Answer:
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How to Solve a Hexagon
Updated October 23, 2018
By Chris Deziel
A polygon is any closed two-dimensional figure with 3 or more straight (not curved) sides, and a 12-sided polygon is known as a dodecagon. A regular dodecagon is one with equal sides and angles, and it's possible to derive a formula for calculating its area. An irregular dodecagon has sides of different lengths and different angles. A six-pointed star is an example. There's no easy way to calculate the area of an irregular 12-sided figure unless you happen to have it plotted on a graph and can read the coordinates of each of the vertices. If not, the best strategy is to divide the figure into regular shapes for which you can calculate the area.
Calculating the Area of a Regular 12-Sided Polygon
To calculate the area of a regular dodecagon, you have to find its center, and the best way to do that is to scribe a circle around it that just touches each of its vertices. The center of the circle is the center of the dodecagon, and the distance from the center of the figure to each of its vertices is simply the radius of the circle (r). Each of the 12 sides of the figure is the same length, so denote this by s.
You need one more measurement, and that's the length of a perpendicular line drawn from the midpoint of each side to the center of the 12-sided shape. This line is known as the apothem. Denote its length by m. It divides each section formed by the radius lines into two right-angled triangles. You don't know m, but you can find it using the Pythagorean theorem.
The 12 radius lines divide the circle you scribed around the dodecagon into 12 equal sections, so at the center of the figure, the angle each line makes with the one next to it is 30 degrees. Each of the 12 sections formed by the radius lines is made up of a pair of right-angled triangles with hypotenuse r and one angle of 15 degrees. The side adjacent to the angle is m, so you can find it using r and the sine of the angle.
Step-by-step explanation:
The area of the polygon is 344.18 square inches.
What is the area?The area is the amount of area occupied by an object's flat (2-D) surface or shape.
Given:
A regular 12-gon has a side length of 8 inches.
Apothem of the polygon,
a = {8/2(tan180/8)}
a = 8/2tan22.5
a = 7.17 inches.
The area of the polygon,
= 12 x 8 x 7.17 / 2
= 344.18 square inches.
Therefore, the area is 344.18 square inches.
To learn more about the area;
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Suppose a triangle has sides 1,1, and 1. Which of the following must be true?
A. The triangle in question is a right triangle.
O B. The triangle in question is not a right triangle.
C. The triangle in question may or may not be a right triangle.
SUBMIT
Answer:
B.it is an equilateral triangle not a right triangle
Wal-Mart conducted a study to check the accuracy of checkout scanners at its stores. At each of the 60 randomly selected Wal-Mart stores, 100 random items were scanned. The researchers found that 52 of the 60 stores had more than 2 items that were priced inaccurately (the national standards allow a maximum of 2 items out of 100 items priced accurately by the scanners). a) Construct a 95% confidence interval for proportion of Wal-Mart stores that have more than 2 items priced inaccurately per 100 items scanned and give a practical interpretation of this interval. (3 Points) b) Wal-Mart claims that 99% of its stores comply with the national standard on accuracy of price scanners. Comment on the believability of Wal-Mart’s claim based on your results in part (a). (1 Point) c) Determine the number of Wal-Mart stores that must be sampled in order to estimate the true proportion to within 0.05 with 90% confidence. (3 Points)
Answer:
a
The 95% confidence interval is
[tex] 0.7811 < p < 0.9529 [/tex]
Generally the interval above can interpreted as
There is 95% confidence that the true proportion of Wal-Mart stores that have more than 2 items priced inaccurately per 100 items scanned lie within the interval
b
Generally 99% is outside the interval obtained in a above then the claim of Wal-mart is not believable
c
[tex] n = 125 \ stores [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 60
The number of stores that had more than 2 items price incorrectly is k = 52
Generally the sample proportion is mathematically represented as
[tex]\^ p = \frac{ k }{ n }[/tex]
=> [tex]\^ p = \frac{ 52 }{ 60 }[/tex]
=> [tex]\^ p = 0.867[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]
=> [tex]E = 1.96 * \sqrt{\frac{ 0.867 (1- 0.867)}{60} } [/tex]
=> [tex]E = 0.0859 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\^ p -E < p < \^ p +E[/tex]
=> [tex] 0.867 - 0.0859 < p < 0.867 + 0.0859 [/tex]
=> [tex] 0.7811 < p < 0.9529 [/tex]
Generally the interval above can interpreted as
There is 95% confidence that the true proportion of Wal-Mart stores that have more than 2 items priced inaccurately per 100 items scanned lie within the interval
Considering question b
Generally 99% is outside the interval obtained in a above then the claim of Wal-mart is not believable
Considering question c
From the question we are told that
The margin of error is E = 0.05
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n= [\frac{1.645 }}{0.05} ]^2 * 0.867 (1 - 0.867 ) [/tex]
=> [tex] n = 125 \ stores [/tex]
What is 5x3,264-3
please help hurry test teacher mean!!!
