1.Perimeter: [tex]\( P ≈ 31.05 \, mm \)[/tex]
2. Apothem: [tex]\( a ≈ 4.89 \, mm \)[/tex]
3. Area: [tex]\( Area ≈ 75.91 \, mm^2 \)[/tex]
So, the area of the regular 15-gon with a radius of 5 mm is approximately [tex]\( 75.91 \, mm^2 \).[/tex]
To find the area of a regular polygon, you can use the formula:
[tex]\[ Area = \frac{1}{2} \times Perimeter \times Apothem \][/tex]
Where:
- Perimeter is the total length of all the sides of the polygon.
- Apothem is the distance from the center of the polygon to the midpoint of any side.
For a regular polygon, the apothem can be calculated using trigonometry. In this case, the regular 15-gon (also called a pentadecagon) has 15 equal sides.
Let's break down the steps:
1. Calculate the Perimeter:
The perimeter of a regular polygon with ( n ) sides can be calculated as [tex]\( P = n \times s \)[/tex], where ( s ) is the length of each side. Since we're given the radius of the polygon, we need to calculate the length of one side using trigonometry.
2. Calculate the Apothem:
The apothem of a regular polygon can be calculated using the formula:
[tex]\[ a = r \times \cos\left(\frac{\pi}{n}\right) \][/tex]
where ( r ) is the radius of the polygon, and ( n ) is the number of sides.
3. Plug the values into the Area Formula:
Once you have both the perimeter and the apothem, you can plug them into the area formula and calculate the area.
Let's do the calculations:
1. Calculate the Perimeter:
The length of one side ( s )) can be calculated using trigonometry. Since we're dealing with a 15-gon, each interior angle is[tex]\( \frac{(15-2) \times 180°}{15} = 156° \).[/tex]
Using the law of cosines:
[tex]\[ s = 2 \times r \times \sin\left(\frac{180°}{15}\right) \][/tex]
[tex]\[ s = 2 \times 5 \times \sin(12°) \][/tex]
[tex]\[ s ≈ 2 \times 5 \times 0.207 ≈ 2.07 \, mm \][/tex]
So, the perimeter (( P )) is:
[tex]\[ P = 15 \times 2.07 ≈ 31.05 \, mm \][/tex]
2. Calculate the Apothem:
[tex]\[ a = 5 \times \cos\left(\frac{\pi}{15}\right) \][/tex]
[tex]\[ a = 5 \times \cos(12°) \][/tex][tex]\[ a = 5 \times \cos\left(\frac{\pi}{15}\right) \][/tex]
[tex]\[ a ≈ 5 \times 0.978 ≈ 4.89 \, mm \][/tex]
3. Plug the values into the Area Formula:
[tex]\[ Area = \frac{1}{2} \times 31.05 \times 4.89 \][/tex]
[tex]\[ Area ≈ \frac{1}{2} \times 31.05 \times 4.89 ≈ 75.91 \, mm^2 \][/tex]
So, the area of the regular 15-gon with a radius of 5 mm is approximately [tex]\( 75.91 \, mm^2 \)[/tex].
If a-b = 4 and ab = 60, what is the value of a + b?
Answer:
a + b = 16 or -16.
Step-by-step explanation:
a - b = 4
ab = 60 so a = 60/b
Substituting for a in the first equation:
60/b - b = 4
60 - b^2 = 4b
b^2 + 4b - 60 = 0
(b + 10)b - 6) = 0
b = 6, -10.
Therefore, from the first equation:
When b = -10 . a + 10 =4 giving a = -6 or
When b = 6, a - 6 = 4 giving a = 10.
So when a = -6, b = -10 and
when a = 10, b = 6.
So a + b is either 16 or -16.
Need help!!!!!!
This is so confusing
Answer:
Omar
Step-by-step explanation:
to find the base, which i am to assume they want to find the triangle base based on the formula they are using,
you should multiply base * height, then divide by 2, since it is a triangle, you not solving for a rectangle.
dividing by 2 and multiplying by 1/2 is the same thing!
so,
1/2 (7* 24) is the right answer to finding the base!
Kari looked at he direct base of 7*28, however, that shape is actually a rectangle... so Kari is wrong because he multiplied that dimension by 1/2, which is the formula for a triangle.
Omar is correct because he chose the dimensions of a triangle, and properly used the triangle formula!
i hope this helped you out!
stay safe!
:)
This graph shows a car moving at a
constant speed. For example, in 8 hours
the car travels 400 miles.
Which equation shows the line on the
graph?
