1.99 ÷ 3 =

Which are true about Figure 1 and Figure 2? Select all that apply.

iogann1982 [59]

Answer:

The figures have the same shape, Corresponding angles have the same measure, Corresponding sides have the same ratio, and The figures are similar.

3 0

3 years ago

A mine elevator was at a depth of -120 feet. After 15 seconds, the mine elevator was at a depth of -30 feet. What expression can

Dafna11 [192]

Answer:

The answers to the given question are:

i. The equipment elevator is at a depth of 176 feet (-176 feet), while the miner's elevator is at a depth of 210 feet (-210 feet) below the surface.

ii. The miner's elevator is deeper than that of the equipment.

The speed of an object is the rate at which the object moves.

i.e. speed =

Thus,

Speed of the equipment elevator = 4 feet per second

Speed of the miner's elevator = 15 feet per second.

Time of descent of the equipment elevator = 30 + 14

= 44 seconds

So that, the distance of the elevator at this time is;

speed =

⇒ distance = speed x time

= 4 x 44

= 176

distance = - 176 feet

The distance of the miner's elevator after 14 seconds is:

speed =

⇒ distance = speed x time

= 15 x 14

= 210

distance = - 210 feet

Thus, after another 14 seconds, the equipment elevator is at a depth of 176 feet (-176 feet), while the miner's elevator is at a depth of 210 feet (-210 feet) below the surface.

Therefore, the miner's elevator is deeper than that of the equipment.

Step-by-step explanation:

done

4 0

1 year 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

what is the area of a triangle if the base is 7 less than 5 times a number and the height is 3 times the number and eight

Flauer [41]

Area of a triangle is half multiplied by the height multiplied by the base.So multiplying the two together and halfing is shown below