Answer:
5x3=15
264-3=261
Step-by-step explanation:
Multiply 5x3 to get 15. And subtract 264 and 3 to get 261.
(5n - 3) - (-2n + 7)
Answer:
7n-10
Step-by-step explanation:
=(5n-3) - (-2n) -7 [Bracket Opens]
=5n - 3 +2n -7 [- × - = +]
=7n - 10 [ addition]
eat breakfast at a cafe. the total check was $5. here's the money he left period why did he pay $5.75?
Answer:
Tip.
Step-by-step explanation:
Since to total is $5 that means all taxes are already counted for.
He added the 75 cents as a tip.
find the slope of the line
Garth is packing boxes with books. The list shows how many books are in each of 10 boxes.
6, 14, 6, 18, 9, 9, 12, 10, 11, 15
Which statement is true about the number of books packed to a box?
:Answer: The answer is C on Edge
Step-by-step explanation:
Answer:
C: The mean number of books to a box is 11.
Step-by-step explanation:
edg2020
pleaseeeee helppppp meee
will give brainliest !
The state fair is a popular field trip destination. This year the senior class at High School A and
the senior class at High School B both planned trips there. The senior class at High School A
rented and filled 5 vans and 9 buses with 309 students. High School B rented and filled 12 vans
and 9 buses with 414 students. Every van had the same number of students in it as did the buses.
How many students can a van carry? How many students can a bus carry?
Answer:
15 students/van
26 students/bus
Devaughn's age is two times Sydney's age. The sum of their ages is 18. What is Sydney's age?
Answer:
Sydney's Age is 6
Step-by-step explanation:
6 x 2 = 12
12 + 6 = 18
Answer:
Sydney is 6
Step-by-step explanation:
You get this by dividing 18 by three, as one set of 6 is Sydney while tcice that is her brother.
George has $15. He tries to buy a movie ticket ($9.00), a pretzel ($2.65), a drink ($1.35), and two veggie cups ($1.74 each) but he does not have enough money. Look at the numerical expression George used?
Answer:
15-9-2.65-1.35-1.74 which is a negative number meaning he doesnt have enough money
Step-by-step explanation:
9(1) + 2.65(1) + 1.35(1) + 1.74(2) = 16.48
The difference between two-thirds of a number and 4 is –92.
Answer:
The difference between 4 is –92 is 132
Answer:
Given - The difference between two- third of a no. and 4 is (-92)
Let the no. be X
TO Find - The no.
Solution -
Let the no. be X
Two - third of a no. = 3/2x
according to the question equation made is-
2/3x - 4 = (-92)
2/3x = (-92)+ (4)
2/3x = ( -88)
X = (-88) × 3/2
X= ( -264/2)
X = (-132)
Pls I need help ASAP!
Mr.Roberson buys 18 quarts of milk each week for his 5 children. How many gallons of milk does this equal?
Answer:
4 and a half gallons of milk
Step-by-step explanation:
4 quarts = 1 gallon
16 quarts = 4 gallon
18 quarts = 4 1/2 gallons
The Child Health and Development Studies investigate a range of topics. One study considered all pregnancies between 1960 and 1967 among women in the Kaiser Foundation Health Plan in the San Francisco East Bay area. Here, we study the relationship between smoking and weight of the baby. The variable smoke is coded 1 if the mother is a smoker, and 0 if not. The summary table below shows the results of a linear regression model for predicting the average birth weight of babies, measured in ounces, based on the smoking status ofthe mother. Estimate Std. Error t value Pr(>|t|)(Intercept) 123.05 0.65 189.60 0.0000smoke -8.94 1.03 -8.65 0.0000The variability within the smokers and non-smokers are about equal and the distributions aresymmetric. With these conditions satisfied, it is reasonable to apply the model. (Note that wedon't need to check linearity since the predictor has only two levels.)(a) Write the equation of the regression line.(b) Interpret the slope in this context, and calculate the predicted birth weight of babies born tosmoker and non-smoker mothers.(c) Is there a statistically significant relationship between the average birth weight and smoking?
Answer:
hmmmmmmmmmmmmmmmm...
Which angle is an exterior angle of the triangle?
Triangle L M N. Angle L is 1, angle M is 2, angle N is 3. Side M N extends to form angle 4.
A. 1
B. 2
C. 3
D. 4
Answer quick pls
Answer:
D
Step-by-step explanation:
Because it is on the outside
Answer:
its c becuase i did the test and got it correctomonzo
Step-by-step explanation:
Laura had 32 dollar off coupons for mini golf course but every buddy else had to pay nine dollars per person the full price what was the total cost of their group of eight to play mini golf
Please help me!!!
Write the following comparison as a ratio reduced to lowest terms.
25 nickels to 25 dimes
Answer:
[tex]N:D = 1: 2[/tex]
Step-by-step explanation:
Given
Represent Nickels with N and Dimes with D
[tex]N=25[/tex]
[tex]D=25[/tex]
Required
Write as a ratio to lowest term
Ratio of Nickels to Dime is represented as N:D
[tex]N:D = 25\ nickels : 25\ dimes[/tex]
Convert nickels to dollar
[tex]N:D = 25\ * \$0.05. : 25\ * \$0.10[/tex]
[tex]N:D = 1.25 : 2.5[/tex]
Divide through by 1.25
[tex]N:D = 1.25/2.25 : 2.5/1.25[/tex]
[tex]N:D = 1: 2[/tex]
Hence, the ratio to lowest term is 1:2
1. Name the two-dimensional shapes that when rotated around the vertical axis form the following three-dimensional solids?
Cone:
Cylinder:
Sphere:
2. Name four, three-dimensional solid objects found in your home, workplace, etc. , and tell what geometric solid each most closely represents.
Object 1:
Object 2:
Object 3:
Object 4:
3. State the volume formulas for a cylinder, sphere, pyramid, and cone.
a. Volume formula for a cylinder:
b. Volume formula for a sphere:
c. Volume formula for a pyramid:
d. Volume formula for a cone:
Problem 1
Answers:
Cone: TriangleCylinder: RectangleSphere: Circle------------------------
Explanation:
Imagine a fan blade rotating. As it rotates really quickly, it occupies a 3D space. Or perhaps imagining rotating eggbeaters is a better thing to have in mind. Those blades spin really fast to form a 3D shape. So that's what's going on with this problem. If you spin a triangle around an axis, a cone will form. The base of the triangle forms the base of the cone. Half the base of the triangle is the radius of the cone. The height of the triangle is the height of the cone.
Similarly, a rectangle rotated around its center axis forms a cylinder. Think of a revolving door. That's often a classic example. Finally, a circle spun around any of its diameters will form a sphere.
========================================================
Problem 2
Answers:
Object 1: Cup = CylinderObject 2: Ball = SphereObject 3: Funnel = ConeObject 4: Paper towel roll = Cylinder-------------------------------
Explanation:
Pick objects around your house that are fairly simple in design and resemble either a cylinder, sphere, or cone. A cup resembles a cylinder just it doesn't have a top to it. A ball is a 3D sphere that has an interior to it, unless the ball is filled with air. A funnel resembles a cone due to its triangular shape of sorts. A paper towel roll (the card board piece or the cardboard plus the actual paper towels) resemble a cylinder as well. You can pick any four other objects you have around your house such as a cylindrical speaker, batteries (shaped as a cylinder), soup cans (also cylinders), and so on.
========================================================
Problem 3
Answers:
a) volume of cylinder = pi*r^2*hb) volume of sphere = (4/3)*pi*r^3c) volume of pyramid = (1/3)*L*W*Hd) volume of cone = (1/3)*pi*r^2*h-------------------------------
Explanation:
These formulas are what you should memorize or have handy on a flashcard. It is possible to derive them, but it would require calculus to do so. Also, such a process is quite length. So memorization or flashcards are the better way to go.
For the cylinder and cone, r is the radius and h is the height. Note how the formulas are nearly identical except the cone has the (1/3) term. This shows that the cone's volume is 1/3 that of the cylinder's volume where they both have the same radius r and height h.
The sphere also deals with the radius r, but we don't have to worry about the height of the sphere (it's really just 2r).
For the pyramid, L,W,H represent the length width and height respectively. The length and width form the base of the pyramid. Recall that L*W*H is the volume of a rectangular block. The volume of a pyramid is 1/3 of that rectangular block's volume.
