Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answers
Answer:
(40/3)*pi
Step-by-step explanation:
lets first find the area of the little circle
A=pi*r^2
A=pi*3^2
A=9pi
Now, lets find the area of the big circle
A=pi*r^2
A=pi*(3+4)^2
A=pi*7^2
A=49pi
now lets subtract the area of the little circle from the area of the big circle
49pi-9pi=40pi, now we found the area of the "bagel)
lets find what portion of the bagel is the shaded region
120/360=1/3
now lets multiply the bagel area by the fraction
40pi*(1/3)=
(40/3)*pi or (40*pi)/3
Area of the shaded regions is equal to 7π/3
What is the area and circumference of a circle?The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.
Given here: radius of the smaller circle= 3 and larger circle =4 cm
Now A = (θ/360°) × πr2
θ is the sector angle subtended by the arcs at the center (in degrees), r is the radius of the circle. If the subtended angle θ is in radians, the area is given by, A = 1/2 × r² × θ.
Thus we have Area ADBC= 1/2 × 16×2π/3 -1/2×9×2π/3
=16π/3 -3π
=7π/3
Hence, Area of the shaded regions is equal to 7π/3
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Related Questions
what is the length of the hypotenuse of a triangle with legs of 8 and 19?
a. 17.2
b. 20.6
c. 297
d. 425
Answers
B
Step-by-step explanation:
in a triangle, what is the 3rd angle measure if the other two angles are each 60
Answers
Explanation: the two other measures add up to 120 degrees. The triangle sum property states that every triangle always adds up to 180 degrees. So, 180 - 120 = 60 degrees. Therefore, the third angle measures 60 degrees.
will mark bianleast plz plz
Which is the best description of the transformation shown?
A pentagon is translated 4 units to the right.
A pentagon is translated 9 units to the right.
A pentagon is reflected across the x-axis.
A pentagon is reflected across the y-axis.
Answers
Answer:
A pentagon is reflected across the y-axis
Add.
3x2 - 5x+1
2x2 +9X-6
+
A. 5x2 + 4x + 7
B. 5x2 - 4x + 5
C. 5x2 + 4x-5
D. 5x2 + 14x-5
Answers
Answer:
C
Step-by-step explanation:
3x2 - 5x+1 + 2x2 +9x-6
Combine like terms
5x2+4x-5 which is C
You are welcome and don't for get to click THANKS
You enjoy reading in your free time and keep every book you have ever read. When you were five, you read 2 books and every year after you tripled the number of books you read. How many books did you have in your bookcase when you were 11 years old?
Answers
The total number of books that we had in out bookcase when we were 11 years old was 2,187 books.
What is a geometric sequence and how to find its nth terms?Suppose the initial term of a geometric sequence is [tex]a[/tex]
and the term by which we multiply the previous term to get the next term is [tex]r[/tex]
Then the sequence would look like
[tex]a, ar, ar^2, ar^3, \cdots[/tex]
(till the terms to which it is defined)
Thus, the nth term of such sequence would be
[tex]T_n = ar^{n-1}[/tex] (you can easily predict this formula, as for nth term, the multiple r would've multiplied with initial terms n-1 times).
What is the sum of terms of a geometric sequence?Lets suppose its initial term is [tex]a[/tex] , multiplication factor is [tex]r[/tex]
and let it has total n terms, then, its sum is given as:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
For this case the initial number of books (2) is multiplied by 3 each year.
So we got:
a = 2,
r = 3
Since a = 2 was for age 5, and if we take age 5 at 1st position, then age 11 is at the 7th position.
The number of books we read at each age is a geometric sequence with initial term 2 and multiplication factor 3.
The sum of its term(which would make it geometric series) will give the total number of books we will have.
Since age 11 is at 7th position, so n = 7
Thus, the total number of books we had in the bookcase when we were 11 years old is:
[tex]S_n = \dfrac{a(r^n-1)}{r-1}\\\\S_7 = \dfrac{2((3)^7-1)}{3-1} = 2187[/tex]
We could've derived it without formula as:
Age 5: 2 booksAge 6: [tex]2 \times 3[/tex] booksAge 7: [tex]2 \times 3^2[/tex] booksAge 8: [tex]2 \times 3^3[/tex] booksAge 9: [tex]2 \times 3^4[/tex] booksAge 10: [tex]2 \times 3^5[/tex] booksAge 11: [tex]2 \times 3^6[/tex] booksTheir sum is 2187.
