What the difference between the lengths of the two routes
Step-by-step explanation:
Comparison of two routes in terms of complexity and length. The blue route (. . .) is the shortest but is complex to explain while the red (---) is simpler although a bit longe
Find the measure of each angle indicated.
P
U
160°
W
95° ?
V
Answer:
? = 65°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ PUV is an exterior angle of the triangle , then
? + 95° = 160° ( subtract 95° from both sides )
? = 65°
10. A pizza with a diameter of 5 inches is divided into 8 sectors
of equal area.
What is the approximate area of each pizza slice? Round
your answer to the nearest hundredth.
O
O
The approximate area of each pizza slice is 2.45 sq inches
What is the approximate area of each pizza slice?From the question, we have the following parameters that can be used in our computation:
Diameter = 5 inches
This means that
Radius, r = 5/2 inches
Evaluate
Radius, r = 2.5 inches
The approximate area of each pizza slice is calculated as
Area = Circle area/number of sectors
So, we have
Area = 3.14 * 2.5^2/8
Evaluate
Area = 2.45 sq inches
Hence, the approximate area of each pizza slice is 2.45 sq inches
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A young couple purchases their first new home in 2011 for $95,000. They sell it to move into a bigger home in 2018 for $105,000. First, we will develop an exponential model for for the value of the home. The model will have the form V(t) = V0e^kt. Let t be years since 2011 and V (t) be the value of the home.
a. The home's value is increasing at a rate of approximately 1.55% per year.
b. The exponential model is V(t) = [tex]95000e^{(0.0155t)}[/tex]
c. The predicted value of the home in 2022 is approximately $123,240.
d. The home's value reached $130,000 approximately 20 years after 2011, which is in the year 2031.
To find the growth rate k, we can use the formula [tex]V(t) = V0e^{(kt)}[/tex]. We have two data points: V(0) = 95000 and V(7) = 105000 (since 2018 is 7 years after 2011). Inputting these values into the formula yields:
V(0) =[tex]V0e^{(0k)}[/tex] = V0
V(7) = [tex]V0e^{(7k)}[/tex]= 105000
When the second equation is divided by the first, the result is:
V(7)/V(0) = [tex]e^{(7k)}[/tex] = 105000/95000 = 1.1053
Taking the natural logarithm of both sides and calculating k yields:
ln(1.1053) = 7k
k ≈ 0.0155
This means that the home's value is increasing at a rate of approximately 1.55% per year.
b. The exponential model is V(t) = [tex]95000e^{(0.0155t)}[/tex].
c. The predicted value of the home in 2022 is approximately $123,240.
To predict the home's value in 2022, we need to find the value of V(t) when t = 11 (since 2022 is 11 years after 2011). Substituting into the exponential model gives:
V(11) = [tex]95000e^{(0.0155*11)}[/tex] ≈ $123,239.62
So the predicted value of the home in 2022 is approximately $123,240.
d. The home's value reached $130,000 approximately 20 years after 2011, which is in the year 2031.
We need to solve for t in equation V(t) = 130,000.
130,000 = [tex]95,000e^{(0.0155t)}[/tex]
Dividing both sides by 95,000 and taking the natural logarithm of both sides, we get:
ln(130,000/95,000) = 0.0155t
Simplifying, we get:
t = (ln(130,000/95,000))/0.0155
t = (ln(1.368)/0.0155
t = 0.313 / 0.0155
t ≈ 20.23
Therefore, the home's value reached $130,000 approximately 20 years after 2011, which is in the year 2031.
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Complete question:
A young couple purchases their first new home in 2011 for $95,000. They sell it to move into a bigger home in 2018 for $105,000. First, we will develop an exponential model for the value of the home. The model will have the form V(t) = V0e^(kt) . Let t be years since 2011 and v (t) be the value of the home.
a. What is the growth rate k for the model? What does that number mean?
b. What is the exponential model?
c. Predict the value of the home in 2022.
d. During what year did the value of the home reach $130,000?
3.) Given the regular polygon. Find the measure of each numbered angle.
m<1 = 30
m<2 = 15
m<3 =
75
Work/expanation:
The b. m<angle1 = 45°,
mangle2 = 67.5°
How to solveAn octagon has 8 sides.
