The product of two rational number is -5. If one of them is -7/15
Answer:
The other is 75/7.
Step-by-step explanation:
Let the other rational number be x, then:
(-7/15) * x = -5
x = -5 * -15/7
= 75/7
Determine if the ordered pair (-2, -4) is a solution for equation 2y - 3x = -2.
Answer:
Step-by-step explanation:
2(-4) - 3(-2) = -2
-8 + 6 = -2
-2 = -2
The angle of elevation of the top of a flag-pole from a point on level ground is 30 degrees. From another point on the ground 20m nearer the flag-pole, the angle of elevation is 60 degrees. Calculate the height of the flag pole
Answer:
<b> <i>
Step-by-step explanation:
Write
a real-world situation that can be
represented by 15 + c = 17.50. Tell what
the variable represents. Then solve the
equation and describe what your answer
represents for the problem situation. Can you also please try to make it something a little original I need help with this ASAP pls.
The given expression is
[tex]15 + c = 17.50[/tex]
We can use this expression to model the cost for a service.
Let's say that your gardener charges an initial amount of $15, and an additional per hour. If the gardener worked only for one hour, and the total cost charged was $17.50, how much was the additional cost?
So, the given expression models this real life situation, we can answer the problem by just solving the equation for [tex]c[/tex]
[tex]15 + c = 17.50[/tex]
[tex]c=17.50-15[/tex]
[tex]c=2.50[/tex]
Answer: Well C equals 2.5. You could use...
You have 3 sticks. one stick is 15 inches long and the other is 17.50. You want to get a small stick to add to the first one so that the first and last stick is equal to the 2nd stick. C is the third stick. 15+C = 17.50. What is the length of C?
Step-by-step explanation:
EASY
Move all terms not containing C to the right side of the equation. C = 2.5
In 2010, the population of Belvedere was estimated to be 39,366 people with an annual rate of increase of approximately 2.8%.
Select the explicit expression that represents the population in the next 6 years.
OA. 39,366(1.0028)5
OB. 39,366(1.28)
OC. 39,366(0.028)
OD. 39,366(1.028)
The exponential function that represents the population in the next six years is given as follows:
[tex]39366(1.028)^6[/tex]
How to model an exponential function?The standard definition of an exponential function is given as follows:
[tex]A(t) = A(0)b^{\frac{t}{n}}[/tex]
The parameters of the exponential function are given as follows:
A(0) is the initial amount.b is the rate of change.n is the time needed for the rate of change.In 2010, the population of Belvedere was estimated to be 39,366 people, hence the parameter a is given as follows:
a = 39366.
The yearly increase rate is of 2.8%, hence the parameter values for b and n are given as follows:
b = 0.028, n = 1.
Then the expression giving the population after t years is of:
[tex]P(t) = 39366(1.028)^t[/tex]
After six years, the expression is given as follows:
[tex]39366(1.028)^6[/tex]
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Find the value of x.
The calculated value of x in the similar triangles is 14 and it is calculated from the ratio 10 : x = 20 : 28
Calculating the value of x in the triangleGiven the triangle
The triangle is a superset of similar triangles
So, we have the following equivalent ratio that can be used to determine teh value of x
The set up of teh ratio is
10 : x = 10 + 10 : 28
Evaluating the like terms, we get
10 : x = 20 : 28
So, we have
x/10 = 28/20
Multiply both sides by 10
x = 14
Hence, the value of x is 14
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I cant figure it out
4x - 4/4x² + x is the value of linear equation.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
28x³ - 28x²/28x⁴ + 7x³
= 28x²( x - 1 )/7x³( 4x + 1)
= 4( x - 1)/x( 4x + 1)
= 4x - 4/4x² + x
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need help on finding d
You are to take multiple-choice exam consisting of 100 questions with 5 possible responses to each question. Suppose that you have not studied and so must guess (randomly select one of the five answers) on each question. Let x represent the number of correct responses on the test (a) What kind of probability distribution does x have? normal distribution uniform distribution geometric distribution binomial distribution (b) What is your expected score on the exam? (Hint: Your expected score is the mean value of the x distribution:)_______
(c) Calculate the variance and standard deviation of X Variance_____
standard deviation ______
(d) Based on your answers to parts (b) and (c), is it likely that you would score over 50 on this exam? Explain the reasoning behind your answer:
A score of 50 is z =__________________ standard deviations above the mean therefore it___________ not likely that you would score over 50 on this exam;,
The probability distribution that X has is a binomial distribution, and the expected score on the exam is 20.
a. The correct probability distribution is a binomial distribution.
