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3 years ago

Write the equation for this line in slope intercept form

Mathematics

1 answer:

elena-s [515]3 years ago

5 0

Answer:

y = $\frac{3}{2}$ x + 2

Step-by-step explanation:

Slope-intercept form is y = mx + b with m as the slope and b as the y-intercept.

The y-intercept is the point where the line intersects the y- axis.

y = mx + 2

The equation to find slope is $\frac{y1-y2}{x1-x2}$ Two points from the line: (0,2) (4,8)

$\frac{8-2}{4-0}$ = $\frac{6}{4}$ = $\frac{3}{2}$

y = $\frac{3}{2}$ x + 2

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Many elementary school students in a school district currently have ear infections. A random sample of children in two different

Marta_Voda [28]

Answer:

Step-by-step explanation:

The summary of the given data includes;

sample size for the first school $n_1$ = 42

sample size for the second school $n_2$ = 34

so 16 out of 42 i.e $x_1$ = 16 and 18 out of 34 i.e $x_2$ = 18 have ear infection.

the proportion of students with ear infection Is as follows:

$\hat p_1 = \dfrac{16}{42}$ = 0.38095

$\hat p_2 = \dfrac{18}{34}$ = 0.5294

Since this is a two tailed test , the null and the alternative hypothesis can be computed as :

$H_0 :p_1 -p_2 = 0 \\ \\ H_1 : p_1 - p_2 \neq 0$

level of significance ∝ = 0.05,

Using the table of standard normal distribution, the value of z that corresponds to the two-tailed probability 0.05 is 1.96. Thus, we will reject the null hypothesis if the value of the test statistics is less than -1.96 or more than 1.96.

The test statistics for the difference in proportion can be achieved by using a pooled sample proportion.

$\bar p = \dfrac{x_1 +x_2}{n_1 +n_2}$

$\bar p = \dfrac{16 +18}{42 +34}$

$\bar p = \dfrac{34}{76}$

$\bar p = 0.447368$

$\bar p + \bar q = 1 \\ \\ \bar q = 1 -\bar p \\ \\\bar q = 1 - 0.447368 \\ \\\bar q = 0.552632$

The pooled standard error can be computed by using the formula:

$S.E = \sqrt{ \dfrac{ \bar p \bar q}{ n_1} + \dfrac{\bar p \bar p}{n_2} }$

$S.E = \sqrt{ \dfrac{ 0.447368 * 0.552632}{ 42} + \dfrac{ 0.447368 * 0.447368}{34} }$

$S.E = \sqrt{ \dfrac{ 0.2472298726}{ 42} + \dfrac{ 0.2001381274}{34} }$

$S.E = \sqrt{ 0.01177284105}$

$S.E = 0.1085$

The test statistics is ;

$z = \dfrac{\hat p_1 - \hat p_2}{S.E}$

$z = \dfrac{0.38095- 0.5294}{0.1085}$

$z = \dfrac{-0.14845}{0.1085}$

z = - 1.368

Decision Rule: Since the test statistics is greater than the rejection region - 1.96 , we fail to reject the null hypothesis.

Conclusion: There is insufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools

5 0

3 years ago

A bag has 30 towels numbered 1 to 30. What's the ratio for odds to evens?

8090 [49]

15:15

Which is simplified to
1:1

Hope this helps!

8 0

3 years ago

Does the table represent an exponential function? Explain.

Ede4ka [16]

Answer:

No, because as the x-values are increasing by a constant amount, the y-values are not being multiplied by a constant amount.

Step-by-step explanation:

We have a set of ordered pairs of the form (x, y)

If a function is exponential then the ratio between the consecutive values of y, is always equal to a constant.

This means that:

\frac{y_2}{y_1}=\frac{y_3}{y_2}=\frac{y_4}{y_3}=by1y2=y2y3=y3y4=b

This is: y_2=by_1y2=by1

Now we have this set of points {(-1, -5), (0, -3), (1, -1), (2, 1)}

Observe that:

\begin{gathered}\frac{y_2}{y_1}=\frac{-3}{-5}=\frac{3}{5}\\\\\frac{y_3}{y_2}=\frac{-1}{-3}=\frac{1}{3}\\\\\frac{3}{5}\neq \frac{1}{3}\end{gathered}y1y2=−5−3=53y2y3=−3−1=3153=31

Then the values of y are not multiplied by a constant amount "b"

5 0

3 years ago

Using 45-in. fabric, Regan needs 2 and one fourth yd for a dress, one fourth yd of contrasting fabric for the band at the bot

Arte-miy333 [17]

Answer:

$7\dfrac14$ yards$