Sum of interior angles = 180° x (n-2) = 180° x (8-2) = 180° x 6 = 1,080°
1,080° ÷ 8 sides = 135° interior angle.
Angle 2 = 135° / 2 = 67.50°
Angle 1 = 180° - 135° = 45°
If these were the choices given:
a. mangle1 = 45°, mangle2 = 135°
b. mangle1 = 45°, mangle2 = 67.5° ⇔ THIS IS THE CORRECT ANSWER.
c. mangle1 = mangle2 = 60°
d. mangle1 = 22.5°, mangle2 = 78.75°
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Pls help me with this problem pls right answer only pls, quick!
Answer:
This is a quadratic function.
Find all solutions of the equation in the interval [0, 27). (Enter your answers as a comma-separated list.)
6 tan²(x) + 6 tan(x) = 0
X =
The solutions are x = 0 and x = 3π/4, written as 0, 2.35619 (in radians).
We can factor out 6 tan(x) from the left-hand side of the equation:
6 tan(x) (tan(x) + 1) = 0
This equation is satisfied if either 6 tan(x) = 0 or tan(x) + 1 = 0.
If 6 tan(x) = 0, then tan(x) = 0. This occurs when x = 0, π, 2π, etc. However, we need to restrict our attention to the interval [0, 27), so the only solution in this case is x = 0.
If tan(x) + 1 = 0, then tan(x) = -1. This occurs when x = 3π/4 + nπ, where n is an integer. However, we need to restrict our attention to the interval [0, 27), so the only solution in this case is x = 3π/4.
Therefore, the solutions of the equation 6 tan²(x) + 6 tan(x) = 0 in the interval [0, 27) are x = 0 and x = 3π/4, which can be written as the comma-separated list: 0, 2.35619.
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HELP PLEASE IM GIVE BRAINLIST
The triangle which could be drawn as per the given description is only option b. isosceles triangle with measure 20° and 80°.
An acute triangle with sides measuring 7, 4, and 2
In an acute triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side .
According to the Pythagorean Theorem.
Here, 7² is greater than (4² + 2²).
So this is not possible.
An isosceles triangle with angles measuring 20° and 80°
In an isosceles triangle, two angles are equal, so if two angle measures 20° and 80°,
Then the third angle measures is
180° - 20° - 80°= 80°
Two angles are congruent implies two sides are congruent.
It is possible to form isosceles triangle.
An obtuse triangle with sides measuring 5, 10, and 15
In an obtuse triangle, the longest side is opposite the largest angle.
Sum of squares of two shorter sides is less than square of longest side according to Pythagorean Theorem.
However, 15²is greater than (5²+ 10²),
so this is not possible.
A scalene triangle with angles measuring 110° and 35°
The sum of the angles of any triangle is 180°,
so the third angle must measure
180° - 110° - 35° = 35°.
Two angles are congruent so it is isosceles triangle.
It is not possible to form scalene triangle.
Therefore, the triangle possible to draw as per the given condition is only option b. isosceles triangle with measure 20° and 80°.
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I need help asap!!!!!!!!!!!!
The falls that make up Niagara Falls are eroding backwards, thus migrating upstream.
They have migrated back 100 feet in the past 50 years. What is the rate of erosion along the falls?
( )Feet per year
The rate of erosion along the falls is given as follows:
2 feet per year.
How to obtain the rate of erosion?The rate of erosion of Niagara Falls is obtained applying the proportions in the context of the problem.
The falls have migrated back 100 feet in the past 50 years, hence the rate of erosion in feet per year is given as follows:
100/50 = 2 feet per year.
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STAINED GLASS Pablo made the stained glass
window shown. He used an inscribed square and
equilateral triangle for the design.
a. Label the angle measures on the outer edge of the
triangle.
b. Label all of the arcs with their degree measure.
a) The angles outside the side PQ measure 65° and 25°
The angles outside the side QR measure 85° and 95°
The angles outside the side PR measure 55° and 35°
b) The arc PR, PQ and PR measure 120°
a)
Let us assume that the inscribed square be ABCD and equilateral triangle is PQR.
Let side PR of triangle intersects the quadrilateral at points M and N.
So, we get a triangle DMN outside the equilateral triangle.
Here, ∠DMN = 55°, ∠D = 90°
So, ∠MND = 180 - (90 + 55)
= 35°
Similarly, side PQ of triangle PQR intersects the quadrilateral at points X and Y.
