(a) The fitted polynomial regression model for the given data is:
y = 338.61 - 0.270x + 0.000249x^2
(b) To test for the significance of regression, we can perform an analysis of variance (ANOVA) test.
(c) To test the hypothesis that β11 = 0, where β11 is the coefficient for x^2 in the polynomial regression model, we can perform a t-test.
(d) To evaluate model adequacy, we can examine the residuals.
(a) To fit a second-order polynomial regression model to the given data, we can use the method of least squares. The model equation takes the form:
y = β0 + β1x + β2x^2
By using the least squares method, we estimate the coefficients β0, β1, and β2 that minimize the sum of the squared residuals. In this case, the estimated coefficients are:
β0 = 338.61
β1 = -0.270
β2 = 0.000249
Therefore, the fitted polynomial regression model for the given data is:
y = 338.61 - 0.270x + 0.000249x^2.
(b) The hypotheses are as follows:
Null hypothesis (H0): β1 = β2 = 0 (no regression)Alternative hypothesis (Ha): At least one of β1 or β2 is not equal to zero (significant regression)The test statistic for the ANOVA test is the F-statistic. By comparing the computed F-statistic with the critical F-value at a significance level of α = 0.05, we can determine whether to reject or fail to reject the null hypothesis. If the computed F-statistic is greater than the critical F-value, we reject the null hypothesis and conclude that there is a significant regression.
(c) The hypotheses are as follows:
Null hypothesis (H0): β11 = 0Alternative hypothesis (Ha): β11 ≠ 0The test statistic for the t-test is computed by dividing the estimated coefficient by its standard error. By comparing the computed t-statistic with the critical t-value at a significance level of α = 0.05, we can determine whether to reject or fail to reject the null hypothesis. If the computed t-statistic falls within the rejection region, we reject the null hypothesis and conclude that there is evidence of a non-zero coefficient β11.
(d) Residuals represent the differences between the observed values and the predicted values from the regression model. If the residuals exhibit random patterns with no apparent trends or patterns, it suggests that the model adequately captures the relationship between the variables. However, if there are systematic patterns or trends in the residuals, it indicates that the model may be inadequate.
We can plot the residuals against the predicted values or the independent variable x to assess their behavior. If the residuals are randomly scattered around zero with no clear patterns, it suggests that the model adequately fits the data. On the other hand, if there are distinct patterns or a significant deviation from zero, it indicates potential issues with the model's adequacy.
In conclusion, fitting a second-order polynomial regression model to the given data provides a fitted equation that can be used for prediction and inference. The significance of the regression can be tested using an ANOVA test, and the significance of individual coefficients, such as β11, can be tested using a t-test. Assessing the residuals helps evaluate the adequacy of the model in capturing the relationship between the variables.
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A factory was ordered to reduce the amount of pollution by 51% in two years with the same percent decrease each year. What is this percentage?
PLEASE HELP!!!
Answer:
30%
Step-by-step explanation:
You want the percentage reduction each year that will result in a reduction of 51% over two years.
Growth factorThe growth factor is 1 added to the growth rate. If the desired growth rate over 2 years is -51%, then the growth factor for that period is ...
1 -51% = 0.49
If the growth factor is the same for each of two years will be ...
(1 +r)² = 0.49 . . . . . . . where r is the growth rate each year
Growth rateSolving for r gives ...
1 +r = √(0.49) = 0.7
r = 0.7 -1 = -0.3 = -30%
The required growth rate each year is -30%.
The pollution must be reduced by 30% each year for 2 years.
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Is any set of ordered pair?
Any set of ordered pair cannot be called as a function , the ordered pairs that in which no two different ordered pairs have the same x coordinate is called as a Function .
What is a Function ?
The set of ordered pair (x,y) is called a function, in which no two different ordered pairs have the same x coordinate. and the equation that produces such a set of ordered pairs can be called as function.
For Example : Let us Consider ordered pairs , F = [tex][(1,5) , (3,6)][/tex] ;
we see that , the element 1 has the image as 5 , and the element 3 has the image as 6 .
So , we can conclude that , the each value of x has exactly only one corresponding value of y .
Therefore , the ordered pair can be called as a function .
The given question is incomplete , the complete question is
Is any set of ordered pair is called a Function ?
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What are the steps in solving systems of equations using substitution method?
The steps in solving systems of equations using the substitution method include simplifying the given equation, solving one of the equations for any unknown value, substituting the step 2 solution in another equation, solving the new equation, and finally solving the equation to find the second variable.
The substitution method is the algebraic method to solve different linear equations. In this method of substitution, the value of one variable from either of the equation is substituted in the other equation.
In this technique the following steps are used to solve an equation by substitution method:
Step 1. Simplify the given equation by removing the parenthesis.
Step 2. Solve one of the equations for any unknown value.
Step 3. Substitute step 2 result in the other equation.
Step 4. Now solve the equation which gets from step 3 obtained using elementary arithmetic operations.
Step 5. Finally, solve the final equation for the second variable.
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What is the slope of Y 10x 1?
The slope of the given equation y = 10x + 1 is 10.
If we draw the graph of the linear equation y = mx + c. The result is a line with m as the slope, and c as the y-intercept. This form of the linear equation y = mx + c is called the slope-intercept form, and the values of m and c are real numbers.
The slope, m, of the line represents the steepness of a line. This is also termed a gradient, sometimes. The y-intercept, c, of the line y = mx + c represents the y-coordinate of the point where the graph of the line intersects the y-axis.
Now, if we equate the standard slope-intercept form of the equation with the given equation, we get
y = mx + c
y = 10x + 1
m = 10 and c = 1
As we know the m is the slope which is equal to 10.
-- The given question is incorrect, the correct form of equation is
"What is the slope of y = 10x + 1?" --
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At charles school, 15 of the 75 students in seventh grade play in the jazz band. How many seventh graders play in the jazz band?.
The jazz band has 15 seventh graders playing according to the ratio.
What is the ratio?A ratio, which is a number, is a way to represent one quantity as a portion of another. A ratio can only be compared when the two numbers in it have the same unit. To compare two objects, ratios are utilized.
Given One fifth of the 75 seventh graders at Charles School participate in the jazz band.
Presented as a ratio
75 pupils, or 1/5 of them, participate in the jazz band.
75 pupils out of the total play in the jazz band.
15 kids in total participate in the jazz band.
15 seventh graders are therefore playing in the jazz band in accordance with the ratio.
Hence, The jazz band has 15 seventh graders playing according to the ratio.
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At Aaron's Automobile's, Bob made $150,000 total in sales and commission last week. If commission is 20%, how much were Bob's sales?
Last week's sales were $______
Answer: 30,000
Step-by-step explanation:
150,000 x 0.2 = 30,000
How do you find an area example?
Answer:
To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area......
Step-by-step explanation:
Write an exponential function that models the info below.
An initial value of 1,425 increasing at a rate of 5%.
Answer:
y = 1425 * (1 + 0.05)^x
Step-by-step explanation:
An exponential function of the form y = a * b^x can be used to model exponential growth or decay, where a is the initial value, b is the base (growth or decay factor), and x is the time period. In this case, the initial value is 1,425 and the rate of increase is 5%. We can write this as an exponential function as follows:
y = 1425 * (1 + 0.05)^x
where y is the final value after x time periods, and x is the number of time periods (in years, for example). To find the value of the function after x time periods, you can substitute the value of x into the equation.
intiderivatives & Indefinite Integrals (x^3-2)dx
The final solution of the given integral ∫ ([tex]x^3[/tex] - 2) dx is ([tex]x^4[/tex])/4 - 2x + C.
To integrate ∫ (x^3 - 2) dx, we use the power rule of integration, which states that ∫[tex]x^n[/tex] dx = ([tex]x^{(n+1)}[/tex])/(n+1) + C, where C is the constant of integration.
In this case, we have [tex]x^3[/tex] as the inside function, so we apply the power rule by raising the exponent by 1 and dividing by the new exponent. This gives us ([tex]x^4[/tex])/4 + C as the antiderivative.
However, we also have the constant term -2. To integrate a constant term, we add it as a separate term to the antiderivative. So the final solution is ([tex]x^4[/tex])/4 - 2x + C.
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Tony and Jacob are selling fruit for a school fundraiser. Customers can buy small boxes of grapefruit and large boxes of grapefruit. Tony sold 12 small boxes of grapefruit and 8 large boxes of grapefruit for a total of $276. Jacob sold 6 small boxes of grapefruit and 9 large boxes of grapefruit for a total of $228. find the cost each of one small box of grapefruit and one large box of grapefruit
The cost of one small box of grapefruit and one large box of grapefruit is
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations with the same unknown variables and the same value of the variables satisfies all such equations. This implies that the simultaneous equations have a common solution. Some of the examples of simultaneous equations are: 2x - 4y = 4, 5x + 8y = 3.
represent small box by x and large box by y
12x + 8y = 276 equation 1
6x + 9y = 228 equation 1
make the coefficients of x equal by multiplying equation 2 by 2
12x + 8y = 276 equation 3
12x + 18y = 456 equation 4
subtract equation 3 from 4
10y = 180
y = 180/10
y = 18
substitute 18 for y in equation 1
12x + 6×18 = 276
12x = 276-108
12x = 168
x = 168/12
x= 14
therefore the cost of one small boxes is $14 and the cost of one large box is $18
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What is the range of a function in Mcq?
The range is found by finding the vertex and noting that it is the minimum or maximum (depending on direction) of the function. You can find the vertex by using -b/2a for the x value and then plugging in to get y value.
What is a function?
A mathematical phrase, rule, or rule that establishes the link between explanatory variables or a dependent variable In mathematics, curves exist everywhere, and they are crucial for constructing physical links in the sciences.
A Method can be defined by a module, an object, or another function. An internal feature of a class is called a method. Methods are listed inside a base class to make the connections between it class and thus the method clear. A method can be called or invoked using different syntax. We can convert a type into an object before being able to access its methods.
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make p subject formula in I=PRT/100
Answer:
P=Ix100/RT
therefore P is made the subject formula
Is 2 or 5 an ordered pair?
Answer:
If it's written like this: (2, 5) then it is a ordered pair
Step-by-step explanation:
What is the coefficient of XYZ?
Therefore , the solution of the given problem of expression comes out to be the coefficient of given expression XYZ is 1.
What exactly does expression mean?By substituting each variable with a number and conducting mathematical functions, an algebraic formula must be checked. The solution variable in the previous example is identical to 6 since 79 + 8 = 87. To evaluate the expression, we can replace the variables values with ones we are familiar with.
Here,
Given :
XYZ
To find the coefficient of given expression ,
Thus,
From observing we can see XYZ
can be written as
=>1*XYZ
Where 1 is coefficient.
Therefore , the solution of the given problem of expression comes out to be the coefficient of given expression XYZ is 1.
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If h(x)=3x+1 and g(x)=x^2-5 Evaluate h(-2)+g(4)
The value of h(-2)+g(4) by substitution is 6
What is substitution of variables?The method of solving "by substitution" works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other. Then you back-solve for the first variable.
For instance if h(x)=3x+1 . This means h(-2) means we are going to substitute -2 for variable x
Therefore h(-2) = 3(-2)+1
= -6+1 = -5
Similarly g(x)=x²-5. This means g(4) means we are going to substitute 4 for x in the equation.
Therefore g(4) = 4²-5
= 16-5 = 11
Therefore h(-2)+g(4) = -5+11
= 6
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i need help on this quiestion
when x is 0.5 then y value is 3, x is 1.5 then y is 9 and x is 4.5 then y is 27.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
A proportion is an equation in which two ratios are set equal to each other
In the given table the value of x is 0.5 and value of y is 3
y/x=3/0.5=6
In the second row the value of x is 1.5 we need to find value of y.
3/0.5=y/1.5
4.5=0.5y
Divide both sides by 0.5
y=9
In third row the value of x is 4.5 and y is 27
Hence, when x is 0.5 then y is 3, x is 1.5 then y value is 9 and x is 4.5 then y is 27.
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Which expression is equivalent to -8.2 - 5?
Choose 1 answer:
A
B
5- (-8.2)
-8.2 + 5
8.25
-8.2+(-5)
The expression equivalent to - 8.2 - 5 is - 8.2 + (-5)
What is an expression?
A mathematical expression is a phrase that includes at least two numbers or variables, and at least one arithmetic operation. The mathematical operations used can be addition, subtraction, multiplication or division.
Note ,
- × - = +
- × + = -
+ × + = +
For the expression - 8.2 - 5
In the above expression, we are subtracting positive integer 5 from -8.2
So we get the answer as
-8.2-5 = = -13.2
Now this is the solution we should get while solving the given options.
a) 5 - ( -8.2) = 5 + 8.2 = 13.2
b) -8.2 + 5 = - 3.2
c) -8.2 -5 [tex]\neq[/tex] 8.25 (as seen above)
d) - 8.2 + ( -5) = -8.2 - 5 = -13.2
Comparing the solutions, we get that option(d) matches with the required answer.
Therefore option(d) is the correct expression that gives the same answer.
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An architect built a scale model of a convention center using a scale in which 5 inches
represents 60 feet. The height of the convention center is 240 feet.
What is the height of the scale model in inches?
F) 0.6 in.
G) 36 in.
H) 20 in.
J) 300 in.
Therefore , the solution to the given problem of perimeter model of the sports stadium has a 12 inch height. The right response is option C.
Define Perimeter.The perimeter of a shape is sometimes refers to as its entire length in geometry. The perimeter of something like a form can be calculated by summing the distances of all of its sides and edges. The lenght of all a form's sides can be added up to find its perimeter. A rectangle that is 24 yards long and 15 yards broad, for instance, will have a perimeter of 78 yards.
Here,
A man can cover 6 miles on foot in 2 hours.
A man will cover 3 miles on foot in one hour.
10 potatoes can be sliced by a machine in 5 minutes.
2 potatoes can be cut by a machine in a minute.
Those are
2 inches per thirty feet
By 30 multiply both sides.
1 foot Equals 2/30 inches.
Now,
1 foot Equals 2/30 inches.
180 times on both sides.
180 feet = 180 x 2/30 inch
180 feet equals 6 by 2 inches.
120 feet equals 12 inches.
Thus,
Considering that a foot equals two inches, a sports arena's height would be 180 feet.
The scale model of both the sports stadium has a 12 inch height.1 foot Equals 2/30 inches.
Now,
1 foot Equals 2/30 inches.
180 times on both sides.
180 feet = 180 x 2/30 inch
180 feet equals 6 by 2 inches.
120 feet equals 12 inches.
Thus,
Considering that a foot equals two inches, a sports arena's height would be 180 feet. The scale model of both the sports stadium has a 12 inch height.
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What are the 3 steps of factoring?
The three steps of factoring include taking the common component out of the polynomial then simplifying the polynomial such that the most simple values are left and finally rearrangement.
If we are provided with the polynomial that is very complex in nature then first thing we have to do in order to solve the problem related to that polynomial is to factorise the polynomial.
The factory of that particular polynomial can be done by taking out the most common component out of the polynomial in a multiplication.
After this we have to simplify the polynomial such that only the simplest values are left in the polynomial and finally we have to rearrange the polynomial because after such operations on that polynomial the polynomial will not be easy to understand in the first look of it.
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5 students are going on a field trip and 5 students are staying at school. What is the ratio of the number of students who are staying at school to the total number of students?
The area of a square living room is 256 ft2
256
ft
2
. Which is the length of the room?
Answer:16ft
√256=16ft
length=16ft
G(1) = 50
G(n) = 8 - g (n-1)
G(2) =
The value of G(2) of the given sequence formula is; -42
How to solve Arithmetic sequence?The general formula for the nth term of an arithmetic sequence is;
aₙ = a + (n - 1)d
where;
a is first term
n is position of term
d is common difference
We have the following parameters;
G(1) = 50
G(n) = 8 - g (n-1)
Thus;
G(2) = 8 - g(2-1)
G(2) = 8 - g(1)
Since (g(1) = 50 ), then we have;
G(2)= 8 - 50
G(2) = -42
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If amy walked 25 seconds how many feet did she travel
(its ratio or unit rates i forgot.)
Feet Second
18. 3.
48. 8.
25
c
If Amy walked 25 seconds, she travelled 150 feet.
What is direct proportion?The definition of direct proportion states that "When the relationship between two quantities is such that if we increase one, the other will also increase, and if we decrease one the other quantity will also decrease, then the two quantities are said to be in a direct proportion". which means the ratio of two quantities is constant.
Given, In table
Relationship between distance and time of Amy travel is given
Feet Second
18 3
48 8
c 25
From the above table ratio between distance and time = Distance/ Time
= 18/3 = 48/8 = c/25
= 6/1 = 6/1 = c/25
⇒ c/25 = 6/1
⇒ c = 6 × 25 = 150
So, In 25 seconds distance will be 150 feet.
Hence, in 25 seconds Amy will travel 150 feet.
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Which side is opposite of 30 in a 30 − 60 − 90 triangle?
The side opposite the 30-degree angle is called the shorter leg in a 30 − 60 − 90 triangle
A right triangle is any triangle that has a 90-degree angle.
A 30-60-90 triangle is a special type of right triangle that has a 30-degree angle and a 60-degree angle in addition to the right angle.
The side opposite the 30-degree angle is called the shorter leg.
The side opposite the 60-degree angle is called the longer leg.
The side opposite the right angle of 90 degrees is called the hypotenuse.
The hypotenuse is twice the shorter leg.
The longer leg is √3 times the shorter side.
if the length of the shorter leg is given, then these properties are used to find the longer side and the hypotenuse.
However, the 30-60-90 properties hold no matter which side is provided.
If the length of the hypotenuse is given, divide it by 2 for the shorter leg. Then multiply that result by √3 to get the length of the longer leg.
If the length of the longer leg is given, divide it by √3 to get the shorter leg. Then, multiply that result by two to get the length of the hypotenuse.
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What is an example of a two-step inequality?
A two-step inequality is an inequality that requires more than one step to solve. An example of a two-step inequality is to solve the inequality 2x - 3 ≥ 5.
Example: Solve the inequality 2x - 3 ≥ 5
Step 1: Isolate the variable by adding 3 to both sides: 2x ≥ 8
Step 2: Divide both sides by 2: x ≥ 4
In this example, the first step is to isolate the variable x by adding 3 to both sides of the inequality. In the second step, we divide both sides by 2 to get the final solution of x ≥ 4.
It's worth noting that this inequality has a solution that is an interval, it is x ≥ 4, which means that all values of x that are greater or equal to 4 are solutions of the inequality.
It's important to keep in mind that inequalities may require multiple steps to solve and may not always have a single solution. It's important to check the solution by substituting back into the inequality to make sure it holds true.
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What is the formula of property?
The formula of commutative property is α + β = β + α or α × β = β × α.
The commutative property is the property that deals with the arithmetic operations of addition and multiplication. So mathematically, if we change the order of the operand and it does not change the result of the arithmetic operation then that particular arithmetic operation is commutative.
If two numbers α and β are given, then the formula of the commutative property of numbers is given as,
α + β = β + α
α × β = β × α
α - β ≠ β - α
α ÷ β ≠ β ÷ α
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Need Answer desperately pls help
Answer:
7) B.
8) D.
Step-by-step explanation:
An architect has designed two tunnels. Tunnel A is modeled by2+7+30x+56=0, and tunnel B is modeled by 2-3x+15y-55-0, where all measurements
are in feet. The architect wants to verify whether a truck that is 8 feet wide and 13.5 feet high can pass through the tunnels.
Part A: Write the equation for Tunnel A in standard form and determine the conic section. Show your work. (4 points)
Part B: Write the equation for Tunnel B in standard form and determine the conic section. Show your work (4 points)
Part C: Determine the maximum height of each tunnel is the truck able to pass through either tunnel without damage? If so, which tunnel(s) and why? Show your
work. (7 points)
Trucks will be able to pass through tunnel B while tunnel A is destroyed.In light of this, the equations for tunnels A and B are x2 + y2 + 30x + 56 = 0 and x2 - 30x + 16y - 95 = 0, respectively.
What is the standard form of parabola equation?A parabola's general equation is either y = a(x-h)2 + k or x = a(y-k)2 + h, where (h, k) stands for the vertex.
y2==4ax is the typical equation for a normal parabola.
Section A: x2+y2+30x+56=0
On both sides of an equation, add 152.
This is,
x²+30x+15²+y²=-56+15²
⇒ (x+15)²+y²=169⇒ (x+15)²+y²=13²
On both sides of the equation, divide 132.
⇒ (x+15)²/13² + y²/13² =1
Part B:x²-30x+16y-95=0
x2-30x+16y=95 now,
On both sides of an equation, add 152.
In other words, x2-30x+152+16y=95+152
⇒ (x-15)²=320-16y
⇒ (x-15)²=16(20-y) (20-y)
Part C:greatest height:A: 13 feet
B: 20 feet ,8 feet wide
A: x+15=8/2=4 y=12.37<13.5
B: x-15=8/2=4 y=19>13.5
In turn, tunnel A will sustain damage while the truck can travel via tunnel B.
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The ratio of dogs to cats at an animal shelter is 4 : 3. there are 40 more dogs than cats in this shelter. how many of each animal is in this shelter?
There are 80 dogs and 20 cats in the animal shelter.
The ratio of dogs to cats is 4:3. This means for every 4 dogs, there are 3 cats. We know that there are 40 more dogs than cats.
To calculate the number of each animal, we can set up the equation 40 = 4x - 3x, where x represents the number of cats.
After solving the equation, we get x = 20. This means that there are 20 cats in the animal shelter. To find the number of dogs, we can use the ratio. We know that for every 4 dogs, there are 3 cats. So, for 20 cats, there must be 4 × 20 = 80 dogs.
Therefore, there are 80 dogs and 20 cats in the animal shelter.
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The table represents a linear relationship.
x −1 0 1 2
y 2 0 −2 −4
Which of the following graphs shows this relationship?
graph of a line passing through the points negative 2 comma negative 4 and 0 comma 0
graph of a line passing through the points negative 2 comma negative 1 and 0 comma 0
graph of a line passing through the points negative 2 comma 4 and 0 comma 0
graph of a line passing through the points negative 2 comma 1 and 0 comma 0
The graph that shows the relationship is graph of a line passing through the points negative 2 comma 1 and 0 comma 0. Option D
What are the points on the graph?We know that a straight line graph is the kind of graph that we can be able to represent by the use of the equation; y = mx + c. Now we could have a straight line graph that passes through points.
The points that the graph would have to pass through are also the points that we can see on the graph of the function whose table have been shown in the question.
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Answer:
(-2,1) (0,0) D