Using the system of equations we get the values of 3 digit number as:
238
Given:
The sum of the digits of a three-digit number is 13.
The tens digit, t, is 1 more than the hundreds digit, h. The units digit, u, is 3 more than the sum of the tens and hundreds digits.
we are asked to determine each digit of the given number:
we frame the equation as:
tens digit (t) = 1+h
hundreds digit (h) = h
units digit (u) = 3+(t+h)
hence,
h + (1+h) + (3+(t+h)) = 13
open the brackets.
h+1+h+3+(t+h)=13
substitute t value from the above mentioned state.
h+1+h+3+((1+h)+h)=13
h+1+h+3+1+h+h=13
arrange the like terms and add.
4h + 5 = 13
4h = 13-5
4h=8
h = 8/4
h = 2
hence we get the hundreds digit as 2.
now substitute it to get t and u value.
t = 1+h
t = 1+2
t = 3
tens digit = 3
u = 3+(t+h)
u = 3+(3+2)
u = 3+5
u = 8
units digit = 8
Hence we get the number as 238 whose sum is 13 when added.
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A cyclist travels 40km between two villages with an average speed of 18km\hr. Find how long the journey takes.
Here the time taken to complete the journey is2 hour 20 minutes
To find it we need to use the formula which include speed, time and distance of total journey.
Speed=Distance/Time
Here we put the number based on the formula,
18km/hr=40km/time
Time=40km/18km/hr
Time=2.2hr or 2 hour 20 minutes
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a problematic case may occur when two variables measured on a sample of individuals have a correlation of less than 1. on average, individuals that are far from the mean on the first measurement will lie closer to the mean on second; this phenomenon is called
Individuals that are far from the mean on the first measurement will lie closer to the mean on second; this phenomenon is called regression towards the mean.
What is regression?
Regression analysis is a group of statistical procedures used in statistical modelling to determine the relationships between a dependent variable and one or more independent variables.
If one sample of a random variable is extreme, the next sampling of the same random variable is likely to be closer to its mean. This is known as regression toward the mean.
Background A statistical phenomenon called regression to the mean (RTM) can cause natural variation in repeated data to appear as actual change. It occurs when measurements that are frequently followed by ones that are more typical of the range are unusually large or small.
Hence, individuals that are far from the mean on the first measurement will lie closer to the mean on second; this phenomenon is called regression towards the mean.
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how to find the points?
As described in the analytic geometry, the points are(1.1, -5 )
What is analytic geometry?The area of algebra known as analytical geometry uses an ordered pair of numbers known as coordinates to determine the position of a point on a plane. It is utilized to model many plane objects, including points, lines, and others. The terms Coordinate geometry and Cartesian geometry are both used to refer to analytical geometry.
We have to locate the point where the line is through the x line and y line coordinates
Therefore the point is (1.1, -5 )
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How many 4-digit numbers can be formed if the number must be divisible by 2 and digits can be repeated?
Answer:
4500
Step-by-step explanation:
This can be solved in more than one way. One method is to use permutations and see which digits can appear how many times in which position in the possible list of even numbers between 1000 and 9999
However, I think approaching this from an arithmetic progression perspective is easier to explain.
An arithmetic progression or sequence is a sequence of numbers such that there is a common difference between consecutive numbers.
For example, 2, 4, 6, 8, 10... is an arithmetic sequence with a common difference.
Given the first term in the sequence, we can find the nth term using the formula:
[tex]a_n = a_0 + (n-1)\cdot d[/tex]
where
[tex]a_n[/tex] is the nth term,
[tex]a_0[/tex] is the first term
[tex]d[/tex] is the common difference
Treating the even numbers from 1000 to 9999 as an arithmetic sequence, we get the following:
[tex]a_0 = 1000[/tex]
[tex]a_n = 9998[/tex] (since the last number has to be even
[tex]d = 2[/tex]
Let [tex]n[/tex] be the number of possible values
Plug this into the formula and solve for [tex]n[/tex]
9998 = 1000 + (n-1)2
9998 = 1000 + 2n - 2
9998 = 998 + 2n
9998-998 = 2n
9000 = 2n
Switch sides:
2n = 9000
Divide by 2 to get
n = 9000/2 or
n = 4500
The weights of Alma and Bella are in the ratio 5:7 respectively.