A y = 2x
B y = 50x
C y = 400x
Answer:
B
Step-by-step explanation:
If you set x to hours and y to the amount of miles, you can multiply the hours to the numbers and equal out your miles. So, if 8 hours is multiplied to 50, it equals out the 400 miles.
convert 20 miles to km
Answer:
32.1869
Step-by-step explanation:
multiply 20 by 1.609
multiplying miles by 1.609 will give you the answer
Answer:
20 miles =32.1869
Step-by-step explanation:
For an approximate result multiply the length value by 1.609.
Can someone please explain how to solve this question? I will give thanks and 5 stars! Whoever answers, thank you!
Answer:
33 1/3%
Step-by-step explanation:
When you roll a die, the possible outcomes are 1,2,3,4,5,6
getting a number less than 5: 1,2,3,4
P( getting a number less than 5)
= number of outcomes that meet conditions / total outcomes
=4/6
= 2/3
Then we flip a coin heads or tails
We want heads
P (heads) = number of outcomes that meet conditions / total outcomes
= 1/2
Since the event outcomes do not depend on each other
P( getting a number less than 5) *P (heads) = 2/3 * 1/2 = 1/3
as a percent
= 33 1/3%
A shop owner bought some T-shirts and purses.
Each T-shirt cost $8 and each purse cost $5
She bought a total of 28 T-shirts and purses.
She spent $161 altogether.
How many T-shirts did she buy? [3 marks]
Answer:
20 t shirt
Step-by-step explanation:
Find the area to this please
Answer:
35
Step-by-step explanation:
please mark brainiest
Identify the graph of g(x) = –x2 + 9x – 20 from the choices below.
The graph of the quadratic function g(x) = -x^2 + 9x - 20 will be a downward opening parabola with vertex at (4.5, 0.25), x-intercepts at (4, 0) and (5, 0), and a y-intercept at (0, -20). To graph it, label the axes as 'f(x)' and 'x' and scale them to include these critical points.
Explanation:The student wants to identify the graph of the quadratic function g(x) = –x2 + 9x – 20. To do this, first note that the standard form of a quadratic function is ax2 + bx + c, where a, b, and c are constants.
In this case, a = -1 (which makes the parabola open downward), b = 9, and c = -20.
The vertex form of a quadratic function is f(x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola. To find the vertex, we can use the formula h = -b/(2a).
For g(x), this gives h = -9/(2 * -1) = 4.5.
We can then find the value of k by substituting h back into g(x), which gives us k = -4.52 + 9(4.5) - 20.
Therefore, k = 0.25.
The vertex of the parabola is at (4.5, 0.25), and because a is negative, the parabola opens downward. The x-intercepts (or roots) of the parabola can be found by factoring the quadratic equation or using the quadratic formula. In this case, the x-intercepts are (4, 0) and (5, 0). Lastly, the y-intercept occurs when x = 0, which for g(x) is -20.
To label the graph, we'd use 'f(x)' for the vertical axis and 'x' for the horizontal axis. The scale of the axes depends on the maximum and minimum x and y values of the graph, which in this instance would include at least the vertex, x-intercepts, and y-intercept.
The box-and-whisker plot shows the average temperatures in Orlando, Florida in January.
51,54,57,60,63,66,69,72,75,78,81,84
Which statement about the temperatures in Orlando must be true?
A. About half of the days in January had average temperatures above 75 degrees.
B. About 50% of the days in January had average temperatures between 66 and 75 degrees.
C. The coldest day in January was 66 degrees.
D. The hottest day in December was 75 degrees.
Answer:
B. About 50% of the days in January had average temperatures between 66 and 75 degrees.
The box ranges from 66 to 75... meaning that most of the days were in those temperatures.
The lines mean that there were only a few days that were in those temperatures.
You're welcome if I'm correct.
The correct answer is about 50% of the days in January had average temperatures between 66 and 75 degrees.
What is the box and whisker plot?A Box and Whisker Plot (also known as a Box Plot) is a visual representation of data distribution through quartiles.
The maximum and minimum value of the function is plotted at the ends of a box and whisker plot.The box in the middle displays the interquartile range, which means that about 50% of values when the data is arranged in ascending or descending order.In the graph given in the question we can clearly see that the interquartile range of the data is lying between the temperatures 66° to 75°, which means that 50% of days in January had the temperature between 66 to 75 degrees.
Hence, Option(c) is correct for the given question.
Learn more about quartiles on:
https://brainly.com/question/11850663
#SPJ2
Find the 72nd term of the arithmetic sequence 11, 7,3,...