So, we get a triangle AXY outside the equilateral triangle.
From triangle PXM we get the measure of angle PXM which is 65 degrees.
As angle PXM and angle AXY are opposite angles, the measure of angle AXY = 65°
∠A = 90°
So, ∠AYX = 180° - (∠A + ∠AXY )
= 180° - (90° + 65°)
= 25°
Let the side QR of triangle PQR intersects the quadrilateral at points L and K.
so we get new quadrilateral LKBC
In this quadrilateral ∠B = 90°, ∠C = 90°
From triangle QYL, we get the measure of angle QLY = 95°
So, the measure of ∠KLB = 95° .......(∠QLY and ∠KLB opposite angles)
So, the remaining angle LKC of quadrilateral LKBC would be,
∠LKC = 360° - (∠B + ∠C + ∠KLB)
∠LKC = 360° - (90 °+ 90° + 95°)
∠LKC = 85°
b)
We know that he angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
so, the measure of arc PR = 120°
the measure of arc PQ = 120°
the measure of arc RQ = 120°
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IVE SPENT TWO DARN DAYS ON THIS QUESTION AND I DON'T GET IM SUPPOSED TO KNOW THIS OMG `
Answer:
A rhombus has four congruent sides.
The diagonals of a rhombus bisect each other and form right angles.
From these:
[tex] {(2y})^{2} + {2}^{2} = {(3y - 2)}^{2} [/tex]
[tex]4 {y}^{2} + 4 = 9 {y}^{2} - 12y + 4[/tex]
[tex]5 {y}^{2} - 12y = 0[/tex]
[tex]5y - 12 = 0[/tex]
[tex]5y = 12[/tex]
[tex]y = 2.4[/tex]
Answer:
y=2.4
Step-by-step explanation:
We know that a rhombus has 4 equal sides, and 2 diagonals which bisect eachother at an angle of 90 degrees.
Simply saying, a rhombus is made up of 4 right angled triangles.
If QR is 3y-2, that means that each other side must be 3y-2 aswell, which means that SQ is also 3y-2
Now we can use the pythagorean theorem to solve for y, given that the base is 2 (length of QU), the height is 2y (length of SU), and the hypotenuse is 3y-2 (length of SQ)
(3y-2)²=2²+2y² (Expand using binomial formula)
9y²-12y+4=4+4y² (Collect similar terms)
5y²-12y=0 (Factor the expression)
y(5y-12)=0
We know that if a product of 2 factors is 0, atleast one must also be 0
So we have to make both factors equal 0
y=0
5y-12=0
5y=12
y=12/5, or 2.4
We see that 2.4 is the only possible solution.
Hope this helps!
A cyclist managed to ride 5 miles against the wind in the same time that it took him to ride 10 miles with the wind. If the wind speed is 4 mph, which equation can be used to calculate the cyclist’s average rate of speed in miles per hour?
Answer:
Step-by-step explanation:
Average Rate of Speed = Distance / Time
Average Rate of Speed = (5 + 10) / (Time with the Wind + Time Against the Wind)
Average Rate of Speed = 15 / (Time with the Wind + Time Against the Wind)
Average Rate of Speed = 15 / (10/4 + 10/6)
Average Rate of Speed = 15 / (2.5 + 1.67)
Average Rate of Speed = 15 / 4.17
Average Rate of Speed = 3.59 mph
Which set of data could be reasonably modeled by a quadratic function?
The quadratic function is represented by option A. both graph.
From the set of data representing in the graph ,
A quadratic function is a second-degree polynomial of the form f(x) = ax² + bx + c, where a, b, and c are constants.
It represents a parabolic curve when plotted on a graph.
Generally, a quadratic function is suitable for modeling data that shows a U-shaped or inverted U-shaped pattern.
Representation of x-axis and y-axis is not clearly specified in the graph .
We assume different conditions.
Projectile motion,
The trajectory of a ball thrown into the air or a projectile fired from a cannon can be modeled by a quadratic function.
Falling objects,
The distance a dropped object falls over time can be modeled by a quadratic function.
Profit vs. production,
The relationship between a company's profit and the level of production can be modeled by a quadratic function.
The profit generally increases with production but eventually reaches a maximum point before declining.
Trajectory of a car,
The distance traveled by a car accelerating from a stationary position can be modeled by a quadratic function.
