15, 16, 16, 18, 20
If the set of data is an even number, like in this case,
Take 2 of the middle numbers:
14 and 15
Add them and divide by 2:
14+15= 29
29 ÷ 2= 14.5
In each of the following cases, would the mean or the median probably be higher, or would they be about equal? a. Prices of all new cars sold in 1 month in a large city. b. Heights of all 7-year-old children in a large city. c. Shoe sizes of adult women.
In the case of prices of all new cars sold in a month in a large city, the mean is likely to be higher than the median.
The reason is, new car prices range from economy to luxury, and there are high-end cars that are more expensive than the average/median cars, which will pull the mean value to a higher level.
In the case of the heights of all 7-year-old children in a large city, the mean and median are likely to be about equal. The reason is, children's heights are likely to be distributed relatively evenly, and the mean and median are typically close together for a normal distribution.
In the case of shoe sizes of adult women, the median is likely to be higher than the mean. The reason is, the distribution of shoe sizes among adult women is likely to be skewed, with more women having shoe sizes near the middle of the distribution, and fewer women having sizes that are either very small or very large. This will pull the median to a higher level than the mean.
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In a group of nine people each person shakes hands with exactly two of the other people from the group. Let N be the number of ways this handshaking can occur. Consider two handshaking arrangements different if and only if at least two people who shake hands under one arrangement do not shake hands under the other arrangement. Find the remainder when N is divided by 1000
Answer:
We can solve this problem using the principle of counting, specifically the handshaking lemma.
The handshaking lemma states that in a group of 2n people, where each person shakes hands with exactly one other person, the number of handshaking arrangements is equal to n!.
In this case, we have 9 people, so n = 4.5. Each person shakes hands with exactly two other people, so the number of handshaking arrangements is (4.5!) / (2!)^4 = 945.
Finally, the remainder when N is divided by 1000 is 945 % 1000 = 945.
Step-by-step explanation:
The heights in cm of 5 students are :60,58,54,56,42
Find the mean deviation for the given data
Answer:
54
Step-by-step explanation:
take the average of the number given
I collect an SRS of size n from a population and compute a 95% confidence interval for the population proportion. Which of the following would produce a new confidence interval with larger width (larger margin of error) based on these same data? (a) Use a larger confidence level. (b) Use a smaller confidence level. (c) Increase the sample size. (d) Use the same confidence level, but compute the interval n times. Approximately 5% of these intervals will be larger. (e) Nothing can guarantee absolutely that you will get a larger interval. One can only say that the chance of obtaining a larger interval is 0.05.
Use a larger confidence level would produce a new confidence interval with larger width (larger margin of error) based on these same data.
How do you calculate the population proportion's 95% confidence interval?
We must determine p′ and q′ in order to construct the confidence interval. p′ = 0.842 is the sample percentage; this is the point estimate of the population proportion.
Since CL = 0.95 is the requested confidence level, the calculation is as follows: = 1 - CL = 1 - 0.95 = 0.05 ( 2) ( 2) = 0.025.
What does confidence interval mean?
When you conduct your experiment again or resample the population in the same way, you may anticipate your estimate to fall inside a specific range of values a certain proportion of the time. This is known as the confidence interval.
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Can someone help me solve this and explain it?
Answer:
a. -0.004
b. -sqrt(20)/70
Step-by-step explanation:
a.
We are given that y = a(x - 70)^2 + 20
And we know that x=0 and y=0
We can substitute these values into the equation:
0 = a(-70)^2 + 20
Simplifying we get:
0 = a(4900) + 20
Subtracting 20 from both sides we get:
-20 = a(4900)
Dividing both sides by 4900 we get:
a = -20/4900
a = -20/4900 = -0.004
So the value of a is -0.004
b.
We are given that y = a(x - 70)^2 + 20
And we know that x=140 and y=0
We can substitute these values into the equation:
0 = a(140-70)^2 + 20
Simplifying we get:
0 = a(70)^2 + 20
Subtracting 20 from both sides we get:
-20 = a(70)^2
Taking the square root of both sides:
sqrt(-20) = a(70)
Dividing both sides by 70:
-sqrt(20)/70 = a
a = -sqrt(20)/70
So the value of a is -sqrt(20)/70
The sum of 11 and three-fourths of a number is less than 112. What are the possible values of the number? Write an inequality that could be used to solve this problem. Use the letter, "x" as a variable and write the inequality so that the term, "x" term comes first. Where necessary, write numbers as fractions (rather than decimals)
The inequality that can be used to solve the possible values of the number is 11 + 3/4x < 112 where the number x is x < 134 2/3
How to write inequality?sum of 11 and three-fourths of a number is less than 112.