Answer:
3124
Step-by-step explanation:
Answer: -273
Step-by-step explanation: To determine the 72nd term, we will want use our explicit formula which is shown below.
[tex]^{a}n = ^{a}1 + (n - 1)d[/tex]
Since we want to find the 72nd term, the [tex]^{a}n[/tex]
in the formula will be changed to [tex]^{a} 72[/tex].
Also, the 72 will be substituted in for the n
that is inside the set of parentheses.
Then [tex]^{a} 1[/tex] will be the 1st term given in our sequence or 11.
Lastly, the d outside the parentheses is the difference between
each of the terms in the sequence which is -4.
So we now have [tex]^{a} 72 = 11 + (72 - 1)(-4)[/tex].
Now we have all the information we need.
Now we can simplify from here.
Make sure to apply your order of operations because
this is where a lot of students make mistake.
Start simplifying inside the parentheses!
(72 - 1) is going to be 70.
So we have [tex]^{a} 72 = 11 + (71)(-4)[/tex].
Then, we have to multiply before we add.
So (71)(-4) is going to be -284.
So we have [tex]^{a} 72 = 11 + (-284)[/tex].
Solving from here, 11 + (-284) simplifies to -273.
This means that the 72nd term of this sequence is -273.
What is the answer to this question
Answer:
A
Step-by-step explanation:
Given the exponential function
f(t) = 228[tex](0.975)^{t}[/tex] ← where t is time in years
Substitute t = 20 into f(t), that is
f(20) = 228 × [tex](0.975)^{20}[/tex] = 228 × 0.60268.... ≈ 137 → A
please solve this question
Given:
Number of mice and frequency
Mean = 7
To find:
The value of x.
Solution:
Number of mice = X
Frequency = Y
XY = Multiply X and Y values.
X Y XY
5 4 20
6 13 78
7 16 112
8 x 8x
9 6 54
Sum of Y = 4 + 13 + 16 + x + 6
= 39 + x
Sum of XY = 20 + 78 + 112 + 8x + 54
= 8x + 264
Mean formula:
[tex]$Mean = \frac{\Sigma XY }{\Sigma Y}[/tex]
[tex]$7=\frac{8x+264}{39+x}[/tex]
Do cross multiplication.
[tex]7(39+x)=(8x+264)[/tex]
[tex]273+7x=8x+264[/tex]
Subtract 264 from both sides, we get
[tex]9+7x=8x[/tex]
Subtract 7x from both sides, we get
[tex]9=x[/tex]
The value of x is 9.
Are these shapes similar?
which expression is equivalent to 9x2 − 16
Answer:
[tex]9 \times 2 - 16 \\ 18 - 16 = 2[/tex]
1.
What is the mean for the following scores: 2, 5, 4, 1, 8?
A. 3
B. 4
c. 5
20
Answer to your question is:
B. 4
Explanation:
2 + 5 + 4 + 1 + 8 = 20
20 ÷ 5 = 4
The mean is found out by adding the scores given and dividing the total by the number of scores.
In the given question the mean of the scores is 4.
The mean is calculated to get an average about something that is given.
Here
n= number of scores= 5
Sum of scores = ∑x= 2+5+4+1+8= 20
Mean = x bar= ∑x/n= 20/5= 4
For different distributions mean may or may not be the middle value.
https://brainly.in/question/8482715
https://brainly.com/question/12844003
If y = 11 inches, z = 14 inches, h = 7 inches, and w = 3 inches, what is the area of the object?
The information given, y = 11 inches, z = 14 inches, h = 7 inches, and w = 3 inches, is not enough to calculate the area of an object unless its shape is known. If it's a rectangular prism, the volume can be calculated. But without further information, we cannot provide a specific area calculation.
Explanation:The type of area an object will have depends on its shape. For example, the area of a rectangle is given by width times height (w * h). Similarly, the volume of a rectangular prism would be length times width times height (l * w * h). However, the given dimensions in the question (y = 11 inches, z = 14 inches, h = 7 inches, and w = 3 inches) are not enough to determine the shape of the object. We need additional information on how these dimensions are related to the shape of the object before we can calculate the area.
If for instance, this object is a rectangular prism, then we could calculate its volume. That volume would be y (depth) * z (width) * h (height). In this case with the provided values, the volume would be 11 inches * 14 inches * 7 inches = 1078 cubic inches.
Without more information on the object’s shape, we can’t make assumptions and provide a definitive calculation of the area.
Learn more about Area Calculation here:https://brainly.com/question/34380164
#SPJ12
What is the perimeter of the rhombus below?