Height vs. time,
The height of an object thrown upwards, such as a bouncing ball, can be modeled by a quadratic function.
The height increases, reaches a maximum point, and then decreases.
Here both the graphs represents the quadratic function.
Therefore, the set of the data clearly modelled the quadratic function is present by option A. Both graph.
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Ethan's class is handing out balloon arrangements consisting of 4 balloons each. Each balloon has an equally likely chance of being red, blue, or yellow. Ethan created a spinner to simulate this probability. Here is Ethan's data from 30 trials of 4 spins on the spinner (r = red, b = blue, y = yellow):
ybrr bybb rbbb rrry rbbb rryy yybb ryry ryyr rbyr ryyr rryy rrrr yrby bbyy byyr byyr byyb rbby ybry rryy rbrr rybb bbbr rrbr ybry ryrr rryb rrrb rryr
According to this data, what is the experimental probability that an arrangement will consist entirely of balloons that are the same color?
0.012
0.1
0.033
0.33
The requried, experimental probability is 0.1. Option B is correct.
To find the experimental probability that an arrangement will consist entirely of balloons that are the same color, we need to count the number of times that Ethan got an arrangement where all four balloons were the same color and divide that by the total number of trials.
Looking through the data, we can see that the following trials had all four balloons the same color:
rrrr
bbbb
yyyy
So, out of 30 trials, there were 3 trials where all four balloons were the same color. Therefore, the experimental probability is:
3/30 = 0.1
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What is the slope of the line passing through points (4, 6) and (2, 4)? A. 3 B. 6 C. 4 D. 2 E. 1
Answer: E. 1
Explanation: The slope (m) of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
We can use this formula to find the slope of the line passing through points (4, 6) and (2, 4):
m = (y2 - y1) / (x2 - x1)
m = (4 - 6) / (2 - 4)
m = -2 / -2
m = 1
The slope of the line passing through points (4, 6) and (2, 4) is 1.
The answer is E) 1.
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The circumference of a circle is 20 � π cm. Find its radius, in centimeters.
The required radius of the circle is 10 cm.
The formula for the circumference C of a circle in terms of its radius r is given by:
C = 2πr
We are given that the circumference of the circle is 20π cm. So we can set this expression equal to 20π and solve for r:
20π = 2πr
Dividing both sides by 2π, we get:
r = 10
Therefore, the radius of the circle is 10 cm.
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Entomologists have discovered that a linear relationship exists between the rate of chirping of crickets of a certain species and the air temperature. When the temperature is 70°F, the crickets chirp at the rate of 120 chirps/min, and when the temperature is 90°F, they chirp at the rate of 200 chirps/min.
(a) Find an equation giving the relationship between the air temperature T and the number of chirps per min N of the crickets.
N =
(b) Use this function to determine the rate at which the crickets chirp when the temperature is 104°F.
chirps/min
An equation giving the relationship between the air temperature T and the number of chirps per min N of the crickets is N = 4T - 160.
The rate at which the crickets chirp when the temperature is 104°F is 256 chirps/min.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided above, the linear relationship can be modeled by using this system of linear equations:
y = mx + c
120 = 70x + c
200 = 90x + c
By solving the system of equations simultaneously, we have:
200 = 90x + 120 - 70x
20x = 80
x = 4.
c = 120 - 70(4)
c = -160
Therefore, the linear relationship is given by;
y = 4x - 160 ≡ N = 4T - 160.
When T = 104°F, N is given by;
N = 4(104) - 160
N = 256 chirps/min.
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Place value of 4 in 265 473
Answer:
The place value of 4 in 265 473 is 40,000
Answer:
Step-by-step explanation:
Order:
3 is in the ones place and has a value of 3
7 is in the tens place and has a value of 70
4 is in the hundreds place and has a value of 400
5 is in the thousands place and has a value of 5000
6 is in the ten thousands place and has a value of 60,000
2 is in the hundred thousands place and has a value of 200,000
The school is planning to add 2 new playgrounds. Each playground will be in the shape of a square that measures by 24m by 24m.What will be the area of the playgrounds?
Answer: 1152 sq m
Step-by-step explanation: 24x24=576+ 24x24=576 so 576+576
Need Help!!!! A pre-image has coordinates J(3, -6) and K(-1, -2). The image has coordinates J'(6, 3) and K'(2, -1). Describe the clockwise rotational path of the line segment.
