The value of X in the given fraction is 1/12
What are improper fractions?A fraction is a mathematical expression that represents a part of a whole or a quotient of two numbers. It is expressed as one integer or number (called the numerator) divided by another integer or number (called the denominator), separated by a line or a slash.
Here, we are going to find the LCM of both 4 and 6 to determine the value of X.
LCM = 12
X = 1/4 - 1/6
X = (3 - 2)/12
X = 1/12
Therefore, we can conclude that the value of X in the given fraction is 1/12.
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Consider the line y= -3/2x-8 . Find the equation of the line that is parallel to this line and passes through the point (-2,3). Find the equation of the line and passes through the point (-2,3)
Answer:
The given line has a slope of -3/2, since it is in the form y = mx + b, where m is the slope. Any line that is parallel to this line will also have a slope of -3/2.
To find the equation of the line that passes through the point (-2,3) and has a slope of -3/2, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope. Substituting in the values we have:
y - 3 = (-3/2)(x - (-2))
y - 3 = (-3/2)x - 3
y = (-3/2)x - 3 + 3
y = (-3/2)x
Therefore, the equation of the line that is parallel to y = -3/2x - 8 and passes through the point (-2,3) is y = (-3/2)x.
Note that this line does not have a y-intercept, since it passes through the point (-2,3) and has a slope of -3/2.
worth 20 points, pls help!!!
The probability that a randomly selected light bulb will last between 750 and 900 hours is given as follows:
P = 47.5%.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.In the context of this problem, we have that:
750 hours is the mean.900 hours is two hours above the mean.The normal distribution is symmetric, hence the probability of an observation between the mean and two standard deviations above the mean is given as follows:
0.5 x 95 = 0.475 = 47.5%.
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Find the value of z such that 0.8904 of the area lies between −z and z. Round your answer to two decimal places.
Answer: Assuming a standard normal distribution, we know that the total area under the curve is equal to 1. Since 0.8904 of the area lies between -z and z, the remaining area (0.1096) lies outside of this range.
Since the normal distribution is symmetric around the mean, the area to the left of -z is the same as the area to the right of z. Therefore, we can find the area to the right of z by subtracting 0.1096 from 1 and dividing by 2:
(1 - 0.1096)/2 = 0.4452
We can use a standard normal distribution table or calculator to find the z-score that corresponds to an area of 0.4452 to the right of the mean. This z-score is approximately 1.70.
Therefore, the value of z such that 0.8904 of the area lies between -z and z is approximately 1.70. Rounded to two decimal places, this is 1.70.
Step-by-step explanation:
One travel bag is 15 inches long, another is 18 inches long, and a third is 21 inches long. They are all 10 inches deep and 15 inches wide. Which travel bag can hold exactly 3,150 cubic inches? Explain your reasoning. 50 points to whoever answers
Answer:
The travel bag that can hold exactly 3,150 cubic inches is the bag that is 21 inches long.
Step-by-step explanation:
The travel bags can be modelled as rectangular prisms.
The formula for the volume of a rectangular prism is:
[tex]\boxed{\textsf{Volume} = l \times w\times d}[/tex]
where:
[tex]l[/tex] is the length.[tex]w[/tex] is the width.[tex]d[/tex] is the depth.Given that all three bags have a depth of 10 inches and a width of 15 inches, we can create an equation for the volume of any of the bags by substituting d = 10 and w = 15 into the formula:
[tex]\begin{aligned}\sf Volume &=l \times w \times d\\&= l \times 15\times10\\&=l \times 150\\&=150\;l\end{aligned}[/tex]
To determine which travel bag can hold exactly 3,150 cubic inches, substitute volume = 3150 into the formula and solve for length, l:
[tex]\begin{aligned}\sf Volume &=150\;l\\\\ \implies 3150&=150\;l\\\\\dfrac{3150}{150}&=\dfrac{150\;l}{150}\\\\21&=l\\\\l&=21\;\sf in\end{aligned}[/tex]
Therefore, the travel bag that can hold exactly 3,150 cubic inches is the bag that is 21 inches long.
Valeria thinks that smoking suppresses a person's appetite so they will weigh less than those who do not smoke. She randomly collected the weights of some smokers and nonsmokers and created the graph shown.
