To find the common roots between two functions, we need to find the roots (or solutions) of each function individually and then identify the shared solutions.
For the function f(x) = x^2 + x - 6, we can find the roots by setting the function equal to zero and solving for x:
x^2 + x - 6 = 0
To factorize this quadratic equation, we need to find two numbers that multiply to -6 and add up to 1 (the coefficient of x). The numbers that satisfy these conditions are 3 and -2:
(x + 3)(x - 2) = 0
Setting each factor equal to zero:
x + 3 = 0 or x - 2 = 0
Solving for x in each equation:
x = -3 or x = 2
Therefore, the function f(x) = x^2 + x - 6 has two roots: x = -3 and x = 2.
To find the common roots between this function and another function, we would need to know the second function. If you provide the second function, I can help determine if there are any shared roots.
Un camión va cargado con 3796 kg de patatas. En una frutería descarga 6 sacos de 50 kg cada uno. ¿ Cuanto pesa ahora la carga del camión?
The current weight of the truck is given as follows:
3496 kg.
How to obtain the current weight of the truck?The current weight of the truck is obtained applying the proportions in the context of the problem.
The initial weight of the truck is given as follows:
3796 kg.
The weight removed from the truck is given as follows:
6 x 50 = 300 kg.
Hence the current weight of the truck is given as follows:
3796 - 300 = 3496 kg.
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From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.
,
,
The x-coordinates where the graphs of the equations intersect are x = -1 and x = 3
How to determine the x-coordinates where the graphs of the equations intersect?From the question, we have the following parameters that can be used in our computation:
y = 2x
y = x² - 3
The x-coordinates where the graphs of the equations intersect is when both equations are equal
So, we have
x² - 3 = 2x
Rewrite the equation as
x² - 2x - 3 = 0
When the equation is factored, we have
(x + 1)(x - 3) = 0
So, we have
x = -1 and x = 3
Hence, the x-coordinates are x = -1 and x = 3
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Question
From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.
y = 2x
y = x² - 3
How do I find the possible degree(s) of a function from the graph alone?
The possible degrees of a function from it's graph are found with the sum of the multiplicities of each root of the function.
How to obtain the x-intercepts of a function?On the definition of a function, the x-intercept is given by the value/values of x for which the function assumes a value of zero.
On the graph, these are the values of x for which the graph of the function crosses or touches the x-axis.
The multiplicity of each root is given as follows:
Even multiplicity when the graph touches the x-axis.Odd multiplicity when the graph crosses the x-axis.Hence the degree is found with the sum of the multiplicities of the zeros of the function.
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Find the measure indicated.
27)
T
A) 59⁰
C) 56°
S
80°
20
Q
B) 50°
D) 37°
R
b)50
since its a Equilateral triangle, then the two base angels have the same measure
abd since both triangles are symmetric, they have the same measurements
so 180-80 = 2x
x = 50⁰
Multiply
19(x + 1 + 9z)
The product of the expressions 19(x + 1 + 9z) is 19x + 19 + 171z
How to evaluate the product of the expressionsFrom the question, we have the following parameters that can be used in our computation:
19(x + 1 + 9z)
When the brackets are opened, we have
19(x + 1 + 9z) = 19 * x + 19 * 1 + 19 * 9z
Evaluate the products of the expression
So, we have the following representation
19(x + 1 + 9z) = 19x + 19 + 171z
Hence, the product of the expressions 19(x + 1 + 9z) is 19x + 19 + 171z
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how to find x values
Answer:
Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find
What is the meaning of "A function f is one-to-one"?
A function f is said to be one-to-one, or injective, if it has the property that for any two different inputs, it produces two different outputs.
What is the meaning of "A function f is one-to-one"?More formally, a function f: X -> Y is one-to-one (or injective) if for every x1, x2 in X, if x1 ≠ x2 then f(x1) ≠ f(x2).
This means that no two different elements of the domain X map to the same element of the codomain Y. If you were to draw a horizontal line through any point on the graph of a one-to-one function in the Cartesian plane, that line would intersect the graph at most one time. This is known as the "horizontal line test" for one-to-one functions.
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Fluency in the conversion of the metric system to the Imperial System is an essential skill in the nursing profession. Think of a situation in which negative effects have occurred due to incorrect dosage calculations? This situation could be a personal experience, the experience of someone you know, or a hypothetical. Explain how this error could have been avoided. How will you ensure that you avoid dosage errors due to metric conversions in your future career as a nurse?
In a hypothetical situation, an incorrect dosage calculation due to an error in metric system to Imperial System conversion could lead to potential harm to the patient. To avoid such errors, it is crucial to ensure accurate and precise conversions between the metric and Imperial systems. As a nurse, I will double-check my calculations, use reliable conversion charts or tools, and consult with colleagues or supervisors when in doubt. Additionally, ongoing education and training on dosage calculations and metric system conversions will be important to maintain proficiency and prevent errors in the future.
~~~Harsha~~~
please answer 5+10+12+6+11+18+17=
Answer:
79
Step-by-step explanation:
add this you have easily find answer
Which is an expression for the volume of the prism (v =lwh)
Show how to calculate the volume in two different ways
The expression that shows the volume of the prism is x³ - x² - 6.
How to find the volume of a rectangular prism?The prism above is a rectangular prism. The volume of the prism can be found as follows:
The volume of the prism can be found as follows:
volume of the rectangular prism = lwh
where
l = length of the basew = width of the baseh = height of the prismTherefore,
volume of the rectangular prism = (x - 3)(x)(x + 2)
volume of the rectangular prism = (x² - 3x)(x + 2)
volume of the rectangular prism = x³ + 2x² - 3x² - 6
volume of the rectangular prism = x³ - x² - 6
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How many tiles can fit in a rectangular floor with length 14 ft and width 6 ft if the square tiles has an edge of 3/4 ft. Show your work
Find w=a+bi=, where a and b are real numbers
√-8+6i
Given statement solution is :- The given expression √(-8 + 6i) does not have a real solution in the form w = a + bi, where a and b are real numbers.
To find the complex number in the form w = a + bi, where a and b are real numbers, we can solve the given expression.
Let's solve √(-8 + 6i) step by step:
First, we can express -8 + 6i in the form a + bi:
-8 + 6i = -8 + 6i + 0i = -8 + 6i + [tex]0i^2[/tex]
Now, we can take the square root of -8 + 6i:
√(-8 + 6i) = √((-8) + 6i + [tex]0i^2[/tex])
Since [tex]i^2[/tex] = -1, we can simplify the expression further:
√(-8 + 6i) = √(-8 - 6 + 6i)
= √(-14 + 6i)
Now, we want to express -14 + 6i in the form a + bi:
-14 + 6i = -14 + 6i + 0i = -14 + 6i +[tex]0i^2[/tex]
Taking the square root, we have:
√(-14 + 6i) = √((-14) + 6i + [tex]0i^2[/tex])
Since [tex]i^2[/tex] = -1, we can simplify the expression further:
√(-14 + 6i) = √(-14 - 6 + 6i)
= √(-20 + 6i)
Now, we want to express -20 + 6i in the form a + bi:
-20 + 6i = -20 + 6i + 0i = -20 + 6i + [tex]0i^2[/tex]
Taking the square root, we have:
√(-20 + 6i) = √((-20) + 6i + [tex]0i^2[/tex])
Since [tex]i^2[/tex] = -1, we can simplify the expression further:
√(-20 + 6i) = √(-20 - 6 + 6i)
= √(-26 + 6i)
Now, we want to express -26 + 6i in the form a + bi:
-26 + 6i = -26 + 6i + 0i = -26 + 6i +[tex]0i^2[/tex]
Taking the square root, we have:
√(-26 + 6i) = √((-26) + 6i + [tex]0i^2[/tex])
Since [tex]i^2[/tex] = -1, we can simplify the expression further:
√(-26 + 6i) = √(-26 - 6 + 6i)
= √(-32 + 6i)
We continue this process until we reach a point where the expression simplifies. However, in this case, we encounter an expression that cannot be simplified further, as the square root of a negative number is not defined in the set of real numbers.
Therefore, the given expression √(-8 + 6i) does not have a real solution in the form w = a + bi, where a and b are real numbers.
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Solve for a. Round your answer to the nearest tenth if necessary. 10.7 N X P 22.2 R 17.8
Answer:
Step-by-step explanation:
the answer is 69 the if we round of
Find the number that belongs
in the green box.
37⁰
64°
[?]
30
Round your answer to the nearest tenth.
Answer:
? ≈ 20.1
Step-by-step explanation:
using the Sine rule in the triangle
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex]
with a = ? , b = 30 , ∠ A = 37° , ∠ B = 64° , then
[tex]\frac{?}{sin37}[/tex] = [tex]\frac{30}{sin64}[/tex] ( cross- multiply )
? × sin64° = 30 × sin37° ( divide both sides by sin64° )
? = [tex]\frac{30sin37}{sin64}[/tex] ≈ 20.1 ( to the nearest tenth )
Here is a rectangle:
2
3
2 cm
Find the area of the rectangle.
cm²
The area of the given rectangle with a length of 3 cm and a width of 2 cm is 6 cm².
To find the area of a rectangle, we multiply its length by its width. In this case, the length of the rectangle is given as 3 cm and the width is given as 2 cm.
Area of the rectangle = Length * Width
Plugging in the given values:
Area = 3 cm * 2 cm
Multiplying 3 cm by 2 cm gives us:
Area = 6 cm²
Therefore, the area of the given rectangle with a length of 3 cm and a width of 2 cm is 6 cm².
The area of a rectangle represents the amount of space enclosed within its boundaries. In this case, since the rectangle is two-dimensional, the area is measured in square units, which in this case is square centimeters (cm²).
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Solve the following equations. Check the solutions. 8x^2 + 11 = 191 + 3x^2, 7x^2 - 15 = 49 + 3x^2, 14x^2 - 157 = 333 + 4x^2
The solutions to the equations are:
x = 6, x = 4, x = 7.
1. 8x² + 11 = 191 + 3x²
Rearranging the equation:
8x² - 3x² = 191 - 11
5x² = 180
Dividing both sides by 5:
x² = 36
Taking the square root of both sides:
x = ±6
Checking the solution:
8(6)² + 11 = 191 + 3(6)²
288 + 11 = 191 + 108
299 = 299
The solution x = 6 satisfies the equation.
2. 7x² - 15 = 49 + 3x²
Rearranging the equation:
7x² - 3x² = 49 + 15
4x = 64
Dividing both sides by 4:
x² = 16
Taking the square root of both sides:
x = ±4
Checking the solution:
7(4)² - 15 = 49 + 3(4)²
112 - 15 = 49 + 48
97 = 97
The solution x = 4 satisfies the equation.
3. 14x² - 157 = 333 + 4x²
Rearranging the equation:
14x² - 4x^2 = 333 + 157
10x² = 490
Dividing both sides by 10:
x² = 49
Taking the square root of both sides:
x = ±7
Checking the solution:
14(7)² - 157 = 333 + 4(7)²
686 - 157 = 333 + 196
529 = 529
The solution x = 7 satisfies the equation.
Therefore, the solutions to the equations are:
x = 6, x = 4, x = 7.
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A collection of coins consists of nickels dimes and quarters. There are four fewer quarters than nickels and 3 more dimes than quarters. How many of each kind of coin are in the collection if the total value of the collection is $6.5?
There are 19 nickels, 15 quarters, and 18 dimes in the collection.
Let's assume that there are n number of nickels in the collection.There are four fewer quarters than nickels, so the number of quarters will be n - 4.
There are 3 more dimes than quarters, so the number of dimes will be (n - 4) + 3 = n - 1.
The value of each nickel is $0.05, the value of each dime is $0.10, and the value of each quarter is $0.25.Using this information, we can form the following equation to represent the total value of the collection:
0.05n + 0.10(n - 1) + 0.25(n - 4) = 6.5Simplifying this equation, we get:0.05n + 0.10n - 0.10 + 0.25n - 1 = 6.50.40n - 1.10 = 6.50
Adding 1.10 to both sides, we get:0.40n = 7.60Dividing both sides by 0.40, we get:n = 19
Therefore, there are 19 nickels in the collection.There are four fewer quarters than nickels, so the number of quarters will be n - 4 = 19 - 4 = 15.
There are 3 more dimes than quarters, so the number of dimes will be (n - 4) + 3 = 15 + 3 = 18.
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6(3x+4)+2(2x+2)+2=22x+31 solve the equation for the given variable
The equation 6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31 has no solution for the variable x.
What is the solutuon to the given equation?Given the equation in the question:
6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31
To solve the equation 6(3x + 4) + 2(2x + 2) + 2 = 22x + 31 for the variable x, we will simplify and solve for x.
Apply distributive property:
6 × 3x + 6 × 4 + 2 × 2x + 2 × 2 + 2 = 22x + 31
18x + 24 + 4x + 4 + 2 = 22x + 31
Collect and combine like terms on both sides:
22x + 30 = 22x + 31
Next, we want to isolate the variable x on one side.
22x - 22x + 30 = 22x - 22x + 31
30 = 31
However, we notice that the x terms cancel out when subtracted:
30 ≠ 31
This means that there is no solution.
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if m∠2=3x+14° and m∠4=2x+6°, what is
The angle m∠HAT in the line segment is 54 degrees.
How to find the angle in a line?When line segment intersect, angle relationships are formed such as
vertical angles, linear angles etc.
Therefore, the angle ∠HAT can be found using the relationship of the angles as follows:
m∠MAH = 3x + 14
m∠HAT = 2x + 6
Therefore,
m∠MAH + m∠HAT = 90 degrees
3x + 14 + 2x + 6 = 90
5x + 20 = 90
5x = 90 - 20
5x = 70
x = 24
Therefore,
m∠HAT = 2x + 6 = 2(24) + 6 = 48 + 6 = 54 degrees
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PLEASE HURRY! When you know the volume of a prism and some dimensions, you can solve for a(n) ____________ dimension.
When you know the volume of a prism and some dimensions, you can solve for an unknown dimension.
How to solve for unknown dimension ?When armed with knowledge about the volume of a prism alongside certain known dimensions, the possibility emerges to determine an elusive dimension within the prism. By leveraging the given information, the missing dimension can be unearthed, unraveling the intricacies of the prism's complete set of measurements.
This calculation empowers us to gain a comprehensive understanding of the geometric structure, further enriching our grasp of its spatial characteristics. The interplay between the volume and the known dimensions acts as a gateway to unlocking the enigma of the unknown dimension.
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The roof gable on Charlene's house has two
equal sides. One angle measures 110.4°. The
other two angles are equal to each other.
Estimate the measure of each of the other
two angles.
Each of the other two angles in the roof gable measures approximately 34.8°.
How to calculate the valueIf the roof gable on Charlene's house has two equal sides, and one angle measures 110.4°, we can determine the measure of each of the other two angles by using the fact that the sum of the angles in a triangle is always 180°.
Let's denote the measure of the other two angles as x.
Since the two equal sides of the gable form an isosceles triangle, the two angles opposite those sides are equal.
Therefore, we have:
x + x + 110.4° = 180°
Combining like terms:
2x + 110.4° = 180°
Now, let's solve for x:
2x = 180° - 110.4°
2x = 69.6°
x = 69.6° / 2
x = 34.8°
Therefore, each of the other two angles in the roof gable measures approximately 34.8°.
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This figure is a rectangular prism.
Select ALL figures that are NOT formed by a horizontal
slice parallel to the base.
A
B
C
D
square
right triangle
isosceles trapezoid
rectangle
“This figure is a rectangular prism” it says at the top btw”
if u do this ty
The horizontal slice of a rectangular prism will always be a rectangle. Therefore, the correct answers are options A, B and C.
A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.
The horizontal cross section of a rectangular prism will always be a rectangle.
Therefore, the correct answers are options A, B and C.
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2. Find the area of the figure below.
1.3 cm
1.3 cm
3 cm
4.2 cm
6.8 cm
5 cm
The area of the figure as shown in the diagram is 30.64 cm².
What is area?The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.
To calculate the area of the figure, we use the formula below
Formula:
A = 2LW+l²................... Equation 1Where:
A = Area of the figure shown in the questionL = Length of the rectangleW = Width of the rectanglel = Length of the squareFrom the diagram,
Given:
L = 5 cmW = 1.3 cml = 4.2Substitute these values into equation 1
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Out of 20 people how many would you expect to say that they like all seasons
Answer:
None
Step-by-step explanation:
Truly, I'm not sure what type of problem this is, but most people don't favor all the seasons. If there is more to the problem, I would be glad to help further.
Answer:
One possible way to estimate how many people out of 20 would say that they like all seasons is to use a simple random sample. A simple random sample is a subset of a population that is selected in such a way that every member of the population has an equal chance of being included. For example, one could use a random number generator to assign a number from 1 to 20 to each person in the population, and then select the first 20 numbers that appear. The sample would then consist of the people who have those numbers.
Using a simple random sample, one could ask each person in the sample whether they like all seasons or not, and then calculate the proportion of positive responses. This proportion is an estimate of the true proportion of people in the population who like all seasons. However, this estimate is not exact, and it may vary depending on the sample that is selected. To measure the uncertainty of the estimate, one could use a confidence interval. A confidence interval is a range of values that is likely to contain the true proportion with a certain level of confidence. For example, a 95% confidence interval means that if the sampling procedure was repeated many times, 95% of the intervals would contain the true proportion.
One way to construct a confidence interval for a proportion is to use the formula:
p ± z * sqrt(p * (1 - p) / n)
where p is the sample proportion, z is a critical value that depends on the level of confidence, and n is the sample size. For a 95% confidence interval, z is approximately 1.96. For example, if out of 20 people in the sample, 12 said that they like all seasons, then the sample proportion is 0.6, and the confidence interval is:
0.6 ± 1.96 * sqrt(0.6 * (1 - 0.6) / 20)
which simplifies to:
0.6 ± 0.22
or:
(0.38, 0.82)
This means that we are 95% confident that the true proportion of people who like all seasons in the population is between 0.38 and 0.82. Therefore, based on this sample and this confidence interval, we would expect between 8 and 16 people out of 20 to say that they like all seasons in the population.
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Eye Color of Males Surveyed
Green
Blue
5
16
Brown
27
Eye Color of Females Surveyed
Blue
Brown
19
18
Green
3
What percent of students in the survey are either female or have green eyes? Round your answer to the nearest tenth.
About % are either female or have green eyes.
What percent of students in the survey are males who do not have green eyes? Round your answer to the nearest tenth.
About % are males who do not have green eyes.
Find the sum of these two percents.
The sum of these two percents is %.
The sum of the percentage of students who are either female or have green eyes and the percentage of males who do not have green eyes is approximately 99.7%.
How to determine the sum of these two percents.The sum of these two percents is %.Percentage of Females: (1918 / (1918 + 516 + 27)) * 100 = (1918 / 2461) * 100 ≈ 78.0%
Percentage of Students with Green Eyes: ((516 + 3) / (1918 + 516 + 27)) * 100 = (519 / 2461) * 100 ≈ 21.1%
Percentage of Students who are either Female or have Green Eyes: 78.0% + 21.1% ≈ 99.1%
Therefore, approximately 99.1% of students in the survey are either female or have green eyes.
Percentage of Males with Green Eyes: (516 / (516 + 3)) * 100 = (516 / 519) * 100 ≈ 99.4%
Percentage of Males who do not have Green Eyes: 100% - 99.4% ≈ 0.6%
Therefore, approximately 0.6% of students in the survey are males who do not have green eyes.
To find the sum of these two percentages:
Sum of Percentages: 99.1% + 0.6% ≈ 99.7%
Therefore, the sum of the percentage of students who are either female or have green eyes and the percentage of males who do not have green eyes is approximately 99.7%.
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a number cube is tossed 60 times Determine the experimental probability of landing on a number less than two
Answer:
1.67% approx
Step-by-step explanation:
To determine the experimental probability of landing on a number less than two when a number cube is tossed 60 times, we need to count the number of times the number on the cube is less than two and divide it by the total number of tosses.
Let's denote the event of landing on a number less than two as "A." We'll count the number of successful outcomes, where the number on the cube is less than two.
Assuming the number cube is fair and unbiased, it has six sides numbered from 1 to 6. Out of these, only one side has a number less than two, which is one.
Now, we can calculate the experimental probability using the formula:
Experimental Probability (P(A)) = Number of successful outcomes / Total number of tosses
In this case, the number of successful outcomes is the number of times the cube lands on a number less than two, which is one. The total number of tosses is given as 60.
Therefore, the experimental probability of landing on a number less than two is:
P(A) = 1 (successful outcomes) / 60 (total number of tosses)
= 1/60
≈ 0.0167 or 1.67%
So, the experimental probability of landing on a number less than two is approximately 0.0167 or 1.67%.
obove answer is correct i think
Andrea has a jug that holds 1.5 liters of chocolate milk. She fills one container with 250 milliliters and another container with 0.6 liters. How much chocolate milk is left in the jug in milliliters?
0.65 mL
249.1 mL
450 mL
650 mL
Answer:
correct answer is 650ml
by what percent will a fraction change if its numerator is decreased by 60% and its denominator is decreased by 20%
Mrs. Brown wants to assign eight homework
problems to her Algebra 1 class tonight. If
there are eleven problems she could choose
from, how many different homework sets
could she assign?
A
88
B
165
C
495
D
990
Mrs. Brown can assign 165 different homework sets to her Algebra 1 class.
We have,
The number of different homework sets Mrs. Brown could assign can be calculated using the combination formula.
In this case, she wants to choose 8 problems out of 11 available problems. The formula for combinations is given by:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of items to choose from and r is the number of items to be chosen.
Using this formula:
C(11, 8) = 11! / (8! x (11 - 8)!)
C(11, 8) = 11! / (8! x 3!)
Simplifying the factorial expressions:
C(11, 8) = (11 x 10 x 9 x 8!) / (8! x 3 x 2 x 1)
The factorial terms cancel out:
C(11, 8) = (11 x 10 x 9) / (3 x 2 x 1)
C(11, 8) = 165
Therefore,
Mrs. Brown can assign 165 different homework sets to her Algebra 1 class.
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Twenty-five students were asked to rate—on a scale of 0 to 10—how important it is to reduce pollution. A rating of 0 means “not at all important” and a rating of 10 means “very important.” Here is a dot plot of their responses.
in the dot plot given, A rating of 6 is not a good description of the center of this data set because it does not accurately represent the most common or typical response.
How is this so?
To determine the center of data set, we typically look for the measure of central tendency, such as the mean, median, or mode.
From the dot plot, we can observe that the mode is at the rating of 10, with six students giving this highest rating. In contrast, the rating of 6 has only two students, making it less representative of the center.
Therefore, a rating of 6 does not accurately capture the overall sentiment or the central tendency of the data set.
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Full Question:
Please see the attached.