If all of a 2D object's sides and angles have different lengths, such shape is said to be irregular.
What is 2D shape?In geometry, a form or figure having length and breadth is referred to as a "2D shape." Due to the lack of a thickness, a third dimension, such as the case of a prism or a cube, two-dimensional or 2D objects are often measured in terms of their two faces.
'2D' refers for 2-dimensional. A 2D shape is any form that has two dimensions. Consider for a moment what it means to have two dimensions. We could only move backwards or forwards in a straight line if we only had one dimension to work with. One dimension is a line.
Cone: Triangle
Cylinder: Rectangle
Sphere: Circle
Therefore, if all of a 2D object's sides and angles have different lengths, such shape is said to be irregular.
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Val is going to plant vegetable seeds in one garden and 5b+2 vegetable seeds in another. How many seeds is Val going to plant?
Answer:
6d+2
Step-by-step explanation:my teacher told me
A shirt had an original price of $15 but has been discounted by 15%. What is the sale price of the shirt?
Answer:
12.75$
Step-by-step explanation:
15$/100=0.15
0.15×15%=2.25
15$-2.25=12.75$
which comparisons can be made using these fraction bars?
Using your own words or illustrations, explain the addition rule for equations. (in other words, don't just restate the rule word for word).
Step-by-step explanation:
This rule states that the same value can be added to both sides of an equation without interfering with the solving process of the equation
JKL is given with J (-1,1), K (4,4), and L (5,1). What is the area of JKL? Justify your response.
9514 1404 393
Answer:
9 square units
Step-by-step explanation:
The base JL is a horizontal line. Its length is 5-(-1) = 6.
The height is the difference between the y-coordinate of K and the y-coordinate of the horizontal line: 4 -1 = 3.
The formula for the area of a triangle is ...
A = (1/2)bh
A = (1/2)(6)(3) = 9 . . . square units
The area of ∆JKL is 9 square units.
Answer:
9 units
Step-by-step explanation:
shorter answer
Solve for x :)
6x + 4x – 6 = 24 + 9x
Answer:
x=30
Step-by-step explanation:
6x+4x-6=24+9x
combine like terms
10x-6=24+9x
add 6 on both sides
10x=30+9x
subtract 9x on both sides
x=30
Hope this helps! :)
Answer right and get branliest
Answer:
8 outfits
Step-by-step explanation:
Each number represent a different shirt and each letter represents a different skirt:
1 2 3 4
A B
Outfits:
1A 2A 3A 4A
1B 2B 3B 4B
(hope this helps, i don't really know how to explain it)
Answer:
I got 8!
Step-by-step explanation:
A car travels 180 miles in 3 hours. how far did it travel in 1 hour
Answer:
60
Step-by-step explanation:
Olivia's goal is to complete 200 sit ups Right now she is up to 50 sit ups What percentage of her goal has she reached?
A(n) _____ transition shows that one event happened before another. Some examples of this type of transition are "so," "therefore," "hence," and "as a result. "A.contras tB.cause-and-effect C.order-of-importance
D.summary
The total cost y is proportional to the number of used books x purchased at a constant price of $4. What equation represents this relationship?
Answer:
Y=x+4
If you think about it it's basically a addition problem.
A farmer must transport a fox, goose and bag of beans from one side of a river to
another using a boat which can only hold one item in addition to the farmer, subject to
the constraints that the fox cannot be left alone with the goose, and the goose cannot
be left alone with the beans. What is the fewest number of trips the farmer has to take
in order to transport all three safely to the other side of the river?
Show working using any appropriate mathematical representation(s)
Answer:
The man in the goose cross the river, with the fox and the beans together, he leaves the goose on the other side and goes back across.
The man then takes the fox across the river, and since he can’t leave the fox in the goose together, he brings that goose back.
Again, since the goose and the beans can’t be left together, he leaves the goose and he takes the beans across and leaves with the fox.
He returns to pick up the goose and heads back across the river one last time.
Step-by-step explanation:
Answer:
4 trips.
Step-by-step explanation:
The man and the goose across the river, leaving the fox and the beans together, he leaves the goose on the other side and goes back across.
The man then takes the fox across the river, and since he can’t leave the fox in the goose together, he brings that goose back.
Again, since the goose and the beans can’t be left together, he leaves the goose and he takes the beans across and leaves with the fox.
He returns to pick up the goose and heads back across the river one last time.
#teamtrees #WAP (Water And Plant)