Answer:
16
Step-by-step explanation:
the perimeter of the given rhombus is 8√5.
To find the perimeter of a rhombus, we need to calculate the sum of the lengths of all four sides.
Given the coordinates of the points touching the graph: (-5,-3), (-1,-1), (3,-3), and (-1,-5), we can calculate the distances between these points to find the lengths of the sides.
Let's calculate the lengths of the sides:
1. Side 1: Distance between (-5,-3) and (-1,-1)
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length = √[(-1 - (-5))^2 + (-1 - (-3))^2]
Length = √[4^2 + 2^2]
Length = √[16 + 4]
Length = √20
Length = 2√5
2. Side 2: Distance between (-1,-1) and (3,-3)
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length = √[(3 - (-1))^2 + (-3 - (-1))^2]
Length = √[4^2 + (-2)^2]
Length = √[16 + 4]
Length = √20
Length = 2√5
3. Side 3: Distance between (3,-3) and (-1,-5)
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length = √[(-1 - 3)^2 + (-5 - (-3))^2]
Length = √[(-4)^2 + (-2)^2]
Length = √[16 + 4]
Length = √20
Length = 2√5
4. Side 4: Distance between (-1,-5) and (-5,-3)
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Length = √[(-5 - (-1))^2 + (-3 - (-5))^2]
Length = √[(-4)^2 + 2^2]
Length = √[16 + 4]
Length = √20
Length = 2√5
Now, we can calculate the perimeter by adding the lengths of all four sides:
Perimeter = Side 1 + Side 2 + Side 3 + Side 4
Perimeter = 2√5 + 2√5 + 2√5 + 2√5
Perimeter = 8√5
Therefore, the perimeter of the given rhombus is 8√5.
What is the circumference of the circle? Use 3.14 for pi
r = 6.4 cm
20 096 cm
40 192 cm
200 96 cm
401 92 cm
Answer:
its
40 192 cm
Step-by-step explanation:
Answer:
40.192cm
Step-by-step explanation:
the circumference of a circle = ?
radius = 6.4cm
recall that,
circumference of a circle = 2πr
circumference of a circle = 2 x 3.14 x 6.4cm
circumference of a circle = 40.192cm
therefore the circumference of a circle whose radius is 6.4cm is evaluated to be equals to 40.192cm.
the answer to your question is option B 40.192cm
What is the range of 16,17,17,18,18,18,19,19,19,19,20,20,20,21,21,22,22,24,25,25
In order to find the range we first have to list the numbers from least to greatest:
16, 17, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 21, 21, 22, 22, 24, 25, 25
range = largest value - smallest value = answer
range = 25 - 16 = 9
range = 19
so, our final answer would be 19.
~ i hope this helps you have a good day/night afternoon~ ~-gabby~
Answer: The answer is 23.
Step-by-step explanation:
Which of the following statements is true regarding a representative sample?
A.
It is at least 1/2 of the total population.
B.
It focuses on a specific group within the population.
C.
It is a group that is fairly proportional to the population.
Answer:
B
Step-by-step explanation:
The following statement is true regarding a representative sample
"It is a group that is fairly proportional to the population".
What is the representative sample?
A representative sample is a subset of a population that is selected in such a way that it accurately reflects the characteristics of the entire population. The goal of a representative sample is to ensure that the sample is as representative as possible of the population as a whole so that the results of a study based on the sample can be generalized to the population.
A representative sample is not necessarily at least 1/2 of the total population (Option A) or focused on a specific group within the population (Option B). It is simply a group that is fairly proportional to the population, meaning that it contains a similar mix of characteristics as the population as a whole.
Hence, the correct answer would be an option (C).
To learn more about representative samples click here:
https://brainly.com/question/15085839
#SPJ3
Express your answer exactly
Answer:
sin(θ) = [tex]\frac{\sqrt{55} }{8}[/tex]
Step-by-step explanation:
See the attachment.
Cosine is adjacent over hypotenuse, so since cos(θ) = 3/8, then the adjacent side of the triangle is 3 and the hypotenuse is 8.
Since is opposite divided by hypotenuse. To find the opposite side, which is the unlabelled side on the graph, we need to use the Pythagorean Theorem:
x = [tex]\sqrt{8^2-3^2} =\sqrt{64-9} =\sqrt{55}[/tex]
So, sin(θ) = [tex]\frac{\sqrt{55} }{8}[/tex].
Hope this helps!
