Answer:
Area_shaded_region = 2 * (√(1 - cos^2(4π/9))) - (16/9)π m^2
Step-by-step explanation:
To find the area of the shaded region, we need to subtract the area of the sector from the area of the triangle formed by the radius and the two radii connecting to the endpoints of the central angle.
First, let's find the area of the sector:
The formula for the area of a sector is (θ/360) * π * r^2, where θ is the central angle and r is the radius.
Given that the radius is 2 m and the central angle is 160°, we have:
θ = 160°
r = 2 m
Converting the angle to radians:
θ_radians = (160° * π) / 180° = (8π/9) radians
Now, we can calculate the area of the sector:
Area_sector = (θ_radians / (2π)) * π * r^2
= (8π/9) / (2π) * π * 2^2
= (4/9) * π * 4
= (16/9)π m^2
Next, let's find the area of the triangle:
The formula for the area of a triangle is (1/2) * base * height.
The base of the triangle is equal to the length of the radius, which is 2 m.
The height of the triangle can be found using the formula h = r * sin(θ/2).
θ = 160°
r = 2 m
Converting the angle to radians:
θ_radians = (160° * π) / 180° = (8π/9) radians
Calculating the height:
h = 2 * sin(θ_radians/2)
= 2 * sin((8π/9)/2)
= 2 * sin(4π/9)
= 2 * (√(1 - cos(4π/9)^2))
= 2 * (√(1 - cos^2(4π/9)))
Now, we can calculate the area of the triangle:
Area_triangle = (1/2) * base * height
= (1/2) * 2 * 2 * (√(1 - cos^2(4π/9)))
= 2 * (√(1 - cos^2(4π/9)))
Finally, we can find the area of the shaded region by subtracting the area of the sector from the area of the triangle:
Area_shaded_region = Area_triangle - Area_sector
= 2 * (√(1 - cos^2(4π/9))) - (16/9)π m^2
This is the exact answer in terms of π, with the correct unit of measurement (m^2).
Which of the following reflective symmetries
apply to the hexagon below?
Symmetry
D
E
F
C
A
Reflective symmetry over AD
Reflective symmetry over CE
B
Applies to th
Yes/No
Yes/No
The table can be filled as Symmetry | Applies to the hexagon Reflective symmetry over AD | Yes Reflective symmetry over CE | No
We are given that;
The hexagon DEFCA
Now,
the hexagon has reflective symmetry over AD, because if we fold it along AD, the vertices B and F will match, as well as the vertices C and E. Therefore, the answer for reflective symmetry over AD is Yes.
However, the hexagon does not have reflective symmetry over CE, because if we fold it along CE, the vertices A and F will not match, nor will the vertices B and D. Therefore, the answer for reflective symmetry over CE is No.
Therefore, Symmetry | Applies to the hexagon Reflective symmetry over AD | Yes Reflective symmetry over CE | No.
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x is proportional to the square root of y, where y > 0
y is increased by 44%
Work out the percentage increase in x
When Y is increased by 44%, X increases by 20%.
If X is proportional to the square root of Y, then we can express this relationship as X = k√Y, where k is the constant of proportionality. Now, let's consider the scenario where Y is increased by 44%.
Let's denote the initial value of Y as Y₀. When Y is increased by 44%, the new value of Y becomes Y₁ = Y₀ + 0.44Y₀ = 1.44Y₀.
Since X is proportional to the square root of Y, we can write the initial value of X as X₀ = k√Y₀, and the new value of X as X₁ = k√(1.44Y₀).
