The remaining time of the trip is 3 5/6 hours.
If a trip from Boston to Washington takes 5 3/4 hours and you have traveled 1/3 of the way, the remaining time of the trip can be calculated by subtracting the time traveled from the total time of the trip.
First, we need to convert 5 3/4 hours to a fraction:
5 3/4 = (5 * 4 + 3)/4 = 23/4
Next, we need to calculate the time traveled so far:
23/4 * 1/3 = 23/12
Now we can subtract the time traveled from the total time of the trip:
23/4 - 23/12 = (23 * 3 - 23 * 1)/12 = 46/12 = 3 10/12 = 3 5/6
Therefore, the remaining time of the trip is 3 5/6 hours.
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Write the equation for g(x)
The equation for g(x) by the given data is g(x) = (-1/4)(x^2).
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that;
The function f(x)=x^2
Now,
Since the function g is a scaled version of f(x) = x^2, we can write:
g(x) = a(x^2)
where 'a' is the scaling factor.
To find the value of 'a', we can use the given point on the graph of g:
g(2) = -1
Substituting x = 2 and g(x) = -1 in the above equation, we get:
-1 = a(2^2)
-1 = 4a
a = -1/4
Therefore, the equation for g(x) will be g(x) = (-1/4)(x^2).
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A political scientist received a grant to fund a research project on voting trends. The budget includes $3,200 for conducting door-to-door interviews on the day before an election. Undergraduate students, graduate students, and faculty members will be hired to conduct the interviews. Each undergraduate student will conduct 18 interviews for$100. Each graduate student will conduct 25 interviews for $150. Each faculty member will conduct 30 interviews for$200. Due to limited transportation facilities, no more than 20 interviewers can be hired. How many undergraduate students, graduate students, and faculty members should be hired in order to maximize the number of interviews? What is the maximum number of interviews?
To maximize the number of interviews, 12 undergraduate students, 4 graduate students, and 4 faculty members should be hired. The maximum number of interviews that can be conducted is 684.
Let x, y, and z be the number of undergraduate students, graduate students, and faculty members hired, respectively. The objective is to maximize the number of interviews, which is given by the function
N = 18x + 25y + 30z.
The total cost of hiring interviewers is given by the function
C = 100x + 150y + 200z.
The constraints are x + y + z ≤ 20 (due to transportation limitations), and C ≤ 3200 (the budget constraint). Using linear programming techniques, we can solve for the optimal values of x, y, and z, which are 12, 4, and 4, respectively.
The maximum number of interviews is 18(12) + 25(4) + 30(4) = 684.
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Find the range, IQR, and MAD of the data set.
15, 22, 16, 13, 14, 20, 40, 44
IQR = 16.5
The range = 31
Mean absolute deviation = 9.5
What is the median?The median is the value that splits the mathematical numbers or expressions in the half. The median value is the middle number of data points. to find the median first arrange the data points in ascending order.
Given:
A data set:
15, 22, 16, 13, 14, 20, 40, 44.
The lower half of median Q1 = (14 + 15)/2 = 14.5
The upper half of median Q3 = (40 + 22)/2 = 31
So IQR = Q3 - Q1 = 31 - 14.5 = 16.5
The range = 44 - 13 = 31
Mean absolute deviation = 9.5
Therefore, MAD = 9.5.
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Help please…………………………………..
The limit of (3x - 3)^(5/2) as x approaches 4, [tex]\lim_{x \to } _4[/tex] (3x - 3)^(5/2) is 243.
What is lim as x approaches 4 (3x-3)^(5/2)?The limit of a function as x approaches a certain value can be thought of as the value that the function approaches as x gets arbitrarily close to that value.
To find the limit of (3x - 3)^(5/2) as x approaches 4, we need to evaluate the expression for values of x that are close to 4 and see what the result approaches.
First, let's substitute 4 for x in the expression:
[tex]\lim_{x \to } _4[/tex] (3x - 3)^(5/2) = (3*4 - 3)^(5/2)
= (9)^(5/2)
= (√9)⁵
= 3⁵
= 243
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Marcy has 20$ she wants to buy a book that is marked down 30% from its original price of 28$ if the sales tax is 2.5% does marcy have enough money to buy the book
Answer:
yes
Step-by-step explanation:
if i did the math right marcy should have enough
PLEASE HELP! A horse's weight decreases by 1/2 pound per week. At this rate, how many weeks will it take for the horse to lose a total of 5 1/2 pounds? Write an expression that could be used to model the situation. State what strategy you will use to answer the question, explain your choice, then find the answer.
