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3 years ago

Find a equation for the line below

Mathematics

1 answer:

LenaWriter [7]3 years ago

3 0

Answer:

y = - $\frac{1}{2}$ x - $\frac{13}{2}$

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 5, - 4) and (x₂, y₂ ) = (- 1, - 6)

m = $\frac{-6+4}{-1+5}$ = $\frac{-2}{4}$ = - $\frac{1}{2}$ , thus

y = - $\frac{1}{2}$ x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 1, - 6), then

- 6 = $\frac{1}{2}$ + c ⇒ c = - 6 - $\frac{1}{2}$ = - $\frac{13}{2}$

y = - $\frac{1}{2}$ x - $\frac{13}{2}$ ← equation of line

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Find p(-4) and p(2) for the function p(x)=11x^5-11x^4-5x^2+15x-8

egoroff_w [7]

hi,

you must replace x by the number between parenthese.

I show you with the first one and let you do the second one

p(x) = 11x^5 -11x^4 - 5x^2 +15x-8

p(-4) = 11 (-4)^5 - 11 (-4)^4 -5(-4)² +15(-4) -8

p(-4) = 11 ( -1024- 256) - 5*16 -60-8

p(-4) = 11 ( -1280) -80-60-8

p(-4) = - 14080 - 148

p(-4) = - 14 228

7 0

3 years ago

Some scientists believe alcoholism is linked to social isolation. One measure of social isolation is marital status. A study of

frez [133]

Answer:

1) H0: There is independence between the marital status and the diagnostic of alcoholic

H1: There is association between the marital status and the diagnostic of alcoholic

2) The statistic to check the hypothesis is given by:

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

3) $\chi^2 = \frac{(21-33.143)^2}{33.143}+\frac{(37-41.429)^2}{41.429}+\frac{(58-41.429)^2}{41.429}+\frac{(59-46.857)^2}{46.857}+\frac{(63-58.571)^2}{58.571}+\frac{(42-58.571)^2}{58.571} =19.72$

4) $df=(rows-1)(cols-1)=(3-1)(2-1)=2$

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} >19.72)=5.22x10^{-5}$

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

"=1-CHISQ.DIST(19.72,2,TRUE)"

Since the p value is lower than the significance level so then we can reject the null hypothesis at 5% of significance, and we can conclude that we have association between the two variables analyzed.

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:

Diag. Alcoholic Undiagnosed Alcoholic Not alcoholic Total

Married 21 37 58 116

Not Married 59 63 42 164

Total 80 100 100 280

Part 1

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

H0: There is independence between the marital status and the diagnostic of alcoholic

H1: There is association between the marital status and the diagnostic of alcoholic

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

Part 2

The statistic to check the hypothesis is given by:

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

Part 3

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:

$E_{1} =\frac{80*116}{280}=33.143$

$E_{2} =\frac{100*116}{280}=41.429$

$E_{3} =\frac{100*116}{280}=41.429$

$E_{4} =\frac{80*164}{280}=46.857$

$E_{5} =\frac{100*164}{280}=58.571$

$E_{6} =\frac{100*164}{280}=58.571$

And the expected values are given by:

Diag. Alcoholic Undiagnosed Alcoholic Not alcoholic Total

Married 33.143 41.429 41.429 116

Not Married 46.857 58.571 58.571 164

Total 80 100 100 280

And now we can calculate the statistic:

$\chi^2 = \frac{(21-33.143)^2}{33.143}+\frac{(37-41.429)^2}{41.429}+\frac{(58-41.429)^2}{41.429}+\frac{(59-46.857)^2}{46.857}+\frac{(63-58.571)^2}{58.571}+\frac{(42-58.571)^2}{58.571} =19.72$

Part 4

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

$df=(rows-1)(cols-1)=(3-1)(2-1)=2$

And we can calculate the p value given by:

$p_v = P(\chi^2_{2} >19.72)=5.22x10^{-5}$

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

"=1-CHISQ.DIST(19.72,2,TRUE)"

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4 years ago

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Ira Lisetskai [31]

The completed factor is (7x+2) (x+5)

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3 years ago

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Westkost [7]

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3 years ago

The equation of a line perpendicular to y = 3 and passes through the point (24, -56).

Lera25 [3.4K]

Answer:

x = 24

Step-by-step explanation:

The given line y = 3 is a horizontal line with slope zero (0).

We wish to find the equation of a line that is perpendicular to y = 3. Such a line would be a vertical one. Vertical lines do not have slopes defined (due to division by zero).

Thus the general form of the equation of this new line is x = c.

This new line passes through (24, -56). Thus, x must be 24: x = 24

3 0

3 years ago