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 Two-thirds divided by one-sixth? An area model with 4 shaded parts and 2 unshaded parts. The shaded parts are labeled two-thirds. 2 3 4 6
Answers
Two thirds divided by one sixth is 4
Answer:
It is number four
Step-by-step explanation:
Martha types a 4−digit code into a keypad to unlock her car doors. The code uses the numbers 1 and 0. If the digits are selected at random, what is the probability of getting a code with exactly two 1's? Enter your answer as a simplified fraction.
The probability of getting two 1's is_________.
Answers
Answer:
3/8
Step-by-step explanation:
1. We list all codes that start with 0 and have 0 as second digit:
2. We list all codes that start with 0 and have 1 as second digit:
3. We list all codes that start with 1 and have 0 as second digit:
4. We list all codes that start with 1 and have 1 as second digit:
5. We find the number of codes which have exactly 2 zeros: 6 codes
6. The total number of outcomes is: 16 codes
7. We find the probability that the number of codes has exactly 2 zeros: 6/16 3/8
Answer:
The probability of getting two 1's is 3/8
Step-by-step explanation:
Martha types a 4−digit code into a keypad to unlock her car doors.
The code uses the numbers 1 and 0
So the sample space of all the possible combinations is given by
1. 0 0 0 0
2. 0 0 0 1
3. 0 0 1 0
4. 0 0 1 1
5. 0 1 0 0
6. 0 1 0 1
7. 0 1 1 0
8. 0 1 1 1
9. 1 0 0 0
10. 1 0 0 1
11. 1 0 1 0
12. 1 0 1 1
13. 1 1 0 0
14. 1 1 0 1
15. 1 1 1 0
16. 1 1 1 1
So there are total 16 possible outcomes.
Now count the number of combinations that has exactly two 1's
4. 0 0 1 1
6. 0 1 0 1
7. 0 1 1 0
10. 1 0 0 1
11. 1 0 1 0
13. 1 1 0 0
So there are 6 possible outcomes with exactly two 1's
The required probability is
P(two 1's) = Number of outcomes with two 1's/Total number of outcomes
P(two 1's) = 6/16
P(two 1's) = 3/8
Therefore, the probability of getting two 1's is 3/8
Easy way to get points: What is 1+2+3+4+5+6+7+8+9+10?
Answers
Answer:55
Step-by-step explanation:addition
Which statements are true regarding the quadratic statement?
Answers
Answer:
E
Step-by-step explanation:
I hope am right coz it seems most appropriate
The shorter leg of a right triangle is 21 feet less than the other leg. Find the length of the two legs if the hypotenuse is 39 feet.
Answers
Answer:
leg 1= 36 feet
leg2 = 15 feet
Step-by-step explanation:
Hi, we have to apply the Pythagorean Theorem:
c^2 = a^2 + b^2
Where c is the hypotenuse of the triangle (in this case the distance between Doreen’s house and the tower) and a and b are the other legs.
leg1 = x
leg2 = x-21 (21 feet less than the other leg)
Replacing with the values given:
39^2 = x^2 + (x-21)^2
1,521 = x^2 + x^2 -42x +441
0 = 2x^2 -42x +441-1,521
0= 2x^2 -42x -1,080
For: ax2+ bx + c
x =[ -b ± √b²-4ac] /2a (quadratic formula)
Replacing with the values given:
x=-(-42)± √(-42)²-4(2)-1080] /2(2)
x= 42± √10,404] /4
x = 42± 102 /4
Positive:
x = 42+102 /4 = 36
leg 1= 36
leg2 = 36-21 =15
Feel free to ask for more if needed or if you did not understand something.
The length of shorter leg is 15 feet and other leg is 36 feet.
Pythagoras theorem:Let us consider that, length of shorter leg is x feet.
So that, length of other leg is [tex](x+21)[/tex] feet.
It is given that, the hypotenuse is 39 feet.
Apply Pythagoras theorem,
[tex]x^{2} +(x+21)^{2} =(39)^{2}\\ \\x^{2} +x^{2} +441+42x=1521\\\\2x^{2} +42x-1080=0\\\\x=15 ,-36[/tex]
Since, side can not be negative.
So that, we have to consider x=15 feet.
Length of other leg[tex]=x+21=15+21=36feet[/tex]
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Declaring war and coining money are considered
states' rights.
implied powers.
national rights.
expressed powers.
Answers
Answer: Expressed powers
Step-by-step
3x-2≤5(x+2) . show all steps please.
Answers
Answer:
-6 ≤x
Step-by-step explanation:
3x-2≤5(x+2)
Distribute
3x-2≤5x+10
Subtract 3x
3x-2-3x≤5x +10-3x
-2 ≤2x+10
Subtract 10 from each side
-2-10 ≤2x+10-10
-12 ≤2x
Divide by 2
-12/2≤2x/2
-6 ≤x
Answer:
Step-by-step explanation:
You have to first use the distributive property of 5(x+2)
That would be 5x+10.
So it would be all together
[tex]3x-2\leq 5x+2[/tex]
to see if it is true
x=2
6-2
[tex]6-2\leq 10+2\\4\leq 12[/tex]
it is true
F(x) = x^2, g(x) = 2/3 x^2 comparison
Answers
Answer:
g(x) is a vertical compression of f(x)
Step-by-step explanation:
Equation of graph 1 :[tex]f(x)=x^2[/tex]
Equation of graph 2 :[tex]g(x)=\frac{2}{3}x^2[/tex]
f(x)→a f(x)
Its is case of vertical stretch or compression
Vertical stretch if |a|>1
Vertical compression if 0<|a|<1
f(x)→a f(x)
So, [tex]x^2[/tex] →[tex]\frac{2}{3}x^2[/tex]
So, [tex]a= \frac{2}{3}=0.67[/tex]
So,0<|a|<1
So,It is a case of vertical compression
So, g(x) is a vertical compression of f(x)
Determine whether the two triangles can be proven congruent using the AAS congruence method. If they can, select the congruence statement. answers: A) ΔABC ≅ ΔEDC B) ΔCBA ≅ ΔCED C) The triangles aren't congruent using AAS. D) ΔCAB ≅ ΔEDC
Answers
Answer:
A) ΔABC ≅ ΔEDC
Step-by-step explanation:
To prove triangles congruent with the AAS method, you need two angles and the non-included side of one triangle to be congruent to the corresponding parts of another triangle.
Let's see what we have in these two triangles.
Side AB is congruent to side ED. This is one pair of sides.
Angle A is congruent to angle E. This is one pair of sides.
Now we need a second pair of angles, that will make the two sides not-included in the angles.
By the congruence of vertical angles, we see that angles ACB and ECD are congruent. This is another pair of congruent angles.
We have two angles and a non-included side of one triangle congruent to two angles and a non-included side of another triangle. The triangles are congruent by AAS.
Answer: A) ΔABC ≅ ΔEDC
What is the base of a triangle that has a height of 6 centimeters and an area of 18 centimeters? Use the formula h = StartFraction 2 A Over b EndFraction, where A represents the area of the triangle, h represents the height, and b represents the length of the base. One-third centimeter Two-thirds centimeters 3 Centimeters 6 Centimetersc
Answers
Answer:
h = 6 cm
Step-by-step explanation:
Atriangle = b×h/2
18cm² = 6cm×h/2
36cm² = 6cm×h
h = 36cm²/6cm
h = 6 cm
Answer:
Base = 6 cm
Step-by-step explanation:
Area of Triangle = [tex]\frac{1}{2} .{base}.{Height}[/tex]
Where A = 18 cm², h = 6 cm
Putting in the above formula
18 = [tex]\frac{1}{2}[/tex](base)(6)
18 = 3(base)
base = 18/3
Base = 6 cm
Alison, the owner of a regional chain of pizza stores, is trying to decide whether to add calzones to the menu. She conducts a survey of 700 people in the region and asks whether they would order calzones if they were on the menu. 46 people responded “yes.” Create a 90% confidence interval for the proportion of people in the region who would order calzones if they were on the menu.Round your answer to four decimal places.
Answers
Answer:
Step-by-step explanation:
Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 700
x = 46
p = 46/700 = 0.066
q = 1 - 0.066 = 0.934
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.05 = 0.95
The z score corresponding to the area on the z table is 1.645. Thus, the z score for a confidence level of 90% is 1.645
Therefore, the 90% confidence interval is
0.066 ± 1.645√(0.066)(0.934)/700
= 0.066 ± 0.0094
The lower limit of the confidence interval is
0.066 - 0.0094 = 0.0566
The upper limit of the confidence interval is
0.066 + 0.0094 = 0.0754
Answer:
(0.0503, 0.0811).
Step-by-step explanation:
The confidence interval for the unknown population proportion p is (p^−z⋆p^(1−p^)n−−−−−−−−√,p^−z⋆p^(1−p^)n−−−−−−−−√). The confidence interval can be calculated using Excel.
1. Identify α. Click on cell A1 and enter =1−0.90 and press ENTER.
2. Thus, α=0.1. Enter the number of successes, x=46, and sample size, n=700, in the Excel sheet in cells A2 and A3. To find the proportion of successes, p^, click on cell A4 and enter =A2/A3 and press ENTER.
3. Thus, p^≈0.0657. Use the NORM.S.INV function in Excel to find z⋆. Click on cell A5, enter =NORM.S.INV(1−A1/2), and press ENTER.
4. The answer for z⋆, rounded to two decimal places, is z⋆≈1.64. To calculate the standard error, p^(1−p^)n−−−−−−−−√, click on cell A6 and enter =SQRT(A4∗(1−A4)/A3) and press ENTER.
5. The answer for the standard error, rounded to four decimal places, is p^(1−p^)n−−−−−−−−√≈0.0094. To calculate the margin of error, z⋆p^(1−p^)n−−−−−−−−√, click on cell A7 and enter =A5*A6 and press ENTER.
6. The answer for the margin of error, rounded to four decimal places, is z⋆p^(1−p^)n−−−−−−−−√≈0.0154. The confidence interval for the population proportion has a lower limit of A4−A7=0.0503 and an upper limit of A4+A7=0.0811. Thus, the 90% confidence interval for the population proportion of people in the region who would order calzones if they were on the menu, based on this sample, is approximately (0.0503, 0.0811).
Yolanda participated in a walkathon in which each kilometer walked raised $10 for charity. Her goal was to raise more than $300 on Saturday and Sunday. She raised $50 on Saturday. Which graph shows all the distances, in kilometers, that Yolanda could have walked on Sunday to reach her goal?
Answers
Answer:
B
Step-by-step explanation:
She needed to raise at least $250
$250 divided by $10 equals 25 km
So she need more than 25km to raise over $300
M is directly proportional to r3
When r = 4, M = 160
a) Work out the value of M when r = 2.
Answers
Answer:
M = 20
Step-by-step explanation:
Given that M is directly proportional to r³ then the equation relating them is
M = kr³ ← k is the constant of proportion
To find k use the condition when r = 4, M = 160, that is
160 = k × 4³ = 64k (divide both sides by 64 )
2.5 = k
M = 2.5r³ ← equation of proportion
When r = 2, then
M = 2.5 × 2³ = 2.5 × 8 = 20
Answer:
M<varies>r³
M=kr³(k= constant)
when M=160,r=4
160=k(4)³
160=64k
k=2.5
therefore,M=2.5r³
when r=2
M=2.5r³
M=2.5(2)³
M=2.5(8)
M=20
Solve this inequality.
-5x + 7 > 42
A. x> 245
B. x < -175
C. x > 7
D. x < -7
Answers
Answer:
x < -7
Step-by-step explanation:
-5x + 7 > 42
Subtract 7 from each side
-5x + 7-7 > 42-7
-5x > 35
Divide each side by -5, remembering to flip the inequality
-5x/-5 <35/-5
x < -7
Which angles are acute?
А в
H
Check all that apply.
Answers
Answer:
The answer is A and D.
Step-by-step explanation:
Acute angles are angles that are less than 90°.
0° < θ < 90°.
So by looking at the diagram, any angles that are smaller than a L-shaped(90°) are all acute angle.
In the diagram shown,
ABCE is a trapezium,
AD is parallel to BC,
DE = 4cm,
Area of ABCE = 60cm^2,
Area of ABCD = 48cm^2,
Work out the values of f and g.
You must show all your working.
Answers
The values of f and g are;
f = 6
f = 6g = 8
We are given the trapezium ABCE where;
AD is parallel to BC
DE = 4 cm
Area of ABCE = 60 cm²
Area of ABCD = 48 cm²
f and g are sides of the rectangle ABCD. Thus;
fg = 48 - - - (eq 1)
Also,for the trapezium ABCE;
½(g + g + 4)f = 60
(2g + 4)f = 120 - - - (eq 2)
From eq 1, f = 48/g
Thus;
(2g + 4) × (48/g) = 120
96 + 192/g = 120
192/g = 120 - 96
192/g = 24
g = 192/24
g = 8
Thus;
8f = 48
f = 48/8
f = 6
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Which ordered pair maximizes the objective function P = 3x + 8y?
оооо
(0, 0)
(2, 7)
(5, 6)
о(8, 1)
Answers
Answer:
(5,6)
Step-by-step explanation:
I think you are asking whats the biggest sum you can get out of the ordered pairs. If you are I'm pretty sure (5,6) is correct. If you are not asking that, I am sorry.
15 POINTS!!!
Solve 3(−3−3x)+4=−5.
The solution is x=___
Answers
One solution was found :
x = 0
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
3*(-3-3*x)+4-(-5)=0
Step by step solution :
Pull out like factors :
-3 - 3x = -3 • (x + 1)
Equation at the end of step 2 :
(-9 • (x + 1) + 4) - -5 = 0
Equation at the end of step 3 :
-9x = 0
Step 4 :
Solving a Single Variable Equation :
4.1 Solve : -9x = 0
Multiply both sides of the equation by (-1) : 9x = 0
Divide both sides of the equation by 9:
x = 0
One solution was found :
x = 0
Select the correct product.
(y+ z)3
y 3+3y2z+ 3yz 2 + z 3
y 3 y+ 3 z
y 3 z 3
y 3 + z 3
Answers
Answer:
Step-by-step explanation:
Please help me! I'm terrible at math
Answers
Answer:
(3.) x = 45
Step-by-step explanation:
Because the lines are parallel and cut by the same line, the angles within are equal as well.
Which means that...
Angle GE = Angle EFD
Therefore (2x-30) = (x + 15)
2x - 30 = x + 15
+30 +30 (add 30 to both sides to get rid of the -30)
2x = x + 45
-x -x (subtract x from both sides to get rid of the single positive x)
x = 45
If the nth term of a sequence is
on what is the 12th term?
If the nth term of a sequence is 28-3n what is the 7th term?
Answers
Answer:
7
Step-by-step explanation:
The nth term is supposed to help us find the value of any number in the sequence. All we have to do is substitute n for 7, in this case
So, this is the general term.
= 28 - 3n
Now, to find the 7th term, we simply replace "n" with "7"
= 28 - 3(7)
Since "n" was being multiplied with 3, 7 is also going to be multiplied with 3.
= 23 - 21
= 2
PLEASE HELP!! 25 POINTS
Answers
Answer:
1. f(x) and g(x)
2. g(x)
3. All
4. F(x) and H(x)
Step-by-step explanation:
graph them
Which algebraic expression is a polynomial with a degree of 5?
Answers
Find the equation of the line, in slope-
intercept form, that passes through the point
(-3. 2) and has slope 3.
of the equation for
Answers
Answer:
y= 3x +11
Step-by-step explanation:
slope-intercept form:
y= mx+c, where m is the gradient and c is the y-intercept.
Given that the slope is 3, m=3
substitute m=3 into the equation:
y= 3x +c
To find the value of c, substitute a coordinate.
When x= -3, y=2,
2= 3(-3) +c
c -9= 2
c= 9 +2 (+9 on both sides)
c= 11 (simplify)
Thus, the equation of the line is y= 3x +11.
Points A B C and D lie on a line consecutively so that AB = BC = CD = 6in. Find the distance between the midpoints of segments AB and CD.
Answers
Answer:
Distance of segments AB and CD = 12
Step-by-step explanation:
AB+BC + CD = 6+6+6 = 18inch
midpoint AB = 6/2 = 3
midpoint CD =6/2 = 3
Midpoint AB+Midpoint CD = 3+3 = 6
To solve we just 18-6 = 12
Distance of segments AB and CD = 12
Answer:
its 12
Step-by-step explanation:
Distance of segments AB and CD = 12
HELP! WILL GIVE BRAINLIEST!
Answers
Answer: The answer is A
Step-by-step explanation: There are different ways to solve this type of problem. One way I would do it is to use a piece of wax paper to trace the shape then rotate the paper to get the answer.
15 pts!!! will mark BRAINLIEST Sharon found a couch for $1,770.00. The sales person said it was on sale for 25% off. How much did Sharon pay for the couch if she also had to pay 6% sales tax on the total?
Answers
Answer:
$1407.15
Step-by-step explanation:
$1,770.00*0.25= $442.5
$1.770-$442.50 = $1327.5
$1327.5*0.06 = $79.65
$1327.50+$79.65 = $1407.15
what is -5+11y-3=25? will mark brainliest!!
Answers
Step-by-step explanation:
-5 +11y -3 = 25
11y = 25 + 5 + 3
11y = 33
y = 33/11
y = 3
-8+11y=25
11y=25+8
11y=33
y=33/11
y=3
I don’t need you to explain just answer.
Answers
Answer:
-4 <x< -2
Step-by-step explanation:
you need to plot the line between -4 and -2
Which of the following is the linear parent function?
A. Fx) = x
B. Fx) =1/x
C. F(x) = |x|
D. F(x) = x^3
Answers
Answer:
A linear parent function is the equation y = x or f(x) = x. A parent function is the simplest equation of a function. Thus, f(x) = x is the simplest of all linear functions and that is the reason why it is called linear parent function
Answer:
F(x) = x
Step-by-step explanation:
A line is of the form
x to the first power
1/x is not x to the first power and makes a curve
|x| makes a v shape
x^3 is a curve