Similar triangles are two triangles with equal ____ angles.
a. vertical
b. corresponding
angles.
c. horizontal
d. elliptical
Similar triangles are defined as two triangles having equal B. corresponding angles, shown by the congruence of vertical angles, alternate interior angles, and the application of the AAA theorem.
Similar triangles are two triangles with equal corresponding angles. According to the question, in the figure, two triangles named triangle ABC and triangle FCE are observed to be similar because they have three sets of congruent angles - vertical angles (Angle ACB \\<=\ Angle FCE), alternate interior angles (Angle CAB \\<=\ Angle CFE), and another set of alternate interior angles (Angle CBA \\<=\ Angle CEF).
This is summed up by the AAA (Angle Angle Angle) theorem which states that two triangles are similar if all their corresponding angles are congruent. An example will be two right triangles which are equal when the hypotenuse and an acute angle of one are equal, respectively, to the hypotenuse and an acute angle of the other. These principles help us understand the similarity of triangles in geometry.
Find the measure of Arc JN
Find the measure of arcJN=
Find the m
Step-by-step explanation:
[tex]m(arc \: JN) = 360 \degree - (60 \degree + 150 \degree) \\ \hspace{57pt}= 360 \degree - 210 \degree \\ \hspace{57pt} = 150\degree \\ \\ m \angle K = \frac{1}{2} \times m(arc \: JN) \\ \hspace{30pt}= \frac{1}{2} \times 150\degree \\ \hspace{30pt} = 75\degree \\ [/tex]
66 times 26 times 60 then multiply 1/2
Answer:
Step-by-step explanation:
51,480 is the answer.
Answer:
51,480
Step-by-step explanation:
66 x 26 = 1,716
1,716 x 60 = 102,960
102,960 x 1/2 = 51,480
The coordinates of trapezoid ABCD are A (-6,3) B (-3,6) C (9,6) and D (-5,-8). Find the coordinates of trapezoid A’ B’ C’ D’ after the translation whose rule is T 3,4.
Answer:
A' (-3,7)
B' (0,10)
C' (12,10)
D' (-2,-4)
Step-by-step explanation:
A' (-6+3 , 3+4) = (-3,7)
B' (-3+3 , 6+4) = (0,10)
C' (9+3 , 6+4) = (12,10)
D' (-5+3 , -8+4) = (-2,-4)
First one that knows the answer
wins brainliest
Answer:
The bakery made a profit of $8,013 during the summer months
Step-by-step explanation:
A profit is made when income is greater than expenses while a loss is made when expenses are greater than income
A loss is a negative profit
In June
Income = $750
Expense:
rent = $890
Operating costs = $975
Total expense = $1,865
Profit = income - expense
profit = $750 - $1865
= -$1115
Therefore, a loss of $1115 was made in June
July
Income = $ 925
Expenses:
Rent = $890
Operating costs = $721
Total expenses = 1611
Profit = $925 - $1611
= -$686
A loss of $686 was made in July
August
Income = $11,250
Expenses:
Rent = $890
Operating costs= $546
Total expense = $1436
Profit = $11,250 - $1436
= $9,814
A profit of $9,814 was made in August
Now let's find the difference between the profit and losses that were made during the summer months. This will be the addition of the profit and losses of all three months
Remember that losses carry a negative sign
$9,814 -$686 -$1115 = $8,013
Therefore, the bakery made a profit of $8,013 during the summer months
What is the height of our classroom door is it a statistical or non statistical question
Answer:
to me should be statistical question
Step-by-step explanation:
not statistical would be only getting one answer but you could have the height in inches, centimeters, feet, meters, etc. which would count as more then one answer being statistical
29+5x=44 whats the valué of x
Answer:
x=3
Step-by-step explanation:
44-29=15
5*3=15
The value of x in the equation 29 + 5x = 44 is solved by isolating x to find that x = 3.
Explanation:To solve the equation 29 + 5x = 44 for x, you should start by isolating the variable on one side. Here's a step-by-step process:
Subtract 29 from both sides of the equation to get 5x = 44 - 29.This simplifies to 5x = 15.To find the value of , divide both sides by 5, leading to .Finally, you get the solution x = 3.Therefore, the value of x in the given equation is 3.
Find the circumference of a circle that has a diameter of 42 m.
Answer:
the answer is 131.95m.
Answer:
Step-by-step explanation:
Circumference = πd
r = diameter/2
C= 42π = 42 XX22/7 =- 6x22=132m
if 3300 equals 4.5 percent what is the price of 100%
Answer:
73333.333
Step-by-step explanation:
100/4.5= 22.222
3300*22.222= 73333.333