To find the percentage increase in X, we can calculate the difference between the new and initial values of X and express it as a percentage of the initial value:
Percentage increase in X = ((X₁ - X₀) / X₀) * 100
Substituting the values, we get:
Percentage increase in X = ((k√(1.44Y₀) - k√Y₀) / k√Y₀) * 100
Simplifying the expression, we find:
Percentage increase in X = ((√1.44 - √1) / √1) * 100
Percentage increase in X = (1.2 - 1) x 100
Percentage increase in X = 0.2 x 100
Percentage increase in X = 20%
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¿Para qué valor de la constante "b" la función real
f(x) = 2bx³ + 2x² − 3 tiene un extremo relativo en x = -1/6
a) b=4
b) b=-4
c) c=-6
d) b=6
e) b=-3
calculate for me question 4, please
Answer:
f(x) = x^2 - 5x + 6
f'(x) = 2x - 5
Since the slope of h(x) is 1/3, the slope of the tangent line to f(x) will have slope -3.
2x - 5 = -3
2x = 2, so x = 1
The local high school is hosting an ice cream social for new students. They
record the ice cream choices of the students throughout the event.
What is the probability that a female student chose strawberry ice cream?
Male
Female
Total
Vanilla Strawberry
6
4
8
9
14
13
Chocolate Total
13
23
21
44
4
17
The probability that a female student chose strawberry ice cream is 7/11 or approximately 0.6364 (rounded to four decimal places).
To calculate the probability that a female student chose strawberry ice cream, we need to consider the total number of female students who made an ice cream choice and the number of female students who chose strawberry ice cream.
From the given information, we have the following breakdown:
Male Female Total
Vanilla 6 4 10
Strawberry 9 14 23
Chocolate 13 4 17
Total 28 22 50
To find the probability, we divide the number of female students who chose strawberry ice cream by the total number of female students:
Probability = (Number of female students who chose strawberry ice cream) / (Total number of female students)
Therefore, the probability of a female student choosing strawberry ice cream is:
Probability = 14 / 22
Simplifying the fraction, we have:
Probability = 7 / 11
Therefore, the probability that a female student chose strawberry ice cream is 7/11 or approximately 0.6364 (rounded to four decimal places).
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please help I don’t know how to do this graph
The graph of the functions f(x) and g(x) is given below.
Given that:
Function, f(x) = x³
Translated function, g(x) = (x + 6)³
If the function is translated by 'h' units horizontally and 'k' units vertically, then x and y are replaced with (x - h) and (y - k), respectively.
The curve of the function g(x) is translated left side by 6 units.
The graph of the functions is given below.
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There are 1000 cubic centimeters and 1 Liters in 1000 cubic millimeters in 1 milliliter. How many cubic millimeters are there in 1000 cubic centimeters
Answer:Set up a proportion, letting = the amount of cubic millimeters in 1,000 cubic centimeters. Solve for : 1,000,000 cubic millimeters are in 1,000 cubic centimeters.
The probability that a machine will produce
all bolts in a production run within
specification is 0.998. A sample of 8
machines is taken at random then the
probability that 7 or 8 machines is:
Select one:
O
a. 0.9999
b. 0.9841
c. 1
d. 0.8
The probability that 7 or 8 machines will produce all bolts within specification is approximately 0.9841.
Using the binomial distribution formula, we get:
P(X = 7) = (8 choose 7) * (0.002)⁷ * (0.998)¹ ≈ 0.0081
P(X = 8) = (8 choose 8) * (0.002)⁸ * (0.998)⁰ ≈ 0.000003
Therefore, P(X = 7) + P(X = 8) ≈ 0.0081 + 0.000003 ≈ 0.9841.
Probability is a branch of mathematics that deals with the study of the likelihood of occurrence of events or outcomes in situations where there is uncertainty or randomness. It is a measure of the degree of uncertainty of an event, typically expressed as a number between 0 and 1. Probability is used to make predictions and decisions in various fields, including science, engineering, economics, finance, and social sciences.
It is based on the analysis of past events or observations, and it enables us to estimate the likelihood of future events or outcomes. Probability theory provides a mathematical framework for modeling and analyzing random phenomena and helps us understand the laws of chance that govern various natural and artificial systems.
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The bedroom, garage, office, and bathroom of a house will be painted, each with a different color. There are 15 colors to choose from. This means that there are ________ color arrangements possible.
Answer: There are 32,760 color arrangements possible for painting the bedroom, garage, office, and bathroom with different colors chosen from 15 options.
