Answers
[tex]\dfrac{60^o}{360^o}=\dfrac{1}{6}[/tex]
The sector is 1/6 of the circle, therefore the area of the sector is 1/6 of area of the circle.
The formula of an area of the circle: [tex]A_O=\pi r^2[/tex]
The area of the sector:
[tex]A_s=\dfrac{1}{6}\cdot\pi\cdot12^2=\dfrac{1}{6}\pi\cdot144=24\pi\ m^2[/tex]
The formula of an area of the equilateral triangle: [tex]A_\Delta=\dfrac{a^2\sqrt3}{4}[/tex]
[tex]A_\Delta=\dfrac{12^2\sqrt3}{4}=\dfrac{144\sqrt3}{4}=36\sqrt3\ m^2[/tex]
The area of the segment:
[tex]A_{sg}=A_s-A_\Delta\to A_{sg}=(24\pi-36\sqrt3)m^2[/tex]
The area of the shaded region:
[tex]A=A_O-A_{sg}\to A=144\pi-(24\pi-36\sqrt3)=144\pi-24\pi+36\sqrt3\\\\=\boxed{A=(120\pi+36\sqrt3)m^2}[/tex]
Related Questions
An earthquake strikes and an isolated area is without food or water. three crews arrive. one can dispense needed supplies in 4545 hours, a second in 9090 hours, and a third in 6060 hours. how long will it take all three crews working together to dispense food and water?
Answers
1 person takes 20h, the second would hake 30h, third 60h.
1/20+1/30+1/60=1/10
If the surface area of a sphere is 256π cm2, what is the radius?
4 cm
8 cm
12 cm
16 cm
Answers
If you rearrange the equation for surface area to solve for r then you can plug the 256pi into the equation and get 8.
The formula for surface area of the sphere is -
Surface area of sphere = 4πr²
Now, the surface area of sphere is given to us as = 256π cm²
Thus,
4πr² = 256π cm²
While equating the equations, we will get
4r² = 256 cm²
r² = 64 cm²
64 is the square of 8, thus the radius of sphere will be = 8 cm.
The correct answer will be = 8 cm radius
Ellen needs to buy 180 inches of ribbon to wrap a present. The store sells ribbon only in whole yards. How many yards does Ellen need to buy to have enough ribbion
Answers
A wood board is one of a 6 different parts in a shelf kit. the width, depth, and height dimensions of the board are 42 inches x 8 inches x .75 inches, respectively. the board is made from southern yellow pine, which has an air dry weight density of .021 lbs/in.3. (watch the units of measure)
Answers
A wood board is one of a 6 different parts in a shelf kit. the width, depth, and height dimensions of the board are 42 inches x 8 inches x .75 inches, respectively. the board is made from southern yellow pine, which has an air dry weight density of .021 lbs/in.3. (watch the units of measure)
1) What is the volume of the wood board? Precision = 0.00
2) What is the surface area of the wood board? Precision = 0.00
3)What is the weight of the wood board? Precision = 0.00
4) If one gallon of paint will cover 35,000 square inches, how many gallons would be needed to give two coats of paint to 15,000 boards? Round your answer to the nearest gallon
Part 1) What is the volume of the wood board? Precision = 0.00
we know that
volume=L*W*H-----> 42*8*0.75----> 252 in³
the answer Part 1) is 252 in³
Part 2) What is the surface area of the wood board? Precision = 0.00
surface area=2*area of the base+perimeter of the base*height
area of the base=42*8----> 336 in²
perimeter of the base=2*[42+8]----> 100 in
height=0.75 in
surface area=2*336+100*0.75----> 672+75----> 747 in²
the answer Part 2) is 747 in²
Part 3)What is the weight of the wood board? Precision = 0.00
we know that
density=mass/volume-----> mass=density*volume
density=0.021 lbs/in³
volume=252 in³
mass=0.021*252----> 5.292 lbs
the answer Part 3) is 5.29 lbs
Part 4) If one gallon of paint will cover 35,000 square inches, how many gallons would be needed to give two coats of paint to 15,000 boards? Round your answer to the nearest gallon
if 1 gallons cover------------> 35000 in²
x -----------------------> 747 in² (one board)
x=747/35000-----> x=0.021 gallons per 1 board
so
15000*0.021------> 320.14 gallons
but remember ------> two coats of paint
so
320.14*2-----> 640.28 gallons------> 640 gallons
the answer Part 4) is 640 gallons
What is the sum os the interior angles of the polygon?
