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3 years ago

The volume of a cube is 74088cm3. find the length of each side?

Mathematics

1 answer:

professor190 [17]3 years ago

4 0

It should be 42 if you have a calculator that allows you to cube root 74088

42•42•42 = 74088

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$2 \frac{4}{6}$

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Write an equation that represents the line. (-3,-6) and (2,-2) use exact numbers

Ilia_Sergeevich [38]

Given:

The line passes through (-3,-6) and (2,-2).

To find:

The equation of line.

Solution:

If a line passes through two points $(x_1,y_1)\text{ and }(x_2,y_2)$ , then the equation of line is

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

The line passes through (-3,-6) and (2,-2). So, the equation of line is

$y-(-6)=\dfrac{-2-(-6)}{2-(-3)}(x-(-3))$

$y+6=\dfrac{-2+6}{2+3}(x+3)$

$y+6=\dfrac{4}{5}(x+3)$

$y+6=\dfrac{4}{5}(x)+\dfrac{4}{5}(3)$

Subtract 6 from both sides.

$y=\dfrac{4}{5}(x)+\dfrac{12}{5}-6$

$y=\dfrac{4}{5}(x)+\dfrac{12-30}{5}$

$y=\dfrac{4}{5}(x)+\dfrac{-18}{5}$

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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

The volume of a cube is 74088cm3. find the length of each side?​

The volume of a cube is 74088cm3. find the length of each side?