35 is a reasonable prediction of the number of times he will select 2 yellow socks?
what is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain to occur. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
What is event?In probability theory, an event is a set of outcomes or a subset of a sample space. In simpler terms, an event is anything that can happen, or any possible outcome of an experiment or observation. An event can be a single outcome, or it can consist of multiple outcomes.
In the given question,
The theoretical probability of drawing two yellow socks with replacement from a bag containing equal numbers of red, yellow, green, blue, and purple socks is:
P(drawing two yellow socks) = P(yellow) * P(yellow) = (1/5) * (1/5) = 1/25
So, the probability of drawing two yellow socks from the bag in any given trial is 1/25.
To predict the number of times the child will select two yellow socks in 175 trials, we can use the formula for the expected value of a discrete random variable:
E(X) = n * p
where E(X) is the expected number of times the event occurs, n is the number of trials, and p is the probability of the event occurring in a single trial.
In this case, n = 175 and p = 1/25. So,
E(X) = 175 * (1/25) = 7
Therefore, a reasonable prediction of the number of times the child will select two yellow socks in 175 trials is 7. Since this prediction is not one of the answer choices, the closest option is 35, which is more than five times the expected value. However, this is within the range of possible outcomes due to the random nature of the experiment.
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Question 19 (2 points)
According to research conducted by the Department of Education, 80% of college
students took a mathematics course as part of their general education requirements.
If ten college students are selected at random, what is the probability at least one of
the ten has not taken a mathematics course?
0.0800
0.1073
0.7927
0.8000
Rounding to four decimal places, the answer is 0.8926. So the probability that at least one of the ten college students has not taken a mathematics course is approximately 0.8926.
what is probability?
Probability is a measure of the likelihood or chance that a particular event will occur. It is usually expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
The probability that a college student has taken a mathematics course is 0.80. Therefore, the probability that a student has not taken a mathematics course is
1 - 0.80 = 0.20.
The probability that at least one of ten college students has not taken a mathematics course can be found using the complement rule. That is, the probability that at least one student has not taken a mathematics course is equal to one minus the probability that all ten students have taken a mathematics course.
The probability that all ten students have taken a mathematics course is:
0.80¹⁰ = 0.1074
Therefore, the probability that at least one student has not taken a mathematics course is:
1 - 0.1074 = 0.8926
Therefore, Rounding to four decimal places, the answer is 0.8926. So the probability that at least one of the ten college students has not taken a mathematics course is approximately 0.8926.
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a relation r is called circular if arb and brc imply that cra. if r is an equivalence relation, then would r be circular?
If a relation R is an equivalence relation, then R will be circular.
If a relation R is an equivalence relation, then it must satisfy three properties: reflexivity, symmetry, and transitivity.
(i) Reflexivity: For any element "a" in the set, "aRa" must be true.
(ii) Symmetry: For any elements "a" and "b" in the set, if "aRb" then "bRa" must be true.
(iii) Transitivity: For any elements "a", "b", and "c" in the set, if aRb and bRc then "aRc" must be true.
A Circular relation is where "aRb" and "bRc" imply "cRa".
This is a stronger condition than the transitivity property of an equivalence relation, which only requires that "aRb" and "bRc" together imply "aRc".
Therefore, a relation that is an equivalence-relation have to be circular.
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The given question is incomplete, the complete question is
A relation R is called circular if "aRb" and "bRc" imply that "cRa". if R is an equivalence relation, then would R be circular?
What rotation centered about the origin maps (4, − 7) to (7,4) ? 90° counterclockwise 180° counterclockwise 270° counterclockwise I don't know. ←
Answer:
What rotation centered about the origin maps (4, − 7) to (7,4) ? 90° counterclockwise 180° counterclockwise 270° counterclockwise I don't know. ←
Step-by-step explanation:
To map the point (4, -7) to (7, 4) by a rotation centered about the origin, we need to find the angle of rotation and direction.