Step-by-step explanation: To determine the number of color arrangements possible for painting the bedroom, garage, office, and bathroom with different colors chosen from 15 options, we need to calculate the number of permutations.
Since each room is assigned a different color, we can arrange the colors in a specific order. The number of ways to arrange 15 colors in 4 distinct positions is given by the permutation formula:
P(n, r) = n! / (n - r)!
where n is the total number of options (15 colors) and r is the number of positions (4 rooms).
Using the formula, the number of color arrangements possible is:
P(15, 4) = 15! / (15 - 4)!
= 15! / 11!
= (15 * 14 * 13 * 12) / (4 * 3 * 2 * 1)
= 32,760
ABCD is a quadrilateral.
a
b) When ABCD is drawn to scale, would
the lines AD and BC be parallel or not? A
You must justify your answer without
using a scale drawing.
Justify your answer
Yes/No
The value of x is 45 in the provided assertion, and the Centerior angles do sum up to 180°, indicating that AD and BC are parallel.
We have,
Parallel in mathematics refers to two lines which never cross one another; picture an equal symbol. Three close pals' parallel lives could be depicted in a tale.
(a)
3x + x + 2x + 90 = 360
6x = 360 - 90
6x = 270
x = 45
(b) The answer will be yes, they would be parallel.
We can justify this using co-interior angles, which state that 2 angles subtended by parallel lines add up to 180°
We can check this with both angles 3x & x, or 2x & 90°.
If AD and BC are parallel, then 3x + x = 180, and since you already found the value of x we can substitute this in:
3(45) + (45) = 180
135 + 45 = 180
180 = 180
So the co-interior angles do add up to 180°, which means that AD and BC are parallel.
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What are the zeros of the function defined by y = x2 + 6x + 5?
There are 8 strawberry plants in each row. Each plant has 11 strawberries on it. What equation could you use to find how many strawberries there are in 7 rows?
8 + 11 x 7 = ___
8 x 11 + 7 = ___
8 x 11 x 7 = ___
8 x 11 ÷ 7 = ___
Write the factored form of the polynomial function with real coefficients, a lead coefficient of 1, and zeros of -4, -2, 4, and 2.
Step-by-step explanation:
Using the roots given in order given:
y= ( x+4)(x+2)(x-4)(x-2) would fit the bill.....
Imagine a clock with the hour hand at 12 and the minute hand at 2. Does the angle formed by the two hands have a measure greater than, less than, or equal to 1/4 turn?
The angle formed by the two hands have a measure less than 1/4 turn
How to relate the measure of the angle to 1/4 turn?From the question, we have the following parameters that can be used in our computation:
A clock with the hour hand at 12 and the minute hand at 2
The turn represented by the above is represened as
Turn = (2 * 30)/360
When simplified, we have
Turn = 1/6
Next, we have
Angle at the turn = 1/4
1/6 is less than 1/4
This means that the angle formed by the two hands have a measure less than 1/4 turn
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What is this expression in simplified form?
✔-1, 728
O A. -12
OB. -36
O C.
-42
OD. -576
If A and B are m × n matrices such that Ax = Bx for all x ∈ R n , then A = B. Please prove this.
From matrix property it can be showed that A=B.
Given,
If A,B and x are matrices with x≠0 and AX=BX
Now.
X must be non-singular matrix because
A[tex]XX^{-1}[/tex]=B[tex]XX^{-1}[/tex]
[tex]XX^{-1}[/tex] = I( identity matrix )
AI = BI
A = B
Hence Proved, A = B .
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Let f(x) = 5 sin(x). Describe the graph of each of the following in terms of the graph off.
1. g(x) = 5 sin(x) + 4
2. h(x) = 5 sin(x + 1)
3. k(x) = 20 sin(x) + 10
4. m(x) = 5 sin(4x - 1)
I
The graph of g(x) will have the same shape as f(x), but every y-coordinate will be increased by 4 units,The graph of h(x) will have the same shape as f(x), but every x-coordinate will be decreased by 1 unit,The graph of k(x) is 20 and every y-coordinate is increased by 10 units and the graph of m(x) is horizontally squeezed.