A) An algebraic expression that could be used to model the situation where a horse's weight decreases by ¹/₂ pounds weekly is w/r, where w is the total weight lost and r is the constant rate of weight loss.
B) Using division operation and decreasing rate, if a horse's weight decreases by ¹/₂ pounds weekly, it will take the horse 11 weeks to lose a total of 5¹/₂ pounds.
What is an algebraic expression?An algebraic expression combines constants, variables, and mathematical operations (+, -, ×, ÷) without the equal sign (=) found in equations.
While equations show the equality of expressions, algebraic expressions merely state values.
Division operation is one of the four basic mathematical expressions, including addition, subtraction, and multiplication.
Division operations involve the dividend, the divisor, the equal sign (=), the division operand (÷), and the result called the quotient.
The total weight loss over time = 5¹/₂ pounds
The constant rate of weight loss = ¹/₂ pounds per week
The number of weeks for the horse to lose 5¹/₂ pounds = 11 weeks (5¹/₂ ÷ ¹/₂).
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Which of the following expressions is equivalent to 17?
Answer:
17^1 . ......................
What is algorithm explain?
Algorithm is a set of instructions for solving a problem or performing a task, typically designed for a computer to follow.
An algorithm is essentially a step-by-step procedure for solving a problem or accomplishing a specific task. It is used in various fields, including mathematics, computer science, engineering, and many others. In computer science, algorithms are essential for software development and programming, as they provide a systematic approach to designing and implementing complex programs. The process of developing an algorithm typically involves breaking down a problem into smaller sub-problems, identifying the key steps required to solve each sub-problem, and then putting the steps together in the correct order to form a complete solution.
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what is parameters ?
Parameters are a set of values or characteristics that help to define or limit a system or process.
In computer programming, parameters are values or arguments that are passed to a function or method to specify how it should operate. Parameters can also be used in mathematical equations, scientific experiments, and other fields to specify conditions or constraints.
For example, in the equation y = mx + b, m and b are parameters that determine the slope and intercept of the line.
In a scientific experiment, parameters might include the temperature, pressure, or other conditions under which the experiment is conducted. In computer programming, parameters can be used to specify the input data, options, or other information that a function or method needs to operate correctly.
Overall, parameters are an important tool for defining and controlling systems, processes, and functions in a wide range of fields. By specifying parameters, we can ensure that a system operates in a predictable and consistent manner, and that we can accurately measure and compare results.
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Give three solutions to the equation y=1/2x+1
Answers:
(12, 7)
(20, 11)
(32, 17)
There are infinitely many possible answers.
=======================================================
Explanation:
The equation given to us is the same as y = 0.5x+1 because 1/2 = 0.5
If we replace x with even numbers, then we'll get whole number outputs for y.
Example: if x = 12, then y = 0.5x+1 = 0.5*12+1 = 7
This leads to (12,7) as one solution to this equation. A solution is a point that is on the line. Use graphing software like Desmos or GeoGebra to confirm.
Another example: if x = 20, then y = 0.5x+1 = 0.5*20+1 = 11. Therefore, another solution point is (20, 11)
Final example: If x = 32, then y = 0.5x+1 = 0.5*32+1 = 17. This gives the point (32,17)
There are infinitely many possible answers since we can replace x with infinitely many real numbers.
Melanie deposits $500 into an account that pays 1.7% annual interest compounded quarterly.
Enter an equation to represent Melanie's account balance after t years.
Melanie's account balance after t years is, A = 500 x [tex](1 + 0.00425)^{4t[/tex].
What is Compound Interest?Compound interest is when you receive interest on both your interest income and your savings.
Given:
Initial deposit = $ 500
Interest rate = 1.7 % = 0.017/4 = annual compounded quarterly
Now, Account balance = Initial deposit x [tex](1 + r)^{4t[/tex]
A = 500 x [tex](1 + 0.00425)^{4t[/tex]
Where:
A = Account balance
4t = Number of quarters (4 x Number of t years)
Suppose we want to calculate the account balance after 4.5 years, then we substitute this way:
A = 500 x [tex](1 + 0.00425)^{4(4.5)[/tex]
A = 500 x (1 + 0.00425)¹⁸
A = 539.66
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A rectangular prism is 9 inches long, 4 inches wide, and 11.6 inches high. What is the volume of the rectangular prism?
Answer:
417.6 in sq
Step-by-step explanation:
9 x 4 x 11.6 = 417.6
How to Write 9 in Roman Numerals?
To write 9 in Roman Numerals, you would use the symbols "IX".
The symbol "I" represents the number 1 and the symbol "X" represents the number 10. When a smaller symbol is placed before a larger symbol, it means that the smaller symbol is subtracted from the larger symbol.
In this case, "I" is placed before "X", so it is subtracted from 10, giving us the value of 9.
Here is a step-by-step explanation:
1. Identify the symbols for 1 and 10: "I" and "X"
2. Place the smaller symbol before the larger symbol: "IX"
3. Subtract the smaller symbol from the larger symbol: 10 - 1 = 9
4. The result is the value of the Roman Numeral: "IX" = 9
Therefore, the Roman Numeral for 9 is "IX".
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Consider the figure shown. SEE EXAMPLE 3 x + 6 cm X X x+6cm a. What expression represents the total area of the four white triangles? b. If the length of each side of the shaded square is 12 cm, what is the total area of the four white triangles?
What is the expanded form of -1/2(14x+50)
Answer:
= - 7x - 25.
Step-by-step explanation:
[tex] \frac{ - 1}{2} (14x \ + 50) \\ \\ = - 0.5(14x + 50) \\ \\ = - 7x + - 25 \\ = - 7x - 25[/tex]
In the year 2000, the population of Mexico was about 100 million, and was growing by approximately 1.53% per year. At this growth rate, the function f(x)=100(1.0153)^x
gives the population, in millions, x
years after 2000. Using this model and a graph of the function, in what year would the population reach 111 million? Round your answer to the nearest year.
The solution is, The population would reach 111 million in next 7 years
What is an exponent in math?An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
here, we have,
given that,
The initial population of Mexico was 100 million
The growth rate of the population is 1.53 %per year
Then the future population of Mexico is given by
P = P_0(1+r)^t
Where P = future population after t years
P_0= initial population
t = time period in years
Substituting the given vales in above equation we get
(1+ 0.0153)^t = 1.11
Taking log on both sides we get
t* log (1.0153) = log(1.11)
solving we get,
t = 6.87
≈ 7 years
The population would reach 111 million in next 7 years.
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PLEASE HELP ME!!!!!!!!!!!!
PICTURE BELOW
In this polygon all angles are right angles
What is the area of this polygon
Enter your answer in the box
The two rectangles are joined to get the shape. And the area of the shape is 258 square feet.
What is the area?The amount region shows how much an area is on a planar or hemispherical cup. Surface region alludes to the region of an open surface or the boundary of a multi-object, while the region of a plane locale or plane field alludes to the region of a structure or planar material.
The shape is a mix of the two rectangular shapes. Then the region is likewise the amount of these two square shapes. Then we have
A = (18 - 8) x (21 - 12) + 21 x 8
A = 10 x 9 + 21 x 8
A = 90 + 168
A = 258 square feet
The two rectangles are joined to get the shape. And the area of the shape is 258 square feet.
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When data are positively skewed, the mean will usually be:a. greater than the medianb. smaller than the medianc. equal to the mediand. positiveData:Data refers to a characteristic of information that is collected for analysis and reference purposes. Data can be measured through various analytical tools to enable one to draw a conclusion. Data collected is used in scientific research and business management; thus, enabling the management to make better-informed decisions.
The right answer is a. The mean is bigger than the median and the mode when the data is positively skewed.
A characteristic of information that is gathered for analysis and reference is referred to as data. Numerous analytical tools can be used to measure data and facilitate conclusion-making. The data gathered is used for corporate management and scientific research, allowing management to make more informed decisions.
The right answer is a. The mean is bigger than the median and the mode when the data is positively skewed. The tail of the data set is said to point to the right when the data is positively skewed. The mean and median, on the other hand, are always lower than the mode in a distribution that is negatively skewed. Skewness, in general, is a distortion that differs from typical data collection.
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Refer to Table 4-1. Suppose that D2 and S1 are the prevailing demand and supply curves for a product. If the demand schedule changes from D2 to D1, then:
Price D 1 D 2 S 1 S 2
$12 5 9 19 14
$10 8 12 17 12
$8 11 15 15 10
$6 13 18 13 8
$4 16 21 11 6
$2 18 24 9 4
equilibrium price increases from $6 to $8.
equilibrium quantity increases from 13 to 18
equilibrium quantity decreases from 15 to 13.
equilibrium price decreases from $6 to $4.
The correct option is A, equilibrium price increases from $6 to $8.
What do you mean by Equilibrium?In economics, equilibrium is a state in which the supply and demand for a product or service are balanced, resulting in a stable price. This can occur in a free market, where the price of a good or service is determined by the interaction of buyers and sellers.