Answers
Calculate the length of AC to one decimal?
Answers
As one side of the rectangle is given length of 4cm, the parallel other must also be equal to 4cm. Hence, Length of A to E is equal to 11cm-4cm=7cm.
Now, we use this length of 7 cm as this is opposite to our desired angle(a colored green) and by making 16cm our hypotenuse we find angle a to be 25.9°. [tex]sin x^{-1}(7/16)=25.9^{o} [/tex]
Next we find angle b by adding angle a with 90. hence getting 115.9°.
Finally we consider our triangle ABC to find the length of AC. We know one angle and length of two sides and can easily use cosine rule to find the remaining length AC. The equation and working is shown in diagram.
Answer= 18.1
92.4 is 150% of what number?
Answers
2. We assume, that x is the value we are looking for.
3. If 92.4 is 100%, so we can write it down as 92.4=100%.
4. We know, that x is 150% of the output value, so we can write it down as x=150%.
5. Now we have two simple equations:
1) 92.4=100%
2) x=150%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
92.4/x=100%/150%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 150% of 92.4
92.4/x=100/150
(92.4/x)*x=(100/150)*x - we multiply both sides of the equation by x
92.4=0.666666666667*x - we divide both sides of the equation by (0.666666666667) to get x
92.4/0.666666666667=x
138.6=x
x=138.6
now we have:
150% of 92.4=138.6
Answer:
Number is 61.6
Step-by-step explanation:
Given : 92.4 is 150%.
To find : what number.
Solution : We have given 92.4 is 150%.
Let the number = x
According to question :
150% of x = 92.4
[tex]\frac{150}{100} *x[/tex] = 92.4
On multiplying both sides by 100
150 x = 92.4 * 100.
150 x = 9240
On dividing both sides by 150 .
x = [tex]\frac{9240}{150}[/tex].
x = 61. 6
Therefore, Number is 61.6
Find the number if the square root of another number that is 6 greater than this number is equal to the number itself.
Answers
Answer:
The number is 3 and the another number is 9
Step-by-step explanation:
Let
x-------> the number
y-----> another number
we know that
[tex]y=x+6[/tex] ----> equation A
[tex]\sqrt{y}=x[/tex] ----> equation B
Substitute equation A in equation B
[tex]\sqrt{x+6}=x[/tex]
squared both sides
[tex]x+6=x^{2} \\x^{2}-x-6=0[/tex]
Using a graphing tool
solve the quadratic equation
see the attached figure
The solution is x=3
Find the value of y
[tex]y=x+6[/tex] -------> [tex]y=3+6=9[/tex]
PLEASE HELP!!!!!!!!!!!!!!!!! What is the simplified form of the expression k^3(k^7/5)^-5
A. k^4
B. 1/k^1/4
C. k^1/4
D. 1/k^4
Answers
= (k^3)(k^(7/5*-5))
= (k^3)(k^-7)
= k^(-7+3)
= k^-4
= 1/k^4
Which is choice D.
A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for soccer or volleyball. Out of the total 80 people who liked soccer, 30 also liked volleyball. There were 45 people who liked volleyball.
Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points)
Like soccer
Do not like soccer
Total
Like volleyball
A
D
G
Do not like volleyball
B
E
H
Total
C
F
I
Part B: What percentage of the survey respondents did not like either soccer or volleyball? (3 points)
Part C: Do the survey results reveal a greater dislike for soccer or volleyball? Justify your answer. (2 points)
Answers
https://brainly.com/question/9914822
_____
A picture of your table would be most helpful.
Which number supports the given conjecture?
If a number is divisible by both 3 and 4, then the number is also divisible by 6.
A.
18
B.
42
C.
48
D.
64
Answers
48/3 = 16
48/4 = 12
48/6 = 8
In a factory, a parabolic mirror to be used in a searchlight was placed on the floor. It measured 40 cm tall and 90 cm wide. Find an equation of the parabola with its vertex at the origin.
Answers
point on the parabola:(45,40)
equation:
45^2=4p(40)
4p=45^2/40=40.625
thus
x^2=(50.625)y
Answer: x^2=(50.625)y
For an angle Θ with the point (12, −5) on its terminating side, what is the value of cosine?
−5
12
negative 5 over 13
12 over 13
Answers
opposite=-5
adjacent=12
thus using using Pythagorean theorem, the hypotenuse will be:
c^2=a^2+b^2
plugging the values we obtain:
c^2=(12)^2+(-5)^2
c^2=144+15
c^2=169
thus
c=13
but
cos θ=adjacent/ hypotenuse
therefore:
cos θ=12/13
Answer is option . D
the perimeter of this figure is 42.5 cm. Find the area of this figure.
Answers
let
AB=x
we know that
perimeter of the figure=10*x
perimeter=42.5 cm
so
42.5=10*x
x=42.5/10
x=4.25 cm
area of the figure=area of rectangle +area of square
area of rectangle=4.25*(4.25*3)----> 54.1875 cm²
area of square=4.25²----> 18.0625 cm²
area of the figure=54.1875+18.0625-----> 72.25 cm²
the answer is
72.25 cm²
Answer:
72.25
Step-by-step explanation:
I just took the test and got it correct
There is a ratio of 5 girls to 3 boys in the class in the chorus.there are 24 boys in the chorus how many girls are in the chorus
Answers
Can somone help me with this 1 problem? QRST is a parallelogram. Determine the measure of ∠Q
Q (4x+10) bottom left
R (9x+1) top left
S (5x-3) top right
T bottom left
Answers
In a rhombus, opposite angles are congruent based on the alternate interior angle theorem. In other words, R and T along with Q and S are both alternate interior angle pairs.
(You can actually test this by printing out a rhombus, cutting out the angles, and matching up the opposite ones.)
We know that Q is equal to 4x + 10, but we need to solve for x. Since Q and S are congruent, we can set them equal to each other:
1) 4x + 10 = 5x - 3
2) 4x + 13 = 5x
3) 5x = 4x + 13
4) x = 13
Now let's plug 13 in for Q:
5) 4(13) + 10 = 52+10 = 62
I got m<Q = 62 degrees. Hope this helps!
In the parallelogram QRST then measure of ∠Q is 62 degrees.
What is Quadrilateral?A quadrilateral is a four-sided polygon, having four edges and four corners.
Given that QRST is a parallelogram.
We have to find the measure of ∠Q.
Both pairs of opposite sides are parallel, quadrilateral QRST is a parallelogram.
∠Q= ∠S
4x+10=5x-3
We have to find the value of to find ∠Q measure.
10+3=5x-4x
13=x
Now let us plug in the value of x in ∠Q measure.
∠Q = 4x+10
Now plug in x value in ∠Q
∠Q = 4(13)+10
=52+10
=62 degrees
Hence, in the parallelogram QRST then measure of ∠Q is 62 degrees.
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A distribution of numbers has the following five-number summary:
20.2, 22.4, 30.0, 37.6, 39.8
True or False? These numbers can be used to calculate the standard deviation of the distribution.
Please Answer quickly! I need this done ASAP! Please.
Answers
The correct answer is:
False.
Explanation:
Using the five number summary, we can estimate the standard deviation.
The quartiles are about 0.67 standard deviations from the mean; this could be used to estimate the standard deviation.
However, we cannot accurately calculate the standard deviation using only the fie number summary.
40 points!!!!!!!!!!!!!! *If one of the legs of a right triangle is 4 in and the hypotenuse is 8 in, find the length of the other leg (use a calculator if necessary). Can you guess the measures of the acute angles?
Answers
the ratio of the sides of the triangle = 8 : 4 :4 sqrt3 = 2:1:sqrt3 so this is a
30-60-90 degree triangle
Multiply the binomial and find the coefficients
(X+y)^1=__×+__y
(×+y)^2=__x^2+__xy+__y^2
(X+y)^3=__×^3+__×^2y+__y^3
(×+y)^4=__×^4+__x^3y+__x^2y^2+__xy^3+__y4
Answers
For this case, rewriting each binomial we have:
(x + y) ^ 1 = 1x + 1y
(x + y) ^ 2 = 1x ^ 2 + 2xy + 1y ^ 2
(x + y) ^ 3 = 1x ^ 3 + 3x ^ 2y + 3xy ^ 2 + 1y ^ 3
(x + y) ^ 4 = 1x ^ 4 + 4x ^ 3y + 6x ^ 2y ^ 2 + 4xy ^ 3 + 1y4
Please help with geometry
Answers
[tex]\pi . {12}^{2} . \dfrac{300}{360} + {12}^{2} \dfrac{ \sqrt{3} }{4} \\ {12}^{2} ( \dfrac{5.\pi}{6} + \dfrac{ \sqrt{3} }{4} ) \\( 120\pi + 36 \sqrt{3} ) {cm}^{2} [/tex]
[tex]\dfrac{60^o}{360^o}=\dfrac{1}{6}[/tex]
The sector is 1/6 of the circle, therefore the area of the sector is 1/6 of area of the circle.
The formula of an area of the circle: [tex]A_O=\pi r^2[/tex]
The area of the sector:
[tex]A_s=\dfrac{1}{6}\cdot\pi\cdot12^2=\dfrac{1}{6}\pi\cdot144=24\pi\ m^2[/tex]
The formula of an area of the equilateral triangle: [tex]A_\Delta=\dfrac{a^2\sqrt3}{4}[/tex]
[tex]A_\Delta=\dfrac{12^2\sqrt3}{4}=\dfrac{144\sqrt3}{4}=36\sqrt3\ m^2[/tex]
The area of the segment: [tex]A_{sg}=A_s-A_\Delta\to A_{sg}=(24\pi-36\sqrt3)m^2[/tex]
The area of the shaded region:
[tex]A=A_O-A_{sg}\to A=144\pi-(24\pi-36\sqrt3)=144\pi-24\pi+36\sqrt3\\\\=\boxed{A=(120\pi+36\sqrt3)m^2}[/tex]
HELPPPPPPPPPPPPP and explain
Answers
There are a number of ways you could do this. The most straight forward might be to simply multiply the second equation to get the answer.
Step One
Multiply the second equation by 2
2(2x^2 + 1/y^2 = 12) Remove the brackets.
4/x^2 + 2/y^2 = 12 * 2
4/x^2 + 2/y^2 = 24
Step Two
Add the new equation and the first original equation
1/x^2 - 2/y^2 = 1
4/x^2 + 2/y^2 = 24
5 / x^2 = 1 + 24
5/x ^2 = 25 Divide both sides by 5
1/x^2 = 5 Reciprocate the x^2 and the 5 (That means turn them upside down.
x^2 = 1/5
Take the square root of both sides.
x = +/- 1/sqrt(5) Rationalize the denominator.
[tex]{x = } \frac{1}{ \sqrt{5} } * \frac{ \sqrt{5} }{ \sqrt{5} }\\ \\{x = } \frac{ \sqrt{5} }{5} [/tex]
Step 3
Place this answer in for x^2 to get y^2. and then y
1/(1/5) - 2/y^2 = 1
Interlude
You can use your calculator to see what 1/(1/5) is. Change the 1/5 to 0.2
1/0.2 = 5 Just put it in as
1
÷
0.2
=
You should get 5
Continued
5 - 2 / y^2 = 1 Subtract 5 from both sides.
- 2/y^2 = 1 - 5
-2 / y^2 = - 4 Divide both sides by - 2
1 / y^2 = -4/-2
1 / y^2 = 2 Now reciprocate both sides.
y^2 = 1/2 Take the square root.
y = +/- 1/sqrt(2) And rationalize the denominator
y = +/- sqrt(2) / 2 Done the same way as for the x.
There's only 1 there. I'll let you find it.
The average age of the children at a campout is shown in the box plot below. Which statement is true about the box plot? The youngest age is 7. It is skewed right. More of the children were close to 12 years old than 6 years old. Half of the children were between 6 and 9 years old.
Answers
The statement that is true about the box plot is that: C. more of the children were close to 12 years old than 6 years old.
What is a Box Plot?A box plot shows how a data is distributed, as it displays the five-number summary.
here, we have,
The five-number summary of the box plot representing the average age of children is:
Min = 6 (youngest age)
Lower quartile (Q1) = 9 (25% of the children are below 9)
Median = 10
Upper quartile = 11 (50%, which is half of the children are between 9 years and 11 years old)
Max = 12 (oldest)
Therefore, the statement that is true about the box plot is that: C. more of the children were close to 12 years old than 6 years old.
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What's the probability a number is odd given that it's an integer between 0 and 11?
Answers
sample space=s={1,2,3....,10}=total 10 numbers
So,
m=total no. of odd numbers{1,3,5,7,9} in our sample space=5 numbers
probability that number is odd=p=m/s
p=5/10=0.5
A teacher asked her students to divide a large number by 50.
• Aslan divided the number by 50.
• Lucy divided the number by 5 and then divided the answer she got by 10.
• Jack divided the number by 10 and then divided the answer he got by 40.
Who among these got the correct answer assuming they did NOT make mistakes in division?
Answers
Answer:
c
Step-by-step explanation:
Aslan and Lucy got the correct answer of x/50, while Jack made a mistake in his calculation.
Explanation:To find out who got the correct answer, we need to evaluate the division calculations of each student. Let's assume the large number is 'x'.
Aslan divided the number by 50, so his answer is x/50.
Lucy divided the number by 5 and then divided the answer by 10, so her answer is (x/5)/10 = x/50.
Jack divided the number by 10 and then divided the answer by 40, so his answer is (x/10)/40 = x/400.
Therefore, both Aslan and Lucy got the correct answer of x/50, while Jack made a mistake in his calculation.
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The mass of a grain of sand is about 10^-3 gram. About how many grains of sand are in a 10kg bag of sand?
Answers
Divide the mass of the bag by the mass of sand. First you need to convert kg to g
About how many grains of sand are in the bag of sand
Answer
10 kg* (1000 g/ 1 kg)* (1 grain of sand/ 10^(-3) g)= 10^7 grains of sand.
(Note that the units cancel out so you get the answer)
The final answer is 10^7 grains of sand.
Hope this helps~
A boy flies a kite with a 100-foot-long string. The angle of elevation of the string is 48°. Find the vertical distance between the kite and the point at which the boy is holding the string.
Answers
sinθ=opposite/hypotenuse
where:
θ=48°
opposite=h
hypotenuse=100 ft
thus
sin 48=h/100
hence
h=100 sin48
h=74.315 ft
Answer: 74.315 ft
Using the sine function of trigonometry, the vertical distance between the kite and the point where the boy is holding the string is calculated to be approximately 74.31 feet when the string's angle of elevation is 48 degrees.
To find the vertical distance between the kite and the point at which the boy is holding the string, we can use trigonometric functions, specifically the sine function which is defined as the ratio of the opposite side to the hypotenuse in a right triangle. Since we know the length of the string, which acts as the hypotenuse of the triangle, and the angle of elevation, we can set up our equation as follows:s
sin(48°) = opposite/hypotenuse
sin(48°) = vertical distance/100 feet
W then multiply both sides by the hypotenuse (100 feet) to solve for the vertical distance:
vertical distance = 100 feet \sin(48°)
To get the numerical value, we use a calculator to find:
vertical distance ≈ 100 feet * 0.7431
vertical distance ≈ 74.31 feet
Therefore, the vertical distance between the kite and the point where the boy is holding the string is approximately 74.31 feet.
Jamal is 167 cm tall. Which expression finds Jamal’s height in dekameters? Use the metric table to help answer the question.
Answers
1 cm is equal to -----------> 0.001 dekameters
so
167 cm------------------> X
x=167*0.001------> x=0.167 dekameters
Expression to finds Jamal’s height in dekameters
[Jamal’s height in cm]*0.001 or [Jamal’s height in cm]/1000
Answer:
It is D
Step-by-step explanation:
What is the equivalent decimal? Drag the answer into the box to match the fraction. 5/45
Answers
what you do is divide 5 into 45 to make it a decimal
If ΔGET≅ΔMAP, then what corresponding parts are congruent? segment TG and segment AM ∠T and ∠P segment MP and segment ET ∠E and ∠M
Answers
Answer:
2nd Option is correct that is ∠T and ∠P.
Step-by-step explanation:
We are given that ΔGET ≅ ΔMAP
We need to find Congruent part from the given options.
Since, we are given the figure of the congruent triangles with marking not any instruction with which vertex is congruent to which vertex.
So, The Given Name of the Congruent triangle.
We deduce that
G ↔ M
E ↔ A
T ↔ P
Using this we get following congruent parts,
GE ≅ MA , GT ≅ MP and ET ≅ AP
∠G ≅ ∠M , ∠E ≅ ∠A and ∠T ≅ ∠P.
Therefore, 2nd Option is correct that is ∠T and ∠P.
Answer:
∠T and ∠P
Step-by-step explanation:
The members of a chorus agree to buy at least 250 tickets for and outside concert. They buy 20 fewer ow tickets that balcony tickets. What is the lowest number of balcony tickets bought
Answers
This is because you can set balcony equal to x and ow equal to x - 20. Then you can add them together and set equal to 250. Simplify and solve for x.