What is an equation of the line that passes through the points (−4,−2) and (−8,3)?

An article reported on the results of an experiment in which half of the individuals in a group of 60 postmenopausal overweight

slavikrds [6]

Answer:

Step-by-step explanation:

From the given information:

Let's first compute the null and alternative hypothesis

Null hypothesis:

$\mathbf{H_o: \mu_1-\mu_2=1}$

Alternative hypothesis:

$H_a :\mu_1 -\mu_2 > 1$

The number of samples is half in a group of 60

i.e

$n_1=n_2 = 30$

the sample mean for sample 1 $\overline x_1$ = 5.7

the standard deviation for sample 1 $s_1$ = 3.1

the sample mean for sample 2 $\overline x_2$ = 3.9

the standard deviation for sample 2 $s_2$ = 2.7

degree of freedom for this test can be computed by using the formula:

$df = \dfrac{\begin {pmatrix} \dfrac{s_1^2}{n_1} + \dfrac{s^2_2}{n_2} \end {pmatrix}^2 } {\dfrac{ (\dfrac{s_1^2}{n_1}^2)}{ n_1-1} + \dfrac{ (\dfrac{s_2^2}{n_2}^2)}{ n_2-1} }$

$df = \dfrac{\begin {pmatrix} \dfrac{3.1^2}{30} + \dfrac{2.7^2}{30} \end {pmatrix}^2 } {\dfrac{ \begin {pmatrix} \dfrac{3.1^2}{30} \end {pmatrix}^2}{ 30-1} + \dfrac{ \begin {pmatrix} \dfrac{2.7^2}{30} \end {pmatrix}^2}{ 30-1} }}$

df = 114.68

The test statistics can be computed as follows:

$t = \dfrac{ \overline x_1 -\overline x_2- (\mu_1 -\mu_2)}{\sqrt{ \dfrac{s_1^2}{n_1} +\dfrac{s_2^2}{n_2} }}$

$t = \dfrac{ 5.7-3.9- (1)}{\sqrt{ \dfrac{3.1^2}{30} +\dfrac{2.7^2}{30} }}$

t = 1.07

Using the level of significance of 0.1, the P-value for the test statistics at the df of 114.68 is:

P-value = 0.143

Decision rule: To reject the null hypothesis if the level of significance is greater than the p-value.

Conclusion: We fail to reject the null hypothesis because the p-value is greater than the level of significance at 0.1.

Thus, it appears that the true average weight loss for the vegan diet does not exceeds that for the control diet by more than 1 kg.

8 0

3 years ago

A total of

Arte-miy333 [17]

Let x equal the number of adult tickets sold.

X + 3X=512
(I put 3x because we know the students sold 3 times as many).
Solve for X.

X+3X=512
4X=512
4X/4=512/4
X=128

3 0

3 years ago

Volume of triangular prism

galina1969 [7]

Answer:

216

Step-by-step explanation:

9 * 6 = 54

54 * 8 = 432

432/2 = 216 is the answer

5 0

3 years ago

Read 2 more answers

A cake manufacturer boxes Swiss chocolate and German chocolate cakes at one site. A box of Swiss chocolate cake contains 0.55 lb

Kobotan [32]

Answer:

2,500 German chocolate cake boxes.

1,500 Swiss chocolate cake boxes.

Step-by-step explanation:

Let 'S' be the number of Swiss chocolate cakes boxed and 'G' the number of German cholocate cakes boxed. If all of the available ingredients are used:

$0.55*S +0.59*G = 2,300\\0.45*S+0.41*G = 1,700$

Solving the linear system above:

$(0.55 *S +0.59*G)- \frac{0.55}{0.45} (0.45*S+0.41*G)= 2,300-\frac{0.55}{0.45}*1,700*\\0.088888*G = 222.222\\G=2,500\\S =\frac{2,300-2,500*0.59}{0.55}\\S=1500$

2,500 German chocolate cake boxes and 1,500 Swiss chocolate cake boxes can be made each day.

6 0

3 years ago

Which value of m will create a system of parallel lines with no solution? y=mx-6 8x-4y=12 A coordinate grid with one line labele

nydimaria [60]

Answer:

A system of parallel lines will be created where the two lines will never meet and have no common solution at a value of m = 2

Step-by-step explanation:

The equation of the given line is 8·x - 4·y = 12

Which gives;

8·x- 12= 4·y

y = 2·x - 3

Given that the line passes through the points (0, -3) and (1, -1), we have;

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

When (x₁, y₁) = (0. -3) and (x₂, y₂) = (1, -1), we have;

$Slope, \, m =\dfrac{(-1)-(-3)}{1-(0)} = 2$

y - (-3) = 2×(x - 0)

y = 2·x - 3 which is the equation of the given line

For the lines 8·x - 4·y = 12, which is the sane as y = 2·x - 3 and the line y = m·x - 6 to have no solution, the slope of the two lines should be equal that is m = 2

Given that the line passes through the point (1.5, 0), we have;

y - 0 = 2×(x - 1.5)

y = 2·x - 3...................(1)

For the equation, y = m·x - 6, when m = 2, we have;

y = 2·x - 6..................(2)

Solving equations (1) and (2) gives;

2·x - 3 = 2·x - 6, which gives;

2·x - 2·x= - 3 - 6

0 = 9

Therefore, a system of parallel lines will be created where the two lines will never meet and have no common solution at a value of m = 2.

4 0

3 years ago