To describe the graphs of the given functions, let's first analyze the effects of the transformations applied to the original function f(x) = 5 sin(x).
1. g(x) = 5 sin(x) + 4:
The function g(x) is obtained by vertically shifting the graph of f(x) by 4 units upward. This means that the graph of g(x) will have the same shape as f(x), but every y-coordinate will be increased by 4 units.
2. h(x) = 5 sin(x + 1):
The function h(x) is obtained by horizontally shifting the graph of f(x) to the left by 1 unit. This means that the graph of h(x) will have the same shape as f(x), but every x-coordinate will be decreased by 1 unit. The period of the function remains the same.
3. k(x) = 20 sin(x) + 10:
The function k(x) is obtained by vertically stretching the graph of f(x) by a factor of 20 and then shifting it 10 units upward. This means that the amplitude of the graph of k(x) is 20 (compared to the amplitude of 5 in f(x)), and every y-coordinate is increased by 10 units.
4. m(x) = 5 sin(4x - 1):
The function m(x) is obtained by compressing the graph of f(x) horizontally by a factor of 4, reflecting it across the y-axis, and shifting it 1 unit to the right. This means that the period of m(x) is 1/4 of the period of f(x), and the graph is horizontally squeezed. The reflection across the y-axis means that the graph of m(x) will be inverted compared to f(x). The amplitude remains the same.
Remember that the graph of the original function f(x) = 5 sin(x) represents a sine wave with an amplitude of 5 and a period of 2π. Applying the transformations described above will modify the position, scale, and shape of the graph, resulting in the respective graphs for each function g(x), h(x), k(x), and m(x).
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A certain car has a fuel efficiency of 28.1 miles per gallon (mi/gal). Express this efficiency in kilometers per liter (km/L).
Answer:
the answer is 10.63km/L.
A multiple choice question has five Anne’ answer options of which two options are correct what is the probability of randomly choosing the correct pair of answer options
Answer:
1/10
Step-by-step explanation:
2/5 * 1/4 = 2/20 = 1/10
2 right answers, 5 possible choices
Select one right choice = 2/5
After selecting one right choice, there are 4 possible choices with one more right choice left.
Select another right choice = 1/4
Does anybody know this? From a group of five boys and three girls, a boy and a girl will be selected to attend a conference in how many ways can the selection be made?
If the Coach chooses the Three-Year Plan, what is the total amount he will spend after 12 months? ANSWER QUICK ILL GIVE BRAINLIST!
Answer:
$17,320 after 12 months.
Step-by-step explanation:
f the Coach chooses the Three-Year Plan, the total amount he will spend after 12 months can be calculated as follows:
First, we need to calculate the total amount of monthly payments made in 12 months:
12 months x $610 per month = $7,320
Then, we need to add the down payment made at the time of purchase:
$7,320 + $10,000 = $17,320
Therefore, if the Coach chooses the Three-Year Plan, he will spend a total of $17,320 after 12 months.
Solve 44 = K + 58 for K
Answer:
-14 = k
Step-by-step explanation:
44 = k+58
Subtract 58 from each side.
44-58 = k+58-58
-14 = k
PLEASE HELP!! WIKL GIVE BRAINLIEST!!
Action. 2,150
Comedy. 1,271
Drama. 829
Romance. 300
The manager of the theater expects to sell 8,000 movie tickets next month. The theater earns $4.53 profit on each movie ticket sold. Based on last month's results, how much profit can the theater manager expect to earn from ticket sales to romance movies next month?
Answer:
$2174.40
Step-by-step explanation:
2150+1721+829+300=5000
They sold 5000 tickets last month.
300÷5000=0.06
So 6% of the tickets each month are romance.
They expect to sell 8000 next month.
8000x.06=480
They should sell 480 romance tickets next month.
480x4.53=2174.40
which represents 10 times the value of the digit 8 in 308.19
Answer: 0
Step-by-step explanation:8th Place 100*10 1000th Place is 0
Which systems is the only inconsistent system?
A.
Y=2x+3
Y=2x-1
B.
Y=x+3
Y=-x+7
C.
Y=x-5
2y=2x-10
D.
Y=x+3
Y=2x+4
Answer:
C
Step-by-step explanation:
Both equations are the same
Find the m angle DEG and angle DEF. H D 6x E 4x° G F
Based on the application of the complementary angles, the measures of the angles are: m<DEG = 54 degrees; mm<GEF = 36 degrees
What are Complementary Angles?When two angles make up a right angle, they are referred to as complementary angles because they add up to 90 degrees when summed.
6x and 4x make up a right angle, this means their sum will give us 90 degrees when we add them up. Therefore:
6x + 4x = 90
10x = 90
Divide both sides by 10
10x/10= 90/10
x = 9
measure of angle DEG = 6x = 6(9) = 54 degrees.
Measure of angle GEF = 4x = 4(9) = 36 degrees
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The figure shows four box-and-whisker plots. These represent variation in travel time for four different types of transportation from the beginning to the end of one route.
Conrad is at one end of the route. He is trying to decide how to get to an appointment at the other end. His appointment is in 30 minutes. Which type of transportation is LEAST likely to take more than 30 minutes?
Select one:
a.
bus
b.
car
c.
subway
d.
train
Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.
How to Interpret a Box-and-whisker Plot?
In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.
The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.
Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.
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Can u find “V”
XXX* YV=••••+666=799Y
The letter "V" in the equation XXX × YV=••••+666=799Y is replaced by the number 89.
How to simplify equations?The equation can be simplified to XXX × YV=1335.
If both sides of the equation are divided by 3, X × YV = 445.
If now all the X's is replaced with 5's, 5 × YV = 445.
This gives the following equation:
5 × YV = 445
Now multiply both sides of the equation by Y, to get 5Y = 445.
This gives us the following equation:
5Y = 445
Finally, divide both sides of the equation by 5, to get Y=89.
Therefore, the letter "V" in the equation XXX × YV=••••+666=799Y is replaced by the number 89.
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Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
The equivalent value of the equation is 18x-9=72 and x=4.5
Given data ,
Let the equation be represented as A
Now , the value of A is
(3/5)(30x-15)=72
On simplifying the equation , we get
3(6x-3)=72
On further simplification , we get
18x-9=72
x=81/18
x=4.5
Hence , the equation is 18x-9=72
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Find the coordinates of the intersection of the diagonals of ABCD
with vertices A(0, 2), B(8, 2), C(4, − 4), and D(−4, − 4).
The coordinates of the intersection of the diagonals are ( , )
If the coordinates of the intersection of the diagonals of ABCD
with vertices A(0, 2), B(8, 2), C(4, − 4), and D(−4, − 4). The coordinates of the intersection of the diagonals are (4/3, 0).
What is the coordinates?Using the two point form of the equation of a line to determine the The equation of the line that contains AC
y₋y₁ = (y₂-y₁)/(x₂-x₁) * (x₋x₁)
where:
(x₁, y₁) and (x₂, y₂)= two points on the line
y - 2 = (-4 - 2)/(4 - 0) * (x - 0)
Simplify
y - 2 = -3/2 * x
2y - 4 = -3x
3x + 2y = 4
Equation of the line that has BD
y - 2 = (-4 - 2)/(8 - (-4)) * (x - 8)
Simplify
y - 2 = -3/4 * x + 9/2
4y - 8 = -3x + 36
3x + 4y = 44
Now let find the point of intersection:
3x + 2y = 4
3x + 4y = 44
Multiplying the first equation by -2
-6x - 4y = -8
Eliminate x
0x + 0y = 36
So,
y = 0
3x + 2(0) = 4
3x = 4
x = 4/3
Therefore the coordinates is (4/3, 0).
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