Which statement correctly compares the distributions?
Responses
A Since the range of nonsmokers is 13 lbs more than that of smokers there is much more variability in their weights.Since the range of nonsmokers is 13 lbs more than that of smokers there is much more variability in their weights.
B On average smokers weighed 35 pounds more than nonsmokers.On average smokers weighed 35 pounds more than nonsmokers.
C Almost half of the smokers weighed more than all of the nonsmokers in the sample.Almost half of the smokers weighed more than all of the nonsmokers in the sample.
D On average, nonsmokers weighed 13 lbs less than smokers.On average, nonsmokers weighed 13 lbs less than smokers.
E Even though smokers on average weighed more than nonsmokers the variability in their weights was about the same.
The correct statement that compares the distributions is:
D On average, nonsmokers weighed 13 lbs less than smokers.
What is the variability?
Variability refers to the amount of spread or dispersion in a set of data. It is a measure of how much the data values in a sample or population differ from each other.
One commonly used measure of variability is the standard deviation, which is the square root of the variance. The variance is the average of the squared differences from the mean.
Looking at the graph, we can see that the center of the distribution of smokers is around 178 lbs, while the center of the distribution of nonsmokers is around 165 lbs. This means that, on average, nonsmokers weigh less than smokers.
Option A is incorrect because the range is not a good measure of variability, and it does not necessarily mean that there is more variability in the weights of nonsmokers.
Option B is incorrect because the graph clearly shows that nonsmokers weigh less on average than smokers.
Option C is incorrect because we cannot make any conclusion about half of the smokers weighing more than all of the nonsmokers from the graph.
Option E is incorrect because the graph shows that the variability in the weights of smokers is greater than that of nonsmokers.
Hence, The correct statement that compares the distributions is:
D On average, nonsmokers weighed 13 lbs less than smokers.
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In a large population, 56 % of the people have been vaccinated. If 5 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?
The likelihood that at least one of the five individuals has received a vaccination is therefore roughly 0.9551, or nearly 95.51%.
what is probability ?Probability is a way to gauge how likely something is to happen. To quantify uncertainty, one uses a mathematical construct. A number between 0 and 1 represents the likelihood of an event, with 0 denoting impossibility and 1 denoting certainty. The ratio of outcomes that lead to an event A to all potential outcomes can be used to calculate the probability of that occurrence. This is stated as follows: Probability of A is equal to the proportion of conceivable possibilities that lead to A.
given
To solve this issue, we may calculate the likelihood that none of the five individuals have had a vaccination and then remove that from one to calculate the likelihood that at least one of them has.
1 - 0.56 = 0.44 is the likelihood that any one person has not had a vaccination. As a result, the likelihood that all five individuals are unvaccinated is:
0.44 x 0.44 x 0.44 x 0.44 x 0.44 = 0.0449 (rounded to four decimal places) (rounded to four decimal places)
By deducting the aforementioned result from 1, we can determine the likelihood that at least one person has had vaccinations:
1 - 0.0449 = 0.9551
The likelihood that at least one of the five individuals has received a vaccination is therefore roughly 0.9551, or nearly 95.51%.
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Solve the inequalities show each solution as an interval on the number line 3x-14≥11-x
Answer:
To solve the inequality 3x - 14 ≥ 11 - x, we need to isolate the variable x on one side of the inequality symbol. We can do this by adding x to both sides and adding 14 to both sides:
3x - 14 + x ≥ 11
Combining like terms, we get:
4x - 14 ≥ 11
Adding 14 to both sides, we get:
4x ≥ 25
Dividing both sides by 4, we get:
x ≥ 6.25
Therefore, the solution to the inequality is x ≥ 6.25, which can be represented as the interval [6.25, ∞) on the number line
matt saves $100 one month, $50 for three months, $150 for four months, and $75 for the rest of the months of that year. how much does he save in one year?
PLEASE HELP
7x+3y=20 and -4x-6y=11 find the value of 3x-3y
Answer:
[tex]3x-3y=31[/tex]
Step-by-step explanation:
Adding the equations yields [tex]3x-3y=20+11=31[/tex].
Let f be a linear function. If (−3) = 5 and f(5) = −27, find f(x).
