The length of the rectangular pool is 98 m.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that the perimeter of a rectangular pool is 368m.
The width of the pool is 86m
We need to find the length of the pool.
Perimeter of rectangle=2(Length+width)
368=2(Length+86)
368=2Length+172
368-172=2length
196=2length
Divide both sides by 2
98=length
Hence, the length of the rectangular pool is 98 m.
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Ahmed sells boxes of pens ($8) and rubber bands ($4). Leona ordered a total of 30 cartons for $220. How many boxes of pens did Leona order?
Leona ordered 25 boxes of pen
How to calculate the boxes of pen that Leona ordered?
Ahmed sells pens for $8 and rubber bands for $4
Leona ordered a total of 30 cartons for $220
The number of boxes that Leona ordered can be calculated as follows
Let x represent the boxes of pen
Let y represent the boxes of rubber bands
x + y= 30.........equation 1
8x + 4y= 220.......equation 2
From equation 1
x= 30 - y
Substitute 30-y for x in equation 2
8(30-y) + 4y= 220
240 - 8y + 4y= 220
240-4y= 220
-4y= 220-240
-4y= -20
y= 20/4
y= 5
Substitute 5 for y in equation 1
x + y= 30
x + 5= 30
x= 30-5
x= 25
Hence Leona ordered for 25 boxes of pen
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Which of the following is NOT divisible by 8?
A. 1,406
B. 1,488
C. 3,608
D, 5,016
Answer: A
Step-by-step explanation:
A man invests his savings in two accounts, one paying
6% and the other paying 10% simple interest per year.
He puts twice as much in the lower-yielding account
because it is less risky. His annual interest is $7612
dollars. How much did he invest at each rate?
Simple Interest Consider making an investment of $100 (the principal) at a 5% yearly rate for a year. Simple interest is calculated as follows: $100 multiplied by.05 percent per year for a total of $5 after a year.
What is the simple interest per year?Let x represent the sum of money invested at a simple interest rate of 6%. Let y represent the sum of money invested at a simple interest rate of 10%.
Decimalize the interest rates as follows: 6% equals 0.06 and 10% equals 0.10. The interest earned on the first account is equal to 0.06 times the interest rate multiplied by the amount invested.
Similar to the first account, the second account's interest earnings are calculated as the interest rate times the amount invested, or 0.10*y.
Now that we have the data from the problem, we need to model the scenario with two equations. Because it is less hazardous, the man invests twice as much in the lower-yielding account. Otherwise put,
[the investment amount at 6%] = [2] * [the investment amount at 10%]
We can represent this relationship in algebra as
x=2y
Therefore, the amount the man earns in interest is $4,180.
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Low density lipoprotein, or LDL, is the main source of cholesterol buildup and blockage in the arteries. This is why LDL is known as "bad cholesterol." LDL is measured in milligrams per deciliter of blood, or mg/dL. In a population of adults at risk for cardiovascular problems, the distribution of LDL levels is normal, with a mean of 123 mg/dL
and a standard deviation of 41 mg/dL.
If an individual's LDL is at least 1
standard deviation or more above the mean, he or she will be monitored carefully by a doctor. What percentage of individuals from this population will have LDL levels 1
or more standard deviations above the mean? Use the 68–95–99.7 rule.
Give your exact answer as a whole number.
16% is the Percentage of individuals from this population who will have LDL level 1.
What is Mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
Given the distribution of LDL levels is normal, with a mean of 123 mg/dL and a standard deviation of 41 mg/dL. If an individual's LDL is at least 1 standard deviation or more above the mean, he or she will be monitored carefully by a doctor.
one standard deviation 68% of data- -95% of data- -3 -2 -1 0
So we want a percentage of individuals with LDL level 1 or more sd above the mean.
So from the above graph, we basically want to know what percentage of the scores are to the right of 1 on the x-axis because we want a percentage of individuals with LDL level 1 or more sd above the mean.
Right of 0 on the x-axis we have 50% of the data.
So by simple calculations
Percentage = 50-34=16%
therefore, the Percentage of individuals from this population who will have LDL level 1 is 16%.
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It is only appropriate and possible to calculate the variance and standard deviation as measures of variability for variables measured using a(n) scale of measurement. O ordinal O ratio O interval or ratio O ordinal or nominal
Variance and standard deviation are measures of variability that are appropriate and possible to calculate for variables measured on an interval or ratio scale of measurement.
Interval scales have a true zero point, meaning that a difference of zero on the scale represents a lack of the characteristic being measured (e.g. temperature measured in degrees Celsius). Ratio scales are similar to interval scales, but also have a meaningful zero point, meaning that a value of zero on the scale represents a complete absence of the characteristic being measured (e.g. height measured in meters).
Variance and standard deviation can be calculated for interval and ratio variables because these scales provide meaningful differences and ratios between values. The calculation of variance involves finding the average squared difference between each value and the mean of the values, while standard deviation is the square root of the variance. Both variance and standard deviation provide information about how spread out the values of a variable are and are useful in statistical analysis.
On the other hand, nominal and ordinal scales only provide categories or rank order for values, without any meaningful differences or ratios between values. As such, it is not appropriate or possible to calculate variance or standard deviation for variables measured on nominal or ordinal scales.
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12. Town A has 4.563 residents.
Town A has 127 more than
4 times the number of residents
of Town B. How many residents
does Town B have?
Answer:
1109
Step-by-step explanation:
4563 = 4b + 127 Subtract 127 from both sides
4436 = 4b Divide both sides by 4
1109 = b
What is the difference?
-11x²-3x+4
(-4x+3)(7x - 3x² - 1)
3x² - 11x +4
-3x² + 3x + 2
32²-112+2
The difference of the algebraic expressions is 3x² - 11x + 4
How to find the difference of algebraic expressions?
An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.
The difference of two algebraic expressions means the subtraction of the expressions. That is:
(-4x+3) - (7x - 3x² - 1) = -4x+3 -7x+3x²+1
= 3x² - 11x + 4
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if the 2 triangles are similar, write the similarity statement? how do you know?
Answer:
measure them goofy
Step-by-step explanation:
stop being dumn
I need full working pleaseee, I'll rate it brainliest
On integrating the function ∫4/(2x-1) dx, the value is obtained as 2 ln (2x + 1) + C.
What is Integration?
The summing of discrete data is indicated by the integration. To determine the functions that will characterise the area, displacement, and volume that result from a combination of small data that cannot be measured separately, integrals are calculated.
The integral is given as - ∫4/(2x-1) dx
Substitute u = (2x - 1) → du/dx = 2 → dx = 1/2 du -
⇒ 2 ∫ 1/u du
The standard integral is -
⇒ ln (u)
Plug in solved integrals -
⇒ 2 ∫ 1/u du
⇒ 2 ln (u)
Undo the substitution u = (2x - 1) -
⇒ 2 ln (2x + 1)
Apply the absolute value function to arguments of logarithm functions in order to extend the antiderivative's domain -
⇒ 2 ln (2x + 1) + C
Therefore, the value is obtained as 2 ln (2x + 1) + C.
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The distance, s (in feet), traveled by a car moving in a straight line is given by the function, st=t2+t where t is measured in seconds. Find the average velocity for the time period from t = 1 to t = 4. Hint: Average velocity is displacement divided by time interval of the displacement.
The average velocity for the time period from t = 1 to t = 4 is 6 feet/s.
The distance driven in a car is shown by
s(t) = t^2 + t
The distance driven in a car at t = 1
s(1) = (1)^2 + 1
s(1) = 1 + 1
s(1) = 2
The distance driven in a car at t = 4
s(4) = (4)^2 + 4
s(4) = 16 + 4
s(4) = 20
Let at t = 1, it is t(1) and at t = 4 it is t(2)
Displacement of car between t(1) and t(4) = s(2) - s(1)
Displacement of car between t(1) and t(4) = 20 - 2
Displacement of car between t(1) and t(4) = 18 feet
Time travel between t(1) and t(4) = 4 - 1
Time travel between t(1) and t(4) = 3
Now,
Average velocity = Displacement of car between t(1) and t(4)/Time travel between t(1) and t(4)
Average velocity = 18/3
Average velocity = 6 feet/s
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The surface area of a cylinder with a radius of 3 inches is 78π
square inches. What is the height of the cylinder in inches? (Do not enter units)
Answer: 10
Step-by-step explanation:
Assuming that pi = 3.14
The height of the cylinder in inches is 10.
What is a cylinder?When two equal or identical and parallel bases are connected in a three-dimensional solid form makes a cylinder. These bases resemble spherical disks.
Given:
A cylindrical shape is given.
And the surface area of the shape is 78π.
And the radius of the cylinder is 3 inches.
That means,
2πrh + 2πr² = 78π
3h + 9 = 39
Subtracting 9 from both sides,
we get,
3h = 39 - 9
h = 30/2
h = 10
The height = 10 inches.
Therefore, the height is 10 inches.
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WILL MARK BRAINLYSINT
You drive a school bus in a suburb. You record the number of minutes that it takes to complete your daily route for two months. The data are listed in a frequency table. You need to describe the typical route time.
Which measure best describes the typical route time?
mean
spread
median
weighted mean
none of the above
The measure best describes the typical route time is, Median. So option C is correct.
What is the median?The middle number or piece of data in a collection is known as the median. Three alternative metrics are employed in mathematics to determine the average value for a given group of integers. They are the mode, median, and mean. The measures of central tendency are this trio of measurements.
Median = {(n+1)/2}th term (for odd)
Median = [(n/2)th term + {(n/2)+1}th term]/2 (for even)
The median is the middle value in a set of data, and is often used to describe the typical or central value in a dataset. Unlike the mean, which can be affected by extreme values, the median is not sensitive to outliers and provides a better representation of the typical value in the dataset.
For example, if the bus route times are listed in a frequency table, the median can be found by ordering the values and finding the middle value (or the average of the two middle values, if the number of observations is even).
In the context of driving a school bus, the median route time would give the most accurate representation of the typical time it takes to complete the daily route, and would provide a better indicator of the bus driver's performance than the mean or any other measures of central tendency.
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For the year ending April 30, Urology Medical Services Co. mistakenly omitted adjusting entries for (1) $1,400 of supplies that were used, (2) unearned revenue of $6,600 that was earned, and (3) insurance of $9,000 that expired. Indicate the combined effect of the errors on (a) revenues, (b) expenses, and (c) net income for the year ended April 30.
(a). Revenues = $6,600.
(b). Expenses = $10400
(c). Net income = $3800
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
Given:
For the year ending April 30,
Urology Medical Services Co. mistakenly omitted to adjust entries for (1) $1,400 of supplies that were used,
(2) unearned revenue of $6,600 that was earned,
and (3) insurance of $9,000 that expired.
(a). Revenues = $6,600.
(b). Expenses = ($1,400 + $9,000).
= $10400
(c). Net income =
($10,400 – $6,600).
= $3800
Therefore, all the required values are given above.
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When teaching an 8th grade lesson on problem solving, Sylvia begins by utilizing a short video clip from the movie, Die Hard 3. Characters, John McClane and Zeus Carver, are challenged with getting exactly 4 gallons of water on a scale using only a 5-gallon and 3-gallon container. The clock is ticking, and they only have seconds to spare. Sylvia uses this video clip as?
When teaching an 8th grade lesson on problem solving, Sylvia begins by utilizing a short video clip. Sylvia uses this video clip as a discrepant event because students attached with science it would look like magic for them.
A discrepant occurrence is an unexpected, counterintuitive result that differs from what an observer would typically anticipate. Oobleck is a classic illustration of a discrepant event.
Most kids (who have never seen it before) wouldn't anticipate that it would have both solid and liquid qualities. They didn't anticipate it to spread out right away once the "ball" was placed on the table instead of rolling into a ball and taking shape.
The main factor is that pupils will develop an obsession with science. They will see this as "magic," and they will be very interested in learning how it worked. After that, they'll be prepared to "amaze" their friends with both the "trick" and their subsequently displayed "smarts."
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If x is normally distributed with mean 140 and standard deviation 20, find P(140 < x < 150) (round off to fourth decimal place).
P(140 < x < 150) is 0.1915 when x is normally distributed with mean 140 and standard deviation 20.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value
μ = mean = 140
σ = standard deviation = 20
z-score(x = 140) = (140 - 140) / 20
z-score(x = 140) = 0
z-score(x = 150) =(150 - 140) / 20
z-score(x = 150) = 0.5
Find the probability that corresponds to the z-score in the z-table. (see attached images)
z-score = 0 probability = 0.5000
z-score = 0.5 probability = 0.6915
This means that there's a probability of 0.500 and 0.6915 that the value of x is less than 140 and 150, respectively.
P(140 < x < 150) = 0.6915 - 0.5000 = 0.1915
Therefore, the probability that the value of x is between 140 and 150 is 0.1915.
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The quotient of 60 and k
Answer: The quotient of 60 divided by k is 60/k.
Step-by-step explanation:
The quotient of 60 divided by k refers to the result of dividing the number 60 by another number k. The division operation can be represented mathematically as 60/k.
In other words, the quotient of 60 and k is a mathematical expression that returns the number that results from dividing 60 by k. The result of this division is a single value which can be a fraction or a whole number, depending on the value of k.
A cashier has a total of .68 cents in Pennies and nickels. There are 2 more Pennies than nickels how many each of these coins does she have?
Answer:
see below
Step-by-step explanation:
pennies = x+2
nickels = x
x*0.05 + (x+2)*0.01 =0.68
0.05x+0.01x+0.02 =0.68
0.06x=0.66
x=11 nickels
pennies = x+2 =13
the two equal sides of an isosceles triangle are given as (x 2) cm and the third side is (x 6) cm. if the perimeter of the triangle is 385 cm, find x.
If the two sides of isosceles triangle are (x+2) cm and third side is (x+6) cm. if perimeter is 385 cm, then the value of x is 125 .
We know that the Perimeter of the triangle is equal to the sum of the lengths of all its sides.
the two sides of isosceles triangle are = (x+2) cm ;
the length of third side of triangle is = (x+6) cm ;
So , we have:
⇒ x + 2 + x + 2 + x + 6 = 385
Simplifying and solving for x:
⇒ 3x + 10 = 385 ;
⇒ 3x = 385 - 10 ;
⇒ 3x = 375 ;
⇒ x = 375/3 = 125
Therefore , the value of x for the isosceles triangle is 125 .
The given question is incomplete , the complete question is
The two equal sides of an isosceles triangle are given as (x+2) cm and the third side is (x+6) cm. if the perimeter of the triangle is 385cm, find the value of x.
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What is the area and perimeter of a square that has side lengths that are all 8 inches long?
Answer:
area: 64
perimeter: 32
Step-by-step explanation:
Answer:
Perimeter: 32 inches Area: 64 inches²
Step-by-step explanation:
1) Perimeter
The perimeter is the length of the outside of the shape. For a square you can either add all the sides up or multiply one side by 4 (this only works for a square which has equal sides)8 × 4 = 32or 8 + 8 + 8 + 8 = 32 inches2) Area
The area is the total space on the inside of a 2d shape and for a square you have to multiply the length of one side by itself (x²)8 × 8 = 64or 8² = 64 inches ²The unit for area must be squared (²)4. The candidates for mayor had
2 debates. The first debate lasted
2/3 hour. The second debate was
3 times as long as the first one.
How many hours long was the
second debate?
Answer:
39 ckfiffiofods9odoxdo
A company charges a 5 flat fee plus 3 per window to wash windows. Might someone have to pay exactly 87 to have their windows washed explain
Someone can't pay exactly 87 to have their windows washed.
How to find the exact amount someone have to pay for the company services?A company charges a 5 flat fee plus 3 per window to wash windows. Therefore, let's find if someone can pay exactly 87 units to have there window washed.
Hence, using equation,
y = 5 + 3x
where
x = number of windows washedy = total costUsing the equation, let's find if someone can use exactly 87 units for the service.
87 = 5 + 3x
87 - 5 = 3x
82 = 3x
divide both sides by 3
x = 82 / 3
x = 27.33
Therefore, someone can't use exactly 87 units because the number of windows washed is in decimal.
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How many inches are in 71.12 cm, show your work!
In 71.12 centimeters, there are 28 inches.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
We have a measurement in centimeters,
= 71.12
And we know 1 inch = 2.54 centimeters
So,
In inches, the mesurement = 71.12/2.54
= 28 inches.
Therefore, the required result is 28 inches.
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A 25-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 12 feet from the base of the building. How high up the wall does the ladder reach?
Answer:
b = 21.93
Step-by-step explanation:
This can be solved using Pythagorean theorem. Basically your hypotenuse or c is the length of the ladder, your base or a value is 12 and you're trying to find the height of the wall which is your b
[tex]a^2 + b^2 = c^2\\c^2 - a^2 = b^2\\(25)^2 - (12)^2 = b^2\\625 - 144 = b^2\\b= \sqrt{481} \\b = 21.93...\\b = 21.93[/tex]
Let w = f(x^2 − y^2, y^2 − x^2), where f is a differentiable two-variable function. Calculate y.∂w / ∂x + x. ∂w / ∂y
The value of y. (∂w / ∂x) + x. (∂w / ∂y) is,
⇒ - 4xy f ' (x² - y², y² - x²)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The two-variable function is,
⇒ w = f (x² - y², y² - x²)
Now, We can differentiate the function as;
⇒ (∂w / ∂x) = f ' (x² - y², y² - x²) × (2x , - 2x)
⇒ (∂w / ∂y) = f ' (x² - y², y² - x²) × (- 2y , 2y)
Thus, The value of y. (∂w / ∂x) + x. (∂w / ∂y) is,
⇒ y. (∂w / ∂x) + x. (∂w / ∂y)
⇒ y × f ' (x² - y², y² - x²) × (2x , - 2x) + x × f ' (x² - y², y² - x²) × (- 2y , 2y)
⇒ - 2xy × f ' (x² - y², y² - x²) - 2xy × f ' (x² - y², y² - x²)
⇒ - 4xy f ' (x² - y², y² - x²)
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What’s the answer to 41
The probability of earning a total of exactly 10 points in 2 turns is 1/8.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
The possibilities to earn exactly ten points occur when the scores in first and second turn are as follows:
(4, 6) or (6, 4)
The probability of getting a 4 in first try and 6 in second try is:
(4, 6) = 1/4 * 1/4 = 1/16
The probability of getting a 6 in first try and 4 in second try is:
(6, 4) = 1.4 * 1/4 = 1/16
The possibilities to earn exactly ten points occur when the scores in first and second turn are as follows:
(4, 6) or (6, 4) = 1/16 + 1/ 16 = 2/16 = 1/8
Hence, the probability of earning a total of exactly 10 points in 2 turns is 1/8.
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20. An event that is impossible has a probability of __________________.
An event that is impossible has a probability of 0.
What is the probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
The probability of an event that is impossible is 0. This means that there is no chance or likelihood of it occurring.
In probability, 0 represents the complete absence of any possibility of an event happening, while 1 represents a certain or guaranteed event.
All other values between 0 and 1 represent varying levels of uncertainty or likelihood.
Hence, An event that is impossible has a probability of 0.
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Can anyonee help me with this question
Answer:
5
Step-by-step explanation:
The first says 4 and 4
They added 4 to the previous cumulative, which was nothing and thru got the cumulative of 4+0=4
The second says 10 and 14
Same thing. Adding 10 to the previous cumulative, which was 4, you get 4+10=14
Let's follow the rules for this next one
We have ? and 19
Adding ? to the previous cumulative, which was 14, you get 14+?=19
Making ? = 5 because that what 19-14 is
Suppose the function f(x) satisfies the conditions: f of x = z ^ 2 + 3/z ^ 2 and F (1) = 2. then F(2) =
The value for the function f(x) = z² + 3/z² for f(2) is 4.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range.
Given:
f(x) = z² + 3/z²
Also we have f(1)= 2 then
f(1) = z² + 3/z²
2 = z² + 3/z²
2z² = [tex]z^4[/tex] + 3
-3 = [tex]z^4[/tex] - 2z²
-3 = z²(z²-2)
So, z²= -3 or z²-2 = -3
z= ±√3i or z =i
Now, F(2) we get
F(2) = z² + 3/z²
= (-1)² + 3/ (-1)²
= 1 + 3
F(2) = 4
Hence, the value of F(2) is 4.
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Fabiola's special seasoning mix has two ingredients. The recipe uses 5 parts thyme
and 3 parts parsley. If she is making 40 tablespoons of the mix, how many
tablespoons of parsley does she need?
A 3 tbsp
C 9 tbsp
B 5 tbsp
D 15 tbsp
D) 15 tablespoons of parsley she needs.
How to find the number of tablespoons?Let's call the number of tablespoons of parsley she needs "x". We know the recipe uses 5 parts thyme to 3 parts parsley, so the total number of parts is 5 + 3 = 8.
Since she's making 40 tablespoons of the mix, each part is equal to 40 / 8 = 5 tablespoons.
So x, the number of tablespoons of parsley, is equal to 3 parts * 5 tablespoons/part = 15 tablespoons.
The answer is D) 15 tablespoons of parsley she needs.
Therefore, we can say she needs 15 tablespoons of parsley.
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Define the term drainage density
Drainage density is a measure of the frequency and spacing of stream channels within a drainage basin, expressed as the ratio of the total length of streams within a given area to the total area of the drainage basin.
What is the function of Drainage density?Drainage density is used to quantify the efficiency of the drainage system in carrying water away from the land surface and helps in understanding the hydrological and geomorphological processes that shape the landscape.
Therefore, a measure of the frequency and spacing of stream channels within a drainage basin, expressed as the ratio of the total length of streams within a given area to the total area of the drainage basin is drainage density.
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