After considering the given data we conclude that the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).
We have to evaluate the center and angle of rotation to explain the clockwise rotation of the line segment.
So in the first step, we can evaluate the midpoint of the line segment JK and the midpoint of the line segment J'K'. we can calculate the vector connecting the midpoint of JK to the midpoint of J'K'. This vector is (4-1, 1-(-4) = (3,5)
The center of rotation is the point that is equidistant from the midpoints of JK and J'K'. We can evaluate this point by finding the perpendicular bisector of the line segment connecting the midpoints.
The slope of this line is the negative reciprocal of the slope of the vector we just found, which is -3/5. We can apply the midpoint formula and the point-slope formula to evaluate the equation of the perpendicular bisector:
Midpoint of JK: (1, -4)
Midpoint of J'K': (4, 1)
The slope of the vector: 3/5
(x₁ + x₂)/2, (y₁ + y₂) /2
Point-slope formula: y - y₁ = m(x - x₁)
Perpendicular bisector: y - (-4) = (- 3/5)(x - 1)
Applying simplification , we get: y = (- 3/5)x - 1.2
To evaluate the center of rotation, we need to find the intersection point of the perpendicular bisector and the line passing through the midpoints of JK and J'K'. This line has slope ( 3 - (4)) /(4 - 1) = 7/3 and passes through the point (4, 1). Applying the point-slope formula, we can evaluate its equation:
y - 1 = (7/3)( x - 4)
Apply simplification , we get: y = (7/3)x - 17/3
To evaluate the intersection point, we can solve the system of equations:
y =(- 3/5)x - 1.2 = (7/3)x - 17/3
Evaluating for x and y, we get x = -6 and y = -1.
Therefore, the center of rotation is (-6, -1).
√( 4 - 1)² + ( 1 - ( - 4))²) = 5√(2)
Distance between image points and center of rotation
√( ( 6 - (-6))² + ( 3 - (-1))² = 13
The ratio of these distances gives us the scale factor of the transformation, which is 13/√2).
The angle of rotation is negative as the image moves clockwise direction. We can apply the inverse tangent function to find the angle of the vector connecting the midpoint of JK to the midpoint of J'K':
Angle of vector: arctan(5/3) = 59.04 degrees
Therefore, the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).
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Select the correct answer. A company manufactures computers. Function N represents the number of components that a new employee can assemble per day. Function E represents the number of components that an experienced employee can assemble per day. In both functions, t represents the number of hours worked in one day. Which function describes the difference of the number of components assembled per day by the experienced and new employees? A. B. C. D. Reset Next
The function that describes the difference of the number of components assembled per day by the experienced and new employees is:
E(t) - N(t)
This is because E(t) represents the number of components assembled by an experienced employee in t hours, and N(t) represents the number of components assembled by a new employee in t hours. Therefore, the difference between the two functions will give us the difference in the number of components assembled per day by the two types of employees.
Out of the given options, option A represents the correct answer:
E(t) - N(t) = (5t) - (3t) = 2t
Therefore, the correct answer is A.
Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and Population 2 does not. The data from these two samples is given below:
Population 1: 69, 68, 62, 68, 68, 62, 69
Population 2: 76, 68, 68, 72, 76, 70, 70, 70
Is there evidence, at an α=0.025
level of significance, to conclude that those who exercise regularly have lower resting heart rates? (Assume that the population variances are equal.) Carry out an appropriate hypothesis test, filling in the information requested.
A. The value of the standardized test statistic:
B. The rejection region for the standardized test statistic:
C. Your decision for the hypothesis test:
A. The value of the standardized test statistic is -2.391.
B. The rejection region for the standardized test statistic is t <-2.160.
C. The decision for the hypothesis test is to reject the null hypothesis.
How to explain the hypothesisEmploying a t-distribution table or calculator along with 13 degrees of freedom (n1 + n2 - 2) enables us to ascertain the rejection region for the t-statistic at an α=0.025 level of significance (two-tailed test):
Rejection Region: t < -2.160 or t > 2.160
Given that -2.391 falls in the rejection region, we repudiate the null hypothesis. At the α=0.025 level of significance, we are provided sufficient evidence to support that those who consistently partake in exercise generally have a lower resting heart rate than those who do not.