The f(x) of the linear function is:
f(x) = -4x - 7
How to f(x) of a linear function?Since f is a linear function. The general form of a linear function is:
y = mx + b
where y = f(x), m is the slope and b is the y-intercept
Since f (−3) = 5, we have:
x = -3 and y = 5
Substitute into y = mx + b:
y = mx + b
5 = -3m + b ---- (1)
Also, f(5) = −27, we have:
x = 5 and y = -27
Substitute into y = mx + b:
y = mx + b
-27 = 5m + b ---- (2)
Solving (1) and (2) simultaneously by elimination method:
-3m + b = 5
5m + b = -27
-8m = 32
m = 32/(-8)
m = -4
Put m = -4 in (1) and solve for b:
-3x + b = 5
-3(-4) + b = 5
12 + b = 5
b = 5 - 12
b = -7
Put m and b into f(x) = mx + b to get f(x). That is:
f(x) = mx + b
f(x) = -4x - 7
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Isabel and Helena have built a frame and covered it with cloth. The frame is in the shape of a right triangle , AABC , with side lengths 6 ft ft, and 10 ft. They use a vertical pole AE to raise corner A 3 ft as shown What is the distance ED from the base of the pole to the edge of the frame? Round to the nearest foot
Step-by-step explanation:
all triangles here are right-angled.
ABC, ADB, ADC, AED.
let's say CD = x, AD = height
just by using Pythagoras :
8² = height² + (10-x)² = height² + 100 -20x + x²
64 = height² + 100 -20x + x²
6² = height² + x²
36 = height² + x²
64-36 = 100 - 20x
28 = 100 - 20x
-72 = -20x
x = 72/20 = 3.6 ft
6² = height² + 3.6²
36 = height² + 12.96
height² = 23.04
height = 4.8 ft
height² = ED² + 3²
23.04 = ED² + 9
ED² = 14.04
ED = 3.746998799... ft ≈ 4 ft
Find the volume of the solid formed by rotating the region enclosed by
x=0, x=1, y=0, y=9+x7
about the x-axis.
V=_____ cubic units
Answer:
Step-by-step explanation:
To find the volume of the solid formed by rotating the region about the x-axis, we can use the method of disks.
At a given value of x, the distance between the curve y = 9 + x^2 and the x-axis is 9 + x^2. Thus, the area of the disk at x is A(x) = π(9 + x^2)^2. The limits of integration are 0 and 1, since the region is bounded by the lines x = 0 and x = 1.
Therefore, the volume of the solid is given by:
V = ∫(0 to 1) π(9 + x^2)^2 dx
Using integration techniques (such as substitution), we can evaluate this integral to get:
V = (112π/5) cubic units (rounded to 3 decimal places)
Therefore, the volume of the solid formed by rotating the region about the x-axis is (112π/5) cubic units
Last month sales were £180,000 this month sales reached £196,200. What percentage increase is this?
Answer:
9%
Step-by-step explanation:
To find the increased amount, subtract this month sales from the last month sales.
Increased amount = 196200 - 180000
= £ 16,200
Now, find the increased percentage using the formula,
[tex]\boxed{\bf Increased \ percentage = \dfrac{Increased \ amount}{Original \ amount}*100}\\\\[/tex]
[tex]= \dfrac{16200}{180000}*100\\\\= 9\%[/tex]
Prove by induction
((x/y)^n+1)<((x/y)^n) n≥1 and 0
[tex] \: [/tex]
((x/y)^(n+1)) > ((x/y)^n) for all n ≥ 1 and x > y > 0.
To prove this statement by induction, we will use the principle of mathematical induction.
Base case: When n = 1, we have:
((x/y)^(1+1)) = ((x/y)^2) = (x^2)/(y^2)
((x/y)^1) = (x/y)
Since x > y > 0, we have x/y > 1. Therefore, (x^2)/(y^2) > (x/y), which means that the base case is true.
Inductive step: Assume that ((x/y)^(k+1)) > ((x/y)^k) for some arbitrary positive integer k. We want to prove that this implies that ((x/y)^(k+2)) > ((x/y)^(k+1)).
Starting with ((x/y)^(k+2)), we can write:
((x/y)^(k+2)) = ((x/y)^(k+1)) * ((x/y)^1)
Using the induction hypothesis, we know that ((x/y)^(k+1)) > ((x/y)^k), and we also know that x/y > 1. Therefore, we have:
((x/y)^(k+2)) > ((x/y)^k) * (x/y)
Simplifying this expression, we get:
((x/y)^(k+2)) > ((x/y)^k) * (x/y)
((x/y)^(k+2)) > ((x^k)/(y^k)) * (x/y)
((x/y)^(k+2)) > ((x^(k+1))/(y^(k+1)))
Therefore, we have shown that ((x/y)^(k+2)) > ((x/y)^(k+1)) for all positive integers k, which completes the inductive step.
By the principle of mathematical induction, we have proven that ((x/y)^(n+1)) > ((x/y)^n) for all n ≥ 1 and x > y > 0.
When a number is decreased by 40% of itself, the result is 54. What is the number?
Answer:
Let's call the number we're trying to find "x".
According to the problem, when this number is decreased by 40% of itself, we get 54.
In other words,
x - 0.4x = 54
Simplifying the left side, we get:
0.6x = 54
Dividing both sides by 0.6, we get:
x = 90
Therefore, the number we're looking for is 90.
How do you solve this?
Answer:
1440
Step-by-step explanation:
explanation in the picture
Solve the systems by substitution.
-6x - 2y = 26
7y+3=x
Answer: The solution to the system of equations by substitution is (x, y) = (10, 1).
Step-by-step explanation:
Jeriel earned $520.80 at his job when he worked for 21 hours. What was his hourly wage, in dollars per hour?
On the double number line below, fill in the given values, then use
multiplication or division to find the missing value.
Jeriel's hourly wage was $24.80/hour.
Define earing and wage?Earnings refer to the total amount of money that someone has earned from work over a given period of time. Wage, on the other hand, specifically refers to the amount of money earned per hour or per unit of work completed.
To find Jeriel's hourly wage, we can divide his total earnings by the number of hours he worked:
hourly wage = total earnings / number of hours worked
In this case, Jeriel earned $520.80 and worked for 21 hours, so his hourly wage is:
hourly wage = $520.80 / 21 hours
hourly wage = $24.80/hour
Therefore, Jeriel's hourly wage was $24.80/hour.
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Jeriel worked 21 hours for $520.80, making his hourly pay:
Jeriel got paid $24.80 per hour.
What is Earnings and wages?No matter if it is paid based on working time, output, piecework, or regular payments, earnings and wages are defined as "the total payment, in cash or in kind, payable to all individuals determined on the payrol in return for work performed during the accounting period."
We may divide Jeriel's overall income by the number of hours he worked to determine his hourly rate:
hourly wage = total earnings / number of hours worked
In this instance, Jeriel worked 21 hours for a total of $520.80, making his hourly rate:
hourly wage = $520.80 / 21 hours
hourly wage = $24.80/hour
Jeriel was therefore paid $24.80 per hour.
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A shower head claims to use 9 gallons of water in 4 minutes. If a shower lasts 11 minutes, how many gallons of water were used? Round your answer to the nearest tenth of a gallon
Answer:
24.8 gallons of water
Step-by-step explanation:
We Know
A showerhead claims to use 9 gallons of water in 4 minutes.
9 / 4 = 2.25 gallons of water per minute.
If a shower lasts 11 minutes, how many gallons of water were used?
We Take
2.25 x 11 = 24.75 gallons of water
So, the answer is 24.8 gallons of water
HELPP!
When are the values of f(x) positive, and when are they negative?
The values of function f(x) positive, and negatives are (-infinity, infinity )
What exactly is a function?A function is a procedure or link that connects every element of one non-empty set A to at least one element of another non-empty set B. The phrases "domain" and "co-domain" are used in mathematics to define a function f between two sets, A and B. The constraint F = (a,b)| is satisfied by all values of a and b.
In the case of the question,
f (x) = x²
f (x) will be positive for all x values. As a result of the function:
x² = x × x
That is, when any number or integer is multiplied by itself, the result is positive. (For example, - - = + and + + = +)
As a result, f (x) = x2 will be positive for (,).
