Answers
Answer: [tex]4\sqrt{26}[/tex]
Step-by-step explanation:
This is a rather tricky question at first, but it's easy when you figure out the trick.
The key here is using the Pythagorean theorem twice.
We see that the big triangle is divided by its height into two smaller ones.
First, use the Pythagorean theorem on the triangle on the left to find the height.
height = [tex]\sqrt{80-64}=\sqrt{16} =4[/tex]
Now that we know the height is 4, we can use the Pythagorean theorem on the triangle on the right to find x.
x = [tex]\sqrt{20^{2}+4^{2} } =\sqrt{416} = 4\sqrt{26}[/tex]
And there we have our final answer.
Related Questions
What are acute triangles called?
Answers
An acute triangle is a sort of triangle in which all three internal angles of the triangle are less than 90°. Acute triangles are also named acute-angled triangles.
A triangle is a fundamental polygon with three sides and three vertices. Since the triangle has three sides, it also has three interior angles. An angle which measures between 0° to 90° is called an acute angle. An acute triangle is a kind of triangle in which all three internal angles of the triangle are less than 90°.
Acute triangles are also called acute-angled triangles. Even though the length of the sides of acute triangles varies, the interior angles are never more than 90°.
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What is the ratio of the least common multiple of 180 and 594 to the greatest common factor of 180 and 594?.
Answers
The ratio of the least common multiple of 180 and 594 to the greatest common factor of 180 and 594 is 7,140:18.
The greatest common factor (GCF) of 180 and 594 is 18.
The least common multiple (LCM) of 180 and 594 is 7,140.
Therefore, the ratio of the LCM to the GCF is 7,140:18.
The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 180 and 594, you can use the prime factorization method. First, you need to prime factorize each number.
180 = 2 x 2 x 3 x 3 x 5 and 594 = 2 x 7 x 17.
Then, you need to identify the greatest common factor among the prime factors of each number. The prime factors of 180 and 594 that are common to both are 2 and 2, which means that the GCF of 180 and 594 is 18. The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. To find the LCM of 180 and 594, you can use the prime factorization method. First, you need to prime factorize each number. 180 = 2 x 2 x 3 x 3 x 5 and 594 = 2 x 7 x 17. Then, you need to identify the least common multiple among the prime factors of each number. The LCM of 180 and 594 is 2 x 2 x 3 x 3 x 5 x 7 x 17, which is 7,140.
Therefore, the ratio of the LCM to the GCF is 7,140:18.
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Your answer
Fabiola Torres found some stale
Skittles sitting in the back of the
fridge. Find the misplaced modifier in the sentence if there is one
Answers
Answer:
The misplaced modifier in the sentence is "sitting in the back of the fridge."
Step-by-step explanation:
It implies that Fabiola Torres is stale and sitting in the back of the fridge, rather than the Skittles.
The correct sentence would be: "Fabiola Torres found some stale Skittles in the back of the fridge."
what is the resulting volume when an isosceles triangle with side lengths 5,5 10 and is revolved about one of its longer sides?
Answers
The resulting volume when an isosceles triangle with side lengths 5, 5 and 10 is revolved about one of its longer sides is approximately 40.11 cubic units.
Let's call the height of the triangle "h" and the radius of the circle created by the revolution "r". We know that the hypotenuse of the triangle (the longer side) is 10, so we can use the Pythagorean theorem to find the value of h:
h = [tex]\sqrt{(10^2 - (5/2)^2)}[/tex] = [tex]\sqrt{25 - 6.25}[/tex] = [tex]\sqrt18.75}[/tex] = 4.33
Now we can use the formula for the volume of a revolution solid to find the volume:
V = (1/3) * π * [tex]r^2[/tex] * h
r is half the side length of the triangle, so:
r=5/2
V = (1/3) * π * [tex](5/2)^2[/tex] * 4.33 = (1/3) * π * 6.25 * 4.33 = 20.55 * π = 40.11 (approximately)
So the resulting volume of the revolved isosceles triangle is approximately 40.11 cubic units.