Thus, the number of books that we had in out bookcase when we were 11 years old was 2187 books.
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8.) The distance from Caleb's house to his school is 15 miles. What
is the distance in feet?
0.) 1760 feet
b.) 2640 feet
C.) 5280 feet
d.) 7920 feet
Answers
Answer:
I think the answer would be 79200 feet as 1 miles = 5280 feet
traductor de español
¡Hola! La siguiente descripción dice que el hogar de Caleb para su escuela es de 15 millas. La pregunta pregunta cuántos pies hay en 15 millas
Respuesta: 79.200.
Razonamiento: El razonamiento para esto es que 1 milla es 5280 pies. Cuando descubras que puedes multiplicar esto por 15 obtendrás 79200
Prueba: 5280
x 15
___________
79200
__________________________________
English Translator
Hello! the following description says that Caleb's house to his school is 15 miles. The question asks how many feet are in 15 miles
Answer: 79200
Reasoning: The reasoning to this is that 1 mile is 5280 feet. When you find out that you can multiply this by 15 you would get 79200
Proof: 5280
x 15
___________
79200
A knitting group used 248 yards of yarn to Knit tassels for snow hats. If 1/2 yard of yarn is used for each tassel,how many tassels did the Knitting group make?
Answers
Answer:
124
Because If u divide 248 by 2 you get 124
Which of the following is the equation of a line in slope-intercept form for a line with slope =1/4 and y-intercept at (0,-1)?
A. y=-1/4x - 1/4
B. y= 1/4x - 1
C. y= 1/4x +1
D. y=4x - 1
Answers
Answer: b.y=1/4x-1
Step-by-step explanation:
Y=mx+b
Y=1/4x-1 because 1/4 is the slope which is what you put in m and -1 is the y-intercept which is where it starts and is what you put in b.
Answer:y=1/4x-1
Step-by-step explanation:
Which is the best estimate for the sum 2/9 +10/11 ?
A. 0 + 0 = 0
B. 12+12=1
C. 1 + 1 = 2
D. 0 + 1 = 1
Answers
Answer:
D
Step-by-step explanation:
Indicate the method you would use to prove the two triangles congruent. If no method applies, enter "none."
SSS
SAS
ASA
AAS
None
Answers
Answer:
SSS Theorem
Step-by-step explanation:
Answer:
SSS
Step-by-step explanation:
They share a side so that's the third side that's the same
i) A fish tank measures 1m long by 40cm wide and 60cm height.
What is the capacity of the fish tank?
ii) How many litres of water does it take to fill it three quarters full ?
Answers
Answer:
1. The capacity of the water tank = 240 litres
2. So it will take 180 litres to fill it three quarters full.
Step-by-step explanation:
Dimensions of a water tank:
1 Meter=100 CM
Length (l) = 100 cm,
wide (w) = 40 cm,
Depth (h)= 60 cm,
Volume of the tank (V)
LWH
100 cm × 40 cm × 60 cm
240,000 cm³
The capacity of the water tank = 240,000 cm³ / 240 litres
(240,000*3)/4 = 180,000 cm3
So it will take 180 litres to fill it three quarters full.
Find the value of x in each case. Give reasons to justify your solutions!
Q ∈ PR
Answers
Answer:
x = 52 Degrees
Step-by-step explanation:
Welp, here I go again
According to the Exterior Angle theorem Angle R + Angle S = Angle PQS
So simplified that'd be (90 + 34) = x + 72
124 = x + 72
x = 124 - 72
x = 52 Degrees
I just want u guys to check it and see if it is right if it is say it is and if not please correct me and tell me the answer :)
Lesson 1 exit ticket Name
Please make a copy and then work on it, thank you!
1, Fill in the chart converting between fractions, decimals and percents.
Fraction Decimal Percent
⅛ 0.125 12.5%
1245/1000 1.245 124.5%
40/100 .4 ⅖ %
Show your work here.
8 times .125 = 1 that is 12.5%.
1.245 = 1245/1000 which is 124.5%.
⅖% is 40% which equals 0.4 or 40/100
2. Using the values from the chart in problem 1, list them from least to greatest.
12.5%
⅖%
124.5%
Answers
The first two values were calculated, but the 0.4 one is wrong.
2/5% would result to 0.4% which is converted to 0.004 so it's wrong.
40/100 would be reduced to 2/5.
2/5 would result to 0.4.
0.4 means 40%.
If the question intentionally gives 2/5%, then you have to compute it all the way back.
2/5% to 0.4% to 0.004 to 4/1000
I have no clue what part is given but you can get the idea where this is going.
The second one depends on the value in question one.
So Good luck!
could someone please help me with this problem?
Answers
Answer:
C
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, 9) and (x₂, y₂ ) = (12, 20)
m = [tex]\frac{20-9}{12-4}[/tex] = [tex]\frac{11}{8}[/tex] → C
Charlie wants to order lunch for his friends. He'll order 5 sandwiches and a $3
kid's meal for his little brother. Charlie has $28. How much can he spend on
each sandwich if they are all the same price?
Choose two answers: one for the inequality that models this situation and
one for the correct answer.
D A. Answer: $5 or less
B. Answer: $7.66 or less
O C. Inequality: 3x+5<28
OD. Inequality: 3x+5 s 28
O E. Inequality: 5x+3 s 28
OF. Inequality: 5x+3228
Answers
Answer:
A
Step-by-step explanation:
Charlie bought a $3 kids meal so 28-3 is 25. Since he wants to buy sandwiches for 5 people, he'll have to divide 25 / 5 which is 5. So $5 or less.
An online store sells old video games and DVDs as a bundle. A bundle of two video games and three DVDs can be purchased for $88. A bundle of one video game and two DVDs can be purchased for $51.50. Find the cost of one video game and the cost of one DVD in the bundle.
Answers
Answer:
idk just did like 9 math problems :/
Step-by-step explanation:
ill come back in an hour
The math department needs to buy new textbooks and laptops for
the computer science classroom. The textbooks cost $89.00 each, and
the laptops cost $395.00 each.
a. If the math department has $7200 to spend and purchases 60
textbooks, how many laptops can they buy?
b. Suppose the math department decided to purchase 35
textbooks instead of 60. How does this change the number of
laptops that they can buy?
Answers
Answer:
a. 4
b. 10
Step-by-step explanation:
A. If the math department buys 60 textbooks, which are $89 each, we need to multiply 60 by $89 to get the amount that the textbooks will cost. This gives us $5340. Since the math department has $7200 to spend, we subtract 5340 from 7200. This gives us $1860 that the math department has left to spend on laptops. Since the laptops cost $395 each, and we have $1860 to spend, we divide 1860 by 395 to figure out how many laptops they can buy. This is 4.7. Since you can't buy 0.7 of a laptop, they can only buy 4 laptops. The final answer is 4.
B. The math department has $7200 to spend and buys 35 textbooks, which are $89 each. Multiply 35 by 89. This is $3115. Subtract this from $7200 to see how much the department has left to spend. The math department now has only $4085 to spend on laptops, which are $395 each. Divide 4085 by 395. This gives us 10.3. We can't buy 0.3 of a laptop, so they can only buy 10 laptops. The answer is 10.
Answer:
A:$7200-$5340
=$1860
They can buy 4 laptops which will cost $1580 and leave you with $280
B: 35 textbooks will cost $3115, which will leave us with $4085, so we can get 10 laptops
Step-by-step explanation:
4. A group of friends rents a boat to spend an afternoon on a lake. The boat rental has a flat fee of $180 for up to three hours and $50 per hour for each additional hour. The first four passengers are included in this cost, but $20 is charged for each additional passenger. Write a linear equation to describe this situation, where c is the total cost of the rental, h is each additional hour (over 3) and p is each additional passenger (over 4).
options:
A. c = 230h + 20p
B. c + 180 = 50h + 20p
C. c = 180 + h + p
D. c = 180 + 50h + 20p
Answers
Answer:
it is D c= 180 + 50h + 20p
Step-by-step explanation:
c is the total cost and the boat is 180 but for additional hour it would be +$50
now the first four passenger is free but if another person comes on then it would be +$20 hope this help
The linear equation which describes the total cost of the rental is c = 180 + 50h + 20p
The correct option is an option (D)
What is a linear equation?"It is an equation in which the highest power of the variable is always 1."
For given example,
The boat rental has a flat fee of $180 for up to three hours.
Fixed rental cost = 180 ...............(1)
The boat rental has $50 per hour for each additional hour.
Let, h is each additional hour (over 3)
So, the rental cost for each additional hour = 50h .............(2)
The first four passengers are included in this cost, but $20 is charged for each additional passenger.