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Given the vector v has an initial point at (0, 0) and a terminal point at (-4, 6), find
the exact value of v.
Answer:
The calculated value of the exact value of v is <-4, 6>
Calculating the exact value of vTo find the exact value of v, we need to determine the components of the vector v.
The horizontal component of v, denoted as v_x, is equal to the change in x-coordinates between the initial and terminal points, which is -4 - 0 = -4.
The vertical component of v, denoted as v_y, is equal to the change in y-coordinates between the initial and terminal points, which is 6 - 0 = 6.
Therefore, the exact value of v is:
v = <v_x, v_y> = <-4, 6>
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Factor out the expression: -2xy3 - 8xy2 + xy
After factoring the given expression -2xy³ - 8xy² + xy, the resultant answer is -2xy²(xy-4).
What are expressions?The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.
A group of terms coupled with the operations +, -, x, or form an expression, such as 4 x 3 or 5 x 2 3 x y + 17.
A statement with an equal sign, such as 4 b 2 = 6, asserts that two expressions are equal in value and is known as an equation.
So, we have the expression:
-2xy³ - 8xy² + xy
Now, factor out as follows:
= -2xy³ - 8xy² + xy
= xy(-2xy² - 8xy)
= -2xy²(xy-4)
Therefore, after factoring the given expression -2xy³ - 8xy² + xy, the resultant answer is -2xy²(xy-4).
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Which represents the solution(s) of the system of equations, y + 4 = x² and y - x = 2? Determine the solution set by graphing.
O (-2, 0)
O (-2, 0) and (2, 0)
O (-2, 0) and (3, 5)
Ono solutions
Based on the given information, the answer is (d) no solutions.
What is a system of equations?
A system of equations is a set of two or more equations that need to be solved together to find the values of the variables that satisfy all of the equations.
To solve the system of equations y + 4 = x² and y - x = 2, we can substitute y - x = 2 into y + 4 = x² and get:
y - x + 4 = x²
y = x² + x + 4
Substituting y = x² + x + 4 into y - x = 2, we get:
x² + x + 4 - x = 2
x² + 3 = 2
x² = -1
This equation has no real solutions for x, which means there is no solution for the system of equations.
Therefore, the answer is (d) no solutions.
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The average temperature at the South Pole is - 45" F. The average
temperature on the Equator is 92º F. How much warmer is the average
temperature on the Equator than at the South Pole?
Answer:
The average temperature on the Equator is 137°F warmer than the average temperature at the South Pole.
76°c
Step-by-step explanation:
A small ferry runs every half hour from one side of a large river to the other. The probability distribution for the random variable = money collected (in dollars) on a randomly selected ferry trip is shown here.
Money collected 0 5 10 15 20 25
Probability 0.02 0.05 0.08 0.16 0.27 0.42
Calculate the cumulative probabilities. Do not round.
(≤0) =
(≤5) =
(≤10) =
(≤15) =
(≤20) =
(≤25) =
The median of a discrete random variable is the smallest value for which the cumulative probability equals or exceeds 0.5.
What is the median of ?
The cumulative probabilities for the given probability distribution were calculated, and the median of the discrete random variable was found to be 20.
To find the median, we need to find the smallest value of the random variable for which the cumulative probability equals or exceeds 0.5.
The cumulative probabilities are:
(≤0) = 0.02
(≤5) = 0.07
(≤10) = 0.15
(≤15) = 0.31
(≤20) = 0.58
(≤25) = 1
The cumulative probability is the sum of the probabilities of all events that have an outcome less than or equal to a given value. For example, the cumulative probability for the event of collecting 5 dollars or less is the sum of the probabilities for collecting 0 dollars and 5 dollars, which is 0.02 + 0.05 = 0.07. Similarly, the cumulative probability for the event of collecting 10 dollars or less is the sum of the probabilities for collecting 0 dollars, 5 dollars, and 10 dollars, which is 0.02 + 0.05 + 0.08 = 0.15. The same process is used to calculate the cumulative probabilities for all other values. The median is the smallest value of the random variable for which the cumulative probability is greater than or equal to 0.5.
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a book sold 33,600 copies in its first month of release. suppose this represents 6.7% of the number of copies sold to date. how many copies have been sold to date? answer to the nearest whole number
First, 6.7 % can be written in decimal form as 0.067 (6.7 / 100 = 0.067).