When they sit 18 feet apart on a seesaw how far from the fulcrum must Alma sit
in order to balance the seesaw
Alma should sit 7.5 feet apart from the fulcrum, In order to balance the seesaw.
What is Ratio ?
A ratio in mathematics demonstrates how many times one number is contained in another. For instance, the ratio of oranges to lemons in a dish of fruit is eight to six if there are eight oranges and six lemons.
Given, The weights of Alma and Bella are in the ratio 5:7 respectively.
∴ Alma's weight = 5/12 and Bella's weight = 7/12.
they are sitting 18 feet apart on a seesaw.
It means the distance between Alma and Bella is 18 feet.
Now, Alma should sit feet far from the fulcrum in order to balance the seesaw :
= Distance between Alma and Bella × Weight of Alma
= 18 feet × 5/12
= 7.5 feet.
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what is the expected sum of the numbers that appear when three fair dice are rolled? (enter the value in decimal format.)
The expected sum of the numbers that appear when three fair dice are rolled, is 10.5.
In the given question we have to find the expected sum of the numbers that appear when three fair dice are rolled.
As we know that a dice have six faces. Each faces are mark from the number 1 to 6.
That means if we rolled a dice then there is possibility of coming six numbers. That numbers are 1, 2, 3, 4, 5, 6.
Now the sum of these numbers is
1+2+3+4+5+6 = 21
Total numbers are 6.
So the expected sum of the numbers that appears when one fair dice is rolled
=21/6
=3.5
Since there are three fair dice that are rolled.
So the expected sum of the numbers that appears when three fair dice are rolled = 3*3.5
The expected sum of the numbers that appears when three fair dice are rolled = 10.5
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suppose a package to be mailed using a certain postal service may not measure more than 114 inches in length plus girth. (length is the longest dimension and girth is the largest distance around the package, perpendicular to the length.) find the greatest volume (in inches cubed) of a rectangular box with square base that may be mailed.
Such a box can hold a maximum volume of (114/2)3 = 9837.4 cubic inches.
A three-dimensional space's occupied volume is measured. [1] It is frequently measured numerically with SI-derived units (like the cubic meter and litre) or with a variety of imperial or US-standard units. In contrast to how much space the container actually occupies, the volume of a container is typically thought of as its carrying capacity, or the amount of fluid (liquid or gas) that it could hold. A shipment cannot be larger than 114 inches in length plus girth if it is going through a specific postal service. The maximum cubic inch volume of a rectangular box with a square base that can be sent is (114/2)3 = 9837.4.
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What is the slope of the line that passes through the points (-5, -9) and
(-5, -13)? Write your answer in simplest form.
Answer:
undefined i
EE
Submit Answer
S
DELL
atten
Answer:
undefined
Step-by-step explanation:
the line has always the same x, so it is a vertical line
A vertical line has an undefined slope
the tigers beat the sharks 2 out of the 3 times they played. they then played more times, and the sharks ended up winning at least 95% of all the games played. what is the minimum possible value for ?
37 is the minimum possible value for N.
Given,
Sharks' current winning percentage is 1/3*100, or 33.33%.
Since Shark's winning rate must be at least 95%, we must determine the lowest number of N that can be used. Sharks must thus win every one of the N games in order to reduce N.
Total matches therefore equal N+3.
When sharks have a 95% winning percentage, tigers will have a 5% winning percentage. And they'll only triumph in two games overall.
Therefore,
2 matchups represent 5% of all matches.
As a result, there were 40 total matches (2/5*100).
So,
N+3 = 40 => N= 37
As an alternative, you can determine the solution by solving the following equation.
2/(N+3) = 5/100
You will obtain N = 37 by solving.
That is,
The minimum possible value for N is 37
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One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 25 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
The measure of the largest angle of the triangle is 93°, while the measure of the smallest and the third angle is 31° and 56° respectively. Considering that the measure of the third angle is 25 degrees more than that of the smallest angle.