This is because the multiple-choice exam consists of 100 questions with 5 possible responses to each question.
The discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome, is known as the binomial distribution with parameters n and p in probability theory and statistics: success (with probability p) or failure (with probability q= 1 - p)
Therefore, this is a classic example of a binomial distribution where there are two outcomes in each trial (success and failure) and the trials are independent of each other.
(b) The expected score on the exam
The expected value of X is given by the formula;
Expected value (E) = np
n is the number of trials (100)
p is the probability of getting the correct answer (1/5).
Therefore, Expected value (E) = np
= 100 × (1/5) = 20
So, your expected score on the exam is 20.
A score of 50 is z = 6 standard deviations above the mean.
Therefore, it is extremely unlikely that you would score over 50 on this exam.
In conclusion, a binomial distribution is the probability that X has. Meanwhile, 20 is the expected score.
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If P --> Q is an existing functional dependency, which of the following is NOT an augmented functional dependency? OPA --> Q O P. X. Y --> Q OP.X --> O Q -->P OP.A-->P
The option that is NOT an augmented functional dependency is: Q --> P, because it removes the attribute from the left-hand side of the existing functional dependency, which is not allowed in an augmented dependency.
Functional dependency: It is a concept in database management systems that describes the relationship between two attributes or sets of attributes in a table. In a functional dependency A → B, A is the determinant or the attribute(s) that uniquely determines the value of B.
Augmented functional dependency : It is formed by adding one or more attributes to the determinant side of an existing functional dependency.
From the given options, the only one that is not an augmented functional dependency is "Q → P". This is because it does not involve adding any attributes to the determinant side of an existing functional dependency.
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the rate of decay of a radioactive substance is proportional to the amount of substance present. this radioactive element has a half-life of 50 days. what percentage of the original sample is left after 85 days?
The percentage of the original sample left after 85 days is approximately 30.73%.
The rate of decay of a radioactive substance is proportional to the amount of substance present. The radioactive decay law states that the amount of a radioactive substance left after t days is given by the formula N(t) = N₀ e^(-kt). Here, N₀ is the initial amount of the substance, and k is the decay constant.
We know that the half-life of the substance is 50 days. This means that N(t) = N₀/2 when t = 50. Therefore, we can use this information to find the decay constant k as follows:
N(50) = N₀ e^(-50k)
N₀/2 = N₀ e^(-50k)
1/2 = e^(-50k)
ln(1/2) = -50kln(e)
ln(1/2) = -50k
0.693 = 50k
k = -0.01386 (approx.)
Therefore, the formula for the amount of substance left after t days is given by N(t) = N₀ e^(-0.01386t). Now, we can use this formula to find the percentage of the original sample left after 85 days as follows:
N(85) = N₀ e^(-0.01386 * 85)
N(85) = N₀ e^(-1.1771)
N(85)/N₀ = e^(-1.1771)
N(85)/N₀ = 0.3073 (approx.)
Therefore, the percentage of the original sample left after 85 days is 30.73% (approx.). The answer is 30.73%.
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Please help me I am stuck on this question
Answer:
9
Step-by-step explanation:
-5 + (-18) +32
-23 + 32
32 -23
assume that when adults with smartphones are randomly selected, % use them in meetings or classes. if adult smartphone users are randomly selected, find the probability that fewer than of them use their smartphones in meetings or classes.
The probability that fewer than 3 of them use their smartphones in meetings or classes is 0.0366.
The binomial probability distribution is a discrete probability law with two parameters: trial number (n) and success probability (p) (p). When there are two mutually exclusive outcomes of finite trials, the binomial distribution is utilised.
