If we inscribe a circle such that it is touching all six corners of a regular hexagon of side 10 inches, what is the area of the Circle that is not covered by the hexagon? ( with explanation )
Answers
Answer:
[tex]\left(100\pi - 150\sqrt{3}\right)[/tex] square inches.
Step-by-step explanation:
Area of the Inscribed HexagonRefer to the first diagram attached. This inscribed regular hexagon can be split into six equilateral triangles. The length of each side of these triangle will be [tex]10[/tex] inches (same as the length of each side of the regular hexagon.)
Refer to the second attachment for one of these equilateral triangles.
Let segment [tex]\sf CH[/tex] be a height on side [tex]\sf AB[/tex]. Since this triangle is equilateral, the size of each internal angle will be [tex]\sf 60^\circ[/tex]. The length of segment
[tex]\displaystyle 10\, \sin\left(60^\circ\right) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}[/tex].
The area (in square inches) of this equilateral triangle will be:
[tex]\begin{aligned}&\frac{1}{2} \times \text{Base} \times\text{Height} \\ &= \frac{1}{2} \times 10 \times 5\sqrt{3}= 25\sqrt{3} \end{aligned}[/tex].
Note that the inscribed hexagon in this question is made up of six equilateral triangles like this one. Therefore, the area (in square inches) of this hexagon will be:
[tex]\displaystyle 6 \times 25\sqrt{3} = 150\sqrt{3}[/tex].
Area of of the circle that is not coveredRefer to the first diagram. The length of each side of these equilateral triangles is the same as the radius of the circle. Since the length of one such side is [tex]10[/tex] inches, the radius of this circle will also be [tex]10[/tex] inches.
The area (in square inches) of a circle of radius [tex]10[/tex] inches is:
[tex]\pi \times (\text{radius})^2 = \pi \times 10^2 = 100\pi[/tex].
The area (in square inches) of the circle that the hexagon did not cover would be:
[tex]\begin{aligned}&\text{Area of circle} - \text{Area of hexagon} \\ &= 100\pi - 150\sqrt{3}\end{aligned}[/tex].
Related Questions
If the Lazy River is 7 ft deep, what is the volume of the Lazy River in cubic feet?
Answers
Answer:
Step-by-step explanation:
A factory sells backpacks for $40 each. The cost to make 1 backpack is $10.00. In addition to the costs of making backpacks, the factory has operating expenses of $12,000 per week. The factory’s goal is to make a profit of at least $9800 each week. Which inequality represents the number of backpacks ,x, that need to be sold each week for the factory to meet this goal?
Answers
Answer:
x (40-10) -12000≥980
The factory must sell 433 backpacks to meet its weekly goal.
Hi, to answer this question we have to write an inequality.
So, since the backpacks (x) are sold by $40 and the cost of making one is $10, the revenue per bag is equal to 40x and the cost is 10x.
12,000 of operating expenses are also expenses.
So, for the profit:
Profit = revenue- cost
P = 40x-10x-12,000
P = x (40-10)-12000
The factory goal is to make a profit of at least $980 each week, so, the profit must be greater or equal than 980.
x (40-10) -12000≥980
Solving for x
30x-12000≥980
30x≥980+12000
30x ≥12980
x≥12980/30
x≥432.6
x≥433 (rounded, because if the sell 432 they will not meet the goal)
The factory must sell 433 backpacks to meet its weekly goal.
Step-by-step explanation:
Which of the following is equivalent to (4 x 10~?) + (5 x 10–?)?
Answers
how to i find b in y=my+b if the slope is undefined?
Answers
Answer:
By finding the y- intercept in the graph.
Step-by-step explanation:
This is the only point in the graph that is on the y axis.
Find the slope of the line which goes through the given points.
d
A(2,8) and B(2,6)
Answers
Answer:
Undefined
Step-by-step explanation:
A slope is found using the formula rise (change in y) over run (change in x). The change in x is 0, and the change in y is -2. The answer is -2/0, but dividing by 0 gives you undefined. Don't believe me? Look at the attached image.
Hope this helps!
Answer:
Undefined
Step-by-step explanation:
Use the formula:
[tex]m=\frac{y+2-y_1}{x_2-x_1}[/tex]
Plug in the numbers/coordinates accordingly:
[tex]m=\frac{6-8}{2-2}[/tex]
[tex]m=\frac{-2}{0}[/tex]
m = undefined
When x = 0, the slope is undefined.
I WILL GIVE YOU BRAINLIEST, AND 30 POINTS SO PLEASE HELP ME, IT'S URGENT!
Answers
Jimmy is in New York City to see a Drake concert. He needs to get
from his Airbnb to the concert venue, so he decides to take a cab.
The cab charges a $3 boarding fee in addition to charging $0.50
per mile traveled. Jimmy gave the driver a $2 tip and paid $10.
How far away was the concert venue?
Answers
Answer:
16
Step-by-step explanation:
y= .5x+3
10=.5x+2
I need help nothing is working for the answer p÷3> 2
Answers
Answer:
p > 6
Step-by-step explanation:
Given
[tex]\frac{p}{3}[/tex] > 2 ( in fractional form )
Multiply both sides by 3 to clear the fraction
p > 6
Answer:
honestly idk
Step-by-step explanation:
it may be p (1/3)
hope this is right:000
Complete the equation of the line through (−10,3) (−8,−8). Use exact numbers. y=
Answers
Answer:
y = -11/2x - 52
Step-by-step explanation:
Now follow the equation for slope: m = change in y / change in x.
[tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{-8-3}{-8--10}[/tex]
[tex]\frac{-11}{2}[/tex]
The slope is -11/2. m=-11/2
Use slope-intercept form:
y=mx+b
Plug in a point and the slope:
-8 = (-11/2)(-8) + b
-8 = 44 + b
b = -52
y = -11/2x - 52
Answer:
-11/2x-52
Step-by-step explanation:
i know it is correct
Which type of sampling method is being employed in the following example: "In order to test out a new dessert available at Chili's restaurants in the metro-Atlanta, everyone at 6 selected Chili's locations are offered to try the new dessert for free on one weekend."
Simple Random Sampling
Sampling of Convenience
Stratified Sampling
Systematic Sampling
Cluster Sampling
Answers
Answer:
Cluster sampling
Step-by-step explanation:
What is the sum of 1-2 and V-18?
Answers
Answer:
v-19
Step-by-step explanation:
Answer:
It depends on what you mean.
Step-by-step explanation:
If its to separate questions,
1-2= 1
V-18= -13
If its one whole question then
1-2 - V-18= 14
1-2 / V-18= -0.07692307692
1-2 * V-18= -13
1-2 + V-18= -12
Hope this helps! :D
PLS HELP I WILL MARK BRAINLIEST (EDITED)
Step 2: Finding the area of triangles
a) The International Space Station has small cupboards that are used for storage. A cupboard door is drawn below.
a rectangle with a line going from the upper left corner to the down right corner. at the left corner, under the line is 60. under the right corner, is 30. there is a square at the down left corner
What is a formula that can be used to find the area of one triangular section of the door? How do you know the formula will work? (3 points)
Answers
Answer:
51.9
Step-by-step explanation:
because one side is 30 and another is 60, you can assume the 3rd side of the triangle is 51.9 because of the 30-60-90 rule which states that if each angle of a triangle is 30, 60, and 90, then the side lengths equal x (30), 2x (60), and x√(3) (~51.9).
The base of the triangle is 51.9 units and the area of the right-angled triangle is 778.5 square units.
What is a right-angle triangle?"A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or anyone angle is a right angle. Therefore, this triangle is also called the right triangle or 90-degree triangle".
For the given situation,
A rectangular door has a diagonal, d = 60
A rectangular door has a height, h = 30
When we draw a diagonal to a rectangle, this portion forms a right-angled triangle. The length of the triangle can be found by using the Pythagoras theorem.
The formula of Pythagoras theorem,
[tex]Hypotenuse^{2} = base^{2}+perpendicular^{2}[/tex]
[tex]Base=\sqrt{(Hypotenuse)^{2} -(Perpendicular)^{2} } \\[/tex]
On substituting the above values,
⇒ [tex]Base = \sqrt{60^{2}-30^{2} }[/tex]
⇒ [tex]Base=\sqrt{2700}[/tex]
⇒ [tex]Base=51.9[/tex]
The formula to find the area of a right-angle triangle, [tex]A = \frac{1}{2}(base)(height)[/tex]
⇒ [tex]A = \frac{1}{2}(51.9)(30)[/tex]
⇒ [tex]A=778.5[/tex]
Hence we can conclude that the base of the triangle is 51.9 units and the area of the right-angled triangle is 778.5 square units.
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Question 15
2 pts
The daily caloric intake for a group of women follows a normal distribution with a mean of
1,750 calories and a standard deviation of 200 calories. What is the z-score for a woman
who had a daily intake of 2,100 calories?
2,091
-1.75
1.75
1.09
Question 16
2 pts
What is it called when you get a positive test result for a disease that you do not have?
False Negative
Margin of Error
Accuracy
True Positive
False Positive
Answers
Answer:
1. Z = 1.75
2. False Positive
Step-by-step explanation:
1. mean = 1750 calories
standard deviation, sd = 200 calories
value of interest, x = 2,100
z-score is computed as follows:
Z = (x - mean)/sd
Z = (2100 - 1750)/200
Z = 1.75
2. A false positive happens, when a negative case is detected as a positive case
Gideon asked 50 students at his middle school which option they would like for lunch: pizza, sandwiches or burritos. Ten students said pizza, 4 said sandwiches and the remaining students answered burritos. What percent of students in the school would you predict would choose burritos based on this survey?
Answers
Answer:
72% of students chose burritos
Step-by-step explanation:
first you would add up the total of kids that said they liked the other two options, which was pizza and sandwiches: 10+4=14
then you would take that number and subtract it from the total of all students: 50-14=36
and then you would take that number and divide it by 50: 36/50=.72
turn that into a percent and you'd get 72%
The graph of Y = COS X+ż is the graph of the y = cos(x) shifted in which direction?
T
2 units to the left
2
units to the right
units up
2 units down
Answers
Answer:
2 units up
Step-by-step explanation:
You're just taking the entire graph of cos(x) and then adding 2 so it moves everything up. If you added 2 to x BEFORE taking the cosine
(like y = cos (x+2) ), then you would shift it left 2. Adding and subtracting from the x moves everything left or right. Adding or subtracting at the end just moves it up and down.
The graph of y = cos x + 2 is the graph of the y = cos(x) shifted in ''2 units up.''
What is Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
To find the graph of y = cos x + 2 is the graph of the y = cos(x) shifted in which direction.
Here, The function is,
⇒ y = cos x
Now, After translate 2 units up, we get;
⇒ y = cos x + 2
Thus, The graph of y = cos x + 2 is the graph of the y = cos(x) shifted in ''2 units up.''
Learn more about the transformation visit:
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Which expression can be used to find the surface area of the following triangular prism?
A. 6+6+33+44+55
B. 6+6+55+55+55
C. 12+12+33+44+55
D. 12+55
Answers
Answer:
C
Step-by-step explanation:
3×4=12
3×11=33
5×11=55
PLEASEEEEE ANSWERRRRRRR!!!!!!!!!!!!
What is the area of figure?
A trapezoid with short base eighteen centimeters, long base thirty-eight centimeters, height sixteen centimeters, and diagonal side lengths twenty centimeters.
A. 320 square centimeters
B. 608 square centimeters
C. 448 square centimeters
D. 560 square centimeters
Answers
Answer:
C. 448 square centimeters
Step-by-step explanation:
38+18/2(16)
=448 square centimeters
:3
jina works mowing lawns and babysitting she earns $7.90 an hour for mowing $7.40 an hour for babysitting how much will she earn for 1 hours of mowing and 5 hours of babysitting
Answers
Answer:
44.90
Step-by-step explanation:
1 hour mowing = 1*7.90 = 7.90
5 hours babysitting = 5*7.40 =37.00
The total is 7.90+37 =44.90
Joe has 7 shirts, 4 pairs of pants and 2 pairs of shoes. He needs to make an outfit containing one of each
item. How many different outfits are possible? (We assume that one different item makes a different outfit)
a
13 outfits
28 outfits
26 outfits
56 outfits
d
Answers
Joe has 56 possible different outfits.
What are combinations?A combination is a mathematical method in which the number of possible ways in which a set of given items can be chosen, such that the order in which it happens does not matter items.
The number of possible outfits can be chosen as shown below:Joe has 7 different choices for shirts.
Joe has 4 different choices for pants.
Joe has 2 different choices for shoes.
This means that number of combinations in which Joe can choose an outfit can be found by multiplying all the choices.
This can be done as shown below:
Number of choices for shirts * Number of choices for pants * Number of choices for shoes
= 7 * 4 * 2
= 56 combinations.
Therefore, we have found that Joe has 56 possible different outfits. The correct answer is option D.
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Maria bought an SUV for 21,000 dollars. Nancy bought a sedan for 2/3 as much. How much less did Nancy spend on her sedan?
Answers
Answer:
7000
Step-by-step explanation:
21,000*(2/3)=14000
21,000-14,000=7000
Answer:
7,000 dollars
Step-by-step explanation:
21,000 divided by 3 is 7,000 = 1/3
So 2/3 = 7,000 x 2 = 14,000
To find how much less Nancy spent on her sedan you do 21,000 - 14,000 = 7,000
PLEASE HELP ASAP worth alot
Answers
Answer:
I believe it is C
Step-by-step explanation:
Hope this helps
and if it at all possible and you mark me brainlyest please
Answer:
5 pts isnt a lot but ok.. and yes it is c
Step-by-step explanation:
Kathy recorded the following measurements of length: 2.5 cm.
2.9 cm, 3.0 cm, 2.5 cm, and 3.1 cm. What is the mean for this
set of values, in cm?
Answers
Answer:
2.8
Step-by-step explanation:
To find the mean add all the values and divide by the amount of values and when you add everything up it is 14 and dividr by 5 to get 2.8
110-
у
70-
y = [ ? ]°
Answers
Answer:
y = 90°
Step-by-step explanation:
y + x = 110° because the sum of two interior angles is equal to an interior angle
x + 70° = y ➡ y - x = 70°
y + x = 110°
y - x = 70° add two equations
2y = 180° (x eliminated -x)
y = 90°
Number 11-16 please help me I must make sure You choose a Method of choice so whichever is easiest .
Answers
Answer:
#11: 1180.428 571
#12: 80.166... repeating
#13: 237.5
#14: 686
#15: 2682.333 repeating
#16: 122
Step-by-step explanation:
Hopes this helps. Also #12 and #15 are repeating. Just FYI.
Evaluate A^2 for A = -4. -16 -8 8 16
Answers
Answer:
The answer is 4^2 (-16)
Step-by-step explanation:
If the associated Linear function of this sequence was graphed, what woulld be its slope?
A) 2
B) 4
C) 8
D)1/4
Answers
Answer:
I think it is A but the other person might be right
what is the gcf of 36 and 78
Answers
Answer:
6
Step-by-step explanation:
36: 2 2 3 3
78: 2 3 13
GCF: 2 3
2x3=6
hope this helps
HAVE noice DAY ^_^13. A circle with radius x is shown below. The diagram is not drawn to scale. (1 point)
What is the value of x? Round the answer to the nearest tenth.
Answers
Answer: 16.1
Step-by-step explanation:
x^2 = 8^2 + (28/2)^2
x^2=64 + 196
x^2= 260
Take the square root of 260 and get 16.1!
The value of x is x=16.1
Chord
The perpendicular from the center of a circle bisects the chord
RadiusA line from the center of the circle to the circumference of the circle is the radius of the circle
Lets connect the center of the circle to the other end of the chord that is at the circumference of circle
The diagram attached below
The line OA from the center bisects the chord
AB= half of 28 = 14
the triangle AOB forms a right angle triangle
apply Pythagorean theorem to find out the value of x
[tex]x^2=8^2+14^2\\x^2= 64+196\\x^2=260\\\sqrt{x^2}=\sqrt{260} \\ x=16.1[/tex]
The value of x is 16.1
Learn more information about 'perpendicular line ' here
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Convert: 15,940 feet = how many miles and feet
Answers
Answer:
3.02 miles
Step-by-step explanation:
Help Me! I'm not good at this! I will mark brainliest!
Answers
Answer:
1.61 * 10 ^8
3.3 * 10^-7
Step-by-step explanation:
Multiply the numbers and then add the exponents
2.3 * 10^1 * 7 * 10^6
2.3 *7 * 10^(1+6)
16.1 * 10^7
We need to make this scientific notation by moving the decimal one place to the left and adding 1 to the exponent
1.61 * 10 ^8
Multiply the numbers and then add the exponents
1.1* 10^-5 3*10^-2
1.1 *3 * 10^(-5+-2)
3.3 * 10^-7
Answer:
1. B
2. C
Step-by-step explanation:
1. 2.3 × 10¹ × 7 × 10⁶
2.3 × 7 × 10^(1+6)
16.1 × 10⁷
1.61 × 10⁸
2. 1.1 × 10^-5 × 3 × 10^-2
1.1 × 3 × 10^(-5-2)
3.3 × 10^-7