Let's use the variable x to represent the number of copies sold to date.
Then we can write and solve the following equation to represent 6.7% of the total sold to date:
0.067 • x = 33600
You can solve this equation by dividing both sides of the equation by 0.067:
0.067 • x = 33600
0.067 0.067
x = 501493
To date, 500000 copies would have been sold rounded to the nearest whole.
Consider this scenario: A town's population has been decreasing at a constant rate. In 2010 the population was 6,100. By 2012 the population had dropped to 5,500. Assume this trend continues. Predict the population in 2016.
Using expression 4 x 300, we can predict that the population of the town in 2016 will be 4,300.
What exactly are expressions?
In mathematics, an expression is a combination of symbols that represent a value or a mathematical relationship between values. An expression can contain numbers, variables, operators, and/or functions, and it can be used to perform operations such as addition, subtraction, multiplication, and division.
Now,
We can use the information given to find the rate of decrease in the population, and then use that rate to predict the population in 2016.
From 2010 to 2012, the population decreased by 6,100 - 5,500 = 600.
This corresponds to a decrease of 600 / 2 = 300 per year, since the decrease is assumed to be constant over time.
Therefore, we can predict the population in 2016 as follows:
From 2012 to 2016 is a time period of 4 years.
At a rate of 300 per year, the population would decrease by 4 x 300 = 1200 over this time period.
Starting from the population in 2012 of 5,500, the predicted population in 2016 is 5,500 - 1,200 = 4,300.
Therefore, based on the given information, we can predict that the population of the town in 2016 will be 4,300.
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If someone has a dog, what is the probability that they also have a cat?
1/6
5/7
5/12
1/3
Answer:
5/12
Step-by-step explanation:
We are only looking at people who have a dog, which is 12
Now we need to determine if they have a cat
P( cat given that they have a dog)
= number of people with a cat/ they have a dog
= 5/ (5+7)
= 5/12
Find the perimeter and total area
The perimeter is 27 feet and the area is 35 square feet
From the question, we have the following parameters that can be used in our computation:
The figure
The perimeter is the sum of tthe side lengths
So, we have
Perimeter = 7.5 + 6 + (6 - 2.5) + 4 + 2.5 + 3.5
Evaluate
Perimeter = 27
The area is calculated as
Area = 6 * 3.5 + 4 * (6 - 2.5)
Evaluate
Area = 35
Hence, teh area is 35 square feet
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Which statement correctly compares the spreads of the distributions?
Penguin Heights at Countyside Zoo
(in cm)
Penguin Heights at Cityview Zoo
(in cm)
00000
OO
+++
35 36 37 38 39 40 41 42 43 44 45
00
00000
35 36 37 38 39 40 41 42 43 44 45
A. The range of penguin heights is greater at Countyside Zoo than at
Cityview Zoo.
B. The ranges of penguin heights are the same.
C. The range of penguin heights is greater at Cityview Zoo than at
Countyside Zoo.
OD. The mode of penguin heights at Countyside Zoo is greater than
the mode at Cityview Zoo.
option C is correct. The range of penguin heights is greater at Cityview Zoo than at Countryside Zoo.
How to calculate data?
Based on the given data, we can see that the penguin heights at Countryside Zoo are distributed more evenly across the range of heights, with heights ranging from 35cm to 45cm, and a fairly consistent distribution across this range. In contrast, the penguin heights at Cityview Zoo are more concentrated around the height of 38cm, with fewer penguins at the extremes of the range.
Therefore, option C is correct. The range of penguin heights is greater at Cityview Zoo than at Countryside Zoo.
Option A is incorrect because the range of penguin heights is greater at Countryside Zoo than at Cityview Zoo.
Option B is incorrect because the ranges of penguin heights are not the same.
Option D is also incorrect because there is no mode of penguin heights at either zoo. A mode is defined as the value that appears most frequently in a distribution. In this case, no height appears more frequently than any other.
In conclusion, we can say that the penguin heights are distributed differently at the two zoos, with Countryside Zoo having a more evenly distributed range of heights, while Cityview Zoo has a more concentrated distribution around a particular height.
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