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Which ones apply to the question
Answer:
1 and 3 are correct.
1 is correct (supplementary angles)
3 is correct (1 and 3 are vertical angles)
a. Express each of the following as a function of 15°
6. tan165°
7. sin285°
Expressing each as a function of 15°, we have 6. tan165° = tan(150 + 15)° and 7. sin285° = sin(270 + 15)°
Expressing each as a functionFrom the question, we have the following trigonometry function that can be used in our computation:
6. tan165°
7. sin285°
The above expressions are tangent and sine functions of 165 and 285 degrees
By mathematical expression, we have
165° = 150 + 15
285° = 270 + 15
This means that we can replace the expressions with 150 + 15 and 270 + 15
So in terms of 15 degrees, we have
6. tan165° = tan(150 + 15)° and 7. sin285° = sin(270 + 15)°
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Write an explicit formula for an, the nth term of the sequence 25,30,35,....
Answer:
[tex]a_{n}[/tex] = 5n + 20
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence
30 - 25 = 35 - 30 = 5
this indicates the sequence is arithmetic with explicit formula
[tex]a_{n}[/tex] = a₁ + d(n - 1)
where a₁ is the first term and d the common difference
here a₁ = 25 and d = 5 , then
[tex]a_{n}[/tex] = 25 + 5(n - 1) = 25 + 5n - 5 = 5n + 20
complete the table AB=1?, BC=3?
Answer:
angle B = 60 degree
AB = 2 cm
BC = 2 cm
Step-by-step explanation:
an equilateral triangle is a triangle with the following properties:
1. all sides equal
2. all angels equal to 60 degree
As a result:
angle B = 60 degree
AB = 2 cm
BC = 2 cm
4.) What is the area of the sector with a central angle of 60° and a radius of 2m?
Round your answer to the nearest tenth or leave in terms of .
area =
A
2 60
B
2/3
m²
Work:
The "area" of sector which is having "central-angle" of 60° and the radius of 2m is 2.094 m².
The "Sector" of circle is defined as region bounded by "two-radii" of circle and arc intercepted between them. The two radii that bound the sector are called the "sides" of the sector.
The center of the circle is called as vertex of the sector. The area of a sector can be found using the formula : A = (θ/360)πr², where θ is = angle of sector;
The measure of "central-angle" is = 60°, and radius of circle is = 2m,
So, Area is = (60/360)π(2)²,
⇒ Area is = 4π/6 ≈ 2.094 m²,
Therefore, area of sector is 2.094 m².
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The given question is incomplete, the complete question is
What is the area of the sector with a central angle of 60° and a radius of 2m?
Fred brought a shirt and a wallet for a total of 34.26 before tax. The price of the wallet was $15 less than the price of the shirt. What was the price of the shirt?
Answer:
The price of the shirt is $24.63.
Step-by-step explanation:
Let's assume the price of the shirt is x. Then the price of the wallet will be x - 15. We know that the total cost before tax is 34.26, so we can set up the equation:
x + (x - 15) = 34.26
Simplifying, we get:
2x - 15 = 34.26
Adding 15 on both sides:
2x = 49.26
Dividing by 2:
x = 24.63
Therefore, the price of the shirt is $24.63.
An English class consists of 23 students, and three are to be chosen to give speeches in a school competition. In how many different ways can the teacher choose the team, given the following conditions? The order of the speakers is not important
Answer: The number of different ways the teacher can choose the team of three students from a class of 23, where the order of the speakers is not important, is 1771.
Step-by-step explanation:
To solve this problem, we can use the combination formula:
nCr = n! / r!(n - r)!
where n is the total number of items, r is the number of items to be selected, and ! represents factorial, which means the product of all positive integers up to the given number.
In this case, we need to choose 3 students out of 23, without regard to the order in which they will speak. Therefore, we need to use the combination formula with n = 23 and r = 3:
23C3 = 23! / (3!(23 - 3)!)
= 23! / (3!20!)
= (23 × 22 × 21) / (3 × 2 × 1)
= 1771
Therefore, there are 1771 different ways the teacher can choose the team of three students for the competition, where the order of the speakers is not important.
evaluate.
20
Σ4 (8)n-1
n = 1
S = [?]
Answer:
32.5861
Step-by-step explanation:
