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1 year ago

Find the slope of the line containing the pair of points. (2, -9) and (12,6)

Mathematics

1 answer:

dusya [7]1 year ago

5 0

Answer:

slope = $\frac{3}{2}$

Step-by-step explanation:

calculate the slope m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (2, - 9 ) and (x₂, y₂ ) = (12, 6 )

m = $\frac{6-(-9)}{12-2}$ = $\frac{6+9}{10}$ = $\frac{15}{10}$ = $\frac{3}{2}$

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A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is current

lapo4ka [179]

Using the z-distribution, we have that:

The hypothesis test is:

$H_0: \mu = 7.4$

$H_1: \mu < 7.4$

The p-value is of 0.0668.

The critical value is $z^{\ast} = -1.28$

b) Since the test statistic is less than the critical value for the left-tailed test, there is enough evidence to conclude that the null hypothesis will be rejected.

Item a:

At the null hypothesis, it is tested if the mean is of 7.4 minutes, that is:

$H_0: \mu = 7.4$

At the alternative hypothesis, it is tested if the mean is lower than 7.4 minutes, that is:

$H_1: \mu < 7.4$

We have the standard deviation for the population, hence, the z-distribution is used.

The test statistic is given by:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

The parameters are:

$\overline{x}$ is the sample mean.

$\mu$ is the value tested at the null hypothesis.

$\sigma$ is the standard deviation of the sample.

n is the sample size.

For this problem, the values of the parameters are: $\overline{x} = 7.1, \mu = 7.4, \sigma = 1.2, n = 36$ .

Hence, the value of the test statistic is:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{7.1 - 7.4}{\frac{1.2}{\sqrt{36}}}$

$z = -1.5$

Using a z-distribution calculator, the p-value is of 0.0668.

Also using a calculator, considering a left-tailed test, as we are testing if the mean is less than a value, the critical value with a significance level of 0.1 is of $z^{\ast} = -1.28$ .

Item b:

Since the test statistic is less than the critical value for the left-tailed test, there is enough evidence to conclude that the null hypothesis will be rejected.

You can learn more about the use of the z-distribution to test an hypothesis at brainly.com/question/16313918

5 0

2 years ago

Question 1 of 3 NE A scale drawing of a fishing boat has a scale of 1 cmn to 2 meters. If the length of the fishing boat is 6 cm

bagirrra123 [75]

Answer:

12 meters

Step-by-step explanation:

Given

$Scale= 1cm:2m$

Required

Determine the measurement when the scale reads 6cm

Represent this scale with x;

Such that:

$Scale = 6cm:x$

Equate

$Scale= 1cm:2m$ and $Scale = 6cm:x$

$1cm:2m = 6cm:x$

Express as fraction

$\frac{1cm}{2m} = \frac{6cm}{x}$

Cross Multiply

$x * 1cm = 6cm * 2m$

$x * 1 = 6 * 2m$

$x = 6 * 2m$

$x = 12m$

3 0

3 years ago

The graph of the equation x + 3y = 6 intersects at the y axis at the point whose coordinates are

svp [43]

Answer:

4. (6,0)

Step-by-step explanation:

Plug the points into the equation.

6+3(0)=6

6+0=6

6=6

5 0

3 years ago

o eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before add

Anna71 [15]

Answer:

Look at your answers for the last question in all four sets. Locate these four elements on the periodic table. Enter the name of the group that all four elements belong to. Watch your spelling! [Hint: If all four answers for the last question are not in the same group on the periodic table, redo your sets or contact your instructor.]

A screen reader friendly version of the periodic table (opens in a new window) is available, as well as a printable, black and white version (opens in a new window).

Step-by-step explanation:

7 0

2 years ago

Over the summer, for every 14 Okra seeds Dana planted, 9 plants grew. If he planted 182 seeds, how many grew into plants?

vova2212 [387]

Simple...

you have: For every 14 seeds that Okra seeds Dana planted 9 of them grew; if he planted 182 seeds..how many grew?

Set up an equation...

$\frac{9}{14} = \frac{x}{182}$

Cross multiply....

14*x=14x

9*182=1638

14x=1638

$\frac{14x}{14} = \frac{1638}{14} =117
$

x=117

This means that, for 182 seeds planted, 117 of them grew to be plants.

Thus, your answer.

3 0

3 years ago

Read 2 more answers