We can start by finding the vector from the origin to (4, -7), which is <4, -7>. We want to rotate this vector to the vector from the origin to (7, 4), which is <7, 4>.
To do this, we need to find the angle between these two vectors. Using the dot product, we have:
<4, -7> · <7, 4> = (4)(7) + (-7)(4) = 0
Since the dot product is zero, we know that the two vectors are orthogonal, and the angle between them is 90 degrees.
To map (4, -7) to (7, 4) with a 90-degree rotation counterclockwise, we can use the matrix:
[0 -1]
[1 0]
Multiplying this matrix by the vector <4, -7>, we get:
[0 -1] [4] = [-7]
[1 0] [-7] [ 4]
which corresponds to the point (-7, 4). This matches our desired endpoint, so the answer is 90° counterclockwise.
Answer:
90° counterclockwise
Step-by-step explanation:
I am not sure if the picture helps or not. I am trying to show that I traced the point (4,-7). Then I have a plus sign at (0,0). I start rotating the tracing paper counterclockwise until I get to the point (7,4). I needed to turn one turn of the plus sign. That would be 90°
Helping in the name of Jesus.
Census data for a certain county shows that 19% of the adult residents are Hispanic. Suppose 92 people are called to jury duty and only 11 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection process? Again run a test using the PHANTOMS method to complete all parts of your problem.
Yes, the apparent under representation of Hispanics on the jury duty calls into question the fairness of the jury selection system, as the results of the hypothesis test suggest that the system may be systematically excluding Hispanics.
To determine whether the apparent underrepresentation of Hispanics on the jury selection system is statistically significant and calls into question its fairness, we need to perform a hypothesis test.
First, we set up the null hypothesis, which is the assumption that there is no difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool. That is, the proportion of Hispanics in the jury pool is expected to be equal to 19%.
The alternative hypothesis is that there is a difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool.
We can use a one-tailed z-test to test the null hypothesis, where the test statistic is calculated as:
z = (p - P) / sqrt(P(1-P)/n)
where p is the proportion of Hispanics in the jury pool, P is the proportion of Hispanics in the county population (0.19), and n is the sample size (72).
Plugging in the values, we get
z = (9/72 - 0.19) / sqrt(0.19*(1-0.19)/72) = -2.39
Assuming a significance level of 0.05, we compare the calculated z-value with the critical z-value of -1.645 (obtained from a standard normal distribution table). Since the calculated z-value is less than the critical z-value, we reject the null hypothesis and conclude that the proportion of Hispanics in the jury pool is significantly different from the proportion of Hispanics in the county population.
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Question 41 (Essay Worth 10 points)
(06.06 HC)
Use specific examples from the history you have learned to compose a well-developed paragraph on the following:
How has the rise of democracy impacted ONE of the following regions: Africa, Asia, or the Caribbean?
Answer:
See below, please.
Step-by-step explanation:
The rise of democracy has had a significant impact on the African continent, with many countries transitioning from authoritarian rule to democratic governance since the 1990s. For example, South Africa emerged from decades of apartheid and transitioned to democracy in 1994, with the election of Nelson Mandela as the country's first black president. Similarly, in Ghana, the return to multiparty democracy in 1992 after years of military rule led to the establishment of a more stable political system.
The impact of democracy has not been uniform across Africa, with some countries experiencing significant challenges in their democratic transitions. For instance, in Zimbabwe, President Robert Mugabe, who came to power after independence in 1980, held on to power for over three decades through rigged elections and suppression of political opposition. It wasn't until a military coup in 2017 that he was forced to step down.
Despite the challenges, democracy has brought about some significant improvements on the African continent. With democratic governance, there has been a greater emphasis on human rights, the rule of law, and good governance. Free and fair elections have become the norm in many African countries, and citizens have become more involved in the political process, leading to greater accountability from leaders.
The rise of democracy in Africa has had both positive and negative impacts, but overall it has contributed to the establishment of more accountable and transparent governance systems. With democratic institutions in place, African nations are better positioned to address the political and socio-economic challenges that they face.
jerome haw 1,040 songs downloaded on his spotify account and 30% of the songs are country songs. How many of the songs are not country
I will mark you brainiest!
SSS is used to prove two triangles are congruent.
A) False
B) True
Answer:
A
Step-by-step explanation:
because___________________________________
Answer:
B) True
Step-by-step explanation:
SSS or Side-Side-Side is used to prove two triangles are congruent.
If a ll b, find the value of x.
Answer:
x = 18
Step-by-step explanation:
Alternate exterior angles are congruent. Set the equations equal to each other and solve for x.
7x + 11 = 10x - 43 Subtract 7 x from both sides
7x - 7x + 11 = 10x - 7x - 43
11 = 3x - 43 Add 3 to both sides
11 + 43 = 3x -43 + 43
54 = 3x Divide both sides by 3
[tex]\frac{54}{3}[/tex] = [tex]\frac{3x}{3}[/tex]
18 = x
Helping in the name of Jesus.
What is the meaning of "The elements of F are all finite sequences (x1, x2, ..., xn) of elements of X "?
This is true, of course. The collection of any and all finite sequence of X's elements, along with the concatenation operation, is referred to as the free fuzzy set F over a set .
What does the math symbol X mean?The sentence xA denotes that x is an element of a set A since the symbol denotes set membership and meaning "is an element of". In those other words, x belongs to the group of (potentially many) items in set A.
What do math components consist of?
Components are also the components that constitute a set. A shared characteristic of the items can define a set. For instance, the set is the collection E of positive roughly equal numbers. Furthermore, F is a semigroup, since the operation of concatenation is associative: if and are elements of F, then Finally, F is a free semigroup over , which means that every element of F can be written uniquely as a product of elements of .
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Solve the equation.
Cos 9= sin 56.3
According to the problem the answer is cos 9 = sin 56.3.
What is cos?Cos is a mathematical function that returns the ratio of the side adjacent to a given angle of a right triangle to the hypotenuse of the triangle. It is one of the most commonly used trigonometric functions and is used in various mathematical calculations such as finding angles, distances, and wave lengths. Cos is often written as cosine and is typically abbreviated as "cos." It can also be written as COS or csc. Cos is typically used in conjunction with sin and tan to measure angles and distances in a triangle. Cos can also be used to calculate wave lengths in physics and to determine the magnitude of a vector in vector calculus. Cos is an important concept in mathematics and is used in many areas of science, engineering, and technology.
Use the identity sin(90°-x) = cos x:
sin 56.3 = cos (90° - 56.3)
cos 9 = cos (90° - 56.3)
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For cos 9°, angle lies between 0° and 90° (First Quadrant). Since cosine function is positive and in the first quadrant, thus cos 9° value = 0.9876883. Also Cos 9 = √(1-sin²(9°)).
What is cos?Cos is a mathematical function that returns the ratio of the side adjacent to a given angle of a right triangle to the hypotenuse of the triangle. It is one of the most commonly used trigonometric functions and is used in various mathematical calculations such as finding angles, distances, and wave lengths. Cos is often written as cosine and is typically abbreviated as "cos." It can also be written as COS or csc.
The value of cos 9 degrees in decimal is 0.987688340, since Cos 9 degrees can also be expressed using the equivalent of the given angle (9 degrees) in radians (0.15707)
Using degree to radian conversion, θ in radians is:
= θ in degrees × (pi/180°)
⇒ 9 degrees
= 9° × (π/180°) rad
= π/20 or 0.1570
∴ cos 9° = cos(0.1570)
= 0.9876883
Since the cosine is the periodic function, we can represent cos 9° as,
So, cos 9 degrees = cos(9° + n × 360°).
⇒ cos 9°
= cos 369°
= cos 729°, and so on.
Cos 9 = √(1-sin²(9°))
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point $p$ lies inside square $abcd$ such that triangle $abp$ is equilateral. find $\angle pcd$ in degrees.
The measurement of angle PCD in equilateral triangle is 67.38°.
Let $s$ be the side length of the square $abcd$, and let $O$ be the center of the square. Then $OP = s/\sqrt{2}$.
Since triangle $ABP$ is equilateral, we have $\angle ABP = 60^\circ$ and $AP=BP=s$. Let $E$ be the foot of the perpendicular from $P$ to $AB$. Then $AE=BE=s/2$ and $EP=s\sqrt{3}/2$.
Since $EP$ is perpendicular to $AB$ and $AB$ is parallel to $CD$, we have $\angle PCD = \angle ACE$.
Since $OP$ is perpendicular to $AB$, we have $\angle OEP = \angle AEP = 30^\circ$. Also, $OE=OP/\sqrt{2}=s/2$.
Using the Pythagorean theorem in triangle $OCE$, we have
CE= [tex]\sqrt{(OE)^{2} + (OC)^{2}} = \sqrt{(s/2)^{2} + s^{2}} = s\sqrt{5}/2[/tex]
Therefore, $\sin \angle ACE = CE/CP = \sqrt{5}/2$. Thus,
∠PCD = ∠ACE = arcsin(√5/2) ≈ 67.38°
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Last night, Roberto spent 90 minutes doing homework, two-thirds of an hour reading, and 540 seconds making his lunch for the next day. How many more minutes did Roberto spend doing homework than he did reading and making his lunch?
The answer is 41 minutes.
explaination:
540 secs = 9 minutes
2/3 of 60 mins= 40 mins
(to find a fraction of a number you divide it by the denominator and times it after by the numerator)
9+40= 49
homework: 90 mins
reading and making lunch: 49 minutes
we want the difference so:
90-49= 41
Roberto spent 41 more minutes doing his homework than reading and making lunch.
C is 2 units closer to B than it is to A, if A = 5, B=15
Answer:
the coordinate of C is 10.5, and the distance between A and C is 10.5 - 5 = 5.5, and the distance between B and C is 15 - 10.5 = 4.5.
Step-by-step explanation:
If C is 2 units closer to B than it is to A, then we can find the distance between A and C and between B and C by using the distance formula:
Distance between two points (x1, y1) and (x2, y2) = sqrt[(x2 - x1)^2 + (y2 - y1)^2]
Let x be the coordinate of C. Then, the distance between A and C is x - 5, and the distance between B and C is 15 - x. We know that the distance between B and C is 2 units greater than the distance between A and C, so we can set up an equation:
15 - x = 2 + (x - 5)
Simplifying and solving for x, we get:
15 - x = 2 + x - 5
18 - x = x - 3
2x = 21
x = 10.5
Therefore, the coordinate of C is 10.5, and the distance between A and C is 10.5 - 5 = 5.5, and the distance between B and C is 15 - 10.5 = 4.5.
of the following values, which is least important to today's college students according to the yearly values survey?
The least important value to today's college students according to the yearly values survey is Political involvement. So the option B is correct.
The survey found that only 32% of college students believed that political involvement was important. This is significantly lower than the other values surveyed such as Financial Success (86%) and Community Involvement (71%). As such, it can be concluded that Political Involvement is the least important value to today's college students.
This may be due to a variety of factors, such as a lack of understanding of the political system, a lack of interest in politics, or a sense that individual political action will not make a difference.
It is important to recognize, however, that political involvement is still an important part of civic engagement and an essential part of the democratic process. As such, college students should strive to become more informed about politics and to find ways to get involved in the political process.
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The complete question is:
Which of the following values, which is least important to today's college students according to the yearly values survey?
A. Career success
B. Political involvement
C. Healthy lifestyle
D. Social media presence
PLEASE HELP 30 POINTS!
Answer:
57
57
123
123
57
57
123
that's all.
Answer:
m<1 = 57°
m<2 = m<1 = 57°
m<3 = x = 123°
m<4 = x = 123°
m<5 = m<1 = 57°
m<6 = m<5 = 57°
m<7 = m<4 = 123°
Step-by-step explanation:
[tex]{ \tt{m \angle 1 + x = 180 \degree}} \\ { \colorbox{silver}{corresponding \: angles}} \\ { \tt{m \angle 1 = 180 - 123}} \\ { \tt{ \underline{ \: m \angle 1 = 57 \degree \: }}}[/tex]
What is the end behavior of the polynomial function?
Answer: D. As x → -∞, y → -∞.
Step-by-step explanation:
The graph shows the function approaching negative infinity on the x-axis (left side). When the x-axis is decreasing, the y-axis is also decreasing towards negative infinity.
8. What is the area of sector EFG? Express the answer
in terms of л.
10
E
128⁰
G
The area of a sector is a region bounded by two radii of a circle and an arc between is (320/9) π sq. units.
What is radius?Radius is a straight line segment that connects the center of a circle or sphere to any point on its circumference or surface, respectively. In other words, it is the distance from the center of the circle or sphere to any point on its edge or surface.
According to question:The given sector is EFG = 128°.
The area of a sector is a region bounded by two radii of a circle and an arc between them.
A = (θ/360) × πr²
Where:
A is the area of the sectorθ is the central angle of the sector in degreesr is the radius of the circleThe fraction (θ/360) represents the fraction of the entire circle that the sector occupies. Multiplying this fraction by the total area of the circle (πr²) gives the area of the sector.
Use the formula for the area of a sector with the central angle in degrees:
A = (n/360) × πr²
From the given figure, n = 128 and r = 10
A = (128/360) × π(10)²
= (320/9) π sq. units.
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The volume, V , of a sphere in terms of its radius, r , is given by V(r)=4/3πr^3 . Express r as a function of V , and find the radius of a sphere with volume of 100 cubic feet.
Round your answer for the radius to two decimal places.
A sphere with volume 100 cubic feet has radius ??
So the radius of the sphere is approximately 2.88 feet (rounded to two decimal places).
What is volume?Volume is the amount of space occupied by a three-dimensional object as measured in cubic units. It is the measure of the amount of material or substance that a container, object, or shape can hold.
Here,
To express r as a function of V, we can rearrange the equation V = 4/3πr³ to solve for r:
V = 4/3πr³
V / (4/3π) = r³
r = ³√(V / (4/3π))
r = ³√(3V / 4π)
To find the radius of a sphere with volume 100 cubic feet, we can substitute V = 100 into the equation:
r = ³√(3V / 4π)
= ³√(3(100) / (4π))
≈ 2.88 units
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what is the ordered pair to this question using substitution? y = −2x − 7
2y − x = 1
Answer: (-3, -1)
Step-by-step explanation:
First, we can use the first equation to solve for one variable in terms of the other.
y = -2x - 7
Next, we can substitute this expression for y into the second equation:
2y - x = 1
2(-2x - 7) - x = 1
Simplifying:
-4x - 14 - x = 1
-5x - 14 = 1
-5x = 15
x = -3
Now that we have the value of x, we can substitute it back into either of the original equations to find y. Using the first equation:
y = -2(-3) - 7
y = 6 - 7
y = -1
Therefore, the ordered pair that satisfies both equations is (-3, -1).
Answer: (-3,-1)
Explanation Step By Step
Which expression represents the distance
between point G and point H?
|-12|16| |-12|+|-9|
1-9|-|-6|
|-12|+|6|
-15
H(-9,6)
G(-9,-12)
15+y
0
-15-
15
Answer:
Step-by-step explanation:
2
PLEASE HELPP DUE TODAY!!!!!
Calculate the value of c in the triangle below.
Answer:
82
Step-by-step explanation:
A human head can be approximated as a sphere with a circumference of 60
centimeters. What is the approximate volume of a human head, rounded to the nearest 1,000
cubic centimeters?(GEOMETRY HELP)
The approximate volume of a human head is 4000 cubic centimeter.
What is the approximate volume of a human head?A sphere is simply a geometrical object that is a three-dimensional analogue to a two-dimensional circle.
The circumference of a sphere is given by the formula:
C = 2πr
Where r is the radius of the sphere. In this case, we are given that the circumference of the sphere (which approximates the human head) is 60 cm, so:
60 cm = 2πr
Solve for r
r = 60/2π
r = 30/π
The volume of a sphere is given by the formula:
V = (4/3)πr³.
Substituting the value we found for r, we get:
V = (4/3) × π × ( 30/π )³
V = (4/3) × π × ( 30/π )³
V = 3647.566 cm³
V = 4000 cm³
Therefore, the volume to the nearest 1,000 cubic cm is 4000 cm³.
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The mean weight of 4 parcels is 8.5kg. Three of them weighed 7.7 kg, 7.6 kg and 8.2 kg.
What is the weight of the fourth parce1?
Answer:
Weight of the fourth parcel will be 10.5 kgStep-by-step explanation:
Weight of first parcal = 7.7 kg Weight of second parcel = 7.6 kgWeight of third parcel = 8.2 kg Mean Weight = 8.5 kgLet weight of fourth parcel be x
Mean = Sum of all values/total number of values.
8.5 = 7.7 + 7.6 + 8.2 + x/4
8.5 = 23.5 + x/4
8.5 × 4 = 23.5 + x
34 = 23.5 + x
34 - 23.5 = x
10.5 = x
Therefore, weight of the fourth parcel will be 10.5 kg
PLS Answer help i will give 10 brainly points if you help
Answer:
12×2, 3×8, 4×6
Step-by-step explanation:
To find the area of a parallelogram, the formula is A = bh.
1. Height: 6 ft
Base: 2 ft
6 × 2 = 12 ft
So it does not work.
2. Height: 12 ft
Base: 2 ft
12 × 2 = 24 ft
So it does work.
3. Height: 10 ft
Base: 14 ft
14 × 10 = 140 ft
So it does not work.
4. Height: 3 ft
Base: 4 ft
3 × 4 = 12 ft
So it does not work.
5. Height: 3 ft
Base: 8 ft
3 × 8 = 24 ft
So it does work.
6. Height: 4 ft
Base: 6 ft
4 × 6 = 24 ft
So it does work.
find all real numbers k for which there exists a nonzero 2 dimensional vector bold v such that begin bmatrix 2
CAN SOMEONE HELP WITH THIS QUESTION?✨
Step-by-step explanation:
my previous answer assumed we need a kind of average change rate.
but it seems you need the immediate change rate ?
or what ? the question does not specify.
I would appreciate if you would leave a comment, when you find that my answer is seemingly not matching some expected answers.
so, let's try now the immediate change rate (as I have no information to go - I have also no information about what you are currently learning in your class, and if you do already derivatives or not, so, this might be now above your learning level ...) :
again, the area between the inner circle and the outer square is
A = As - Ac = s² - pi×r²
where s is the square's side length, and r is the radius of the circle.
the immediate change rate of that area is the sum of first derivatives of A based on both used variables multiplied by their individual change rates :
dA/dt = dAs/ds × ds/dt - dAc/dr × dr/dt
and this is then calculated for the given data point (s = 16, r = 3) and the individual change rates of the variables (ds/dt = 2 meters/minute, dr/dt = 1 meter/minute).
so, we have
dA/dt = 2s × 2 - 2×pi×r × 1
as (s²)' = 2s, (pi×r²)' = 2×pi×r
dA(16, 3)/dt = 2×16×2 - 2×pi×3×1 = 64 - 6pi =
= 45.15044408... meters²/minute ≈
≈ 45.15 meters²/minute
so, you see, for a curved function (not a line) there has to be a difference between the average change rate between 2 points and the immediate change rate directly at a point.
