The three methods which are used to represent a set are word description, roster method and set-builder notation.
What is a set?
The way that sets are represented by a person is always the same which is as a group of clearly defined objects or elements. A capital letter designates a set. The cardinal number of a set is the number of elements in the finite set.
The three methods used to represent a set are as follows;
1. Word description
It is the method of representing a set under which we simply use words for describing the elements of the given set.
For example: A is the set of all natural numbers less than 8.
2. Roster method
It is the method of representing a set under which the elements of the set are listed by separating them with commas and in curly brackets.
For example: A = {1,2,3,4,5,6,7}
3. Set-builder notation
It is the method of representing a set under which only the property of the elements of the given set are written.
For example: A = {x ,x ∈ N and x<8}
Hence, the above stated methods are used to represent a set.
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4. The area covered by a lake is 11 square kilometers. It is decreasing exponentially at a
rate of 2 percent each year and can be modeled by A(t) = 11 -0.98¹.
a. By what factor does the area decrease in 10 years?
b. By what factor does the area decrease each month?
Answer:
a. To find the factor by which the area decreases in 10 years, we can use the formula for exponential decay: A(t) = A0 * e^(-kt) where A0 is the initial area, k is the decay constant, and t is the time in years.
Given that A(t) = 11 -0.98^t.
so, we can say k =0.98
The area after 10 years will be:
A(10) = 11 - 0.98^10
The decrease factor is:
(A(10)/A(0)) = (11 - 0.98^10)/11
b. To find the factor by which the area decreases each month, we can first convert the annual decay rate to a monthly rate by dividing by 12, since there are 12 months in a year.
So, the monthly decay rate is 0.98/12 = 0.0816
Then we can use the formula for exponential decay again with the new decay rate:
A(t) = A0 * e^(-kt)
The area after 1 month will be:
A(1/12) = 11 - 0.0816^(1/12)
The decrease factor is :
(A(1/12)/A(0)) = (11 - 0.0816^(1/12))/11
if i helped you, can you mark my answer as best?
QUICKKKK I NEED HELP Quadrilateral ABCD is given, the interior angle at vertex B is 97 degrees and the exterior angle at vertex A is 88 degrees. Lines AB and CD are parallel. What is the most precise name for this given special quadrilateral? What is the measure of angle 1? What is the measure of angle 2?
The measure of angle 1 is 92 and the measure of angle 2 is 83.
What are lines and angles?Lines are straight with little depth or width. Perpendicular lines, intersecting lines, transversal lines, and other types of lines will be covered. An angle is a shape formed by two rays emerging from a common point. In this field, you may also come across alternate and corresponding angles.
Given that ABCD is given, the interior angle at vertex B is 97 degrees and the exterior angle at vertex A is 88 degrees. Lines AB and CD are parallel.
The measure of angle 1 is,
∠1 = 180 - 92 = 88
The measure of angle 2 is,
∠2 = 180 - 97 = 83
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Julieta went shopping for a new phone. Sales tax where she lives is 7%. The price of the phone is $29. Find the total price including tax. Round to the nearest cent.
The total amount of money that the phone will cost including tax would be = $31.03
What is cost price?Cost price is the amount of money that a seller tags a particular product which is usually after the tax fees and other service fees has been added apart from the actual price of the product.
The price of the phone = $29
The percentage of tax = 7% of 29
= 7/100 × 29
= 203/100 = $2.03
Therefore, the total amount of money that the phone will cost including tax would be = 29 + 2.03 = $31.03
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Please help me asap, it's missing :/
Step-by-step explanation:
g(f(x)) means that we first take x and calculate f(x).
then we take that result and use as input value for g(x).
x = -5
f(-5) = (-5)² + -5 - 12 = 25 - 5 - 12 = 8
and now
g(8) = -2×8 - 15 = -16 - 15 = -31
g(f(-5)) = -31
An isosceles triangle has two sides of length p and one length m. In terms of these lengths, write calculator-ready formulas for the sizes of the angles of this triangle. Please state your approach with a diagram and provide supporting theorems and properties used. Thank you!
The angle of your initial isosceles triangle was cut in half by drawing the vertical, therefore you multiply by two to determine theta top.