Here, p is each additional passenger (over 4)
So, the rental cost for each additional passenger = 20p ..................(3)
From (1), (2) and (3),
the required linear equation would be,
c = 180 + 50h + 20p
Therefore, the linear equation which describes the total cost of the rental is c = 180 + 50h + 20p
The correct option is an option (D).
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The graph shows the relationship between the volume of rectangular prism and the volume of a square pyramid with an identical base and height. What is the slope of the line?
O-3
O-1/3
O1/3
O 3
Answers
Answer:
3. Do Δy/Δx
Step-by-step explanation:
Do 10/3, which is an estimate. You get an answer of 3.3. Intuitively this makes sense because the slope is a constant positive value. And 1/3 is way too small of a number to describe the steepness shown
Or actually, do 3/1 because that would give the slope from x=0 to x=1. Since the slope is constant, that answer will apply for every single point on the function
What is the most efficient way to solve this equation?
18c = 108
Divide both sides by 18
Multiply both sides by 108.
Multiply the left side by 18.
Divide both sides by c.
Please don’t guess :(
Answers
Answer:
Divide both sides by 18
Step-by-step explanation:
This is the most efficient way to solve this equation because you can find the variable (c) in one step.
At Work-It-Out, a gym membership is $50 per month with no registration fee. At Get Fit, the registration fee is $100 and membership costs $30 per month. Which equation could be used to find the number of months, m, for which the total cost of both gyms is the same? 100+30m=50m 50m=30+100m 100+50m=30m 50m=100−30m
Answers
Answer:
Step-by-step explanation:
50x=30x+100
The equation is 100 + 30m = 50m and the no. of months for which total cost of both the gyms will be same is 5 months.
What is a linear equation ?A linear equation is an algebraic equation in which a variable has a highest degree of 1.
According to the given question At Work-It-Out, a gym membership is $50 per month with no registration fee and At Get Fit, the registration fee is $100 and membership costs $30 per month.
Given no. of months is m.
∴ 50m = 30m + 100
50m - 30m = 100.
20m = 100
m = 5.
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Solve the following system:
y = x + 3
4x + y = 18
Your answer:
(6, 3)
(3, 6)
(−3, 6)
(3, −6)
Answers
Answer:
B (3,6)
Step-by-step explanation:
y = x + 3
then we will use this y to substitute the other y
4x + y = 18
4x + (x +3) = 18
4x + x + 3 = 18
5x = 18 - 3
5x = 15
x = 15/5 = 3
then we can find the value of y
y = x + 3 = 3 + 3 = 6
so the (x,y) is (3,6)
Which function has a domain and range that includes all real values?
Answers
You're supposed to post all the photos in a single question. Anyway, this is the one that has a domain and range of all real values.
We can see a domain of all real values -- there's no x that's not included.
We can see the range of all real values -- there's no y that's not included.
Answer:
I think its c...
Step-by-step explanation:
Given the objective function C=3x−2y and constraints x≥0, y≥0, 2x+y≤10, 3x+2y≤18, identify the corner point at which the maximum value of C occurs.
Answers
Answer:
Step-by-step explanation:
Find the maximum value of
C = 3x -2y Objective function
subject to the following constraints.
Constraints
x ≥ 0
y ≥ 0
2x + y ≤ 10 vertex 1 : when x=0 then y=10 (0,10)
3x + 2y ≤ 18 vertex 2 : y=0, then x=6 ( 6,0)
two equations together to determine vertex 3 :
3x+2y = 18
2x+y = 10
x=2, y= 6
The feasible region determined by the constraints is
shown. The three vertices are (0, 10), and (6, 0), (0,9)
and (2,6)
First evaluate C = 3x -2 y at each of the vertices.
At (0, 10): C = 3(0) - 2(10) = -17
At (6, 0): C = 3(6) - 2(0) = 18
At ( 2,6) : C = 3(2) -2(6) = -6
At (0,9) : C = 3(0)-2(9)= -18
the maximum value occur on 18 when x=9 and y=0
Given the objective function is [tex]C=3x-2y[/tex] and the contraints as follows:
[tex]x\geq 0\\ y\geq 0\\ 2x+y\leq 10\\ 3x+2y\leq 18[/tex]
Find the intersecting point of [tex]x=0[/tex] and [tex]2x+y=10[/tex].Substitute 0 for [tex]x[/tex] in [tex]2x+y=10[/tex].
[tex]2(0)+y=10\\ y=10[/tex]
So, the intersecting point is [tex](0,10)[/tex].
Find the intersecting point of [tex]y=0[/tex] and [tex]2x+y=10[/tex].Substitute 0 for [tex]y[/tex] in [tex]2x+y=10[/tex].
[tex]2x+0=10\\ 2x=10\\ x=5[/tex]
So, the intersecting point is [tex](5,0)[/tex].
Find the intersecting point of [tex]x=0[/tex] and [tex]3x+2y=18[/tex].Substitute 0 for [tex]x[/tex] in [tex]3x+2y=18[/tex].
[tex]3(0)+2y=18\\ 2y=18\\ y=9[/tex]
So, the intersecting point is [tex](0,9)[/tex].
Find the intersecting point of [tex]y=0[/tex] and [tex]3x+2y=18[/tex].Substitute 0 for [tex]y[/tex] in [tex]3x+2y=18[/tex].
[tex]3x+2(0)=18\\ 3x=18\\ x=6[/tex]
So, the intersecting point is [tex](6,0)[/tex].
Find the intesecting point of [tex]2x+y=10,3x+2y=18[/tex].Add [tex]-2[/tex] times [tex]2x+y=10[/tex] to [tex]3x+2y=18[/tex].
[tex]-2(2x+y)+3x+2y=-2(10)+18\\ -4x-2y+3x+2y=-20+18\\ -x=-2\\ x=2[/tex]
Substitute [tex]x=2[/tex] in [tex]2x+y=10[/tex]:
[tex]2(2)+y=10\\ 4+y=10\\y=6[/tex]
So, the intersecting point is [tex](2,6)[/tex].
The origin [tex](0,0)[/tex] is also a intersecting point of [tex]x\geq 0,y\geq 0[/tex].Corner points:
The corner points are the boundary points of the bounded region of the given constraints.
The bounded region of the given constraints is shown below.
From the graph notice that the shaded region is the required bounded region of the given constraints.The boundary points are [tex](0,0),(5,0),(0,9),(2,6)[/tex].Evaluate the objective function [tex]C=3x-2y[/tex]at these boundary points:
At [tex](0,0)[/tex]:
[tex]C=3(0)-2(0)\\C=0[/tex]
At [tex](5,0)[/tex]:
[tex]C=3(5)-2(0)\\C=15[/tex]
At[tex](0,9)[/tex]:
[tex]C=3(0)-2(9)\\C=-18[/tex]
At[tex](2,6)[/tex]:
[tex]C=3(2)-2(6)\\C=6-12\\C=-6[/tex]
From the above calculated values, one can notice that the maximum value of [tex]C[/tex] is 15 and it is obtained at [tex](5,0)[/tex].
Hence, the maximum value of [tex]C[/tex] is 15 occurs at the corner point [tex](5,0)[/tex].
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When Grace runs the 400 meter dash, her finishing times are normally distributed with a mean of 76 seconds and a standard deviation of 2 seconds. What percentage of races will her finishing time be faster than 79 seconds, to the nearest tenth?
Answers
Answer:
0.07
Step-by-step explanation:
If you cut a 12-inch loaf of bread into -inch slices, you would have ______
slices of bread.
Answers
Answer:
12 divided by 1/2 = 24
Step-by-step explanation:
Consider the function f(x) = x5 – 3x2 + 5x. Let g(x) = f(–x + 4). Which shows the graphs of f(x) and g(x)
Answers
Answer:
The first graph
Step-by-step explanation:
I think it is the first one because I remember doing this. If this is wrong please forgive me. Have a wonderful day!
First graph shows the function f(x) and g(x).
What is graph?" Graph is representation of the coordinates on the coordinate plane along x-axis and y-axis."
According to the question,
Given function,
[tex]f(x) = x^{5} -3x^{2} +5x\\\\g(x) = f(-x+4)[/tex]
Plot the given functions on the graph we get,
Compare the drawn graph with the given graph.
First graph is same as graph drawn for the function f(x) and g(x).
Hence, we conclude that first graph shows the function f(x) and g(x).
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A calculator that is regularly priced $20 is on
sale for 40% off. What is the sale price of the
calculator?
Answers
Answer:
$12.00
Step-by-step explanation:
a product that normally costs $20 with a 40 percent discount will cost you $12.00, and you saved $8.00.
Find the coordinate of point X inside segment BE that is 3/4 the
distance from B to E.
Answers
Answer:
i really dont know
Step-by-step explanation:
this is confusing
Use the distributive property to write the expression without parentheses. Then simplify.
[tex]-\frac{1}{6} (6y+7)[/tex]
Answers
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment
