Answers
52.38 inch² & 261.90 inch²
Step-by-step explanation:Here we need to find the area of the sector . So according to formula we know the area of sector as ,
\(\boxed {\sf Area_{(sector)}= \dfrac{\theta}{360}\times \pi r^2 }\)
Here we can see that the central angle subtended by the arc is 60° and the radius of the circle is 10 inches . So the required area would be ,
=> Area = ∅/ 360° × π r²
=> Area = 60°/360° × 22/7 × (10in.)²
=> Area = 1/6 * 22/7 * 100 in²
=> Area = 52 .380 in²
★ Hence the area of the red sector is 52.38 inch²._________________________________
Now let's find out the area of blue sector .The angle subtended by the arc will be (360-60)°=300° .
=> Area = 300/360 × 22/7 × 100 in²
=> Area = 261. 90 in²
★ Hence the area of blue sector is 261.90 inch².\(\boxed{\red{\sf Area _{(red \ sector )} = 52.38 in^2 }}\)
\(\boxed{\blue{\sf Area _{(blue \ sector )} = 261.90 in^2 }}\)
Related Questions
An aircraft landing gear has a probability of 10-5 per landing of being damaged from excessive impact. What is the probabiliry rhar the landin[ gear will survive a 10,000 landing design life without damage
Answers
The probability that the landing gear will survive a 10,000 landing design life without damage is approximately 0.905.
Given, The probability of an aircraft landing gear being damaged due to excessive impact is 10-5 per landing.In other words, the probability of the landing gear being damaged due to excessive impact is 1 out of 100,000.
Therefore, the probability of the landing gear not being damaged due to excessive impact is
1 - (1/100,000) = 99,999/100,000.
To find the probability that the landing gear will survive a 10,000 landing design life without damage, we need to find the probability that the landing gear will not be damaged in each of the 10,000 landings.
Using the formula for independent events, we can find the probability of the landing gear not being damaged in 10,000 landings: P(surviving 10,000 landings)
= (99,999/100,000)^10,000
= 0.905
Thus, the probability that the landing gear will survive a 10,000 landing design life without damage is approximately 0.905.
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Match each expression with its value. −9 7 −2 Undefined h( 3.999 ) h(4) h(4.0001) h(9)
Answers
The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.
Let's match each expression with its corresponding value:
Expression: -9
Value: -9
Expression: 7
Value: 7
Expression: -2
Value: -2
Expression: Undefined
Value: Undefined
Expression: h(3.999)
Value: Undefined
Expression: h(4)
Value: 8
Expression: h(4.0001)
Value: Undefined
Expression: h(9)
Value: Undefined
Now let's explain the reasoning behind each value:
The expression -9 represents the number -9, so its value is -9.
Similarly, the expression 7 represents the number 7, so its value is 7.
The expression -2 represents the number -2, so its value is -2.
When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.
For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.
The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.
Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.
Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.
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In an initial survey designed to estimate the percentage of time air-express cargo loaders are idle, an analyst found that loaders were idle in 5 of the 55 observations.a. What is the estimated percentage of idle time
Answers
The estimated percentage of idle time for air-express cargo loaders is approximately 9.09%.
To calculate the estimated percentage of idle time, we need to divide the number of observations in which the loaders were idle by the total number of observations and multiply by 100.
In this case, the loaders were idle in 5 out of 55 observations. Dividing 5 by 55 gives us 0.0909. Multiplying this by 100, we find that the estimated percentage of idle time is approximately 9.09%.
This means that, based on the initial survey, it is estimated that the loaders are idle approximately 9.09% of the time. This information provides an insight into the frequency or occurrence of idle periods for the air-express cargo loaders and can be used to evaluate their efficiency or productivity.
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A square playground is covered with pebbles, except for two equal sized triangular portions that have grass. How many square feet do the pebbles cover?
Answers
The pebbles cover an area of 147 sq ft. We can use the Pythagorean theorem to find the solution.
Let's call the length of the third side of the triangle "x".
Since the two triangles are equal in size, and they share two sides with the square, we can use the Pythagorean theorem to find x.
a² + b² = c²
7² + 7² = c²
49 + 49 = c²
98 = c²
c = sqrt(98)
c = 7sqrt(2)
So each triangle has a base of 7ft and a height of 7sqrt(2)ft.
Area of each triangle = (base * height) / 2 = (7 * 7sqrt(2)) / 2 = 24.5 sq ft
Since there are two triangles, the total area of the grass is 24.5 sq ft * 2 = 49 sq ft
The square has an area of 14ft * 14ft = 196 sq ft
The pebbles cover an area of 196 sq ft - 49 sq ft = 147 sq ft.
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Complete question is in the image attached
how many base cases does a proof by the weak form of the principle of mathematical induction require?
Answers
The answer is two base cases, using induction.
What is induction ?
Weak induction is when an inductive mathematical proof holds true for all integers in a set of countable proofs. Natural numbers typically use this. The base step and inductive step are used to prove a set, making it the simplest type of mathematical induction.
Two examples make up an induction proof. Without requiring any prior knowledge of other examples, the first, or base case, establishes the claim for n = 0. The induction process, which is used in the second case, demonstrates that if the assertion is true for any particular scenario where n = k, it must also be true for the subsequent case where n = k + 1.
If a statement true for n= k, accordily to induction it have to hold good for n = k+1,
Hence, base cases does a proof by the weak form of the principle of mathematical induction requires 2 bases.
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1. The graph of y = x2 is translated 4 units down and 3 units to the left. It is also stretched by a factor
of 4, then reflected in the x-axis.
Answers
Answer:
ok so first ur gonna do 4x3=12 then
Step-by-step explanation:
For annually compounded interest, what rate would result in a single investment doubling in 3 years?
Answers
Work Shown:
\(A = P*(1+r/n)^{n*t}\\\\2P = P*(1+r/1)^{1*3}\\\\2 = (1+r)^{3}\\\\(1+r)^{3} = 2\\\\1+r = \sqrt[3]{2}\\\\r = -1+\sqrt[3]{2}\\\\r \approx 0.25992\\\\\)
That converts to 25.992% after moving the decimal point two spots to the right. Round this value however your teacher instructs.
complete the square to rewrite the following equation in standard form
Answers
By completing the square, the equation in standard form is (x - 2)² + (y + 4)² = 4².
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represent the coordinates at the center of a circle.r represent the radius of a circle.From the information provided below, we have the following equation of a circle:
x² - 4x + y² + 8y = -4
x² - 4x + (-4/2)² + y² + 8y + (8/2)² = -4 + (-4/2)² + (8/2)²
x² - 4x + 4 + y² + 8y + 16 = -4 + 4 + 16
(x - 2)² + (y + 4)² = 16
(x - 2)² + (y + 4)² = 4²
Therefore, the center (h, k) is (2, -4) and the radius is equal to 4 units.
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Complete Question:
Complete the square to rewrite the following equation in standard form. x² - 4x + y² + 8y = -4.
Which number line model represents the expression -\dfrac23+\left(-\dfrac13\right)−
3
2
+(−
3
1
)minus, start fraction, 2, divided by, 3, end fraction, plus, left parenthesis, minus, start fraction, 1, divided by, 3, end fraction, right parenthesis?
Choose 1 answer:
Answers
Answer:
: If you cut it in 2 equal-sized pieces and eat one, you have eaten ... whole number - you will get a fraction equivalent to 1/ 2
Answer:
XD yall all ways doing this to me so yall somthings don't give me the Answer
Step-by-step explanation:
A regular octagon has an area of 288 square centimeters and an apothem of 12 cm. what is the length of each side of the octagon?
Answers
The length of each side of the octagon is 6 cm
What is an octagon?It is a polygon with eight sides and eight angles. There are a total of 20 diagonals in it. All its interior angles sum up to 1080°.
Given that, a regular octagon has an area of 288 square centimeters and an apothem of 12 cm.
We need to find the side of the octagon,
We know that area of the octagon = 8/2 × side × apothem
Therefore,
288 = 8/2 × side × 12
side = 288 / 48
side = 6
Hence, the length of each side of the octagon is 6 cm
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Trigonometry
Find the value of x in the given
right triangle.
12
x = [ ?]
5
Enter your answer as a decimal rounded to the
nearest tenth
![TrigonometryFind the value of x in the givenright triangle.12x = [ ?]5Enter your answer as a decimal](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/qFjaIvwHL6uSmUfzBfVtXiUBA9DKuPkw.png)
Answers
Answer:
x ≈ 65.4 °
Step-by-step explanation:
cos x = \(\frac{adjacent}{hypotenuse}\)
Cos x = \(\frac{5}{12}\)
Cos x = 0.4167
x = Cos⁻¹ (0.1467)
x ≈ 65.4 °
X=65.4°
\(solution \\ cos \: x = \frac{5}{12} \\ x = {cos}^{ - 1} \frac{5}{12} \\ x = 65.3756 \\ x = 65.4\)
hope this helps..
Good luck on your assignment
U(C,l)=20C 2/3
+4l 2/3
where C>0 denotes household consumption of papayas and 0≤l≤h denotes household leisure. A) (15 points) Solve for the household's papaya consumption demand function C D
(ω,Π,h), its leisure demand function, l D
(ω,Π,h), and its labour supply function, N S
(ω,Π,h) B) (10 points) Determine whether each of these functions are decreasing in, increasing in, or independent of each of the following parameters and provide economic intuition for your results: C) (10 points) Determine whether the labour supply function is decreasing in, increasing in, or independent of ω (you can do this by computing the partial derivative of N S
(ω,Π) with respect to ω and determining if it is negative, positice, or zero OR by choosing some arbitrary values for h and Π and calculating N S
for various values of ω to determine how N S
changes when ω changes). Explain what your result must imply about the relationship between the substitution effect and the income effect of a change in the real wage on the household's optimal leisure choice in this economy. D) (10 points) Suppose the coefficient on leisure in the utility function increases from 4 to 5. Determine whether this decreases, increases, or has no effect on the household's labour supply and papaya consumption demand and provide economic intuition for your answer. l+N=h where h= Total time Λ= lisure, N= hours worked Lets form Budget constraint ⇒
⇒
c=π+ωN
c=π+ω(h−l)
c+ωl=π+ωh
Now we have to Maximize: 20c 2/3
+4l 2/3
Subject to: c+ωl=π+ωh Ligrange is given by: α=20c 2/3
+4l 2/3
+α(π+ωh−c−ωl) First Oeder Condition: ∂c
∂L
=0⇒20( 3
2
) c 1/3
1
=α→(2)
∂l
∂α
=0⇒4( 3
2
) l 1/3
1
=αω⇒(3)
Dividing (2) from (3) we get: c 1/3
5l 1/3
= ω
1
⇒c=(5w) 3
l=125w 3
l Rultriy this in (1) we get: 125ω 3
l+ωl=π+ωh ⇒l= 125ω 3
+ω
π+ωh
→h leesure demand function. ⇒C=125ω 3
l ⇒C=125ω 3
[ 125ω 3
+ω
π+ωh
]→ Bread Cousumption ⇒N=h−l= 125ω 3
+ω
π+ωh
] function. ⇒N S
= 125ω 3
+ω
125ω 3
h−π
→ lakar Supply function.
Answers
The household's papaya consumption demand function is C_D(ω, Π, h) = 125ω^(3/5)[125ω^(3/5) + Π + ωh]^(2/3). The leisure demand function is l_D(ω, Π, h) = 125ω^(3/5)[125ω^(3/5) + Π + ωh]^(1/3), and the labor supply function is N_S(ω, Π, h) = h - l_D(ω, Π, h).
To solve for the household's papaya consumption demand function, we substitute the given utility function U(C, l) = 20C^(2/3) + 4l^(2/3) into the budget constraint c + ωl = Π + ωh.
Using the Lagrange multiplier method, we form the Lagrangian function L = 20C^(2/3) + 4l^(2/3) + α(c + ωl - Π - ωh).
Taking first-order conditions with respect to C and l, we obtain two equations: 20(2/3)C^(-1/3) = α and 4(2/3)l^(-1/3) = αω.
Dividing the two equations, we find C^(1/3)/l^(1/3) = ω^(1/5), which implies C = 125ω^(3/5)[125ω^(3/5) + Π + ωh]^(2/3).
Substituting this result into the budget constraint, we solve for l and find l = 125ω^(3/5)[125ω^(3/5) + Π + ωh]^(1/3).
Finally, the labor supply function is obtained as N_S = h - l_D.
In summary, the household's papaya consumption demand function is C_D(ω, Π, h) = 125ω^(3/5)[125ω^(3/5) + Π + ωh]^(2/3), the leisure demand function is l_D(ω, Π, h) = 125ω^(3/5)[125ω^(3/5) + Π + ωh]^(1/3), and the labor supply function is N_S(ω, Π, h) = h - l_D(ω, Π, h).
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A student uses the equation tan theta= s^2/49 o represent the speed, s, in feet per second, of a toy car driving around a circular track having an angle of incline theta where sin theta =1/2
Answers
After finding the value of theta, the speed of the toy car driving around the circular track with an angle of incline theta, where sin(theta) = 1/2, is equal to √(7√3) feet per second.
The equation tan(theta) = s^2/49 represents the speed, s, in feet per second, of a toy car driving around a circular track with an angle of incline, theta, where sin(theta) = 1/2.
To solve this problem, we need to use the given information about sin(theta) to find the value of theta. Since sin(theta) = 1/2, we can determine that theta is equal to 30 degrees.
Now that we know the value of theta, we can substitute it into the equation tan(theta) = s^2/49. Plugging in 30 degrees for theta, the equation becomes tan(30) = s^2/49.
The tangent of 30 degrees is equal to √3/3. So, we have √3/3 = s^2/49.
To solve for s, we can cross multiply and solve for s^2. Multiplying both sides of the equation by 49 gives us 49 * (√3/3) = s^2.
Simplifying, we get √3 * 7 = s^2, which becomes 7√3 = s^2.
To find the value of s, we take the square root of both sides. So, s = √(7√3).
Therefore, the speed of the toy car driving around the circular track with an angle of incline theta, where sin(theta) = 1/2, is equal to √(7√3) feet per second.
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You buy a pair of jeans at a department store. A receipt, titled "Department Store". It shows the bill for a pair of jeans. Jeans, 39.99; Discount, negative 10.00; Subtotal, 29.99; Sales Tax, 1.95; Total, 31.94. The line at the bottom reads, Thank You. a. What is the percent of discount to the nearest percent? The percent of discount is %. b. What is the percent of sales tax to the nearest tenth of a percent? The percent of sales tax is %. c. The price of the jeans includes a 60% markup. After the discount, what is the percent of markup to the nearest percent? The percent of markup is %.
Answers
Answer:
25%
6.5%
35%
Step-by-step explanation:
Given the invoice :
Bill for a pair of Jean
Jeans ______39.99
Discount ___ - 10.00
Subtotal ____ 29.99
Sales tax ____ 1.95
Total _______ 31.94
A) % of discount to the nearest %
Discount amount = % discount * price
10 = x% * 39.99
10/39.99 = x%
0.2500625 = x%
x = 0.2500625 * 100%
% discount = 25%
% of sales tax:
Sales tax amount = % tax * Subtotal
1.95 = x% * 29.99
1.95/29.99 = x%
0.06502 = x%
x = 0.06502 * 100%
x = 6.5%
Markup before discount = 60%
Markup after discount = (60 - 25)% = 35%
The perimeter of an equilateral triangle is 126mm.
State the length of one of its sides.
Answers
Answer:
126 mm / 3 = 42 mm
The length of each side of this equilateral triangle is 42 mm.
Which student's answer most accurately describes the solution to the inequality x less-than negative 3? Andie's Solution -contains only negative rational numbers -has a lower limit of –3 and no maximum value Bobby's Solution -contains positive and negative rational numbers -has an upper limit of –3 and no minimum value Carrie's Solution -contains positive and negative rational numbers -has a lower limit of –3 and no maximum value Deshawn's Solution -contains only negative rational numbers -has an upper limit of –3 and no minimum value Andie's Bobby's Carrie's Deshawn's
Answers
Answer: bobby
Step-by-step explanation:
Answer:
Its Carrie’s
The person who is above is wrong
Step-by-step explanation:
99999 help me plz plz plz plz
Answers
Answer:
hi
Step-by-step explanation:
i think 10 in
hope it helps
Answer:
10
Step-by-step explanation:
The triangles are the same size, and if you look at the picture, you can see that MN and QR are the same, making QR 10 in.
Plsss help plssssssss
Answers
X:2
Y:6
Answer:
x = 2
y = 6
Step-by-step explanation:
We have a system of equations and are asked to solve for x and y.
y = -2x + 10
y = 3x
Since both equations start with y, we can subtitute.
3x = -2x + 10
Solve for x :
Add 2x to both sides :
5x = 10
Divide 5 from both sides :
x = 2
Now substitute x in the second equation because it's more easier :
y = 3(2)
3(2)
6
y = 6
what is the answer to this ?
Answers
-25x + 40
Step-by-step explanation:
-8 (4x-5) + 7x
-32x + 40 + 7x
-32x +7x + 40
-25x + 40
Use the solution method from this example to find a basis for the given subspace. S = span {[1 -1 0 2], [3 -5 4 8], [0 1 -2 -1]} Give the dimension of the basis. v
Answers
Answer:
Step-by-step explanation:
The dimension of the basis is {[1 0 0 2], [-1 1 0 0]}.
To find a basis for the subspace S = span {[1 -1 0 2], [3 -5 4 8], [0 1 -2 -1]}, we can use the same method as in the example. First, we put the vectors in a matrix and row-reduce it:
[1 -1 0 2]
[3 -5 4 8]
[0 1 -2 -1]
R2 - 3R1 -> R2
R3 -> R3 + 2R1
[1 -1 0 2]
[0 -2 4 2]
[0 1 -2 -1]
-1/2R2 -> R2
[1 -1 0 2]
[0 1 -2 -1]
[0 1 -2 -1]
R3 - R2 -> R3
[1 -1 0 2]
[0 1 -2 -1]
[0 0 0 0]
We can see that the last row is all zeros, so we have only two pivots and one free variable. This means that the dimension of the subspace S is 2. To find a basis, we can write the pivots as linear combinations of the original vectors:
[1 -1 0 2] = [1 0 0 2] + [-1 1 0 0]
[0 1 -2 -1] = [0 1 -2 -1]
Therefore, a basis for S is {[1 0 0 2], [-1 1 0 0]}.
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the perimeter of a pool table is 30ft. The table is twice as long as it is wide. What is the length of the pool table?
Answers
10 ft pls like if it helped
Find the radius of convergence R of the series. [infinity] Σn=1 (7^n (x + 6)^n)/√n R = Find the interval of convergence I of the series. (Enter your answer using interval notation.) I =
Answers
The radius of convergence R is infinite.∞Σn=1(7^n(x+6)^n)/√n.
The interval of convergence I is (-∞,∞).
The given series is: ∞Σn=1(7^n(x+6)^n)/√nTo find the radius of convergence (R), we will apply the Ratio Test. The Ratio Test states that if the limit of the ratio of the absolute values of the (n+1)th term and the nth term of the given series exists, then the series is absolutely convergent. If the limit is infinity, then the series is divergent. If the limit is zero, then the series is conditionally convergent.Let's apply the Ratio Test on the given series: limn→∞|(7^(n+1) (x+6)^(n+1))/√(n+1) | / |(7^n (x+6)^n)/√n | limn→∞ |7^(n+1) (x+6)^(n+1)|/ |7^n (x+6)^n| √n/√(n+1) limn→∞ |7(x+6)|/√(n+1) = 7|x+6|* limn→∞1/√(n+1) = 0The limit exists and is zero. Thus, the series is absolutely convergent. Hence, the series is convergent for all values of x. Therefore, the radius of convergence R is infinite.∞Σn=1(7^n(x+6)^n)/√nThe interval of convergence (I) of the given series is the set of values of x for which the series converges. From the Ratio Test, we have proved that the series is convergent for all values of x. Therefore, the interval of convergence I is the set of all real numbers. Hence, the interval of convergence I is (-∞,∞).
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Which is equivalent to 4(x – 1)?
Answers
Answer:
=4*x-4*1
= 4x - 4 is equivalent to 4(x-1)
Write a conjecture that describes the pattern in each sequence. Then use your conjecture to find the next item in the sequence. 1, 10, 100, 1000
Answers
The conjecture that describes the pattern in each sequence is *10, the next item in the sequence. 1, 10, 100, 1000 is 10000.
What is a geometric sequence and how to find its nth terms?Suppose the initial term of a geometric sequence is a
and the term by which we multiply the previous term to get the next term is r
Then the sequence would look like
\(a, ar, ar^2, ar^3, \cdots\)
(till the terms to which it is defined)
Thus, the nth term of such sequence would be T_n = ar^{n-1} (you can easily predict this formula, as for nth term, the multiple r would've multiplied with initial terms n-1 times).
Given;
The following sequence that can be used in our computation:
1,10,100,1000
In the above sequence, we can see that 4 is added to the previous term to get the current term
Using the above as a guide,
Next term = 1000*10
Evaluate
Next term = 10000
Therefore, the next term of sequence will be 10000.
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Give me a step by step answer for 15 x 64
( please make it simple) thanks
Answers
Step-by-step explanation:
15 x 64 = 15 x (60 + 4)
= (15x60) + (15x4)
= 900 + 60
= 960
can I get help with this please
Answers
Answer:
10d or less
Step-by-step explanation:
Joanne would want $50 left, and she has $250. 20 - 50 is 200. 20 goes into 100 5 times.
20 goes into 200 10 times. You just add five. (20, 40, 60, 80, 100)
If she wants at least $50 left, she would have to limit how many Dvd's she buys to 10 or less.
(MARK BRAINLIST)
ANYONE KNOWS ANY CHINESE DRAMA PLEASE TELL ME SOME DRAMAS
THANK YOU!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Spirit Realm
Hello, My Shining Love
Find the exact length of the third side.
4
2
Answers
Answer:
Step-by-step explanation:
4-2<x<4+2
2<x<6
x = 3, 4 or 5
i assume u r talking about triangle
Solve = 3/5k + 7/10 = 11/15k – 2/5
Answers
i get 11/2 is this wright answer??
IF YOU MIGHT KNOW THIS THEN TRY IT/ BRIANLIEST
Answers
Answer letter d