Sum of interior angles of a triangleIn any given triangle, the sum of its interior angles is equal to 180°.
Let the smallest angle be represented by x, so that the other angles are 3x and x + 25.
thus
x + 3x + x + 25 = 180° {collect like terms}
5x + 25° = 180°
5x + 25° - 25° = 180° - 25° {subtract 25° from both sides of the equation}
5x = 155°
x = 155°/5 {divide through by the coefficient of x}
x = 31°
thus the other angles are derived by substituting the value 31° for x as follows;
3(31) = 93°
31° + 25° = 56°
Therefore, the largest angle of the triangle 93°, the smallest angle is 31° and the measure of the third angle is 56°.
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The French club wants to make and sell some pizzas for a fundraiser. It will cost
$250 to rent the equipment to make the pizzas and $2 worth of ingredients to
make each pizza. The pizzas will be sold for $4.50 apiece.How many pizzas must
be made and sold for the French club to make a profit of at least $500?
The number of pizzas that must be sold to make at least a profit of $500 is 220.
How many pizzas must be sold?Profit is total revenue less total cost.
Profit = revenue - cost (price of one pizza x number of pizzas sold) - [cost to rent the equipment + (cost of one pizza x number of pizzas made)] ≥ profit
$4.50p - ($250 + $2p) ≥ $300
$4.50p - $250 - $2p ≥ $300
$2.50p ≥ $300 + $250
$2.50p ≥ $550
Divide
p ≥ $550 / 2.50
p ≥ 220
This illustrates the concept of inequality.
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10 POINTS
AE bisects BD; AB is congruent to DE
prove:
triangle ABC congruent triangle EDC
Given that, AB ≅ ED, CA ≅ CE, and AE bisects BD, the two-column proof that shows ΔABC is congruent to ΔEDC by SSS Congruence Theorem.
What is the SSS Congruence Theorem?The side-side congruence theorem (SSS) states that if two triangles has three pairs of sides that are congruent to each other, then both triangles are congruent.
We are given the following information that is;
AE bisects BD; AB is congruent to DE
Since AE bisects BD, thus the third pair of sides of ΔABC and ΔEDC, BC and CD, will be congruent.
This implies that both triangles has three pairs of congruent sides (AB ≅ ED, CA ≅ CE, and BC ≅ CD), meets the criterion of the SSS Congruence Theorem.
Therefore, ΔABC ≅ ΔEDC by SSS Congruence Theorem.
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circle the number that are divisible by both 5 and 2 (25,40,55,70,80,95)
Answer:
40, 70, 80
Step-by-step explanation:
It would have to be numbers that end in 0. Numbers that are divisible by 5 end in 0 or 5, but numbers divisible by 2 do not end in 5, so only the numbers that end in 0 are divisible by 2 and 5.
By using compatible numbers, the estimate is
Use a calculator to multiply 92 × 12. What do you get?
Circle whether the estimates were all less than or greater than
the actual product.
By using compatible numbers, the estimate is 900
Using a calculator, the actual product is 1104The estimates were less than the actual product.How to estimate the product expression?From the question, we have the following expression that can be used in our computation:
92 x 12
From the question, we are to make use of compatible numbers
This means that we have the following approximation
92 = 90
12 = 10
Next, we estimate the product using approximated values
i.e.
Product = Approximation of 92 x Approximation of 12
Substitute the known values in the above equation, so, we have the following representation
Product = 90 x 10
Evaluate the products
Product = 900
Using a calculator, we have
Product = 92 * 12
Evaluate the products
Product = 1104
900 is less than 1104
Hence, the estimate is less than the actual product
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given the equation y = 3x, complete the table of values.
(just give me the output numbers)
given the equation y = 3x, complete the table of values.
x = -2
y = 3x
y = 3(-2)
y = -6
______________________
x = -1
y = 3x
y = 3(-1)
y = -3
______________________
x = 0
y = 3x
y = 3(0)
y = 0
______________________
x = 1
y = 3x
y = 3(1)
y = 3
______________________
x = 2
y = 3x
y = 3(2)
y = 6
______________________
possible points: 7.14 question the student council is selecting officers for the next school year from the 7 freshmen, 4 sophomores, and 6 juniors that are running for the 5 officer positions available. at least three officers must be juniors. how many different possibilities are there for the 5 different officer positions?
The 5 separate possibility that officer seats may be filled in 336 different ways.
7 + 4 + 6 = 17 students are running for the 5 officer positions. If at least 3 of the 5 positions must be filled by juniors, there are 6 ways to choose which 3 juniors will fill these positions.
Then there are 7 + 4 - 3 = 8 remaining students 3 juniors and 5 from the remaining sophomores and freshmen to fill the remaining 2 positions.
There are 8 ways to choose the first of these 2 positions and 7 ways to choose the second, so there are a total of 6 × 8 × 7 = 336 ways to choose the officers.
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help help help help help
The y value of the y-intercept is 146 feet while the slope is -4 feet per second
How to find the y value of the y-intercept and the meaning?it was given that Kaliel starts at a height of 142 feet. That means at time 0 second (the start), he is at height 142 feet. So this is y-intercept i.e. time = 0 (x-axis), height = 146 (y-axis)
Thus, the y value of the y-intercept is 146 feet
In this case, the slope is defined as the rate of change in height with time i.e the rate at which he descends
Slope = Change in height / Change in time
From the table, the time given is 8 and 13 when the height is 110 and 94. Slope will be:
Slope = (94-110) /(12-8)
Slope = -16/4
Slope = -4
This implies he descends at a rate of 4 feet per second.
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Plot the points (-5, 3) and (-4, 9) and find the slope.
Answer:
Slope M=6
Step-by-step explanation:
suppose the roots of the equation 2x 2 − 5x − 6 = 0 are α and β. without explicitely solving for the roots, find the quadratic equation with roots 1 α and 1 β
The quadratic equation with the roots 1/α and 1/β using the given equation is equal to
As given in the question,
Given equation is:
2x²−5x−6=0
Roots of the given equations are α and β
Compare with standard quadratic equation:
ax² + bx + c = 0
a = 2 , b= -5 , c = -6
Sum of the roots are:
α + β = -b/a
= -( -5/2)
= 5/2
Product of the roots
αβ = c/a
= -6/2
= -3
Now ,
( α + β )/ αβ = (5/2) / -3
⇒1/ β + 1/α = -5/6
⇒ 1/α + 1/β = -5/6
And ,
1/αβ = -1/3
Quadratic equation with roots 1/α and 1/β is given by:
x² - ( 1/α + 1/β)x + 1/αβ =0
⇒x² - (-5/6)x + (-1/3) = 0
⇒x² + (5/6)x -(1/3) =0
Therefore, the quadratic equation with roots 1/α and 1/β is equal to
x² + (5/6)x -(1/3) =0
The complete question is :
Suppose the roots of the equation 2x²−5x−6=0 are α and β.Find the quadratic equation with roots 1/α and 1/β.
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nic and tim each purchased one raffle ticket. if a total of 10 raffle tickets are sold and two winners will be selected, what is the probability that both nic and tim win?
The probability of both Nic and Tim winning the raffle at the same time is 1/100.
Probability is a mathematical measurement of a likelihood of an event to happen. Given that both Nic and Tim each purchase one raffle ticket out of 10 tickets and that there will be two winners selected, the odds of either Nic or Tim winning the raffle out of 10 ticket is 1/10.
Since the odds of either Nic or Tim winning the raffle ticket is 1 out of 10 or 1/10, we can then calculate the mathematical probability of two events occurring at the same time with a multiplication rule formula as follows:
1/10×1/10=1/100
Hence, the odds of both Nic and Tim winning at the same time is 1 out of 100 or 1/100.
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A lake contains 4 distinct types of fish. Suppose that each fish caught is equally likely to be any one of these types. Let Y denote the number of fish that need be caught to obtain at least one of each type.
(a) Give an interval (a, b) such that (b) Using the one-sided Chebyshev inequality, how many fish need we plan on catching so as to be at least 90 percent certain of obtaining at least one of each type?
a= μ-3.16*σ , b= μ+3.16*σ if each fish caught is equally likely to be any one of these 4 distinct types.
