What is the slope of a line PARALLEL to the graph?<br><br> A) -3<br> B) 0<br> C) 3<br> D) -1/3

Olin [163]

The value for X is 2

5 0

3 years ago

A field researcher is gathering data on the trunk diameters of mature pine and spruce trees in a certain area. The following are

lidiya [134]

Answer:

As the pvalue of the test is 0.02097 < 0.1, using a .10 significance level, he can conclude that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree.

Step-by-step explanation:

Using a .10 significance level, can he conclude that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree

The null hypothesis is that they are equal(that is, subtraction between the means is 0), while the alternate hypothesis is that they are greater(that is, subtraction between the means is larger than 0). So

$H_0: \mu_1 - \mu_2 = 0$

$H_a: \mu_1 - \mu_2 > 0$

In which $\mu_1$ is the mean pine trees height while $\mu_2$ is the mean spruce trees height.

The test statistic is:

$z = \frac{X - \mu}{s}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis and s is the standard error.

0 is tested at the null hypothesis:

This means that $\mu = 0$

Mean trunk diameter (cm) 35 30:

Pine trees - 35

Spruce trees - 30

The sample mean is given by the subtraction of the means. So

$X = 35 - 30 = 5$

Sample Size 40 80

Population variance 160 160

This means that the standard error for each sample is given by:

$s_1 = \frac{\sqrt{160}}{\sqrt{40}} = 2$

$s_1 = \frac{\sqrt{160}}{\sqrt{80}} = \sqrt{2}$

The standard error of the difference is the square root of the sum squared of the standard error of each sample.

$s = \sqrt{2^2 + (\sqrt{2})^2} = \sqrt{6} = 2.4495$

Test statistic:

$z = \frac{X - \mu}{s}$

$z = \frac{5 - 0}{2.4495}$

$z = 2.04$

Pvalue of the test:

Probability of a sample mean larger than 5, which is 1 subtracted by the pvalue of Z when X = 5.

Looking at the z-table, z = 2.04 has a pvalue of 0.9793.

1 - 0.9793 = 0.0207

As the pvalue of the test is 0.02097 < 0.1, using a .10 significance level, he can conclude that the average trunk diameter of a pine tree is greater than the average diameter of a spruce tree.

8 0

3 years ago

You roll two fair dice, one green and one red. (a) Are the outcomes on the dice independent? Yes No (b) Find P(1 on green die an

navik [9.2K]

Answer:

1) yes ; 2) 1/36 ; 3) 1/36 ; 4) 1/18

Step-by-step explanation:

Given the following :

Two fair dice : 1 green ; 1 red

A) Are the outcomes on the dice independent:

Yes, becomes the outcome of the green dice does not have any effect on the outcome of the red dice.

B) Find P(1 on green die and 5 on red die).

Probability = (number of required outcome) / (total possible outcomes)

Total outcomes of a dice = 6

P(1 on green) = 1 / 6

P(5 on red) = 1/6

P(1 on green die and 5 on red die) :

(1/ 6) × (1/6) = 1/36

C) Find P(5 on green die and 1 on red die)

P(5 on green) = 1/6

P(1 on red) = 1/6

Find P(5 on green die and 1 on red die):

1/6 × 1/6 = 1/36

D) Find P((1 on green die and 5 on red die) or (5 on green die and 1 on red die))

P(5 on green die and 1 on red die) = 1/36

P(1 on green die and 5 on red die) = 1/36

P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)) =

P(5 on green die and 1 on red die) + P(1 on green die and 5 on red die)

= (1/36 + 1/36) = 2 /36 = 1/18

8 0

3 years ago

PLEASE HELP ITS GEOMETRY :OO

Nezavi [6.7K]

Answer:

center of circle: (0,6)

radius: 4

the point (sqrt17,7) is NOT located on this circle. It is outside of the circle. This circle cuts off at (sqrt15,7), therefor (sqrt17,7) is not included

7 0

3 years ago

A triangle with constant base b and height h is changing with time where h(t)=3t +1. What is the rate of change of the area of t

Keith_Richards [23]

The rate of change of the area of the triangle when t=1 is also equal to 3.

<h3>Rate of change</h3>

Given the function of height of a triangle expressed as:

h(t) = 3t + 1

The rate of change is expressed as

dh/dt = 3

The rate of change of the area of the triangle when t=1 is also equal to 3.

Learn more on rate of change here: brainly.com/question/8728504

5 0

2 years ago

What is the slope of a line PARALLEL to the graph? A) -3 B) 0 C) 3 D) -1/3