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Iriss needs to incorporate at least 165 daisies in her floral arrangements for a wedding. Each centerpiece will have 15 daisies, and each bouquet will have 5 daisies. Write an inequality to represent the situation, if c represents the number of centerpieces Iris makes, and b represents the number of bouquets.
Answers
The inequality that represents the situation is 15c + 5b ≥ 165.
What is inequality?
Inequality means not equal. Generally, if two values are not equal, we use the “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
We can start the inequality by using the following equation:
15c + 5b ≥ 165
This equation represents the total number of daisies used in the floral arrangements.
The left side of the inequality is the total number of daisies used in centerpieces (15c) plus the total number of daisies used in bouquets (5b), and it must be greater than or equal to 165 (the minimum number of daisies needed for the wedding).
Hence, the inequality that represents the situation is 15c + 5b ≥ 165.
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Marcus starts with $5 in his piggy bank. He receives a $10.00 allowance each week. Each week he saves $7.00 of his allowance in his piggy bank. His goal is to save at least $47.00 to buy a game. After how many weeks will he be able to buy the game? Select all possible answers.
Answers
The number of weeks that he will be able to buy the game will be 6 weeks.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Marcus starts with $5 in his piggy bank. He receives a $10.00 allowance each week. Each week he saves $7.00 of his allowance in his piggy bank. His goal is to save at least $47.00 to buy a game.
Let 'x' be the number of weeks. Then the inequality is given as,
$5 + $7x ≥ $47
Simplify the inequality, then we have
$5 + $7x ≥ $47
$7x ≥ $42
x ≥ 6 weeks
The number of weeks that he will be able to buy the game will be 6 weeks.
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rewrite in standard form please
Answers
The standard form of the equation y - 11 = (-4/3)(x+7) is 3y = -4x + 5.
What is standard form?
The general method of representing any kind of notation is known as the standard form. The equation's standard form, which is also known as the approved form of an equation, is represented by the standard form formula.
The given equation is -
y - 11 = (-4/3)(x+7)
The standard form of the equation is y = mx + b.
Solving the equation -
y - 11 = (-4/3)(x+7)
3(y-11) = -4(x+7)
3y - 33 = -4x - 28
3y = -4x - 28 + 33
3y = -4x + 5
Therefore, the standard form is 3y = -4x + 5.
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The length of a table is three times as long as its width. The width of the table is 5x+2.
What is an algebraic expression for the length of the table? (Hint: Use the Distributive Property.)
EXPLAIN the steps that you took to find your answer.
Answers
Answer:
length = 15x + 6
Step-by-step explanation:
given the length is 3 times the width, then
length = 3(5x + 2) ← distribute parenthesis by 3
= 15x + 6
A car is traveling at a constant speed. The table below represents the time it takes the car to travel several distances. What does the slope represent in terms of given context? A. The car is traveling 30 minutes per mile. B. The car’s speed is 30 miles per hour. C. The car’s speed is 2 miles per hour. D. The car is traveling 2 minutes per mile.
Answers
The slope represented in terms of the given context will be 2 minutes per mile. Then the correct option is D.
What is speed?Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Time
A car is traveling at a constant speed. The table below represents the time it takes the car to travel several distances.
The slope of the car is given as,
Slope = 30 / 15
Speed = 2 minutes per mile
The slope represented in terms of the given context will be 2 minutes per mile. Then the correct option is D.
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five runners, p,q,r,s,t, have a race, and p beats q, p beats r, q beats s, and t finishes after p and before q. who could not have finished third in the race?
Answers
The statement also says that t finishes after p and before q. This means that t cannot have finished third, as that position is already occupied by q.
In a race involving five runners, p, q, r, s, and t, it is possible to deduce the order of finish based on the information given. According to the statement, p beats q and p beats r, indicating that p finished first in the race. Additionally, q beats s, so q must have finished second.
Therefore, t must have finished either fourth or fifth.One could also deduce that T could not have finished fourth in the race.
As T finishes before Q who is in the 2nd place and after P who is in the first place.It is important to note that this conclusion is based on the information given and cannot be confirmed without additional information.
For example, if it were specified that t finished just milliseconds after p and just before q, it would not be possible to determine whether t finished fourth or fifth.
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The expression -370+13m represents a submarine that began at a depth of 370 feet below sea level and ascended at a rate of 13 feet per minute. What was the depth of the submarine after 9 minutes?
Answers
Answer:
Depth after 9 minutes is -253 feet
Step-by-step explanation:
Since we can find the submarine's depth as a function of time, m (in minutes), lets use the function to calculate the answer.
We are given the equation for depth: Depth(m) = -370+13m
Depth(x) means that the equation will tell us the submarine's depth after m minutes. The equation is missing the units, but we know from the statement that the initial depth is -370 feet and the rate of ascention is +13 feet/min. So we can enhance the equation by rewriting it with the units.
Depth(m) = -370ft+13(feet/minute)*m [m is minutes]
The sub's depth after 9 minutes is:
Depth(9) = -370ft+13(feet/minute)*(9 minutes)
Depth(9) = -370ft + 13*(9)
Depth(9) = -370+117
Depth(9) = -253 feet
allow for classification of individuals based on some attribute or characteristic.
Answers
Individuals can be categorized using qualitative (or categorical) factors based on a trait or characteristic. Individuals are measured numerically through quantitative variables.
There are counts of the participants or observations in each category in qualitative or categorical data. Frequently, percentages or other ratios are used to describe this data (eg, risks). There are two types of categorical data: nominal and ordinal. Nominal variables don't have numerical values; instead, they have two or more categories with "names" (from the Latin nominalis, which means belonging to names). Furthermore, they lack any inherent or natural order. Sex (male or female), marital status (single, married, or divorced), and the reason for a spinal cord injury are examples of nominal variables.
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Demonstrate the translation of a line segment of 3 units to the left and 5 units down if the endpoints of the line segment are (−2, 7) and (0, 3).(1 point) Responses (−5, 2) and (−3,−2) left parenthesis negative 5 comma 2 right parenthesis, and , left parenthesis negative 3 comma negative 2 right parenthesis (1, 2) and (3,−2) left parenthesis 1 comma 2 right parenthesis, and , left parenthesis 3 comma negative 2 right parenthesis (−7, 4) and (−5, 0) left parenthesis negative 7 comma 4 right parenthesis, and , left parenthesis negative 5 comma 0 right parenthesis (−5, 7) and (−3, 3) left parenthesis negative 5 comma 7 right parenthesis, and , left parenthesis negative 3 comma 3 right parenthesis
Answers
The endpoints of the line segment after translation will be (−5, 2) and (−3, −2). Then the correct option is A.
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
The translation does not change the shape and size of the geometry. But changes the location.
The endpoints of the line segment are (−2, 7) and (0, 3).
Translate the points 5 units down and 3 units left. Then the points are given as,
(−2 − 3, 7 − 5) and (0 − 3, 3 − 5)
(−5, 2) and (−3, −2)
The endpoints of the line segment after translation will be (−5, 2) and (−3, −2). Then the correct option is A.
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After a large number of drinks, a person has a blood-alcohol level of 200 mg/dL (milligrams per deciliter). If the amount of alcohol in the blood decays exponentially, and after 2 hours, 112. 5 mg/dL remains, find an exponential model for the person's blood-alcohol level f(t) where t is the time in hours.
Also, Use your model to estimate the person's blood-alcohol level after 4 hours. (Round your answer to one decimal place)
Answers
So, the person's blood-alcohol level is estimated to be 40 mg/dL after 4 hours.
An exponential model for the person's blood-alcohol level can be represented by the function f(t) = A * e^(-kt) where A is the initial blood-alcohol level, k is the decay constant and t is the time in hours.
To find the decay constant k, we can use the known information that after 2 hours, 112.5 mg/dL remains. We can substitute the known values into the exponential function, and solve for k:
f(2) = A * e^(-2k) = 112.5
A = 200 mg/dL
200 mg/dL = 112.5 * e^(-2k)
k = ln(200/112.5)/(-2)
Using this value of k, we can now find the blood-alcohol level after 4 hours:
f(4) = A * e^(-kt) = 200 * e^(-k*4)
f(4) = 200 * e^(-1.6) = 200 * 0.20 = 40 mg/dL
Therefore, the person's blood-alcohol level is estimated to be 40 mg/dL after 4 hours.
It's worth noting that this model is based on the assumption that the blood-alcohol level decays exponentially, and many other factors like body weight, gender, metabolism, and the amount of alcohol consumed can affect the actual blood-alcohol level.
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- 5/8 + 67/8
23/3 - (- 17/4)
- 29/6 - 20/3
pls solve this for me
Answers
Answer:
-5/8+67/8. -5+67/8. 62/8
Step-by-step explanation:
help me I'm stuck solve c
5
Answers
Answer: I believe it is infinitely many solutions
Step-by-step explanation:
2023
Answer:
Step-by-step explanation:
The first equation is already in slope intercept form - y=mx+b
the second equation we would to get y by itself.
so 7x - 6y = 12 subtract 7x from both sides
-6y= -7x + 12 I put the 7x first to keep the y=mx+b form
y = (-7x + 12) / -6 divide both sides by -6
y = 7/6 x -2
so your two equations are now
y = 7/6x + 2
y = 7/6x - 2
you can graph the equation by putting a point in for x and solving for y.
y = 7/6 (0) +2
y = 2
so your first point is (0,2)
try a different value for x
y = 7/6 (6) + 2
y = 7 + 2 (multiplying by 6 cancels out the 6 denominator)
y = 9
so another point is (6, 9)
in the formula y = mx + b , b is the y intercept
so the line will intercept Y at 2 and there will be a point at (6,9)
Do the same for the other equation. It will be exactly the same except that the y intercept will be at -2, not 2.
We have found more than one solution, so the answer can not be one solution or no solutions. By process of elimination we have infinitely many solutions.
Lashanda sold t-shirts at a festival. She made $6 for each t-shirt she sold. Her expenses were $30. If she made a profit of $84, how many t-shirts did she sell?
Write an equation that could be used to answer the question above. First, chose the appropriate form. Then, fill in the blanks with the numbers 6, 30, 84. Let x represent the number of t-shirts.
A. _x + _ = _
B. _x - _ = _
Answers
Answer:
The appropriate form for this equation is B. 6x - 30 = 84. This equation can be used to calculate the number of t-shirts Lashanda sold. By solving the equation, we can determine that she sold 14 t-shirts.
Step-by-step explanation:
Latrell and his family are season ticket holders for their favorite baseball team. Last year, the cost of season tickets was $1,310. This year, the cost is $1,441. What was the percent of increase in the cost of season tickets?
Answers
Answer:
To find the percent of increase in the cost of season tickets, we can use the following formula:
(New cost - Old cost) / Old cost x 100 = % increase
Using the given information:
(1,441 - 1,310) / 1,310 x 100 = 10.06%
So, the percent of increase in the cost of season tickets is 10.06%.
Explain how to write algebraic expressions. What are some key words you should look for? How can you check your work?
Answers
Algebraic expressions can be written by using the key words to write an operation.
What are Algebraic Expressions?Algebraic Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
In order to write an algebraic expression from a written statement, we have to understand the key words and their translation to mathematical operation.
Some of the keywords are :
Addition : sum, added to more than, increased by, .......
Subtraction : Difference of, difference between, less than, decreased by, ..........
Multiplication : product, times, multiplied by, ......
Division : ratio of, quotient of, .......
So for example, sum of 6 and a number which is 2 times x can be written as 6 + 2x.
Hence in order to write the expressions, know the key words.
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Point D is the centroid of triangle ABC use the given information to find the value of X. DF = 4x-1 and BD = 6x+4
Answers
The value of x is 2.5.
What is the Centroid Theorem?The centroid theorem states that, the centroid of a triangle equals two-third of the distance from each midpoint of a triangle to each vertex.
Given;
BD = 6x+4
DF = 4x-1
Now,
BD = 2/3(BF)
BD = 2/3(BD+DF)
Substituting the values of BD and DF
4x + 5 = 2/3(6x+4+4x-1)
4x + 5 = 2/3(10x+3)
4x - 6x -20x/3 = 1
(-6x-20x)/3=1
26x/3=1
x=3/26
Therefore, based on the centroid theorem, the value of x will be 3/26.
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8x3 + 125 which expression represents the correct factorization of the polynomial?.
Answers
The expression that represents the correct factorization of the polynomial 8x³ + 125 exists (2x + 5) (4x² - 10x + 25)
What is meant by polynomial expression?Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable).
A polynomial is not an expression that contains a variable with exponents that are negative or fractional, divides by a variable, or has a variable inside a radical.
Let the given polynomial expression be 8x³ + 125
The expression 8x³ + 125 can be rewritten as (2x)³ + 5³
By using the sum of cubes formula, we get
(2x)³ + 5³ = (2x + 5)( ((2x)² - 2x(5) + 5²)
8x³ + 125 = (2x + 5) (4x² - 10x + 25)
Therefore, the expression that represents the correct factorization of the polynomial 8x³ + 125 is (2x + 5) (4x² - 10x + 25)
The complete question is:
A polynomial expression of degree three is shown below. 8x^3 + 125 Which expression represents the correct factorization of the polynomial?
A (2x + 5)(4x + 10x + 25)
B (2x + 5)(4x + 10x-25)
C (2x + 5)(4x - 10x +25)
D (4x + 25)(2x - 10x+5)
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What is the simplest form of 6/9
Answers
Answer: 2/3, or 0.6666666667
Step-by-step explanation:
Answer:
The simplest form of 6/9 is 2/3.
Step-by-step explanation:
1) Divide both the numerator and denominator by three(does not apply to all situations).
2) Outcome should be 2/3 or .666
someone buys a watch for y including sales tax at 15%. show that the sales tax paid is 3y/23
Answers
The sales tax paid 1.15=3y/23
What is Sales tax?
Government-imposed consumption taxes on the purchase of goods and services are known as sales taxes. Typically, a sales tax is assessed at the point of sale, paid to the store, and then forwarded to the government. A company is responsible for paying sales taxes in a specific jurisdiction if it has a nexus there. Depending on the local rules, this could be a physical location, a worker, an affiliate, or some other kind of presence.
Step by step Explaination:
Sales tax: 15%
Converting 15%=15/100
=0.15
To show sales tax paid is 3y/23
0.15=3y/23
Multiply both side by 23
23*0.15=3y
3.45=3y
Divide both sode by 3
3.45/3=y
y=1.15
The sales tax paid 1.15=3y/23(as the purchase price includes sales tax).
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Write an algebraic expression for the verbal expression "six meters less than four times the width"
4w-6
6-4w
Answers
The spoken statement "six metres less than four times the width is 4w -6" has an algebraic equivalent.
An algebraic expression:
An expression that has been created utilizing integer variables, constants, and algebraic operations is known as an algebraic expression. 3x 2 2xy + c is a nice illustration of an algebraic expression.
As per the data given in the above question are as bellow,
Let's say the value is v.
To get: the product of w multiplied by four.
As a consequence, we must multiply w and 4 the result we get 4w.
To get: the subtract 6 meter less than four times the width.
As a consequence, we must subtract 6 meter less than four times the width the result we get 4w -6.
The following is the mathematical expression.
4w-6
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1/6 x a = 4
a -4 5/8 = 2 6/7
Answers
69Answer:
Step-by-step explanation:
because I love 69
PLS DO NUMBER 3 WILL MARK BRAINLIEST AND ADD 100 MORE POINTS HURRY PLEASE! THANK YOU
Answers
The difference between the y-intercepts of the lines y = 5x + 3 and
y = (17/2)x - 19 is 22 units.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
The given equation of the line in slope intercept form is y = 5x + 3.
The slope of the line given in the table is,
m = (32 - 15)/(6 - 4).
m = 17/2.
Now, 15 = (17/2)×4 + b.
15 = 34 + b.
b = - 19.
So, The required equation of the line is y = (17/2)x - 19.
The difference between the y-intercepts of the lines y = 5x + 3 and
y = (17/2)x - 19 is 3 - (- 19) = 22 units.
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What is the slope of y =- 2x?
Answers
The slope of y = -2x is -2.
The slope of a linear equation is a measure of how steep the line is. In other words, it represents the rate of change of the dependent variable (y) with respect to the independent variable (x).
In the equation y = -2x, the coefficient of the x term is -2, which means that for every unit increase in x, the value of y will decrease by 2 units. So the slope of this line is -2.
The slope can also be thought of as the tangent of the angle the line makes with the x-axis. In this case, the slope being -2, means the angle of the line with the x-axis is negative, which means the line is going downward and to the left.
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How do you plot a log log graph?
Answers
The required way to plot the graph of log function is described.
What is the graph of log function?It can be represented graphically as follows: The graph of any function's inverse function is the reflection of the function's graph about the line y=x. The reflection of the preceding graph about the line y=x is the graph of the logarithmic function y=log3(x), which is the inverse of the function y=3x.
According to question:The function loglog(X, Y) shows the x- and y-coordinates on the x- and y-axes, respectively, using a base-10 logarithmic scale. Specify X and Y as vectors of the same length in order to visualise a set of coordinates connected by line segments. You must provide at least one of X or Y as a matrix in order to plot several sets of coordinates on the same set of axes.
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negative one fifth times the quantity 3 minus 12 timws the quantity one third squared end quantity end quantity
Answers
The expression - 1/5× ( 3 - 12 × (1/3)² is simplified to -1/3
What is a fraction?A fraction can be described as the part of a whole element, number or variable.
The types of fractions are;
Complex fractionsProper fractionsMixed fractionsImproper fractionsSimple fractionsFrom the information given, we have that;
- 1/5× ( 3 - 12 × (1/3)²
find the square
- 1/5 × ( 3- 12 × 1/9)
multiply the values
-1/5 × ( 3 - 4/3)
expand the bracket
- 1/5 × (9 -4 /3)
- 1/5 × 5/3
-5/15
- 1/3
Hence, the value is -1/3
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allow for classification of individuals based on some attribute or characteristic. Quantitative Variables. provide numerical measures of individuals.
Answers
Qualitative variables allow for the classification of individuals based on some attribute or characteristic.
A qualitative variable, additionally referred to as categorical, is one wherein the variable categories aren't described as numbers but alternatively by using verbal groupings. There are classifications of specific statistics: nominal and ordinal. Nominal variables have “names,” not numerical values.
Quantitative variables are any variables in which the facts constitute amounts (e.g. height, weight, or age). specific variables are any variables wherein the information constitutes companies. Qualitative Variables. additionally referred to as specific variables, qualitative variables are variables without a natural feel of order. They're consequently measured on a nominal scale. Qualitative records are information describing the attributes or homes that an object possesses. The residences are categorized into training that may be assigned numeric values. but, there may be no significance to the statistics values themselves, they genuinely constitute attributes of the object worried.
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