Let
The unknown number = x
11 + 3/4x < 112
Subtract 11 from both sides
3/4x < 112 - 11
3/4x < 101
divide both sides by 3/4
x < 101 ÷ 3/4
multiply by the reciprocal of 3/4
x < 101 × 4/3
x < 404/3
x < 134 2/3
Therefore, the inequality which represents the situation is 11 + 3/4x < 112.
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What is the answer for this equation 4x+5x+7+x+2
it depends on what x is but simplified that equation is 9x+9+x
What is the solution to this system of equations?
4x-3y=26
3x+2y=11
A:(5,-2)
B:(-2,5)
C:(5,2)
D(8,2)
Answer:
Option A: (5,-2)
Step-by-step explanation:
4x - 3y = 26
3x + 2y = 11
from equ 1 make x the subject formular | equ means equation
4x - 3y = 26
4x = 26 + 3y
x = (26 + 3y)/4
Substitute x = (26 + 3y)/4 into equ 2
3((13+3y)/4) + y = 11
(39+17y)/4 + y = 11
39/4 + 17y/4 + y = 11
39/4 + 17y/4 = 11
17y/4 = 11 - 39/4
17y/4 = -17/2
17/4y/17/4 = -17/2/17/4
y = -2
Substitute y = -2 into equ 2
3x + 2y = 11
3x + 2(-2) = 11
3x - 4 = 11
3x = 11 + 4
3x = 15
3x/3 = 15/3
x = 5
(x,y) = (5,-2)
Rate my answer :)
Please help!!! Thx so much!!!!!
Answer:
AB = 49
ABC = 253
BAC = 156
ABC = 311
Step-by-step explanation:
The whole circle is 360
360 - 107 - 49 = 204
We now know the measurement of the 3 sections shown.
AB = 49
ABC = 49 + 204 = 253
BAC = 107 + 49 = 156
ACB = 107 + 204 = 311
Norfolk Sporting Goods purchases merchandise with a catalog list price of $40,000. The retailer receives a 30% trade discount and credit terms of 2/10, n/30. What amount should Norfolk pay if paid within discount period?1. Create the table that contains the following information for the last
quarter where data required for this exercise is available.
Please note that using the data for previous years and/or previous
estimates will produce grade zero for this part of the project.
Omit the intermediate lines found in Tables 7 and 8 on the web site.
Gross domestic product
Gross national product
Net national product (you should calculate it as Gross national product minus
Consumption of fixed capital)
National income
Personal income
Personal Disposable Income
Personal Savings
Present the information that you received in your project.
To answer the relevant part of the question, the amount that Norfolk should pay within the discount period is $23,520.
What is the discount period?The discount period is based on the credit terms.
For instance, 2/10, n/30 show the discount and credit terms. The explanation is that a 2% cash discount will be received by the customer if payment is made within 10 days of purchase.
Furthermore, the customer's credit period expires after 30 days. Thus, from day 11 to day 30, the customer does not qualify for cash discounts.
The catalog list price = $40,000
Trade discount = 40%
Discounted price = $24,000 ($40,000 x (1 - 40%)
Cash discount = $480 ($24,000 x 2%)
Cash payment = $23,520 ($24,000 - $480)
Thus, Norfolk Sporting Goods will pay $23,520 if it utilizes the discount.
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Q. What angle corresponds to angle 6?
Answer:
angel 2
Step-by-step explanation:
Angle 2 corresponds to angle 6.
A coffee machine dispenses coffee into paper cups. You’re supposed to get 10 ounces of coffee, but the amount varies slightly from cup to cup. Here are the amounts measured in a random sample of 20 cups. Is there evidence that the machine is shortchanging customers? (You may assume that the number of ounces dispensed in normally distributed)
9.9 , 9.7 ,10.0 ,10.1 , 9.9 , 9.6 , 9.8 , 9.8 , 10.0 , 9.5 ,10.1 , 9.9 , 9.6 , 10.2 , 9.8 , 10.0 , 9.9 , 9.5 , 9.9 , 9.7
a) Find a 95% confidence interval for the number of ounces dispensed by the machine.
b) Write a sentence giving your results in the context of the problem.
c) What does 95% confidence mean in this problem?
d) Does your confidence interval suggest that the company is or is not short-changing their customers? Explain
The mean of the sample data is 9.91 ounces and the standard deviation is 0.16 ounces.
To find the 95% confidence interval, we need to calculate the mean and standard deviation of the sample data. The 95% confidence interval can then be calculated as the mean ± 1.96 times the standard deviation, which is (9.59, 10.23) ounces.
b) The 95% confidence interval for the number of ounces dispensed by the machine is (9.59, 10.23) ounces.
c) 95% confidence means that if the same experiment were to be repeated 100 times, 95 of the confidence intervals would contain the true mean.
d) The confidence interval does not suggest that the company is short-changing their customers because it includes 10 ounces, which is the expected amount of coffee to be dispensed.
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What is the difference 2/9 -1/3
For each part, compare distributions (1) and (2) based on their means and standard deviations. You do not need to calculate these statistics; simply state how the means and the standard deviations compare. Make sure to explain your reasoning. Hint: It may be useful to sketch dot plots of the distributions.
(a) (1) 3, 5, 5, 5, 8, 11, 11, 11, 13
(2) 3, 5, 5, 5, 8, 11, 11, 11, 20
(b) (1) -20, 0, 0, 0, 15, 25, 30, 30
(2) -40, 0, 0, 0, 15, 25, 30, 30
(c) (1) 0, 2, 4, 6, 8, 10
(2) 20, 22, 24, 26, 28, 30
(d) (1) 100, 200, 300, 400, 500
(2) 0, 50, 300, 550, 600
We have compared the given standard distributions based on their means and standard deviations.
What is the standard deviation?
Standard deviation is a statistical measure of the spread of a dataset, defined as the square root of its variance. It is a way to quantify the amount of variation or dispersion of a set of data values.
(a) The means and the standard deviations of both distributions (1) and (2) are the same. The only difference is that there is an outlier in (2) with the value of 20 that doesn't exist in (1)
(b) The means of both distributions (1) and (2) are the same. However, the standard deviation of distribution (2) will be larger than distribution (1) because the values of distribution (2) are farther away from the mean than the values of distribution (1)
(c) The means of both distributions (1) and (2) are different, Distribution (2) has larger mean than Distribution (1). Also, the standard deviation of distribution (2) will be larger than distribution (1) because the values of distribution (2) are farther away from the mean than the values of distribution (1)
(d) The means of both distributions (1) and (2) are different, Distribution (2) has smaller mean than Distribution (1). Also, the standard deviation of distribution (2) will be larger than distribution (1) because the values of distribution (2) are farther away from the mean than the values of distribution (1)
Hence, we have compared the given standard distributions based on their means and standard deviations.
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two consecutive whole numbers, each less than 20, are multiplied and the product is increased by 17. There are exactly two values of the lesser of two consecutive numbers of which the result is not a prime number. Find both values of the lesser numbers?
The two Consecutive number is 16 and 17.
What is consecutive number?
Numbers that follow one another sequentially are known as consecutive numbers. Every time there are two numbers, there is a 1 difference. The mean and median of a sequence of numbers are equal. If n is a number, then it follows that n, n+1, and n+2 are also numbers. Examples. 1, 2, 3, 4, 5.
Here the according to the question those two consecutive number are multiplied and increased by 17 and answer is not prime number. Now,
=> 1× 2+17 = 2+17 = 19(prime number)
=> 2×3+17=6+17=23(prime number)
=> 3×4 +17 = 12+17 = 29(prime number)
=> 4×5+17 = 20+17 = 37(prime number)
=> 5×6+17 = 30+17 = 47(Prime number)
=> 6×7+17 = 42+17 = 59(prime number)
=> 7×8+17 = 56+17 = 73(prime number)
=> 8×9+17 =72+17 = 89(prime number)
=> 9×10+17 = 90+17= 107(prime number)
=> 10×11+17=110+17 = 127(prime number)
=> 11×12+17=132+17 =149(prime number)
=> 12×13+17=156+17 = 173(prime number)
=> 13×14+17=182+17 = 199(prime number)
=> 14×15+17=210+17 = 227(prime number)
=> 15×16+17 = 240+17=257 (prime number)
=> 16×17+ 17= 272+17 = 289( not prime number)
Hence the two consecutive number is 16 and 17.
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which of the following actions would cause alex's set of ordered pairs to no longer define a function?
Alex's set of ordered pairs would no longer define a function if any of the following actions were taken:
Adding a second ordered pair with the same first coordinate but a different second coordinateRemoving an ordered pair from the setModifying an ordered pair so that the first coordinate is different from its original valueReordering the ordered pairs in the setChanging the domain or range of the function
A set of ordered pairs defines a function if, for every element in the domain (the set of first coordinates), there is exactly one element in the range (the set of second coordinates).
For example, if Alex's set of ordered pairs is {(1,2), (2,3), (3,4)}, it would no longer define a function if a new ordered pair of (2,5) is added to it, as it would mean that there are now two different second coordinates (3,5) for the first coordinate 2. This would violate the rule that every element in the domain must have exactly one corresponding element in the range. Similarly, removing one of the ordered pairs, changing the order of the ordered pair, or changing the domain or range would cause the set to no longer to define a function.
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Please hurry!
A box of apples sells for $17. At this rate, which expression represents the cost, in dollars, of 100 apples?
A) 5/17•20
B)5/20•17
C)100/17•20
D)100/20•17
E)17•5•20
Answer: D
Step-by-step explanation: A box of apples consists of 20 apples. Since there are a total of 100 apples, you want to find how many boxes makeup 100 apples. 100/20. Then, you would want to multiply that by the cost of each box (i.e. 5 boxes times 17). This is what is done in D when the order of operations is followed.
A triangle has a side lengths of 17 feet, 26 feet, and 16 feet. Is it a right triangle
Answer: No, it is not a right triangle
Step-by-step explanation:
a=17
b=16
c=26
a^2 + b^2 = c^2 (C will always be the longest side)
17^2 + 16^2 = 26^2
49 + 256 = 676
305 is not equal to 676
Answer:
to test if this is a right triangle, test the side lengths with the Pythagorean theorem
a^2 + b^2 = c^2
Step-by-step explanation:
c is the hypothenuse, the longest side of a right triangle
a and b are the legs of the right triangle.
a = 16
b = 17
c = 26
16^2 + 17^2 = 26^2 ?
256 + 289 = 676?
545 ≠ 676
NO, this triangle is NOT a right triangle
write the equation of the trigonometric graph. use a positive coefficient on sine for this activity.
The different values of x in the equation y = 3 sin (x + π/2) to determine the values of y for different values of x.
The equation of the trigonometric graph is given by y = A sin (Bx + C).
Here, A is the amplitude, B is the angular frequency, and C is the phase shift.
Let's assume that A = 3, B = 1, and C = π/2.
Therefore, the equation of the trigonometric graph is given by y = 3 sin (x + π/2).
To calculate the value of y, we can substitute values of x in the equation.
Let's consider x = 0.
Therefore, the value of y is given by y = 3 sin (0 + π/2).
Using the trigonometric identity sin (π/2 + x) = cos x, we get y = 3 cos 0.
Since cos 0 = 1, y = 3.
Hence, the value of y for x = 0 is 3.
Similarly, we can substitute different values of x in the equation y = 3 sin (x + π/2) to determine the values of y for different values of x.
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methods for solving systems of linear equations
( graphing )
how to graph
Y= 2x+6
Y=2x+2
locate the point of the intersection of the two lines
( , ) ?
Answer: imma be honnest im just trying to get points rn.
Step-by-step explanation: i have no idea but thank you for your time reading my nonescence.
The vertices of ABC are A(3,1), B(1,5), and C(5,3). Graph the image of ABC
after a composition of the transformations in the order they are listed.
Translation: (x,y)-(x-6,y+1)
Rotation: 90° about the origin
A“= (_,_)
B“= (_,_)
C“= (_,_)
The area of rectangle ABCD exists 12 sq. units.
What is meant by vertices?A polygon's vertex is a location where the sides or edges of the item or two rays or line segments meet. Vertex is a noun, whereas vertices is the plural.
Vertices are the points at which the edges of the three-dimensional shape converge. Edges are the lines that separate two faces, while faces are flat surfaces.
One of the items that are linked together in a graph is called a vertex (or node). The terms "edges" or "links" refer to the connections between the vertices. a network with ten nodes (or vertices) and eleven edges (links).
The coordinates of point D exists (3,3).
Area of rectangle ABCD = l × b = AB × BC
On further calculation we get
Area of rectangle ABCD = 6 × 2
Area of rectangle ABCD = 12 sq. units
Therefore, the area of rectangle ABCD exists 12 sq. units.
The complete question is:
Three vertices of a rectangle ABCD are A(3,1), B(-3, -1) and C(-3, 3). Plot these points on the graph paper and find the coordinates of the fourth vertex D. Also, find the area of the rectangle ABCD.
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use what you know about inverse functions to determine the derivative of the inverse function beginning with f ( f -1(x)).
The inverse function of f (x) = 1/3x - 2 is f⁻¹(x) = 3(x + 2), the value of a is 3, and the value of x-intercept is x = -2.
To find the inverse of the given function as it is not a one to one function (has the same value f(x) for more that one value of x) you restrict the domain to get a function one to one.
What is a function?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
Given:
f (x) = 1/3x - 2
Find its inverse as shown below,
Add 2 to x and then divide by 1/3 as shown below,
f⁻¹(x) = (x + 2) / 1/3
f⁻¹(x) = 3(x + 2)
compare with f⁻¹(x) = a (x + 2)
a = 3
Calculate the x-intercept by putting f(x) = 0
0 = x + 2
x = -2
In a quadratic function as given use the vertex to restrict the domain; restrict the domain using coordinate x of the vertex.
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given the list of item ids and a maximum number o fitem deletion m return the number of unique items remained in bag
The function uniqueItems takes a list of items and a maximum number of item deletions and returns the number of unique items remained in the bag.
def uniqueItems(items, m):
uniqueItems = set(items)
return len(uniqueItems) - m
items = [1,2,3,4,5,6]
m = 2
print(uniqueItems(items, m)) # 4
# First, we create a set using the items list to get a collection of unique items
uniqueItems = set(items) # {1, 2, 3, 4, 5, 6}
# Then, we subtract the maximum number of items to be deleted from the length of the set to get the number of unique items remained
return len(uniqueItems) - m # 4
The function uniqueItems takes a list of items and a maximum number of item deletions and returns the number of unique items remained in the bag.
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Provide the equation of all vertical line that violate the vertical line test. Please help
The vertical line that violates the vertical line test is given as follows:
x = -3.
When does a relation represents a function?A relation represents a function when each input value is mapped to a single output value.
For the relation graphed, we have that at x = -3, there are two closed bounds of the function, meaning that the input x = -3 is mapped to multiple outputs and thus the relation is not a function.
This also means that a vertical line traced at x = -3 would cross the graph of the function at two points, thus violating the vertical line test.
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A teacher’s cabinet has 56 black dry erase markers and 14 red dry erase markers. Which proportion can be used to determine p, the percent of dry erase markers that are red?
The percent of dry erase markers that are red is 25
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
Given;
Number of black dry erase markers= 56
Number of red dry erase markers= 14
Now,
14/56=x/100
56x=1400
x=25
Therefore, the value of red marker in percent will be 25%
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^UVW & ^ UXY are shown below.
Which statement is true ?
Answer:
They have to be similar because careful inspection will show all of their angles (the two triangles) are equal.
One can start with the fact that the two triangles have a common angle.
CAll it x.
x * 40 + q = 180
x + 50 + r = 180
q and r must equal 50 and 40 to satisfy the sum of the interior angles must sum to 180.
A rectangular paperboard measuring 26 in long and 20 in wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed?
The perimeter of a two-dimensional shape is the distance around the shape. In this case, the paperboard has a semicircle cut out of it, so the perimeter of the paperboard that remains after the semicircle is removed is the distance around the remaining rectangular shape.
To calculate the perimeter of the remaining rectangular shape, you can use the formula: 2(length + width) = 2(26 in + 20 in) = 2(46 in) = 92 in.
It is important to note that the perimeter is a measure of the distance around a two-dimensional shape and it doesn't take into account the area inside the shape. Also it is measured in units, in this case inches.
I hope this helps :)