Overall, equilibrium is a fundamental concept in many different fields, representing a state of balance or stability in a system or situation.
If the demand schedule changes from D2 to D1, then the demand curve shifts to the left. As a result, the new equilibrium point will be where the new demand curve (D1) intersects with the supply curve (S1).
From the table, we can see that the new equilibrium point is at a price of $8 and a quantity of 15. Therefore, the equilibrium price increases from $6 to $8, but the equilibrium quantity decreases from 15 to 13.
So the correct answer is: equilibrium price increases from $6 to $8.
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Write a system of linear inequalities represented by the graph Inequality 1: Inequality 2:
The system of linear inequalities that represents the graph is:
y ≥ x - 2
y ≥ -3x + 2
How to Write a System of Linear Inequalities Represented by a Graph?The system of linear inequalities for the given graph can be written as explained below.
Inequality 1:
Slope (m) = rise/run = 3/3 = 1
The y-intercept (b) = -2
Since the line is a solid line and the shaded region is above the line, the inequality sign to use is, ≥. Therefore, substitute m = 1 and b = -2 into y ≥ mx + b:
y ≥ x - 2
Inequality 2:
Slope (m) = rise/run = -3/1 = -3
The y-intercept (b) = 2
Since the line is a solid line and the shaded region is above the line, the inequality sign to use is, ≥. Therefore, substitute m = -3 and b = 2 into y ≥ mx + b:
y ≥ -3x + 2
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The bill is $60.55 and you have to pay 8% tax. What is the new total?
Answer:
$65.394
Step-by-step explanation:
The bill is $60.55, and you have to pay 8% tax.
8% = 0.08
60.55 times 0.08 = $4.844
So, the
8% tax = $4.844
What is the new total?
We take
60.55 + 4.844 = $65.394
So, the new total is $65.394
Answer:
$65.39
Step-by-step explanation:
multiply 60.55 by .08. then add 4.84 to 60.55
Jayden measured a desk to be 4 feet. The actual measurement is 3.2 feet. What is Jayden's percent error?
The percentage error made by the person is 25%.
What is percentage error?To get the percentage error, multiply the relative error by 100%. In other words, first, calculate the difference between the true value and the measured value. Then, divide the obtained difference by the true value. Then take the absolute value of the obtained result and multiply it by 100%.
The measured value is 4 feet.
The true value is 3.2 feet.
So, the difference between the true value and the measured value is (4 feet - 3.2 feet), that is, 0.8 feet.
Now, divide the obtained difference by the true value.
(0.8 feet)/(3.2 feet) = 1/4
= 0.25
To get the percentage error, take the absolute value of the obtained result and multiply it by 100%.
|0.25|×100% = 0.25×100%
= 25%
Therefore, the obtained answer is 25%.
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Find The Value Of X.d
The value of the variable x as required to be determined from the given image is; 11.
What is the value of the variable, x?As evident in the task content; it can be inferred that there are similar triangles from the image.
Since the ratio of corresponding sides of similar triangles are equal; we have that;
x / 22 = (9+3) / (9+3+12)
x / 22 = 12 / 24
x = (22 × 12) / 24
x = 11.
Ultimately, the value of x from the given image is; 11.
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What is the volume of the cylinder? Round to the nearest hundredth and approximate using π = 3.14. cylinder with a segment from one point on the circular base to another point on the base through the center labeled 2.8 feet and a height labeled 4.2 feet.
10.39 cubic feet
25.85 cubic feet
36.93 cubic feet
73.85 cubic feet
The volume of cylinder is 25.85 cubic feet
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The formula for volume of cylinder V=πr²h
Where V is volume, r is radius of cylinder and h is height of cylinder.
The cylinder has a height of 4.2 feet and
a segment from one point on the circular base to another point on the base through the center labeled 2.8 feet, which is equal to the diameter of the circular base.
Diameter =2.8 feet
Radius =1.4 feet.
V=3.14×1.4²×4.2
V = 25.85 cubic feet
Hence, the volume of cylinder is 25.85 cubic feet
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Answer:
b or 25.85
Step-by-step explanation: V=pir^2h
the radius is half of the diameter so it would be 1.4. then do 1.4 and square it, getting 1/96. then, multiply 1.96, 4.2, and pi, or 3.14 in this case. After multiplying those, you get 25.8484848, or 25.85.
Hope this helps!
A bakery makes cylindrical mini muffins that measure 2 inches in diameter and 1 and three fourths inches in height. If each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? Approximate using pi equals 22 over 7.
103 and 5 over 7 in2
84 and 6 over 7 in2
66 and 1 over 7 in2
17 and 2 over 7 in2
The required paper over a total of 6 mini muffins of cylindrical shape is (A) 103 5/7 in².
What is a cylinder?One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid.
It is regarded as a prism with a circle as its base in basic geometry.
In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.
So, the cylinder formula:
= 2πrh+2πr²
Now, insert values as follows:
= 2πrh+2πr²
= 2π1*1.75+2π1²
= 17.27 inches
Paper to wrap 6 muffins:
= 17.27*6
= 103.62
Which is close to option (A)
Therefore, the required paper over a total of 6 mini muffins of cylindrical shape is (A) 103 5/7 in².
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Complete question:
A bakery makes cylindrical mini muffins that measure 2 inches in diameter and 1 and three-fourths inches in height. If each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? Approximate using pi equals 22 over 7.
A. 103 and 5 over 7 in2
B. 84 and 6 over 7 in2
C. 66 and 1 over 7 in2
D. 17 and 2 over 7 in2
Answer:
(A) 103 5/7 in².
Step-by-step explanation:
PLEASE THANK AND RATE 5 STARS
Which equation can be used to solve the problem
Answer:
Second one
20/50=v/100
Step by step explanation:
Cross multiplying;
(20×100)÷50 = v
v = 40
Help me I don’t get it
The inequality is solved using graphical method to give a solution of
(-3, 3)How to the table of value to plot the graphThe system of equation are y ≥ 1/3 x + 4 and y ≤ -5/3 x - 2
Using x values of -5, 0, 5
y ≥ 1/3 x + 4
x = -5, y ≥ 1/3 (-5) + 4, y ≥ 7/3
x = 0, y ≥ 1/3 (0) + 4, y ≥ 4
x = 5, y ≥ 1/3 (5) + 4, y ≥ 17/3
table of values
x y
-5 7/3
0 4
5 17/3
y ≤ -5/3 x - 2
x = -5, y ≥ -5/3 (-5) - 2, y ≤ 19/3
x = 0, y ≥ -5/3 (0) - 2, y ≤ -2
x = 5, y ≥ -5/3 (5) - 2, y ≤ -31/3
table of values
x y
-5 19/3
0 -2
5 -31/3
The graph is attached and the solution is (-3, 3)
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What are the properties of determinants problems?
Properties of determinants are Reflection Property, Reliable scales Property, Scalar Multiple Property, Switching Property and All-zero Property.
1. Reflection Property: The determinant remains unchanged when its columns turn into rows and vice versa. The reflection property is what is used to describe this.
2. If every element in a row (or column) is zero, the determinant is zero, according to the all-zero property.
3. Reliable scales (Repetition) Property: If every element in a row or column is proportional to or identical to every element in another row, the determinant is zero (or column).
4. When any two of the determinant's rows (or columns) are exchanged, the sign of the determinant changes.
5. Scalar Multiple Property: If all of a determinant's components in a row (or column) are multiplied by a non-zero constant, the determinant is multiplied by that constant.
6. Factor Property: If a determinant Δ becomes zero when we put x = α, then (x – α) is a factor of Δ.
Hence this is all about determinants problems.
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When you multiply a number by a fraction, will the product be larger or smaller than the largest factor?
Answer: smaller
Step-by-step explanation:
hope this helpsss
Answer:
The answer to this question depends on the values of the numbers involved. In general, when you multiply a number by a fraction, the product will be smaller than the largest factor if the fraction is less than 1. For example, if you multiply 5 by 1/2, the product is 2.5, which is smaller than 5. On the other hand, if you multiply a number by a fraction that is greater than 1, the product will be larger than the largest factor. For example, if you multiply 5 by 2/1, the product is 10, which is larger than 5.
In conclusion, the size of the product obtained from multiplying a number by a fraction depends on the values of the numbers involved and can be either smaller or larger than the largest factor.
Suppose you translate the graph of y = 3/4 so that the new graph has asymptotes at x = -5 and y = 14. What is the equation for the
new graph?
Answer: The graph of y = 3/4 is a horizontal line with y-intercept at 3/4. When this graph is translated, its y-intercept changes, while its slope remains the same.
Since the new graph has asymptotes at x = -5 and y = 14, the new equation must be of the form y = m(x + 5) + 14, where m is the slope of the original line, which is 3/4. Substituting the values, we get:
y = (3/4)(x + 5) + 14
So the equation of the translated graph is y = (3/4)(x + 5) + 14.
Step-by-step explanation: