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Each equation represents a linear relationship. Examine each and determine the slope and y- intercept

marysya [2.9K]

Answer:

Slope is -3/7. Y intercept is 250/7.

Step-by-step explanation:

Since they asking for the slope and y intercept, let put it in slope intercept form.

$y = mx + b$

where m is the slope and b is the y intercept.

The equation given is in standard form so we will convert it to slope intercept.

$3x + 7y = 250$

$7y = 250 - 3x$

$y = \frac{250}{7} - \frac{3}{7} x$

$y = - \frac{3}{7} x + \frac{250}{7}$

The slope is -3/7

The y intercept is 250/7

6 0

2 years ago

A college infirmary conducted an experiment to determine the degree of relief provided by three cough remedies. Each cough remed

KiRa [710]

Answer:

$p_v = P(\chi^2_{4,0.05} >3.81)=0.43233$

Since the p values is higher than the significance level we FAIL to reject the null hypothesis at 5% of significance, and we can conclude that we don't have significant differences between the 3 remedies analyzed. So we can say that the 3 remedies ar approximately equally effective.

Step-by-step explanation:

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Assume the following dataset:

NyQuil Robitussin Triaminic Total

No relief 11 13 9 33

Some relief 32 28 27 87

Total relief 7 9 14 30

Total 50 50 50 150

We need to conduct a chi square test in order to check the following hypothesis:

H0: There is no difference in the three remedies

H1: There is a difference in the three remedies

The level os significance assumed for this case is $\alpha=0.05$

The statistic to check the hypothesis is given by:

$\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$

The table given represent the observed values, we just need to calculate the expected values with the following formula $E_i = \frac{total col * total row}{grand total}$

And the calculations are given by:

$E_{1} =\frac{50*33}{150}=11$

$E_{2} =\frac{50*33}{150}=11$

$E_{3} =\frac{50*33}{150}=11$

$E_{4} =\frac{50*87}{150}=29$

$E_{5} =\frac{50*87}{150}=29$

$E_{6} =\frac{50*87}{150}=29$

$E_{7} =\frac{50*30}{150}=10$

$E_{8} =\frac{50*30}{150}=10$

$E_{9} =\frac{50*30}{150}=10$

And the expected values are given by:

NyQuil Robitussin Triaminic Total

No relief 11 11 11 33

Some relief 29 29 29 87

Total relief 10 10 10 30

Total 50 50 50 150

And now we can calculate the statistic:

$\chi^2 = \frac{(11-11)^2}{11}+\frac{(13-11)^2}{11}+\frac{(9-11)^2}{11}+\frac{(32-29)^2}{29}+\frac{(28-29)^2}{29}+\frac{(27-29)^2}{29}+\frac{(7-10)^2}{10}+\frac{(9-10)^2}{10}+\frac{(14-10)^2}{10} =3.81$

Now we can calculate the degrees of freedom for the statistic given by:

$df=(rows-1)(cols-1)=(3-1)(3-1)=4$

And we can calculate the p value given by:

$p_v = P(\chi^2_{4,0.05} >3.81)=0.43233$

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(3.81,4,TRUE)"

Since the p values is higher than the significance level we FAIL to reject the null hypothesis at 5% of significance, and we can conclude that we don't have significant differences between the 3 remedies analyzed.

4 0

3 years ago

The square root of -108 minus the square root of -3

Lady_Fox [76]

square root(-108) - square root(-3) =8.66025404 i

6 0

3 years ago

Sarawongs school is selling tickets to the anual talent show on the first day of ticket sales the school sold 1 adult ticket and

vaieri [72.5K]

Price of one adult ticket is $9 and price of one student ticket is also $9.

Step-by-step explanation:

Let,

Adult ticket = x

Student ticket = y

According to given statement;

x+2y=27 Eqn 1

2x+2y=36 Eqn 2

Subtracting Eqn 1 from Eqn 2;

$(2x+2y)-(x+2y)=36-27\\2x+2y-x-2y=9\\x=9$

Putting x=9 in Eqn 1;

$9+2y=27\\2y=27-9\\2y=18$

Dividing both sides by 2;

$\frac{2y}{2}=\frac{18}{2}\\y=9$

Price of one adult ticket is $9 and price of one student ticket is also $9.

Keywords: linear equations, subtraction

Learn more about linear equations at:

#LearnwithBrainly

4 0

3 years ago

Find the equation of the parabola with its focus at (6,2) and its directrix y = 0. Question 17 options: A) y = –1∕4(x – 6)2 + 1

Law Incorporation [45]

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8 0

3 years ago