What is meant by Chebyshev inequality?Chebyshev's inequality is a probability theory that ensures that, over a vast range of probability distributions, no more than a particular proportion of values would be present within a selected limits or range as from mean. In other words, only a certain fish caught will be discovered within a given range of the distribution's mean.
The formula for which no more than a particular number of values can exceed is 1/K2; in other words, 1/K2 of a distribution's values can be more than or equal to K standard deviations away from the distribution's mean. Furthermore, it asserts that 1-(1/K2) of a distribution's values must be within, but not include, K standard deviations of the distribution's mean.
How to solve?
from Chebyshev's inequality for Y
P(| Y - μ|≤ k*σ ) ≥ 1-1/k²
where
Y = the number of fish that need be caught to obtain at least one of each type
μ = expected value of Y
σ = standard deviation of Y
P(| Y - μ|≤ k*σ ) = probability that Y is within k standard deviations from the mean
k= parameter
thus for
P(| Y - μ|≤ k*σ ) ≥ 1-1/k²
P{a≤Y≤b} ≥ 0.90 → 1-1/k² = 0.90 → k = 3.16
then
P(μ-k*σ≤ Y ≤ μ+k*σ ) ≥ 0.90
using one-sided Chebyshev inequality (Cantelli's inequality)
P(Y- μ≥ λ) ≥ 1- σ²/(σ²+λ²)
P{Y≥b} ≥ 0.90 → 1- σ²/(σ²+λ²)= 1- 1/(1+(λ/σ)²)=0.90 → 3= λ/σ → λ= 3*σ
then for
P(Y≥ μ+3*σ ) ≥ 0.90
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What is the equation of the line that passes through the point (4,6)(4,6) and has an undefined slope?.
Answer:
x = 4
Step-by-step explanation:
A line with undefined slope is a vertical line.
Vertical lines have equation in the form:
x = anumber
In this case they gave you the info you need (4,6) The 4 is the x and the 6 is the y. (4,6) is in the form (x,y).
So x is 4.
x = 4
Use the information given to enter an equation in standard form.
Slope is 7, and (1, 8) is on the line.
The linear equation associated with slope is 7, and (1, 8) is on the line is y = 7x + 1.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant b.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
A linear equation or function is given as ;
y = mx + b
Now,
At x = 0 ⇒ y = b so it will be a y-intercept.
Put m = 7 , x = 1 and y = 8
8 = 7(1) + b
b = 1
Thus, y = 7x + 1
Hence "The linear equation associated with slope is 7, and (1, 8) is on the line is y = 7x + 1".
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c. find the mean, median, and standard deviation of heating degree days (hdd), broken down by season, for the california (code 0499). (ignore the first and last rows for the given location, the ones that contain -9999, the code for missing values.) round your answers to two decimal places, if necessary.
mean =1.532
median = 6.98
standard deviation = 3.5
mean for heating degree days and broken down by season for the california
according to the given values we find the mean
mean =
-1.45+ -2.5+-4.5+1.056+3.67+6.98+3.78+2.67+4.87+3.45+2.97+-4.06/12
=1.532
median for heating degree days and broken down by season for the california
according to the given values now we find the median
median = 6.98
standard deviation for heating degree days and broken down by season for the california
according to the given values now we find the standard deviation
standard deviation = square root of ∑([tex]x_{i}[/tex]- μ)^2/n
= 3.5
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the ratio of buses to cars entering the lot was 2 to 11. if 650 vehicles entered the lot altogether. how many were cars?
The number of cars were are, 550.
What is Vehicle?
A device, typically with wheels and an engine, used to move people or things, particularly on land: Yesterday evening, a truck driver was killed when his car flipped over. Buses, trucks, and other road vehicles are included. A farm vehicle is a tractor.
Wagons, bicycles, motorized (cars, trucks, buses, mobility scooters for the disabled), railed (trains, trams), amphibious (screw-propelled, hovercraft), watercraft, and aircraft are all examples of vehicles (airplanes, helicopters, aerostats)
The ratio of buses to cars entering the lot was 2 to 11.
650 vehicles entered the lot altogether.
Base on the given information,
650 x 11 ÷ (2 + 11)
Simplifying,
7150 ÷ 13
⇒ 550
Hence, the number of cars were are, 550.
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A hive of bees contains 27 bees when it is first discovered. After 4 days, there are 45 bees. It is determined
that the population of bees increases exponentially.
How many bees are will there be after 40 days? Round your answer to the nearest whole number.
After 40 days 4467 bees will be the population after 40 days.
What is an exponential function?An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
Given here: A hive of bees contains 27 bees when it is first discovered. After 4 days, there are 45 bees. The population of bees also increase exponentially.
let the function that gives the population of bees after given days
f(x)=aˣ27
a⁴×27=45
a= [tex]\sqrt[4]{45/27}[/tex]
a=1.1362
Thus for x= 40 we have f(40)=1.1362⁴⁰×27
= 4465.69
=4467 (approx)
Hence, After 40 days 4467 bees will be the population after 40 days
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(Angle Relationships
Which angle is supplementary to LPM?
O. KPL
NPI
ONPL
OMPN
44. 2 80. 2
55. 6
P
124. 4°
55. 6°
The ∠MPN is supplementary to ∠NPI.
What is the supplementary angles?
Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because the sum of 130° and 50° is equal to 180°.
Supplementary angles sum to 180°.
(Note that supplementary angles don't have to be next to each other).
Given ∠NPI = 55.6°.
Therefore, to find the measure of the angle that is supplementary to ∠NPI, subtract the measure of ∠NPI from 180°:
⇒ 180° - ∠NPI = 180° - 55.6° = 124.4°.
The angle that measures 124.4° is ∠MPN.
Therefore, The ∠MPN is supplementary to ∠NPI.
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Note : Given question is incomplete, the complete question is:
Which angle is supplementary to ∠NPI?
five angles all with common vertex of P, with angle NPI measuring 55.6 degrees, angle IPK measuring 44.2 degrees, angle KPL measuring 80.2 degrees, angle LPM measuring 55.6 degrees, and angle MPN measuring 124.4 degrees
∠IPK
∠NPL
∠MPN
∠LPM
Determine whether the equation 3(4g+6)=2(6g+9) has one solution, no solution, or infinitely many solutions.
Answer:
one solution
Step-by-step explanation:
A minivan is traveling at 80.5 kilometers per hour. Cargo is strapped to the roof at a height of 1.75 meters. The car hits a concrete barrier, and the cargo is ejected from the roof. Use the following two equations to determine how long it takes for the cargo to hit the ground and how far it travels in the horizontal direction. Let y represent height in meters, x represent horizontal distance in meters, and t represent time in seconds. Equation 1: y = -4.9t2 + 1.75 Equation 2: y = -0.0081x2 + 1.75
The time taken for the cargo to hit the ground will be 0.6 seconds and it travels in the horizontal direction for around 14.69 feet.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here,
The calculations are attached in images.
To calculate t we will use that is y because at the moment of cargo will have a height 0, so we get,
= −4.9t² +1.75
-1.75=-4.9t²
t²=-1.75/-4.9
t²=√0.3571
=0.6 seconds
Now we will calculate x, then y = 0
because since the cargo will be on the ground it will no have height, so
0= -0.0081x²+1.75
-1.75 =-0.0081x²
x²=-1.75/-0.0081
x= √216.04 = 14.69 feet
It will take the cargo 0.6 seconds to hit the ground, and it will travel 14.69 feet in a horizontal direction.
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if the correlation between two variables is close to 0, you can conclude that a scatterplot would show
Scatterplots would show no straight‑line pattern, but there might be a strong pattern of another form.
The correlation coefficient between the values is close to 0, which means that there is no pattern of any form, hence, the scatterplot would show a cloud of points with no visible pattern
A scatter plot is a form of plot or mathematical diagram that uses Cartesian coordinates to display values for typically two variables for a collection of data. It is also known as a scatter graph, scatter chart, scattergram, or scatter diagram. One more variable can be shown if the points are color-, shape-, or size-coded. The data are represented as a set of points, where each point's position on the horizontal axis is determined by the value of one variable and its position on the vertical axis by the value of the other variable.
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