A company is designing a new logo that is comprised of four identical sectors of circles that have central angles
that measure 30º. A portion of the logo is shaded. The distance from the center, C, to point A is 8 inches
and the distance from point A to point B is 3 inches.
Determine the area of the logo that is shaded to the nearest tenth of a
square inch. Show the work that leads to your answer.
Answers
============================================================
Explanation:
The radius of the larger circle is CB = CA+AB = 8+3 = 11 inches.
The area of the larger circle with this radius is...
A = pi*r^2
A = pi*11^2
A = 121pi
The area of the smaller circle (radius CA = 8 inches) is
A = pi*r^2
A = pi*8^2
A = 64pi
The difference is 121pi-64pi = 57pi
This represents the exact area of the full ring. Refer to figure 1 below. Specifically the red region of that figure.
However, we don't want the full ring. We only want a small fraction of it (as figure 2 shows, which is the original diagram your teacher gave you). Specifically, we want (4*30)/360 = 120/360 = 1/3 of the full ring. The 4*30 refers to the idea we have four copies of the 30 degree angle.
So we'll take 1/3 of the 57pi to get (1/3)*57pi = (57/3)pi = 19pi
-----------------------------------
The value 19pi is the exact area of the entire shaded region.
From here, you can use a calculator to determine that
19pi = 19*3.1415926535898 = 59.6902604182061 which rounds to 59.7
If your teacher insists you use pi = 3.14, then 19*pi = 19*3.14 = 59.66 which also rounds to 59.7
Related Questions
Solve the system by substitution.
y = -X
y = - 4x + 12
Answers
Answer:
The answer is ( - 8, 8) in point form or in x = -8 , y= 8 in equation form.
Answer:
Step-by-step explanation:
y = -x
y = -4x + 12
-x = -4x + 12
x = 4
y = -x = -4
Could someone help me please.
Answers
Answer:
D
Step-by-step explanation:
The expression is equal to 1/300
D is the only other one equal to 1/300
omplete the statement with always, sometimes, or never. Explain your reasoning. A median is __________ the same line segment as a perpendicular bisector.
Answers
A median is sometimes the same line segment as a perpendicular bisector.
A perpendicular bisector is a segment, line or plane that is perpendicular to a line segment and passes through the midpoint of that line segment. A median, on the other hand, is a line segment joining a vertex of a triangle to the midpoint of the opposite side. Both these concepts are significant in the study of geometry.
A median and a perpendicular bisector can coincide if and only if the triangle is isosceles, that is, two of its sides are of equal length. Since the two concepts are based on different conditions, the line segments or planes may or may not be identical. Thus, a median is sometimes the same line segment as a perpendicular bisector.
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Which are true and which are false?
Answers
Answer:
true
Step-by-step explanation:
if the first table in a cartesian join has five rows and the second table has three rows, the results will consist of ____________________ rows.
Answers
In a Cartesian join, also known as a cross join, each row from the first table is combined with each row from the second table.
If the first table has 5 rows and the second table has 3 rows, the result of the Cartesian join will consist of 5 * 3 = 15 rows.
A paper company needs to ship paper to a large printing business. The paper will be
shipped in small boxes and large boxes. The volume of each small box is 6 cubic feet
and the volume of each large box is 13 cubic feet. A total of 19 boxes of paper were
shipped with a combined volume of 156 cubic feet. Determine the number of small
boxes shipped and the number of large boxes shipped.
There were
Submit Answer
small boxes shipped and
large boxes shipped.
Answers
There were 13 small boxes shipped and 6 large boxes shipped.
Let's denote the number of small boxes as 's' and the number of large boxes as 'l'.
According to the given information, the volume of each small box is 6 cubic feet, so the total volume of all small boxes can be calculated as 6s cubic feet.
Similarly, the volume of each large box is 13 cubic feet, so the total volume of all large boxes can be calculated as 13l cubic feet.
We are also given that the combined volume of all the boxes is 156 cubic feet, so we can write the equation:
6s + 13l = 156 ...(1)
Additionally, we know that a total of 19 boxes were shipped, so we can write another equation:
s + l = 19 ...(2)
Now, we have a system of equations (equation 1 and equation 2) that we can solve simultaneously to find the values of 's' and 'l'.
To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method here.
From equation 2, we can rewrite it as s = 19 - l.
Substituting this value of s into equation 1, we get:
6(19 - l) + 13l = 156
Simplifying the equation:
114 - 6l + 13l = 156
Combining like terms:
7l = 42
Dividing both sides by 7:
l = 6
Now, we can substitute this value of l back into equation 2 to find the value of s:
s + 6 = 19
s = 13
The number of small boxes shipped is 13, and the number of large boxes shipped is 6.
There were 13 small boxes shipped and 6 large boxes shipped.
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Jackson was solving the problem below for k. However, he made a mistake.
19 - 2k = 3k - 1
+3k +3k
19 +1k = -1
-19 -19
k = -20
Part A: Identify the FIRST mistake Jackson made.
Part B: Solve for k.
Answers
Part B: 19 - 2k = 3k - 1
Subtract 3k from both sides
19 - 5k = - 1
Subtract 19 from both sides
- 5k = -20
Divide by -5 on both sides
K=4
Which relation is a function?
O {(0, -9), (-2, -3), (-2, 0), (-3, -2)}
O {(0, -9), (-9, -2), (0, -3)}
O {(0, -9), (-9, 0), (-3, -3)}
O {0, -9, -2, -3}
Answers
Answer:
C
Step-by-step explanation:
Here, we want to select the option that present a function
For a set of points to be a function, we have that every single x value is directly mapped to a single y value
As we can see, this is correct only for the third option
There is no repetition of x-values or y-values
Every x value is directly linked to a different y-values
Answer:
C
Step-by-step explanation:
Here, we want to select the option that present a function
For a set of points to be a function, we have that every single x value is directly mapped to a single y value
As we can see, this is correct only for the third option
There is no repetition of x-values or y-values
Every x value is directly linked to a different y-values
shryia read a 481 481481-page-long book cover to cover in a single session, at a constant rate. after reading for 1.5 1.51, point, 5 hours, she had 403 403403 pages left to read. how fast was shryia reading? pages per hour how long did it take her to read the entire book? hours
Answers
Shryia was reading at a speed of 524.67 pages per hour, and it took her approximately 917.06 hours to read the entire book.
To find Shryia's reading speed, we can use the formula:
\(reading speed = (total pages - pages left) / time\)
We are given that the book has 481481481 pages, and after reading for 1.5 1.51, point, 5 hours, Shryia had 403403403 pages left to read. So, the total number of pages she read is:
481 - 403 = 787
The time taken to read these pages is:
1.5 hours
So, her reading speed is:
reading speed = 787 / 1.5 = 524.67 pages per hour
To find how long it took her to read the entire book, we can use the formula:
time = total pages / reading speed
So, the time taken to read the entire book is:
time = 481481481 / 524.67 ≈ 917.06 hours
Therefore, Shryia was reading at a speed of 524.67 pages per hour, and it took her approximately 917.06 hours to read the entire book.
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Probability and Statistics - Colored Points Six points are drawn from uniform distribution U10,1]. The first three points are marked green and the next three are marked red on the real line. What is the probability that all adjacent points differ in color? Pick one of the choices 1/20 1/10 1/6 1/5 Clear selection Probability and Statistics - Dice Consider an unbiased six-faced dice with integers 1 through 6 marked on the faces. Assume the dice is thrown repeatedly, until the sum of the numbers cast till that point is a multiple of 6. What is the expected number of throws? Pick one of the choices 03 4.5 Clear selection
Answers
The probability that all adjacent points differ in colour is \(\frac{1}{5}\).
What is probability ?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Have given ,
We have first three colour Green that is g1 , g2 and g3
And We have next three colour red that is r1 , r2 and r3
The probability that all adjacent points differ in colour = 3! * \(^{4}C_{3}\) 3! / 6!
=> \(\frac{ 3! * 4! *3!}{6!}\)
=> \(\frac{1}{5}\)
The probability that all adjacent points differ in colour is \(\frac{1}{5}\).
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please help with this question!
Answers
Answer: The first 3 options
Step-by-step explanation:
You have to make sure that the given variable would be able to equal -5. The \(\geq\) sign in the second and third answer show that the variable could be equivalent to -5.
Answer:
g > -7, f ≤ -5 and g ≥ -5
Step-by-step explanation:
the < and > symbols mean less than and greater than respectively, but not including. Therefore -5 cannot be a valid solution if the range is (for example) g > -5. However, ≤ and ≥ mean less/greater than or equal to, so -5 would be a valid solution for g ≥ -5 (for example).
please view the image and answer the questions.
This is College Algebra.
Answers
Step-by-step explanation:
x² - 9
1. There is no common factor other than 1.
2. √x² = x; √9 = 3
3. a = x; b = 3
4. x² - 9 = (x - 3)(x + 3)
a pizza shop runs a special where you can buy a large pizza with one cheese, one vegetable, and one meat for $9. You have a choice of seven Cheese's, 11 vegetables, and 6 Meats. Additionally, you have a choice of Three crusts and two sauces. How many different variations of the pizza special are possible?
Answers
The possible number of pizza special is (7 x 11 x 6 x 3 x 2 = 2772 variations.
3, 9, 15,.
Find the 45th term.
Answers
The 45th term of the sequence is 267.
The 45th term of a sequence can be calculated using the formula:
Tn = a + (n – 1)d
Where,
Tn = the nth term
a = the first term
n = the term position
d = the common difference
In this sequence, the first term is 3, the common difference is 6, and the term position is 45.
Therefore, the 45th term of the sequence is:
T45 = 3 + (45 – 1)6
T45 = 3 + (44)6
T45 = 3 + 264
T45 = 267
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For a car to qualify as a High Occupancy Vehicle (HOV), it must have at least _____ people.
A.
4
B.
2
C.
varies
D.
3
Answers
Answer: i would like to sad it varies
Step-by-step explanation: the number of people required for a Vehicle to be an HOV i would say exactly 2 and greater. The state Laws also applies, so i'll add that onto it varies
#11 i
Solve the system of linear equations.
6x+2y = 16
2x - y = 2
Answers
Answer:
Point slope form of the equations:
y = -3x + 8
y = 2x - 2
Solution to the system of equations:
(x, y) ==> (2, 4)
Step-by-step explanation:
6x + 2y = 16
2x - y = 2
6x + 2y = 16
2(2x - y = 2) ==> 4x - 2y = 4
6x + 2y = 16
4x - 2y = 4
10x = 20
/10 /10
x = 2
Now, we solve for y:
6x + 2y = 16
6(2) + 2y = 16
12 + 2y = 16
-12 -12
2y = 4
/2 /2
y = 2
(x, y) ==> (2, 2)
Point-slope forms:
6x + 2y = 16
-6x -6x
2y = -6x + 16
/2 /2
y = -3x + 8
2x - y = 2
-2x -2x
-1y = -2x + 2
/-1 -1
y = 2x - 2
Hope this helps!
Which value could be substituted for the variable to make the equation
TRUE? w-11 =15
Answers
Answer:
26 - 11 = 15
Step-by-step explanation:
Find the Partial Differential Equations:
∂^2u/∂x^2 = 1/2 ∂u/∂t , u(0,t) = u (3,t) = 0
u(x,0) = 5 sin 4πx-3 sin2πx+1/2 sin πx
Find the Partial Differential Equations:
Utt-Uxx = 0 , u(x,0) = 1 , ut(x,0)=0
u(0,t) = u(π)t=0
Answers
In the first problem, the partial differential equation is given as ∂^2u/∂x^2 = 1/2 ∂u/∂t, with boundary conditions u(0,t) = u (3,t) = 0 and initial condition u(x,0) = 5 sin 4πx-3 sin2πx+1/2 sin πx.
This is a wave equation with non-homogeneous initial condition and homogeneous boundary conditions. The solution can be obtained using separation of variables and applying the appropriate boundary conditions. The general solution will be a linear combination of sine and cosine functions with coefficients determined by the initial condition.
In the second problem, the partial differential equation is given as Utt-Uxx = 0, with boundary conditions u(0,t) = u(π,t) = 0 and initial conditions u(x,0) = 1 and ut(x,0) = 0.
This is a wave equation with homogeneous boundary conditions and non-homogeneous initial conditions. The solution can be obtained using the method of characteristics, where the solution is expressed in terms of a function of the characteristic variables.
The general solution will be a linear combination of two functions, one dependent on x+ct and the other dependent on x-ct, where c is the speed of the wave. The coefficients will be determined by the initial conditions.
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Please help math 100 points! Decimal Rounding
Answers
Answer:
a: 0.5 + 0.3 = 0.8
b: 2.7 + 28.2 = 30.9
c: 3.1 + 2.4 + 9.9 = 15.4
d: 15.2 + 1.4 + 0.8 = 17.4
e: 39.2 + 2.5 + 0.8 = 42.5
Step-by-step explanation:
I did the assignment and I got it right
Solve for x in the equation x2 + 4x-4=8.
O x = -6 or x = 2
X=-2+2/2
O x = -2 or x = 6
O x=2+2V5
Answers
\( {x}^{2} + 4x - 4 = 8 \\ = > {x}^{2} + 4x - 4 - 8 = 0 \\ = > {x}^{2} + 4x - 12 = 0 \\ = > {x}^{2} + 6x - 2x - 12 = 0 \\ = > x(x + 6) - 2(x + 6) = 0 \\ = > (x - 2)(x + 6) = 0 \\ = > x = 2 \: \: \: or \: \: \: x = - 6 \)
Answer:
x = -6 or x = 2
Hope you could get an idea from here.
Doubt clarification - use comment section.
Which expressions are equivalent to 4b? 1.b+2(b+2b)
2.3b+b 3.2(2b)
Answers
Answer:
b+2(b+2b) = 7b so this is incorrect.
3b + b = 4b (correct)
2 * 2b = 4b (correct)
The answer is 3b + b and 2 (2b)
fill in the blank. _____sample
The population is first split into groups. The overall sample consists of every member from some of the groups. The groups are selected at random.
Example—An airline company wants to survey its customers one day, so they randomly select 555 flights that day and survey every passenger on those flights.
Why it's good: A cluster sample gets every member from some of the groups, so it's good when each group reflects the population as a whole.
Answers
it is important to consider the potential for intra-cluster similarity, as individuals within the same cluster may be more similar to each other than to individuals in other clusters.
What is intra-cluster sample?A cluster sample is a sampling technique where the population is divided into clusters or groups, and a subset of clusters is selected at random to form the overall sample. In this type of sampling, all members of the selected clusters are included in the sample.
In the given example, the airline company selects 555 flights as clusters and surveys every passenger on those flights. Each flight represents a cluster, and by selecting random flights, the company includes every passenger on those selected flights in the survey.
This cluster sampling approach is suitable when each group or cluster is representative of the overall population. It is useful when it is impractical or costly to sample every individual unit within the population, but the selected clusters are expected to reflect the characteristics of the entire population.
Cluster sampling allows for more practical data collection, particularly when dealing with large populations or geographically dispersed units. However, it is important to consider the potential for intra-cluster similarity, as individuals within the same cluster may be more similar to each other than to individuals in other clusters.
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Pleasehelp Name the reciprocal
Answers
Answer:
x = 12
Step-by-step explanation:
3/4x = 9
x = 9/1(4/3)
x = 12
Which words correctly complete the statement below?
APQR is dilated with the center of dilation at the origin and a scale factor of 0.5 to
obtain AP'Q'R'. The triangles' corresponding angles are
and their
corresponding sides are
; therefore, the triangles are
Answers
Answer:
A)congruent, proportional, similar
Step-by-step explanation:
Liam puts $800 in a savings account at an annual interest rate of 2%. If Liam does not withdraw or deposit any money, what is the interest that Liam will earn at the end of six months?
Answers
Answer:
$8
Step-by-step explanation:
Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution.
The amounts of time employees of a telecommunications company have worked for the company are normally distributed with a mean of 5. 4 years and a standard deviation of 2. 1 years. Random samples of size 12 are drawn from the population and the mean of each sample is determined
Answers
Using the central limit theorem to find the mean is 5.4 and the standard error of the mean of the indicated sampling distribution is 0.6.
We must utilize the central limit theorem to determine the mean and standard error of the mean of the sample distribution in the given query.
Considering the posed query,
The company has a mean age of 5.4 years and is normally distributed.
2.1 years of standard deviation.
The population is sampled at random with an n = 12 size, and the mean of each sample is calculated.
The mean is determined using the central limit theorem.
μ(x) = μ = 5.4
The standard error of the mean of the indicated sampling distribution is:
σ(x) = σ/√n
σ(x) = 2.1/√12
σ(x) = 2.1/3.5
σ(x) = 0.6
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enter the equation of the line in the form =mx where m is the slope .
Answers
Answer:
y = 3x
Step-by-step explanation:
The line goes up 3 and goes across by 1. Using the rise over run structure, it will be 3/1 or 3. m is equal to the slope, making it y = 3x, since y doesn't intercept anything, you don't need to put + anything at the end. Hope I helped. :D
The center of a circle is at (10, -4) and its radius is 11.
What is the equation of the circle?
(x-10)² + (y + 4)² = 11
O (x-10)² + (y + 4)² = 121
(x + 10)² + (y - 4)² = 11
O (x + 10)² + (y - 4)² = 121
Answers
Answer:
(x - 10)² + (y + 4)² = 121
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (10, - 4 ) and r = 11 , then
(x - 10)² + (y - (- 4) )² = 11² , that is
(x - 10)² + (y + 4)² = 121
Tim buys a torch and a battery. The torch costs 11 times as much as the battery. Tim pays with a £10 note and gets £4.84 change. How much did the battery cost?
Answers
Write an equation that you can use to find the number of refills Keith bought. A restaurant sells a coffee refill mug for $6.75. Each refill costs $1.25. Last month Keith spent $31.75 on a mug and refills. (use x for your variable and do not use $ in your answer) *
Answers
Answer:
6.75+1.25x=31.75
Step-by-step explanation:
let x be the number of refils
also given is that the cost of one refill is $1.25
hence the total refil will be 1.25x
given that the cost of a mug is $6.75
6.75+1.25x=31.75
therefore the expression that can be used to solve for the number of refills is
6.75+1.25x=31.75