At the instant when dp/dt=41 and c = 15, the value of dc/dt is -0.273333.
The derivative of p with respect to time t is given by:
dp/dt = 2p dp/dc * dc/dt
Since dp/dt = 41, we have:
41 = 2p dp/dc * dc/dt
To find dp/dc, we can use the relationship between p and c:
p^2 = (20-c)^3
Taking the derivative of both sides with respect to c, we get:
2p dp/dc = -3(20-c)^2
Substituting this expression into the equation for dp/dt, we get:
41 = 2p * (-3(20-c)^2) * dc/dt
Plugging in the value of c = 15, we find:
41 = 2 * p * (-3(5)^2) * dc/dt
Using the relationship p^2 = (20-c)^3, we can find p:
p = sqrt((20-c)^3) = sqrt((20-15)^3) = sqrt(5^3) = 5
Substituting the value of p into the equation for dp/dt, we get:
41 = 2 * 5 * (-3(5)^2) * dc/dt
Solving for dc/dt, we find:
dc/dt = 41 / (2 * 5 * (-3(5)^2)) = 41 / (2 * 5 * (-3 * 5^2)) = 41 / (-150) = -41/150 = -0.273333...
So the value of dc/dt at the instant when dp/dt = 41 and c = 15 is approximately -0.273333.
Correct Question :
the positive variables p and c change with respect to time t. the relationship between p and c is given by the equation p2= (20−c)3. at the instant when dp/dt=41 and c = 15 what is the value of dc/dt?
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Answer:
[tex]-\frac{82\sqrt{5} }{15}[/tex]
Step-by-step explanation:
[tex]p^{2} =(20-c)^{3}[/tex]
[tex]2p(\frac{dp}{dt}) =3(20-c)^{2}(-\frac{dc}{dt} )[/tex]
Took the derivative of both sides ^
It gives you [tex]\frac{dp}{dt} =41[/tex] and [tex]c=15[/tex], so you just need [tex]p[/tex]
[tex]p=\sqrt{(20-15)^{3} } =5\sqrt{5}[/tex]
Now plug in
[tex]2(5\sqrt{5} )(41)=3(20-15)^{2} (-\frac{dc}{dt} )[/tex]
[tex]-\frac{410\sqrt{5} }{75} =\frac{dc}{dt}[/tex]
[tex]-\frac{82\sqrt{5} }{15} =\frac{dc}{dt}[/tex]
Assume that you graph lines f and g on the same coordinate plane and they intersect at point (4, 5). Which of the following statements is NOT true.
The statement that is not true is the fourth one.
"Other points that are on line f are also solutions of the system".
Which one of the given statements is not true?We know that the graphs of lines f and g intercept at the point (4, 5). So trivially, the point (4, 5) belongs to both graphs.
That also means that (4, 5) is the solution of the system of equations:
y = f(x)
y = g(x).
And because these two are lines, these will intercept only once, then (4, 5) is the only solution of the system.
That means that the correct option (the false statement) is the fourth one.
"Other points that are on line f are also solutions of the system".
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i cant do this! help
Answer:
r= 45 s=5
5(r-s)= 45-5= 40
Step-by-step explanation:
5(9-1) <--- You substitute the values
(5*9-5*1)<--- Multiply
45-5<--- Subtract
40 <-- Answer
r= 45
s=5
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{5(r - s)}\\\mathsf{= 5(9 - 1)}\\\mathsf{= 5(9) + 5(-1)}\\\mathsf{= 45 - 5}\\\mathsf{= 40}\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{40}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
A cylindrical tube must hold between 300 and 350 cubic centimeters of
sand. The diameter of the tube is 6.6 cm. How tall is the tube?
Sort the following to show those heights that would produce a volume
in the desired range, those that produce a volume that is below the
desired range, and those that produce a volume greater than the desired range.
The given heights of the cylinder are arranged as follows:
heights that would produce a volume in the desired range are: 8.9 cm. 10.1 cm, 9.5 cm, and 9.3 cmheights that produce a volume that is below the desired range are: 8.1 cm and 8.4 cmheights that produce a volume greater than the desired range are: 10.9, and 11.3What is the required height of the given cylinder?The volume of a cylinder is given by the formula below:
V = πr²h
where;
V is the volume of the cylinder
π = 22/7
r is radius; r = diameter/2
h is height
The volume of the cylinder is between 300 and 350 cubic centimeters.
For the 300 cm³ cylinder
h = v/πr²
r = 6.6/2 or 3.3 cm
h = 300/(22/7 * 3.3)
h = 8.7 cm
For the 350 cm³ cylinder
h = v/πr²
r = 6.6/2 or 3.3 cm
h = 350/(22/7 * 3.3)
h = 10.2 cm
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the area of a rectangular wall of a barn is square feet. its length is feet longer than the width. find the length and width of the wall of the barn.
The length and width of the wall of the barn are 12 feet and 6 feet respectively.
The formula for area of rectangle is -
Area of rectangle = length × width
Let the width of rectangle be x. So, the length of rectangle = x + 6. Keep the values in formula to find the length and width of the barn.
x × (x + 6) = 72
Performing multiplication
x²+ 6x - 72 = 0
x² + 12x - 6x - 72 = 0
x (x + 12) -6(x + 12) = 0
x = 6 and - 12
Thus, width of rectangle = 6 feet
Length of rectangle = x+ 6
Length of rectangle = 6 + 6
Length of rectangle = 12 feet
Thus, length and width are 12 and 6 feet.
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The complete question is -
The area of a rectangular wall of a barn is 72 square feet. Its length is 6 feet longer than the width. Find the length and width of the wall of the barn.
if the probability that one of these circuit boards is defective is 0.75, what is the probability of simple event {ddnn}?
Answer:
Step-by-step explanation:
=0.25
Casho spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -10.4°F. Between 9 am and noon, the temperature rose 9.5°F. Between noon and 3 pm, the temperature went down 10°F. Between 3 pm and 6 pm, the temperature went down 18.6°F. What was the temperature at 6 pm?
The temperature at 6pm is -29.5 °F.
What is changes in temperature ?The rise in temperature serves as a visual representation of how rapidly the temperature changes over time. Any period of time, such as from one day to the next or from one year to the next, could be taken into account. To determine the temperature increase, you simply need to use simple subtraction.
Here , The temperature at 9 am = -10.4 °F
Between 9 am and noon, the temperature rose 9.5°F.
= -10.4 + 9.5
= -0.9 °F
Between noon and 3pm the temperature went down 10°F
= -0.9 F - 10°F
= -10.9°F
Now again the temperature went down 18.6°F then,
= -10.9°F - 18.6 °F
= -29.5 °F
Hence, the temperature at 6pm is -29.5 °F.
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At a restaurant the total bill on the percentage of the bill left as a tip and represented in a scatter plot the best fit line is represented by the equation y = -0.632 + 27 + 1 where X represents the total bill in dollars
The percentage of the bill left as a tip is 17.62%
How to estimate the percentage of the bill left as a tipFrom the question, we have the following parameters that can be used in our computation:
y = -0.632x + 27.1
When the total bill is $15, we have
y = -0.632 * 15 + 27.1
Evaluate
y = 17.62
Hence, the percentage is 17.62
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Given the curve y2 = x in the xy-plane, for what value of y, if any, does the derivative of y with respect to x not exist?a. y=0b. y=-1c. y= - (1/ ln 2)d. for no value of y
The derivative of y with respect to x exist for all values of y, that is it does not exist for no value of y.
Therefore the answer is d. for no values of y
The curve y^2 = x is a parabolic function and its derivative is continuous for all x in its domain, which is x >= 0. The derivative of this function, which is y' = (dy/dx) = 1/2 * √x, is well-defined for all x >= 0 and therefore, the derivative exists for all values of y, including y = 0 and y = -1.
In general, a function is said to be differentiable at a point if its derivative exists at that point, and the derivative provides information about the rate of change of the function at that point.
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Which nonparametric equation can be used to graph the curve described by the
parametric equations?
The non parametric equation described by the parametric equation is given as follows:
D. y = 324(x - 3)^4 - 7.
How to obtain the non-parametric curve?The parametric curve is defined as follows:
[tex]x = \frac{1}{3}\sqrt{t} + 3[/tex]y = 4t² - 7.Isolating t on the first equation, we have that:
[tex]\frac{1}{3}\sqrt{t} = x - 3[/tex]
[tex]\sqrt{t} = 3(x - 3)[/tex]
t = 9(x - 3)² -> applying the square root to both sides.
Replacing on the second equation, the equation of the non parametric function is given as follows:
y = 4t² - 7
y = 4[9(x - 3)²]² - 7.
y = 324(x - 3)^4 - 7.
Meaning that option D is the correct option.
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Please help me with this geometry question
Please help me answer this question on equations of lines. 10 points and brainliest available.
Answer:
a) (0,1)
b) k = 6.5
Step-by-step explanation:
When a line crosses the y-axis at a point, the point's x-coordinate must be 0. Let's substitute the value of x into the equation of the line to find its y-coordinate.
y - 4x = 1
Rearrange terms to isolate y.
y = 4x + 1
Substitute x = 0 into the equation.
When x = 0, y = 4(0) + 1
y = 0 + 1
y = 1
Thus, the coordinates of the point is (0, 1).
---
The second question uses the general equation of a straight line which is y = mx + c where m is the gradient of the line and c is the y-intercept of the line. As you can see from the graph drawn, the line cuts the y-intercept at (0, -3) so c = -3. You are given the y-coordinate of the point (which is 10) so you can find the x-coordinate (k) by substituting the value of y into the equation of the line once again.
y = 2x + c
You know the value of c from the y-intercept. c = -3
y = 2x - 3
Substitute y = 10 into the equation.
When y = 10, 10 = 2x - 3
10 + 3 = 2x
2x = 13
x = 6.5 when y = 10
Thus, the value of k is 6.5.
Let T: R³ → R² be the linear transformation that first projects points onto the yz-plane and then reflects around the line y=-z. Find the standard matrix A
for T.
A function T:Rn -- > Rm that meets the criteria listed below is said to be linear (or to be a linear map). T(x+y)=T(x)+T(y)
What is linear transformation in R?A function T:Rn -- > Rm that meets the criteria listed below is said to be linear (or to be a linear map).T(x+y)=T(x)+T(y)
T(ax)=aT(x) for any vectors x, y, and any scalar a.
Finding out if a given function f(x) is a linear transformation or not is rather straightforward. Take a moment to consider each term in each f(x) component. For f to be a linear transformation, each of these terms must be an integer multiplied by one of the components of x.As a result, only the function f(x,y,z)=(3xy,3z,0,z2x) is a linear transformation, while neither g(x,y,z)=(3xy,3z+2,0,z2x) nor h(x,y,z)=(3xy,3xz,0,z2x) are.transform in a linear fashion. The nonlinear component 3xz of the function h renders it ineligible. What happens to the g function? The issue arises in the second component 3z+2 since the term 2 is a constant and does not include any x, y, or z components from our input vector.The second requirement stated above is clearly broken by the function g. Each linear transformation must fulfill T(0)=0 but g(0,0,0)=(0,2,0,0), as seen in particular if you set a=0 in that second condition. In comparison to the criterion for a function whose graph is a line that is taught in elementary school, the condition for a linear transformation is more stringent. If b is not zero, then the single variable function f(x)=ax+b is not a linear transformation.The fact that linear transformations, which rely on matrix vector multiplication, and matrices have a one-to-one connection is a useful property of a linear transformation. As a result, the matrix connected to a linear transformation can be discussed without ambiguity T(x).To Learn more About Linear Function Refer To:
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.
Lee pays 2.12 × 10^3 dollars for one year's tuition at Naylor University. His sister attends Ledgewood College and pays 3.28 × 10^3 dollars in tuition for her first year. How much tuition does the family pay altogether for one year? Write your answer in scientific notation. Provide a coefficient accurate to the nearest hundredth.
Answer:
below
Step-by-step explanation:
Add the two numbers together
(2.12 + 3.28 ) x 10^3 = 5.40 x 10^3 dollars
Drag each part of the expression to categorize it as a term or a coefficient in the expression.
Parts that are neither a term nor a coefficient belong in the "Neither One" category.
3x2+6x+7
Terms = 3x² , 6x , 7
Coefficients = 3,6
Neither One = x²
How to find the calculation?A quantity or number that is combined with a variable is known as a coefficient.
Adding a variable to a number produces a coefficient.
The variable next to it is often multiplied by an integer.
Three terms make up the trinomial: 3x² + 6x + 7
3x²
6x
7
Enter the first column as a result.
The coefficients at and are respectively 3 and 6.
The second column should have these two integers.
x² is not a term (because 3x² is a term) and is not a coefficient, because coefficients are numbers.
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(1 point) is the conditional statement "if a human being has 7 heads, then they have 11 arms" true or false? explain
As per the concept of reasoning, the conditional statement is false.
The term reasoning in math is called as students who genuinely make sense of mathematical ideas can apply them in problem solving and unfamiliar situations and can use them as a foundation for future learning.
Here we have the conditional statement "if a human being has 7 heads, then they have 11 arms".
And here we need to find out whether this statement is true or false.
While we looking into the given statement we have identified that this is false because this statement is missing the necessary or sufficient words.
Simply said that it is not possible situation.
Therefore the statement is false.
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The line segment joining the points A (5, 3) and B (-3, 11) is divided by the point C (3,5) in the ratio
(a) 1:3 (b) 3:1 (c) 2:3 (d) 3:2
Are the two triangles similar?
Answer:
Similar by SAS
Step-by-step explanation:
:)
Select the functions f(x)=√x+5 and g(x)=√5-x. Select the Operation fXg and Combine Functions box, and slowly slide the x-slider to the right to graph the function (fg)(x) Note that the graph is a semicircle. Find the equation of this semicircle by simplifying (fXg)(x) Use the interactive figure to find your answer. Use the left and right arrow keys to move along a slider as needed.
For the function the equation of this semicircle by simplifying (fog)(x) is √(√5 - x) + 5.
A function is a mathematical rule that assigns a unique output to each input.
In this problem, we have two functions, f(x) = √x + 5 and g(x) = √5 - x.
Here we need to find the composition of these two functions, denoted by (f∘g)(x) or f(g(x)), we substitute the output of one function as the input of the other.
So,
=> (f∘g)(x) = f(g(x))
=> f(√5 - x) = √(√5 - x) + 5.
So, to find the equation of the semicircle in this case, we can simplify the expression (f∘g)(x) and rearrange it in the standard form of a circle.
The center of the semicircle can be found by setting x = 0, which gives us the y-coordinate of the center, and y = 0, which gives us the x-coordinate of the center.
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Bob is an artist and creates 3 sketches in 45 minutes. Write and solve a proportion to find how many sketches the artist can create in 8 hours.
The sketches after 8 hours is 32
How to determine the sketches after 8 hoursFrom the question, we have the following parameters that can be used in our computation:
Bob is an artist and creates 3 sketches in 45 minutes
This means that
3 sketches = 45 minutes
Convert minutes to hour
3 sketches = 3/4 hour
Multipy both sides by 8
So, we have
8 * 3 sketches = 3/4 * 8 hours
Multipy both sides by 4/4
So, we have
32 sketches = 8 hours
Hence, the sketches is 32
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suppose i want to calculate the derivative of some function at some point let's say i use a third-order accurate method for doing this. if i find that the error is when , what will the error be when ?
The error is when h is some value, the error will be when h/2.
The error of a third-order accurate numerical differentiation method scales with the fourth power of the step size, i.e. if the step size is halved, the error will decrease by a factor of 2⁴=16. So if the error is when h is some value, the error will be when h/2.
Error in Third-Order Numerical DifferentiationThe error in numerical differentiation methods can be approximated using Taylor series expansions. For a third-order accurate method, the error term in the Taylor series would be proportional to h⁴. Hence, reducing the step size by a factor of two would reduce the error by a factor of 2⁴ = 16. This relationship between step size and error holds for small step sizes. For larger step sizes, the error may not decrease in such a simple manner and other factors such as the smoothness of the function being differentiated and the presence of singularities or discontinuities may come into play.
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Solve the following inequality, 8 < 2(7-g), representing the solution on a number line.
Answer:
To solve the inequality 8 < 2(7-g), we first need to simplify the right side of the inequality.
2(7-g) = 2 * 7 - 2 * g = 14 - 2g
Now we can compare the left and right sides of the inequality:
8 < 14 - 2g
To isolate g, we'll add 2g to both sides:
8 + 2g < 14
2g < 6
To divide by 2, we'll divide both sides by 2:
g < 3
So the solution to the inequality is g < 3, which can be represented on a number line as:
(negative infinity, 3)
So the values of g that satisfy the inequality are any real number less than 3.
Step-by-step explanation:
Answer:
g < 3
Step-by-step explanation:
8 < 2(7 - g)
8< 14 - g
-6 < -g
g < 3
On a number line, because there is no equal, so this will be an open circle to the left of 3.
What is the area of the parallelogram?
(2,3)
(2-5)
(6, 1)
(6.-7)
Answer:
32
Step-by-step explanation:
The area of a parallelogram is bh where b = base, h = height
This is one of the questions where plotting the points and seeing the parallelogram is vital
See the attached figure
height h = |difference between x-coordinates of A and C| =
= |6 - 2| = 4.
This will be the same as |difference between x-coordinates of B and D
base b = |difference between y-coordinates of A and B| = |1-(-7)| = 8.
This will be same as |difference between y-coordinates of C and D|
Area = bh = 8 x 4 = 32
special right triangle
Due to the equal sides of the equilateral triangle, a = 6[tex]\sqrt{3}[/tex] and b = 6[tex]\sqrt{3}[/tex] how it is shown in figure 60°, 60°.
what is triangle ?Because that it has three sections and three vertices, a triangle qualifies as a polygon. It belongs to the fundamental geometric shapes. Triangle ABC is the term used to refer to a triangle with the points A, B, and C. Once the three factors are not collinear, a unique plane composite triangle from Euclidean geometry are discovered. Triangles are polygons because they have three sides or three corners. The points where the four structures of the triangle converge are referred to as the triangle's corners. Three triangle angles are multiplied to yield 180 degrees.
given
as shown in the figure
∠60° , ∠60° and side 6[tex]\sqrt{3}[/tex]
Due to the equal sides of the equilateral triangle, a = 6[tex]\sqrt{3}[/tex] and b = 6[tex]\sqrt{3}[/tex] how it is shown in figure 60°, 60°.
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math ia on how airlines decide to sell tickets
Tickets are sold by airlines based on availability and demand. To increase their amount of earnings, they consider things like flight capacity, the time of year that people travel, the number of tickets available, and pricing.
Tickets are sold by airlines based on availability and demand. To choose the best course of action for their firm, they carefully analyse variables including aeroplane capacity, travel season, seat availability, and cost. Airlines assess the current market and forecast future trends using sophisticated mathematical models. This aids them in figuring out the ideal quantity of tickets to market and the finest selling price. To make sure that their tickets are reasonably priced, airlines also take into account the demand for their flights and the competition from other airlines. In order to make their tickets appealing to customers, airlines may consider promotional activities and unique offers. Airlines may increase their revenue by selling tickets at the proper price by studying the data and making wise judgements.
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Dan, Juan, and Thuy are sharing 4 oranges equally. How
many oranges does each person have?
Answer: 1 1/3
Step-by-step explanation: To find this answer, we simply divide the people by the oranges. So, 4 / 3 is 1.3333333333333...... We round this to about 1.3. So, that as a fraction is 1 1/3. So, each person gets 1 1/3. To check, we multiply 1 1/3 by 3 (people) and we get 4. I hope this helped!
The velocity of sound in dry air increases as the temperature increases. At 40 degree C, sound travels at a rate of about 355 meters per sound. At 49 degree C it travels at a rate of about 360 meters per second. a. Write a linear equation in slope-intercept form, for the velocity v of sound as a function of the temperature T. b. Use this equation to find the velocity of sound at 60 degree C.
The linear equation in slope-intercept form for the velocity of sound as a function of temperature is v = 0.068T + 293.2, where v is the velocity of sound and T is the temperature in degrees Celsius. Using this equation, the velocity of sound at 60°C is 339.6 m/s.
The velocity of sound in dry air increases as the temperature increases. At 40°C, sound travels at a rate of about 355 m/s, and at 49°C, it travels at a rate of about 360 m/s. To write a linear equation in slope-intercept form for the velocity of sound as a function of the temperature, first calculate the slope of the line by finding the difference in velocity divided by the difference in temperature: (360 - 355) / (49 - 40) = 0.068. This slope can be written as the coefficient of the T-term in the equation. To find the y-intercept, plug in the temperature at which the velocity was measured (40°C) and the corresponding velocity (355 m/s) into the equation of the form v = mT + b. Solving for b yields 293.2. Therefore, the linear equation in slope-intercept form is v = 0.068T + 293.2. To find the velocity of sound at 60°C, plug in 60 for T in the equation and solve for v, which yields 339.6 m/s.
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If 2/9 is equivalent to zero point X repeating what is the value of X
[tex]\dfrac{2}{9} = 2\div 9 = 0.2222222222222...[/tex]
x is 2.
of a group of patients having injuries, 28% visit both a physical therapist and a chiropractor while 8% visit neither. say that the probability of visiting a physical therapist exceeds the probability ofvisiting achiropractor by 16%. what is the probability of a randomly selected person from this group visiting a physical therapist?
The probability of a randomly selected person from this group visiting a physical therapist will be 68.
In a group of patients having injuries, 28% visit both a physical therapist and a chiropractor while 8% visit neither
A = Visiting a physical therapist
B = Visiting a chiropractor
The probability of visiting a physical therapist exceeds the probability of visiting a chiropractor by 16%.
Pr(A union B)' = .08
Pr(A union B) = 1 - .08 = .92
Pr(A intersect B) = .28
Pr(A) = Pr(B) + .16
Pr(A union B) = Pr(A) + Pr(B) - Pr(A intersect B)
.92 = [Pr(B) + .16] + Pr(B) - .28
.92 = 2Pr(B) - .12
1.04 = 2 Pr(B)
.52 = Pr(B)
Since, Pr(A) = Pr(B) + .16 then P(A) = .52 + .16 = .68.
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Using algebraic techniques, find the roots of:h(x)=x^3−2x^2+9x−18
The roots of h(x)=x³−2x²+9x−18 is 2, -3i and 3i.
What is Factorization?The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.
Given:
h(x)=x³−2x²+9x−18
so, (x-2) is the solution of h(x).
Now, the synthetic division
(x-2) | x³−2x²+9x−18 | x² + 9
x³ −2x²
__________
0 + 9x - 18
9x - 18
__________
0
now, again factorize x² + 9 = 0
x = ±3i
Hence, the roots are 2, -3i and 3i.
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A lawn care specialist chooses a random sample from the yard and determines the number of weeds in the sample. The results of the sample are shown in the table below
No, this is not a representative sample because each type of weed should be represented in proportion to the number of weeds actually present in the yard.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
A representative sample has to be in proportion, and the diagram shows that the greater part is not represented in proportion. Because it is not represented in proportion, it is not a representative sample.
No, this is not a representative sample because each type of weed should be represented in proportion to the number of weeds actually present in the yard.
Hence, No, this is not a representative sample because each type of weed should be represented in proportion to the number of weeds actually present in the yard.
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