Mathematics: Which table of values represents a linear equation

Which table of values represents a linear equation, №13785438, 22.05.2023 09:01

Mathematics

Iwill make brainliest ! 1) is the function described by the points in this table linear or nonlinear? x y −2 4 0 8 1 10 2 12 3 14 a)linear b)nonlinear 2) which table could be a partial set of values for a linear function? x y 0 0 1 2 2 8 3 18 x y 0 3 1 5 2 7 3 9 x y 0 9 1 8 2 5 3 0 x y 0 1 1 2 2 5 3 10 3) is this function linear or nonlinear? y=2x2−4 a)nonlinear b)linear 4)select linear or nonlinear to correctly classify each function. function linear nonlinear 72=x3+y y+1=5(x−9) 7y + 2x = 12 4y = 24 5) a function is represented by the values in

Step-by-step answer

P Answered by Specialist

47

1)

Answer

a) linear

Explanation

There is a simple way to tell if a function is linear from a table: look at the x and y-values; if the y-values are increasing or decreasing by the same amount when their corresponding x-values increases or decreases by the same amount, you have a linear function; otherwise, you don't.

Look at the table

From 0 to 1 x is increasing by 1; from 8 to 10 (the corresponding values), y is increasing by 2

From 1 to 2 x is increasing by 1; from 10 to 12, y is increasing by 2

So, every time that x increases by 1, y increases by 2; therefore, we have a linear function.

Notice that form -2 to 0 x is increasing by 2; from 4 to 8 increasing by 4, which is the same rate as before (when x increases 1, y increases 1)

2)

Answer

xy

03

15

27

39

Explanation

When x increases by 1, y increases by 2; therefore we have a linear function.

If you look at the first and third tables, y increases at different amounts every time x increases by 1; therefore, they are not linear functions.

In the first table when x increases by 1, y increases by 2, 4, or 10. Therefore, the table is not a linear function.

Similarly, in the third table when x increases by 1, y increases by 1, 3, or 5. Therefore, the table is not a linear function.

3)

Answer

a) nonlinear

Explanation

A linear function is function of the form: y=mx+b or Ay+Bx=C where is the independent variable and is the dependent variable.

In a linear function the coefficient of the variables is always 1.

Notice that the coefficient of the independent variable , in the function y=2x^2-4 , is 2; therefore the function is nonlinear.

4)

Answer

2=x3+y Nonlinear

y+1=5(x−9) Linear

7y + 2x = 12 Linear

4y = 24 Linear

Explanation

2=x3+y The coefficient of the independent variable, x, is 3; therefore, the function is not linear.

y+1=5(x−9) We can simplify the expression to get:

y+1=5x-45

y=5x-46

Since y=5x-46 is in the form y=mx+b, we have a linear function.

7y + 2x = 12

Since 7y + 2x = 12 is a function of the form Ay + Bx = C, it is a linear function

4y = 24 We can siplify to get:

$y=\frac{24}{4}$

y=6

Since y=6 is a function of the form y = mx+b (with m=0), it is a linear function.

5)

Answer

b) is not

Explanation

From 22 to 20, x decreases by 2; from 26 to 22, y decreases by 4. So, when x decreases by 2, y decreases by 4.

From 16 to 14, x decreases by 2; from 20 to 18, y decreases by 2. So, when x decreases by 2, y decreases by 2.

When x decreases by 2, y decreases by 4 or 2; therefore the function represented in the table is not a linear function.

Mathematics

Iwill make brainliest ! 1) is the function described by the points in this table linear or nonlinear? x y −2 4 0 8 1 10 2 12 3 14 a)linear b)nonlinear 2) which table could be a partial set of values for a linear function? x y 0 0 1 2 2 8 3 18 x y 0 3 1 5 2 7 3 9 x y 0 9 1 8 2 5 3 0 x y 0 1 1 2 2 5 3 10 3) is this function linear or nonlinear? y=2x2−4 a)nonlinear b)linear 4)select linear or nonlinear to correctly classify each function. function linear nonlinear 72=x3+y y+1=5(x−9) 7y + 2x = 12 4y = 24 5) a function is represented by the values in

Step-by-step answer

P Answered by Specialist

47

1)

Answer

a) linear

Explanation

There is a simple way to tell if a function is linear from a table: look at the x and y-values; if the y-values are increasing or decreasing by the same amount when their corresponding x-values increases or decreases by the same amount, you have a linear function; otherwise, you don't.

Look at the table

From 0 to 1 x is increasing by 1; from 8 to 10 (the corresponding values), y is increasing by 2

From 1 to 2 x is increasing by 1; from 10 to 12, y is increasing by 2

So, every time that x increases by 1, y increases by 2; therefore, we have a linear function.

Notice that form -2 to 0 x is increasing by 2; from 4 to 8 increasing by 4, which is the same rate as before (when x increases 1, y increases 1)

2)

Answer

xy

03

15

27

39

Explanation

When x increases by 1, y increases by 2; therefore we have a linear function.

If you look at the first and third tables, y increases at different amounts every time x increases by 1; therefore, they are not linear functions.

In the first table when x increases by 1, y increases by 2, 4, or 10. Therefore, the table is not a linear function.

Similarly, in the third table when x increases by 1, y increases by 1, 3, or 5. Therefore, the table is not a linear function.

3)

Answer

a) nonlinear

Explanation

A linear function is function of the form: y=mx+b or Ay+Bx=C where is the independent variable and is the dependent variable.

In a linear function the coefficient of the variables is always 1.

Notice that the coefficient of the independent variable , in the function y=2x^2-4 , is 2; therefore the function is nonlinear.

4)

Answer

2=x3+y Nonlinear

y+1=5(x−9) Linear

7y + 2x = 12 Linear

4y = 24 Linear

Explanation

2=x3+y The coefficient of the independent variable, x, is 3; therefore, the function is not linear.

y+1=5(x−9) We can simplify the expression to get:

y+1=5x-45

y=5x-46

Since y=5x-46 is in the form y=mx+b, we have a linear function.

7y + 2x = 12

Since 7y + 2x = 12 is a function of the form Ay + Bx = C, it is a linear function

4y = 24 We can siplify to get:

$y=\frac{24}{4}$

y=6

Since y=6 is a function of the form y = mx+b (with m=0), it is a linear function.

5)

Answer

b) is not

Explanation

From 22 to 20, x decreases by 2; from 26 to 22, y decreases by 4. So, when x decreases by 2, y decreases by 4.

From 16 to 14, x decreases by 2; from 20 to 18, y decreases by 2. So, when x decreases by 2, y decreases by 2.

When x decreases by 2, y decreases by 4 or 2; therefore the function represented in the table is not a linear function.

Mathematics

Which of the following statements concerning the linear correlation coefficient are true? i: if the linear correlation coefficient for two variables is zero, then there is no relationship between the variables. ii: if the slope of the regression line is negative, then the linear correlation coefficient is negative. iii: the value of the linear correlation coefficient always lies between -1 and 1. iv: a linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of -0.82. a) ii and iii b)

Step-by-step answer

P Answered by Master

7

1) A) II and III

2) A) Critical values: r = plusminus 0.396, significant linear correlation

3) Yi= 0.41 + 0.37Xi

Step-by-step explanation:

Hello!

The objective of the linear correlation analysis is to test if there is an association between two study variables (X₁ and X₂).

Pearson's Coefficient of correlation

For Variables with a bivariate normal distribution (X₁, X₂)~N₂(μ₁; μ₂; σ₁²; σ₂²; ρ)

To do so, the study parameter is the population coefficient of correlation (ρ) - Rho- (If you were to make a graphic of the correlation line, Rho represents the slope)

Sample coefficient of correlation: r

It takes values between -1 and 1

This coefficient gives an idea of the degree of correlation between the variables.

If ρ = 0 then there is no linear correlation between X₁ and X₂ Graphically, the slope is cero

If ρ < 0 then there is a negative association between X₁ and X₂ (i.e. when one variable increases the other one decreases) In a graphic, the slope of the line is negative.

If ρ > 0 then there is a positive association between X₁ and X₂ (i.e. Both variables increase and decrease together)

The closer to 1 or -1 the coefficient is, the stronger the association between variables. Using the absolute value of the correlation coefficients you can compare them, the greater the value, the stronger is the association between variables. For example, if you were to have two coefficients r₁= -0.24 and r₂= 0.67 then the absolute values are Ir₁I= 0.24 and Ir₂I= 0.67 you can see that the coefficient of the second sample is bigger than the first sample, that means that there is a stronger correlation in the second sample than the first one.

The non-parametric coefficient of correlation has the same characteristics.

1) Statements:

I: If the linear correlation coefficient for the two variables is zero, then there is no relationship between the variables. FALSE, when r=0 then there is no linear association between the two variables, this doesn't mean that there isn't any other type of association between them.

II: If the slope of the regression line is negative, then the linear correlation coefficient is negative. TRUE

The regression and correlation analyses are closely linked because for a regression equation to be reasonable, the sample points must be linked to the equation and the correlation coefficient between both variables must be large when the degree of association is high and small when The degree of association is low in addition to being independent of the units.

The regression analysis tests whether or not there is an association between both variables and the correlation analysis indicates the degree of that association.

If the slope of the regression is negative, then the correlation coefficient is negative.

III: The value of the linear correlation coefficient always lies between -1 and 1. TRUE, it is one of the characteristics of the correlation coefficient.

0.62 suggests a stronger linear relationship than a linear correlation coefficient of -0.82. FALSE, to check wich correlation coefficient shows a stronger correlation look at their absolute values, the one that is closer to 1 is the stronger, Ir₁I= 0.62 < Ir₂I= 0.82

Correct

A) II and III

2) Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r = 0.523, n = 25

For this, you have to use a Table of cumulative probabilities for the linear correlation coefficient. (I've used Pearson)

For a two-tailed test (H₀: ρ=0)

$r_{n-2; \alpha/2}= r_{23; 0.025}=$ ± 0.396

Against r = 0.523, the decision is to reject the null hypothesis. There is a linear correlation between the two study variables.

Correct

A) Critical values: r = plus-minus 0.396, significant linear correlation

3) Construct a scatterplot for the given data. Check 1st attachment for Data and Scatterplot.

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

Equation of regression:

Yi= a + bXi

a= $(\frac{sum Yi}{n})$ +b $(\frac{sum Xi}{n})$

b= $\frac{sum XiYi*\frac{(sum Xi)(sum Yi)}{n} }{/(sumXi^2)-\frac{(sumXi)^2}{n} }$

Using the given Data:

∑Xi= -11

∑Xi²= 201

∑Yi= 0

∑Yi²= 176

Mean X= -1.10

Mean Y= 0

a= 0.41

b= 0.37

Yi= 0.41 + 0.37Xi

4) Managers rate empoyees acording to job performance and attitude. The results fro several randomly selected empoyees are given below.

Performance: 59; 63; 65; 69; 58; 77; 76; 69; 70; 64

Attitude: 72; 67; 78; 82; 73; 87; 92; 83; 87; 78

No question found?

I hope it helps!

Mathematics

Which of the following statements concerning the linear correlation coefficient are true? i: if the linear correlation coefficient for two variables is zero, then there is no relationship between the variables. ii: if the slope of the regression line is negative, then the linear correlation coefficient is negative. iii: the value of the linear correlation coefficient always lies between -1 and 1. iv: a linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of -0.82. a) ii and iii b)

Step-by-step answer

P Answered by Master

7

1) A) II and III

2) A) Critical values: r = plusminus 0.396, significant linear correlation

3) Yi= 0.41 + 0.37Xi

Step-by-step explanation:

Hello!

The objective of the linear correlation analysis is to test if there is an association between two study variables (X₁ and X₂).

Pearson's Coefficient of correlation

For Variables with a bivariate normal distribution (X₁, X₂)~N₂(μ₁; μ₂; σ₁²; σ₂²; ρ)

To do so, the study parameter is the population coefficient of correlation (ρ) - Rho- (If you were to make a graphic of the correlation line, Rho represents the slope)

Sample coefficient of correlation: r

It takes values between -1 and 1

This coefficient gives an idea of the degree of correlation between the variables.

If ρ = 0 then there is no linear correlation between X₁ and X₂ Graphically, the slope is cero

If ρ < 0 then there is a negative association between X₁ and X₂ (i.e. when one variable increases the other one decreases) In a graphic, the slope of the line is negative.

If ρ > 0 then there is a positive association between X₁ and X₂ (i.e. Both variables increase and decrease together)

The closer to 1 or -1 the coefficient is, the stronger the association between variables. Using the absolute value of the correlation coefficients you can compare them, the greater the value, the stronger is the association between variables. For example, if you were to have two coefficients r₁= -0.24 and r₂= 0.67 then the absolute values are Ir₁I= 0.24 and Ir₂I= 0.67 you can see that the coefficient of the second sample is bigger than the first sample, that means that there is a stronger correlation in the second sample than the first one.

The non-parametric coefficient of correlation has the same characteristics.

1) Statements:

I: If the linear correlation coefficient for the two variables is zero, then there is no relationship between the variables. FALSE, when r=0 then there is no linear association between the two variables, this doesn't mean that there isn't any other type of association between them.

II: If the slope of the regression line is negative, then the linear correlation coefficient is negative. TRUE

The regression and correlation analyses are closely linked because for a regression equation to be reasonable, the sample points must be linked to the equation and the correlation coefficient between both variables must be large when the degree of association is high and small when The degree of association is low in addition to being independent of the units.

The regression analysis tests whether or not there is an association between both variables and the correlation analysis indicates the degree of that association.

If the slope of the regression is negative, then the correlation coefficient is negative.

III: The value of the linear correlation coefficient always lies between -1 and 1. TRUE, it is one of the characteristics of the correlation coefficient.

0.62 suggests a stronger linear relationship than a linear correlation coefficient of -0.82. FALSE, to check wich correlation coefficient shows a stronger correlation look at their absolute values, the one that is closer to 1 is the stronger, Ir₁I= 0.62 < Ir₂I= 0.82

Correct

A) II and III

2) Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r = 0.523, n = 25

For this, you have to use a Table of cumulative probabilities for the linear correlation coefficient. (I've used Pearson)

For a two-tailed test (H₀: ρ=0)

$r_{n-2; \alpha/2}= r_{23; 0.025}=$ ± 0.396

Against r = 0.523, the decision is to reject the null hypothesis. There is a linear correlation between the two study variables.

Correct

A) Critical values: r = plus-minus 0.396, significant linear correlation

3) Construct a scatterplot for the given data. Check 1st attachment for Data and Scatterplot.

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

Equation of regression:

Yi= a + bXi

a= $(\frac{sum Yi}{n})$ +b $(\frac{sum Xi}{n})$

b= $\frac{sum XiYi*\frac{(sum Xi)(sum Yi)}{n} }{/(sumXi^2)-\frac{(sumXi)^2}{n} }$

Using the given Data:

∑Xi= -11

∑Xi²= 201

∑Yi= 0

∑Yi²= 176

Mean X= -1.10

Mean Y= 0

a= 0.41

b= 0.37

Yi= 0.41 + 0.37Xi

4) Managers rate empoyees acording to job performance and attitude. The results fro several randomly selected empoyees are given below.

Performance: 59; 63; 65; 69; 58; 77; 76; 69; 70; 64

Attitude: 72; 67; 78; 82; 73; 87; 92; 83; 87; 78

No question found?

I hope it helps!

Mathematics

1. write a function rule for finding the amount of daily pay, p, in the following situation: a bus driver gets paid $100 each day plus $0.20 per kilometer, k. (1 point) 100 = 0.20 × k p = 0.20 × 100 × k p = 0.20k + 100 0.20k = 100 + p use the table below to answer the following question. 2. do the values in the table represent a linear function? if so, what is the function rule? (1 point) the values do not show a linear function. yes, the values show a linear function: y = x + 4. yes, the values show a linear function: y = 2x + 2. yes, the values

Step-by-step answer

P Answered by Master

16

1.
To figure out how much the bus driver gets paid everyday you will need this function.
P = 0.20K + 100

2.
the table:(x)(-2,0,2,4 (y)-4,0,4,8
The values in the table do represent a linear function.

Y = 2X

Plug in values from the table

-4 = 2(-2)
-4 = -4

3.
Connexus login?

4.
The equation that shows the total cost of a cup of frozen yogurt is Y = 1.25X + 3; $8.00.

Mathematics

1. write a function rule for finding the amount of daily pay, p, in the following situation: a bus driver gets paid $100 each day plus $0.20 per kilometer, k. (1 point) 100 = 0.20 × k p = 0.20 × 100 × k p = 0.20k + 100 0.20k = 100 + p use the table below to answer the following question. 2. do the values in the table represent a linear function? if so, what is the function rule? (1 point) the values do not show a linear function. yes, the values show a linear function: y = x + 4. yes, the values show a linear function: y = 2x + 2. yes, the values

Step-by-step answer

P Answered by Specialist

16

1.
To figure out how much the bus driver gets paid everyday you will need this function.
P = 0.20K + 100

2.
the table:(x)(-2,0,2,4 (y)-4,0,4,8
The values in the table do represent a linear function.

Y = 2X

Plug in values from the table

-4 = 2(-2)
-4 = -4

3.
Connexus login?

4.
The equation that shows the total cost of a cup of frozen yogurt is Y = 1.25X + 3; $8.00.

Mathematics

Use the table below to answer the following question. 2. do the values in the table represent a linear function? if so, what is the function rule? (1 point) the values do not show a linear function. yes, the values show a linear function: y = x + 4. yes, the values show a linear function: y = 2x + 2. yes, the values show a linear function: y = 2x.

Step-by-step answer

P Answered by Specialist

10

The values in the table do represent a linear function.

Y = 2X

Plug in values from the table

-4 = 2(-2)

-4 = -4

Mathematics

Use the table below to answer the following question. 2. do the values in the table represent a linear function? if so, what is the function rule? (1 point) the values do not show a linear function. yes, the values show a linear function: y = x + 4. yes, the values show a linear function: y = 2x + 2. yes, the values show a linear function: y = 2x.

Step-by-step answer

P Answered by Specialist

10

The values in the table do represent a linear function.

Y = 2X

Plug in values from the table

-4 = 2(-2)

-4 = -4