All categories

3 years ago

For the data in the table tell whether y varies directly with X if it does write an equation for the direct variation

Mathematics

1 answer:

frozen [14]3 years ago

5 0

a) Option B Direct variation, y=1.8x is correct option.

b) Option A Not a direct variation is correct option.

Step-by-step explanation:

a) for the data in the table tell whether y varies directly with X if it does write an equation for the direct variation

The direct variation is represented by:

$y=kx \,\,or\\\frac{y}{x}=k$

We need to find k.

Given the values of x and y in table we will find k. if value of k is constant, so x and y varies directly

$\frac{5.4}{3}=1.8\\\frac{12.6}{7}=1.8\\\frac{21.6}{12}=1.8$

Since value of k is constant i.e 1.8 so, y varies directly with x.

Option B Direct variation, y=1.8x is correct option.

b) For the data in the table tell whether Y varies directly with x if it does write an equation for the direct variation.

The direct variation is represented by:

$y=kx \,\,or\\\frac{y}{x}=k$

We need to find k.

Given the values of x and y in table we will find k. if value of k is constant, so x and y varies directly

$\frac{1}{-2}=-\frac{1}{2}\\\frac{6}{3}=2\\\frac{11}{8}=1.3$

Since value of k is not constant so, y doesn't varies directly with x.

Option A Not a direct variation is correct option.

Keywords: Direct variation:

Learn more about Direct variation at:

#learnwithBrainly

You might be interested in

Please help i’ll give brainliest

Natalija [7]

Problem 1 Answer: x = 2/3y+8

Show Work:

Step 1: Add 2y to both sides.

3x−2y+2y=24+2y

3x=2y+24

Step 2: Divide both sides by 3.

3x/3 = 2y+24/3

x = 2/3y+8

Problem 2 Answer: x=−2y+48

Show Work:

Add -2y to both sides.

x+2y+−2y=48+−2y

x=−2y+48

8 0

3 years ago

Drag and drop each verbal phrase next to the algebraic expression that models it.

Aleksandr-060686 [28]

Answer: first one is : the base salary of an employee and a 9% salary increase; second one is : the price of a winter coat and a 90% discount ; third one is : the number of students attending school last year and a 90% increase from last year ; fourth one is : the cost of groceries and a 9% discount with coupons

Step-by-step explanation:

6 0

3 years ago

For simple linear regression, y = β0 + β1x + u, which one of the following statements is true?

RSB [31]

Answer:

Option a) u is called the "error term". It is the error we make in prediction

Option d) x is called the independent variable because x is independent from y and u.

Step-by-step explanation:

We are given the following information in the question:

$y = \beta_0 + \beta_1x + u$

where y is the dependent variable, x is the independent variable.

$\beta_0$ : It is the value of y when x is zero, that is y-intercept.

$\beta_1$ : It is the coefficient of x in predicting the dependent variable y.

u is the error term.

An error term represents the margin of error.
It refers to the sum of the deviations within the regression line, that is the difference between the predicted value and the observed value of y.

Thus, Option A) u is the error term and Option D) x is called the independent variable because x is independent from y and u are the correct answer.

6 0

3 years ago

Write 3.7 repeating as a mixed number

otez555 [7]

Explanation

3.7

3.0

0.7

This is because...

⋅

And also because...

0.7

⋅

4 0

3 years ago

A study of pollutants showed that certain industrial emissions should not exceed 2.3 parts per million. You believe a particular

Musya8 [376]

Answer:

$t=\frac{3.3-2.3}{\frac{0.4}{\sqrt{9}}}=7.5$

The degrees of freedom are given by:

$df=n-1=9-1=8$

And the p value would be:

$p_v =P(t_{(8)}>7.5)=0.0000346$

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 2.3 ppm the safe limit

Step-by-step explanation:

Information provided

$\bar X=3.3$ represent the sample mean in ppm

$s=0.4$ represent the sample standard deviation

$n=9$ sample size

$\mu_o =2.3$ represent the value to verify

$\alpha=0.05$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

System of hypothesis

We want to verify if the true mean is higher than 2,3 ppm, the system of hypothesis would be:

Null hypothesis: $\mu \leq 2.3$

Alternative hypothesis: $\mu > 2.3$

The statistic for this case is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing the info given we got:

$t=\frac{3.3-2.3}{\frac{0.4}{\sqrt{9}}}=7.5$

The degrees of freedom are given by:

$df=n-1=9-1=8$

And the p value would be:

$p_v =P(t_{(8)}>7.5)=0.0000346$

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 2.3 ppm the safe limit

6 0

4 years ago