What are angles of triangle?The sum of the two interior angles that are not adjacent to it equals the exterior angles of a triangle, but the interior angles of a triangle always add up to 180°. Subtracting the angle of the desired vertex from 180° is another method for determining a triangle's exterior angle.The sum of a triangle's angles in a Euclidean space equals the straight angle. Three angles make up a triangle, one at each vertex and two on either side. If there are additional geometries for which this total is different, it has long been unknown.The top of the triangle can be connected to the base by a vertical line if you have two p side-lengths and one m side-length. With hypotenuse p and base 1/2*m, this will result in two equal right triangles.You may determine the base angles by using:
theta_base = arcos(m/2p)
The top angle can be calculated using:
theta_top = 2*arcsin(m/2p)
The angle of your initial isosceles triangle was cut in half by drawing the vertical, therefore you multiply by two to determine theta top. Therefore, arcosin(m/2p) would only return the first half of the angle value.To learn more about angles of triangle refer to:
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the sum of a number with the square of its following algebraic language
[tex]\bold{n + (n+1)^{2}}[/tex]
Step by step explanation:An unknown number can be interpreted with any letter of the alphabet, they will be our unknowns to be able to form an algebraic expression.
Well, in this case, I will use the variable n, to name the unknown number.
Let "n" be the number, the square of it is; n² and the following number results from adding the unit; then (n + 1) will be the next of the number.
(grouping the data the following algebraic expression is obtained):
[tex]\bold{n + (n+1)^{2}}[/tex]
Answer:
(n + 1 )
Let "n" be the number, the square of it is; n² and the following number results from adding the unit; then (n + 1) will be the next of the number.
..
Suppose that x is an int variable and y is a double variable and the input is: 10 20.7 Choose the values after the following statement executes: cin >> x >> y;.a. x=10,y=20 b. x=10,y=20.0c. x=10,y=20.7 d. x=10,y=21.0
x is an int variable and y is a double variable and the input is: 10 20.7.The output will be x = 10, y = 20.7
given that
x is an int variable
y is a double variable
The C++ double should have a floating-point precision of up to 15 digits as it contains a precision that is twice the precision of the float data type.
When you declare a variable as double, you should initialize it with a decimal value. For example, 3.0 is a decimal number. However, if you initialize it with 3, it will also work fine because although 3 and 3.0 seem to be identical i.e., an integer, there is a big difference in their internal representation.
the input is: 10, 20.7
after execution of the statement
cin >> x >> y
The output will be x = 10, y = 20.7
because x is declared as integer variable so it will print the same
y is declared as double integer variable so it will print same as given input , if it is declared as integer variable then it will be printed as 20
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Polynomial 1: 4x2
+ 5x − 4
Polynomial 2: 4x2
+ 4x − 2 What is the product of the two polynomials?
Responses
A 32x4
+ 36x3
− x2
+ 26x + 432 x 4 + 36 x 3 − x 2 + 26x + 4
B 16x4
+ 36x3
− x2
+ 26x + 416 x 4 + 36 x 3 − x 2 + 26x + 4
C 8x4
+ 18x3
− 4x2
− 26x + 88 x 4 + 18 x 3 − 4 x 2 − 26x + 8
D 16x4
+ 36x3
− 4x2
− 26x + 8
The product of the two polynomials is 16x^4 + 36x^3 - 4x^2 - 26x + 8. The solution is obtained by the method of polynomial multiplication.
What is polynomial multiplication?
The process of multiplying two or more polynomials together is known as polynomial multiplication. To obtain the final polynomial, the terms of the first and second polynomials are multiplied. We can multiply polynomials in a variety of ways depending on the kinds we are using. Each form of polynomial has a different set of guidelines for multiplication. Polynomials are multiplied by multiplying the coefficient by another coefficient and the variable by another variable.
We are given two polynomials
Polynomial 1: 4x^2 + 5x − 4
Polynomial 2: 4x^2 + 4x − 2
Multiplying both, we get
⇒(4x^2 + 5x − 4)*(4x^2 + 4x − 2)
⇒16x^4 + 16x^3 - 8x^2 + 20x^3 + 20x^2 - 10x - 16x^2 - 16x + 8
⇒16x^4 + 36x^3 - 4x^2 - 26x + 8
Hence, the product of the two polynomials is
16x^4 + 36x^3 - 4x^2 - 26x + 8.
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based on your answer(s) to part (a), complete the following statement to represent the length of candle remaining in terms of the burned length b .
The length of the remaining candle is equal to the total length of the candle minus the length of the candle that has been burned, or (total length - b).
The length of the remaining candle can be calculated by subtracting the length of the candle that has been burned (b) from the total length of the candle. This is because when a candle is burned, the length of the candle decreases. To calculate the remaining length of the candle, start by determining the total length of the candle. Then, subtract the length of the candle that has been burned (b). The result is the length of the remaining candle. The formula for this calculation is (total length - b). The length of the candle remaining is (b - 2). For example, if the total length of the candle is 6 inches and 2 inches of the candle have been burned, the remaining length of the candle would be 4 inches (6 - 2 = 4).
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A complete question: Based on your answer(s) to part (a), complete the following statement to represent the length of candle remaining in terms of the burned length bb.
simplify 4x to the power of 3 to power of 5
The simplified form of the given expression is 1073741824x¹⁵.
What is the exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
The given expression is ((4x)³)⁵
= (4x)¹⁵
= 1073741824x¹⁵
Therefore, the simplified form of the given expression is 1073741824x¹⁵.
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Evaluate this expression for the given values of x and y 2xy x=5 y= -3 FAST QUICK I WILL GIVE BRAINLIEST
The sum of the measures of two complementary angles is 90°. If one angle measures 27° more than twice the measure of the other, find the measure of the smaller angle.
The smaller angle measures ____ Degrees
Answer:
21°
Step-by-step explanation:
Let smaller angle be x
Bigger angle = 2x + 27
Since they are complementary they all sum up to 90°
Therefore 2x + 27 + x = 90
3x = 90 - 27
3x = 63
x = 21, therefore the smaller angle is 21°
If y varies directly as x and the constant of variation is -2, which equation represents this relationship
The equation represents this relationship between the variables 'x' and 'y' will be y = -2x.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
If y varies directly from x. Then the proportionality is given as,
y ∝ x
If the proportionality signature is removed then a constant is introduced. Then the equation is given as,
y ∝ x
y = kx
The constant of variation is -2. Then the equation is given as,
y = - 2x
The equation represents this relationship between the variables 'x' and 'y' will be y = -2x.
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John can mow his lawn in 3 hours and his sister, Julie, can mow it in 2 hours. How long will it take them to mow their lawn if they work together?
A. 1 hour 12 minutes
B. 1 hour 15 minutes
C. 1 hour 20 minutes
D. 1 hour 30 minutes
E. 1 hour 35 minutes
It would take 12 minute for them to mow their lawn if they work together
What is an equation?An equation is an expression showing the relationship between numbers and variables.
John can mow his lawn in 3 hours and his sister, Julie, can mow it in 2 hours.
Let t represent the time it would take them to mow their lawn if they work together, hence:
(1/3hours) * t + (1/2hours) * 2 = 1
t(1/3 + 1/2) = 1
(5/6)t = 1
t = 6/5 hours = 1 hour 12 minutes
It would take 12 minutes
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Write the solution set in interval notation and graph the inequality.
Set-Builder Notation: {x | 5/7
The set X can therefore be written as follows: The expression "A is the set of elements x such that x is a natural number less than 7" can be translated as "A is the set of elements x such that x is a natural number less than 7." A = x: x N, x 7 is another way to express the above set.
What is the Set Builder Form or Rule Method?If a set's components share a characteristic, the characteristic can be used to define the components. For instance, the natural numbers 1, 2, 3, 4, 5, and 6 in the set A have a trait in common that all of their members fall below the number 7. This trait is not shared by any other natural numbers. The set X can therefore be written as follows:The expression "A is the set of elements x such that x is a natural number less than 7" can be translated as "A is the set of elements x such that x is a natural number less than 7."A = x: x N, x 7 is another way to express the above set.The expression "the set of all natural numbers smaller than seven" can also be used to denote set A.The common property of the elements of a set is described in this instance inside braces. A set-builder form, often known as a rule technique, takes this simple structure.The Complete Question is Set Builder .
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Point D is the centroid of ABC DE=11. Find CD and CE.
The measure of CD and CE in the centroid are 22 and 33 respectively.
What is Centroid?
Centroid is a term used in mathematics to refer to the center of mass of a geometric object. It is typically represented by a point, which is the average of all points in the object. The centroid is often used as a reference point for other calculations or for the positioning of objects.
From the given diagram, the following are true:
CD = 2DE
Given that DE = 11
CD = 2(11)
CD =22
Similarly;
CE = CD + DE
CE = 22 + 11
CE = 33
Hence the measure of CD and CE are 22 and 33 respectively.
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. Fractions less than 1/2
Answer:
[tex]\frac{1}{x} ; x > 2[/tex]
Step-by-step explanation:
A fraction less than one half would have to be one out of a larger number than two.
Basically, let's change the denominator to "x"
[tex]\frac{1}{x}[/tex] -> for this fraction to be less than 2, x always has to be greater than two
Height of redwood trees is normally distributed, with a mean of 360 feet, and a standard deviation of 10 feet. Using this information and a z-score table, find the percentile for a redwood tree that is 375 feet tall. a. 13thb. 95th c. 80thd. 93rd
The percentile for a redwood tree that is 375 feet tall would be 93rd percentile. This is because the z-score of 1.5 (375-360/10) corresponds to a percentile of 93.
Step 1: Find z-score
z-score = (375-360)/10 = 1.5
Step 2: Find percentile
Using a z-score table, the percentile corresponding to a z-score of 1.5 is 93.
Therefore, the percentile for a redwood tree that is 375 feet tall is 93rd percentile.
The percentile of a redwood tree that is 375 feet tall can be determined using a z-score table. The z-score of a data point is the difference between the data point and the mean, divided by the standard deviation. In this case, the z-score is (375-360)/10 = 1.5. This z-score corresponds to a percentile of 93 on a z-score table. Therefore, the percentile for a redwood tree that is 375 feet tall is 93rd percentile. This means that 93% of redwood trees are shorter than 375 feet tall. It also means that only 7% of redwood trees are taller than 375 feet tall. This information can be used to compare the size of a particular redwood tree to other redwood trees.
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Given the following histogram for a set of data, how many values in the data set are greater than 6.5 and less than 9.5?
Given the following histogram (image now attached), for a set of data, the number of values in the data set that are greater than 6.5 and less than 9.5 is: 14 (Option D)
What is a histogram?A histogram is a rough depiction of the numerical data distribution. Karl Pearson was the first to coin the phrase.
A histogram is a graph that depicts the frequency distribution of a few data points from a single variable. Histograms frequently divide data into "bins" or "range groups" and count the number of data points that belong to each of those bins.
Between 6.5 and 9.5 there are 3 bars. Their heights are:
3, 6, 5, 4, and 3. Adding the values, we have:
3 + 6 + 5 = 14
Thus, the values in the data set are greater than 6.5 and less than 9.5 are 14.
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Full Question:
See attached image.
Mrs. Smith is upgrading all 6 of the family phones and wants them to be
protected. New phone cases cost $45 each and screen protectors cost $25
each. Write an expression and use the distributive property to find how
much Mrs. Smith will spend to protect the new phones.
Answer:
6(45 + 25)
Step-by-step explanation:
12% of x =360 hhhhhhhhhhhhhhhhhhhhhhhhh
Answer:
x = 3000
Step-by-step explanation:
Answer:
x=3000
Step-by-step explanation:
Given that, 12% of x=360
or, (x)× (12÷100)=360
or, (12x ÷100)=360
or, 12x=36000
or, x=36000÷12
or, x=3000
I need help with the question below
Answer:
see below
Step-by-step explanation:
there are 3 points given
diff in y / diff in x = slope
so plug in any 2 points' Y and x and get the slope
because it's downward shaped, you know the slope MUST be negative.
so diff in Y = 23-29 = -6
diff in X = 3-7 =2
so slope is +3
intercept is given, when x=0 y = 32
it represents what F is when it's 0C°
express the column matrix b as a linear combination of the columns of a. (use a1, a2, and a3 respectively for the columns of a.) a
We solve this system of equations and we can note that the system don't have a solution, so the vector b is not a linear combination of a1, a2, and a3.
First of all we put the vectors in terms of different variables, such as:
a1(1,-2,0)=(a,-2a,0);
a2(0,1,3)=(0,b,3b);
a3(6,-6,18)=(6c,-6c,18c);
To know that a vector is a linear combination we need to express it like a sum of other different vectors.
(2,-2,6)=(a,-2a,0)+(0,b,3b)+(6c,-6c,18c)
(2,-2,6)=(a+0+6c,-2a+b-6c,0+3b+18c)
We express this sum like a system of equations.
a+6c=2
-2a+b-6c=-2
3b+18c=6
We solve this system of equations and we can note that the system don't have a solution, so the vector b is not a linear combination of a1, a2, and a3.
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Find the standard parametrization for the line segment joining the points below. Draw coordinate axes and sketch the segment, indicating the direction of increasing t for the
parametrization. (0,0,0) and (5,3,7/2)
The parameterization equation for (0,0,0) and (5,3,7/2) is[tex]\frac{x}{5}=\frac{y}{3}=\frac{z}{3.5}[/tex]. Equation of parameterization is what it is.
How do you calculate parametrization?mathematical formulas
[tex]$$\begin{aligned}& x=0+5 t \\& y=0+3 t \\& z=0+3.5 t\end{aligned}$$[/tex]
Equations with symmetry
[tex]\frac{x}{5}=\frac{y}{3}=\frac{z}{3.5}[/tex]
A straight line is the most straightforward curve to parametrize. It is possible to parametrize a line that passes through the origin along the vectors a, b. X is equal to AT and Y is BT. Two vectors parallel to the plane and a point on the plane must be located in order to find a parametrization. On the plane, finding a location is simple. We may use any number for x and y to determine z using the plane's equation. In the event when x and y are both 0, equation (1) states that
z= 18 x + 2 y 3 = 180 + 2 (0) 3= 6.
The process of locating parametric equations of a curve, a surface, or, more generally, a manifold or a variety, described by an implicit equation, is known as in mathematics, and is most commonly used in geometry.
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A data analyst wants to demonstrate how the population in Charlotte has increased over time. They create the chart below. What is this type of chart called?
Line chart
Area chart
Column chart
Bar chart
The Line chart should be used by the data analyst.
Option (A) is correct.
What is a line chart?
A line chart is a type of chart that is used to display a series of data points over time. It shows how a variable changes over time by connecting data points with lines. The line chart is commonly used to display trends, patterns and changes over time in continuous data.
Line chart
This type of chart is called a line chart. A line chart is a type of chart that is used to display a series of data points over time. It shows how a variable changes over time by connecting data points with lines. The line chart is commonly used to display trends, patterns and changes over time in continuous data.
It uses a horizontal x-axis and a vertical y-axis, with the data points connected by a line. It is great for visualizing trends and changes in data over a period of time, and it can be used to compare multiple variables at once.
Hence, the Line chart should be used by the data analyst.
Option (A) is correct.
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A survey was conducted that asked 1018 people how many books they had read in the past year. Results indicated that x=14.1 books and s=16.6 books. Construct a 99% confidence interval for the mean number of books people read. Interpret the interval. Construct a 99% confidence interval for the mean number of books people read and interpret the result. Select the correct choice below and fill in the answer boxes to complete your choice. (Use ascending order. Round to two decimal places as needed.) A. There is a 99% probability that the true mean number of books read is between nothing and nothing. B. There is 99% confidence that the population mean number of books read is between nothing and nothing.
There is 99% confidence that the population mean number of books read is between 1.51 and 26.69. This confidence interval indicates that there is a 99% probability that the true mean number of books read by people in the past year falls between 1.51 and 26.69.
Confidence interval for the mean = (x - z(s/√n), x + z(s/√n))
Where x is the sample mean, s is the sample standard deviation, n is the sample size, and z is the critical value for the given confidence level (in this case, 99%).
Therefore, the confidence interval for the mean number of books read is:
(14.1 - 2.58(16.6/√1018), 14.1 + 2.58(16.6/√1018))
= (1.51, 26.69)
This confidence interval indicates that there is a 99% probability that the true mean number of books read by people in the past year falls between 1.51 and 26.69. In other words, it is likely that the average number of books read by people in the past year is between these values. This interval is an estimate of the population mean and the confidence level indicates how confident we can be that the true mean falls within this range.
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There are 40 female performers in a dance recital. The ratio of men to women is 5 to 8 How many men are in the dance recital?
Answer: there would be 8 men
Step-by-step explanation:
can you give me brainliest
Answer: I believe there would be 25 men
Step-by-step explanation: We can see there are 40 women and the ration is 5 (men) to 8 (women)
If we take 40 and divide it by 8 we get 5
so for every 8 women there are 5 men and we do that 5 times
we get: 40 women and 25 men.
which of the following are magnitudes for rotational symmetry of the isosceles trapezoid below about the marked point?
The isosceles trapezoid has rotational symmetry about the marked point. This means that when the trapezoid is rotated by an angle of 360°, it will look the same as it did before. Since the trapezoid has 4 sides, the rotational symmetry is 4-fold, or 4 magnitude. Therefore, the answer is b) 4.
The correct answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.The answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.
The isosceles trapezoid has rotational symmetry about the marked point. This means that when the trapezoid is rotated by an angle of 360°, it will look the same as it did before. Since the trapezoid has 4 sides, the rotational symmetry is 4-fold, or 4 magnitude. Therefore, the answer is b) 4.
The correct answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.The answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.
The complete question is :
Which of the following are magnitudes for rotational symmetry of the isosceles trapezoid below about the marked point?
a) 2
b) 4
c) 6
d) 8
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a 2.5 nm torque is applied to a flywheel for 10.0 seconds. if the flywheel is initially at rest and its moment of inertia is 2.0 kg m2, determine its angular momentum. group of answer choices
The angular momentum of the flywheel is equal to the product of the applied torque, the time interval, and the moment of inertia. Therefore, the angular momentum of the flywheel will be 2.5 Nm × 10.0 s × 2.0 kg m2 = 50 kg m2/s.
1. Determine the angular momentum of the flywheel:
Angular momentum = Torque × Time × Moment of Inertia
= 2.5 Nm × 10.0 s × 2.0 kg m2
= 50 kg m2/s
The angular momentum of an object can be determined from the product of the applied torque, the time interval, and the moment of inertia. The moment of inertia is the rotational inertia of an object, which is the resistance to changes in its angular velocity. The angular momentum of the flywheel in this question is equal to the product of the applied torque, the time interval, and the moment of inertia. Therefore, the angular momentum of the flywheel will be 2.5 Nm × 10.0 s × 2.0 kg m2 = 50 kg m2/s. This means that the flywheel will have an angular momentum of 50 kg m2/s after the 10-second interval when the torque is applied. The angular momentum of the flywheel will remain constant until another torque is applied to change it.
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In a class of 40 students, 8 are in the drama club, 12 are in the art club, and 5 are in the music club. If a student is selected at random, what is the probability that the selected student is in none of the clubs listed?
Considering the definition of probability, the probability that the selected student is in none of the clubs listed is 0.375 or 37.5%.
Definition of probabilityProbability is the greater or lesser chance that a given event will occur.
In other words, the probability establishes a relationship between the number of favorable events (number of cases in which event A may or may not occur) and the total number of possible events through the Laplace's Law as follow:
P(A)= number of favorable cases÷number of total cases
Probability that the selected student is in none of the clubs listedIn this case, you know:
Total number of students = 40 (number of possible cases)Total number of students in drama club= 8Total number of students in art club= 12Total number of students in music club= 5Total number of students in a club= 8 + 12 + 5= 25Total number of students in none of the clubs listed= 40 - 25= 15 (number of favorable cases)Replacing in the definition of probability:
P(A)= 15÷40
Solving:
P(A)= 0.375
Expressed as a percentage:
P(A)= 37.5%
Finally, the probability is 0.375 or 37.5%.
Learn more about probability:
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