The probability that a specific 3 people all use their smartphones in meetings or class is 0.53³.
Probability that remaining 7 people do not use their phone is 0.47⁷
¹⁰C₃ = 10*9*8/(3*2*1) = 120.
Thus, the probability of exactly 3 people using their smartphones in meetings or in class is 10C3*0.533*0.477, or 0.0905.
So, adding up the 3 possibilities (that 0 of them, 1 of them, or 2 of them use their smartphones in meetings or class) we get
¹⁰C₀*0.530*0.4710 + ¹⁰C₁*0.531*0.479 + ¹⁰C₂*0.532*0.478 = 0.0366.
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Complete question:
Assume that when adults with smartphones are randomly selected, 53% use them in meetings or classes. If 10 adult smartphone users are randomly selected, find the probability that fewer than 3 of them use their smartphones in meetings or classes.
Use the diagram shown. Lines p and q are parallel.
Select all the correct measures for ∠1, ∠2,
and ∠3.
Answer:
<1= 61
<2= 61
<3= 119
Step-by-step explanation:
Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree.
Distance from the base of tower to the airplane = 706ft.
What is Angle of Depression?The term "angle of depression" called angle created when an observer looks down at an item and the horizontal line intersects with the line of sight. It determines how our field of vision shifts as we glance down. Say you are standing in your kitchen and gazing straight, and suddenly you spy an insect crawling on the floor.
Given, Angle of Depression=12°
Height of tower=150ft
For AB parallel to CD
∠ACD=∠cAB=12°
Tan12°=BC/AB
AB=BC/Tan12°
AB=706ft
Hence, Distance from the base of tower to the airplane = 706ft.
Diagram is attached below;
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Round your answer to the nearest hundredth
Answer:
AB ≈ 4.73
Step-by-step explanation:
using the sine ratio in the right triangle
sin25° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{2}{AB}[/tex] ( multiply both sides by AB )
AB × sin25° = 2 ( divide both sides by sin25° )
AB = [tex]\frac{2}{sin25}[/tex] ≈ 4.73 ( to the nearest hundredth )
Use the table you created to play the "Two Spinner
Game" below.
For this game, we say the spinners "match" if they
land on the same color (e.g., both red, or both blue).
How do you win? Once again, that's your choice:
(1) If the spinners MATCH, you win.
(2) If the spinners DO NOT MATCH, you win.
Which game would you be more likely to win?
Therefore, you would be more likely to win the game by choosing option (2) - winning if the spinners do not match.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in many areas of mathematics, science, engineering, finance, and other fields to model and analyze uncertain situations. It helps to make predictions, to assess risks and opportunities, and to make informed decisions based on available information. Probability theory provides a foundation for statistical inference, which is used to draw conclusions from data and to test hypotheses about the underlying population.
Here,
In the "Two Spinner Game", there are two possible outcomes for each spin - a match or a non-match. The probability of the spinners matching is the probability of both spinners landing on the same color. Let's say that there are 3 red sections, 3 blue sections, and 2 green sections on each spinner.
The probability of the first spinner landing on red is 3/8, and the probability of the second spinner landing on red is also 3/8. Therefore, the probability of both spinners landing on red (a match) is (3/8) x (3/8) = 9/64.
Similarly, the probability of both spinners landing on blue (another match) is (3/8) x (3/8) = 9/64, and the probability of both spinners landing on green (a match) is (2/8) x (2/8) = 4/64.
The probability of the spinners not matching is the probability of them landing on different colors. There are 3 different pairs of colors that are not a match: red-blue, red-green, and blue-green. The probability of each of these pairs is (3/8) x (3/8) = 9/64.
So, there are 6 possible outcomes, and the probability of winning by a match is 9/64 + 9/64 + 4/64 = 22/64, or about 34.4%. The probability of winning by a non-match is 3 x 9/64 = 27/64, or about 42.2%.
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Find $\sin X,\ \sin Z,\ \cos X,\ $ and $\cos Z$. Write each answer as a simplified fraction and rounded to four decimal places
The result of each trigonometric functions are:
a) sin X = 7√149 / 149
b) sin Z = 10√149 / 149
c) cos X = 10√149 / 149
d) cos Z = 7√149 / 149
In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse, and the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. Using this trigonometric functions, we can calculate sin X, sin Z, cos X, and cos Z as follows
sin X = YZ / XZ = 7 / √149
cos X = XY / XZ = 10 / √149
sin Z = XY / XZ = 10 / √149
cos Z = YZ / XZ = 7 / √149
To simplify these fractions, we can rationalize the denominator by multiplying the numerator and denominator by √149:
sin X = 7√149 / 149
cos X = 10√149 / 149
sin Z = 10√149 / 149
cos Z = 7√149 / 149
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The given question is incomplete, the complete question is:
Find sin X, sin Z, cos X, and cos Z. Write each answer as a simplified fraction.
You need to get to class, 24 meters away, and you can only walk in the hallways at about 1.5 m/s. How much time will it take to get to your class?
It will take 16 seconds to get to your class.
Solution:[tex]\bold{Distance}=\bold{Speed }\times \bold{Time}[/tex]
[tex]200m = 1.5m\div s \times t[/tex]
Now solve for t to get the time in seconds[tex]24=1.5\times t[/tex] (We want to get t by itself, so lets get rid of the [tex]\times1.5[/tex] by dividing both sides by 1.5)
[tex]24\div1.5 = t[/tex][tex]t = 16 \ \text{seconds}[/tex]
Therefore, it will take 16 seconds to get to your class.
4 more than 3 times a number is 5
Answer:
0.33
Step-by-step explanation:
To solve this, you first write the problem as an algebra equation as follows: 3x + 4 = 5
Then you solve the equation by subtracting 4 from both sides, and then divide both sides by 3. Here is the math to illustrate better:
3x + 4 = 5
3x + 4 - 4 = 5 - 4
3x = 1
3x/3 = 1/3
x = 0.33
Answer = 0.33
Find the distance between 2-4i and 6+i
Answer:
22
Step-by-step explanation:
2-4i and i=6
2-4(6)
=22
=
Suppose that a new employee starts working at $7.32 per hour and receives a 4% raise each year. After time t, in years, his hourly wage is given by the equation y = $7.32(1.04). Find
the amount of time after which he will be earning $10.00 per hour.
After what amount of time will the employee be earning $10.00 per hour?
years (Round to the nearest tenth of a year as needed.)
HELP PLEASE
Using the equation [tex]y = $7.32(1.04)^t[/tex], the amount of time after which the employee will be earning $10.00 is about 9.64 years, or approximately 9 years and 8 months.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
We can start by setting up the equation for the employee's hourly wage y after t years -
[tex]y = $7.32(1.04)^t[/tex]
We want to find the amount of time t after which the employee will be earning $10.00 per hour, so we can set y equal to 10 and solve for t -
[tex]10 = $7.32(1.04)^t[/tex]
Dividing both sides by $7.32, we get -
[tex]1.367 = 1.04^t[/tex]
Taking the natural logarithm of both sides, we get -
[tex]ln(1.367) = ln(1.04^t)[/tex]
Using the property of logarithms that [tex]ln(a^b) = b ln(a)[/tex], we can simplify the right-hand side -
ln(1.367) = t ln(1.04)
Dividing both sides by ln(1.04), we get -
t = ln(1.367)/ln(1.04) ≈ 9.64
Therefore, the employee will be earning $10.00 per hour after about 9.64 years.
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Using c use the best term to identify the following.
The correct definition for the lines drawn to circle with centre C are:
FA is an secant.CD is the radius of the circle.DE is the diameter.EB is the tangent on the circle.Explain about the circle?A circle is a spherical shape without boundaries or edges.
A radius describes the distance radiating from the centre.The Diameter passes through the centre of the circle in a straight line.The distance travelled through a circle is its circumference.A line that precisely crosses a circle at one point is said to be tangent.The circular region is divided into two sections by a circle's chord. The term "circular segment" refers to each component.The major segment and minor segment are distinguished by the arcs they contain. The major segment contains the minor arc.Thus, on the basis of propertied of circle, the correct definition for the lines drawn to circle with centre C are:
FA is an secantCD is the radius of the circle.DE is the diameter.EB is the tangent on the circle.know more about the circle,
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At the bookstore, best-sellers are normally $19.95 each. During the store-wide 20% off sale, how much would it cost you, before tax, to buy two best-sellers?
F. $3.99
G. $7.98
H. $15 96
J. $31.92
K. $39.90
Step-by-step explanation:
20% off means you pay 80 % of the original price for two books
80% * ( 2 x 19.95 ) = .8 ( 39.90) = $ 31.92
HW4 Distance on the Coordinate Plane
Find the perimeter of the trapezoid.
456
P
B
G
10
Units
The required perimeter of the trapezoid is22 units.
How to find the perimeter of trapezoid?The given vertices of the trapezoid are (1,3), (4,7), (9,7), and (9,3). To find the perimeter of the trapezoid, we need to add up the lengths of all four sides.
We can use the distance formula to find the length of each side of the trapezoid:
[tex]{Side 1: }&(1,3) \text{ to } (4,7) \&d = \sqrt{(4 - 1)^2 + (7 - 3)^2} = \sqrt{9 + 16} = 5 \\\text{Side 2: }&(4,7) \text{ to } (9,7) \&d = \sqrt{(9 - 4)^2 + (7 - 7)^2} = \sqrt{25} = 5 \\\text{Side 3: }&(9,7) \text{ to } (9,3) \&d = \sqrt{(9 - 9)^2 + (3 - 7)^2} = \sqrt{16} = 4 \\\text{Side 4: }&(9,3) \text{ to } (1,3) \&d = \sqrt{(1 - 9)^2 + (3 - 3)^2} = \sqrt{64} = 8\end{align*}[/tex]
Therefore, the perimeter of the trapezoid is:
[tex]$\begin{align*}P &= \text{Side 1} + \text{Side 2} + \text{Side 3} + \text{Side 4} \&= 5 + 5 + 4 + 8 \&= 22\end{align*}[/tex]
Thus, the perimeter of the trapezoid is22 units.
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The net of a triangular prism is shown. a) Work out the length x. b) Work out the area of the shaded face. 3 cm 7 cm 5 cm 8 9 cm Not drawn accurately
The length of the side on the prism is 5cm. The area of the shaded region is 72 cm².
What is area?Area is the total amount of area occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the region that its boundary encloses. The quantity of unit squares that span a closed figure's surface is its area. Square units like cm² and m² are used to quantify area. A shape's area is a two-dimensional measurement.
The region inside the perimeter or boundary of a closed shape is referred to as the "area". Such a shape has at least three sides that can be joined together to create a boundary. The "area" formula is used in mathematics to describe this type of space symbolically.
In this figure,
The 5cm flap will be adjacent to the side x. Therefore,
Length of the side x= 5cm
Area of the shaded region= l×b
because the shaded region is a rectangle.
area= 9*x
=9*5= 45 cm²
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Given
\qquad m \angle AOCm∠AOCm, angle, A, O, C is a straight angle.
\qquad m \angle BOC = 6x + 29^\circm∠BOC=6x+29
∘
m, angle, B, O, C, equals, 6, x, plus, 29, degrees
\qquad m \angle AOB = 3x + 124^\circm∠AOB=3x+124
∘
m, angle, A, O, B, equals, 3, x, plus, 124, degrees
Find m\angle BOCm∠BOCm, angle, B, O, C:
The angle BOC on the line AOC is found to be 47 degrees in magnitude.
When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together.
Hence, AOC is a straight angle, BOC is equal to 6x+29°, and AOB is equal to 3x+124°.
It is common knowledge that a straight angle measures 180 degrees.
As the angle ∠BOC+∠AOB=∠AOC is essentially a straight line, we are assuming that it is 180 degrees, which also satisfies the requirement that all angles on the line add to 180 degrees.
6x+29°+3x+124°=180°
9x+153°=180°
9x=27°
x=3°
Hence, ∠BOC=6x+29°
=6×3+29°
= 47°
So, the value of ∠BOC is 47°.
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How many squares would need to be shaded to represent 3/5
The correct answer is three squares. To represent 3/5, 3 out of 5 squares need to be shaded.
What is fraction?Fractions written using a numerator (the number on top) and a denominator (the number on the bottom) that indicate how many parts make up the whole.
This can be seen visually if you draw 5 squares in a row and shade in 3 of them. Since fractions are a representation of the part-whole relationship, the numerator of the fraction (3) indicates the number of parts of the whole (5) that are shaded.
Fractions can be used to represent a variety of ratios, from unit fractions (1/2 or 1/3) to more complex fractions (3/5 or 7/9). To answer the question, "How many squares would need to be shaded to represent 3/5?", it is important to understand that the numerator of the fraction (3) indicates the number of parts of the whole (5) that are shaded.
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We need to shade 3/5 or 60% of the small squares in the bigger square which is 54 small squares.
What is fraction?Fractions written using a numerator (the number on top) and a denominator (the number on the bottom) that indicate how many parts make up the whole.
For this problem, we need to shade 3/5 or 60% of the small squares in the bigger square.
To calculate the number of small squares that need to be shaded, we must first calculate the total number of small squares within the bigger square.
We can do this by multiplying the number of squares in the rows(10) by the number of squares in the columns(9), which in this case is
10 x 9 = 90.
Now that we know the total number of small squares, we can calculate the number of small squares that need to be shaded.
To do this, we need to multiply the total number of small squares (90) by by the fraction we are trying to represent (3/5).
90 x 3/5 = 54.
This means that 54 small squares need to be shaded to represent 3/5.
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Connor bought a box of mini peanut butter cookies to take on a trip. On the back of
The
box, he reads that 10 cookies weigh 30 grams.
) How much does each cookie weigh?
Use the daily data for IBM below: RIBM is the log return of IBM adjusted closing prices. Is there evidence of volatility clustering using 15 lags? ret_ibm= diff(log(price_ibm)) nobs 714.000000 Mean 0.000187 Stdev 0.011466 Skewness -0.418588 Kurtosis 5.958068 Jarque - Bera Normalality Test X-squared: 1085.9541 P VALUE < 2.2e-16 Box-Ljung test data: ret_ibm X-squared = 16.355, df = 15, p-value = 0.3588 Box-Ljung test data: ret ibm 12 X-squared 39.655, df - 15, p-value -0.0005112 BOX-Ljung test data: relibm 2 X-squared - 39.655, df - 15, p-value = 0.0005112 Since the p-value>5% for the Box-Ljung Q test of returns we do not reject the null hypothesis and find no evidence of volatility clustering. Since the p-value>5% for the Box-Ljung Q test of returns we do not reject the null hypothesis and find evidence of volatility clustering. Since the p-value<5% for the Box-Ljung Q test of squared returns we reject the null hypothesis and find no evidence of volatility clustering. Since the p-value< 5% for the Box-Ljung Q test of squared returns we reject the null hypothesis and find evidence of volatility clustering.
The p-value for the Box-Ljung Q test of returns is greater than 5%, which means that we do not reject the null hypothesis and find no evidence of volatility clustering in the raw returns.
What is p value?In statistics, p-value is a measure of the strength of evidence against the null hypothesis. It is defined as the probability of obtaining the observed results, or results more extreme, assuming that the null hypothesis is true.
The null hypothesis is a statement that assumes there is no significant difference or relationship between two groups or variables being compared. The alternative hypothesis is the statement that there is a significant difference or relationship.
Given by the question.
Based on the information provided, we can conclude that there is evidence of volatility clustering in the IBM data using 15 lags. This is indicated by the p-value being less than 5% for the Box-Ljung Q test of squared returns. Therefore, we reject the null hypothesis and find evidence of volatility clustering.
However, since the test is conducted on squared returns, it is the p-value for this test that is more relevant in assessing volatility clustering.
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