I hope this works now for you.
and here now the original answer for an average change rate :
right now the radius is 3 m, and the square side lengths are 16 m.
1 minute ago the radius was 2 m, and the square side lengths were 14 m.
the area between the circle and the square is always the area of the square minus the area of the circle.
these areas are right now
circle : pi×3² = 9pi m²
square : 16² = 256 m²
area between = 256 - 9pi = 227.7256661... m²
these areas were one minute ago
circle : pi×2² = 4pi m²
square : 14² = 196 m²
area between = 196 - 4pi = 183.4336294... m²
the change rate of the area between the circle and the square is
227.7256661... - 183.4336294... = 44.29203673... m² per minute
Give the interval(s) on which the function is continuous.
g(t) = 1/√16-t^2
The function g(t) is defined as:
g(t) = 1/√(16-t^2)
The function is continuous for all values of t that satisfy the following conditions:
The denominator is non-zero:
The denominator of the function is √(16-t^2). Therefore, the function is undefined when 16-t^2 < 0, or when t is outside the interval [-4,4].
There are no vertical asymptotes:
The function does not have any vertical asymptotes, because the denominator is always positive.
Thus, the function g(t) is continuous on the interval [-4,4].
What is the percent of change from 100 to 85?
Hi!
The percent change is 15%.
Hope this helps!
~~~PicklePoppers~~~
HELP MY TEST IS DUE TONIGHT
find the area of the trapezoid
Show work:
Answer:
A = 32
Step-by-step explanation:
A= (a+b divided by 2) mulitiplied by height
a = 6
b = 2+6+2 = 10
h = 4
a+b = 6 + 10= 16
16 divided by 2 = 8
8 x 4 = 32
Therefore, the area is 32.
19
The diagram shows a sector OBC of a circle with centre O and radius (6 + x) cm.
B
A
es 50°
6 cm
DX
find the value of x.
Give your answer correct to 3 significant figures.
x cm
A is the point on OB and D is the point on OC such that OA = OD = 6 cm
Angle BOC= 50°
Given that
Diagram N
accurately
the perimeter of sector OBC= 2 x the perimeter of triangle OAD
The value of the variable, x, obtained using the formula for the perimeter of a sector of a circle is; x = 6 cm
What is a sector of a circle?A sector of a circle is the region of the circle that has two radii of the circle and the arc between the two radii as the boundary of the region.
The perimeter of a sector of a circle can be obtained using the formula;
Perimeter = 2·r + (θ/360°) × (2·π·r)
The radius of sector OAD, r = 6 cm
Therefore;
The perimeter of sector OAD = 2 × 6 + (50/360) × 2 × π × 6 = 12 + 5·π/3
The perimeter of sector OBC = 2 × The perimeter of sector OAD
Therefore;
The perimeter of sector OBC = 2 × (12 + 5·π/3) = 24 + 10·π/3
Which indicates;
The perimeter of sector OBC = 2 × (6 + x) + (50/360) × 2 × π × (6 + x)
2 × (6 + x) + (50/360) × 2 × π × (6 + x) = (5·π·x + 30·π + 36·x + 216)/18
24 + 10·π/3 = (5·π·x + 30·π + 36·x + 216)/18
432 + 60·π = 5·π·x + 30·π + 36·x + 216
432 - 216 + 60·π - 30·π = x·(5·π + 36)
216 + 30·π = x·(5·π + 36)
6 × (5·π + 36 ) = x·(5·π + 36)
x·(5·π + 36) = 6 × (5·π + 36 )
x = 6 × (5·π + 36 )/(5·π + 36 ) = 6
x = 6 cm
Learn more on the sector of a circle here: https://brainly.com/question/9790386
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