Answer:
![h = \frac{v}{\pi r^2}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7Bv%7D%7B%5Cpi%20r%5E2%7D)
Step-by-step explanation:
You transcribed the equation incorrectly, but that's okay as I do know the correct volume formula. That is:
v = πr²h
In other words, the volume of a cylinder is simply the area of one of its circular ends, multiplied by its length. Now that we have that, let's solve for h:
![v = \pi r^2h\\\\\frac{v}{\pi} = r^2h\\\\\frac{v}{\pi r^2} = h\\\\h = \frac{v}{\pi r^2}](https://tex.z-dn.net/?f=v%20%3D%20%5Cpi%20r%5E2h%5C%5C%5C%5C%5Cfrac%7Bv%7D%7B%5Cpi%7D%20%3D%20r%5E2h%5C%5C%5C%5C%5Cfrac%7Bv%7D%7B%5Cpi%20r%5E2%7D%20%3D%20h%5C%5C%5C%5Ch%20%3D%20%5Cfrac%7Bv%7D%7B%5Cpi%20r%5E2%7D)
So the height of the cylinder can be calculated given the volume and the radius, simply by dividing the volume by pi times the square of its radius.
Answer:
The simplified expression is: 12(7m - 6n)
Step-by-step explanation:
Greatest common factor between 84 and 72
We keep dividing 84 and 72, while they can be divided by the same factor. So
84 - 72| 2
42 - 36|2
21 - 18|3
7 - 6
So the greatest common factor is 2*2*3 = 12.
Rewrite 84m - 72n as a product of two factors
Evidencing 12
![84m - 72n = 12(\frac{84m}{12} - \frac{72n}{12}) = 12(7m - 6n)](https://tex.z-dn.net/?f=84m%20-%2072n%20%3D%2012%28%5Cfrac%7B84m%7D%7B12%7D%20-%20%5Cfrac%7B72n%7D%7B12%7D%29%20%3D%2012%287m%20-%206n%29)
Answer:
-47
Step-by-step explanation:
-8(5)+-7
= -40 -7 (+ gets elimanated by the -)
= -47
Answer:
The value of the test statistic is z = -0.877.
Step-by-step explanation:
Testing the difference in mean time spent on housework between husbands and wives.
At the null hypothesis, we test if there is no difference, that is, the subtraction of the means is 0:
![H_0: \mu_H - \mu_W = 0](https://tex.z-dn.net/?f=H_0%3A%20%5Cmu_H%20-%20%5Cmu_W%20%3D%200)
At the alternate hypothesis, we test if there is a difference, that is, the subtraction of the means is different from 0.
![H_1: \mu_H - \mu_W \neq 0](https://tex.z-dn.net/?f=H_1%3A%20%5Cmu_H%20-%20%5Cmu_W%20%5Cneq%200)
The test statistic is:
![z = \frac{X - \mu}{s}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7Bs%7D)
In which X is the sample mean,
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](https://tex.z-dn.net/?f=%5Cmu%20%3D%200)
For the wives the mean was 7 hours/week and for the husbands the mean was 4.5 hours/week. The standard deviation of the differences in time spent on house work was 2.85.
This means that ![X = 4.5 - 7 = -2.5, s = 2.85](https://tex.z-dn.net/?f=X%20%3D%204.5%20-%207%20%3D%20-2.5%2C%20s%20%3D%202.85)
What is the value of the test statistic for testing the difference in mean time spent on housework between husbands and wives?
![z = \frac{X - \mu}{s}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7Bs%7D)
![z = \frac{-2.5 - 0}{2.85}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B-2.5%20-%200%7D%7B2.85%7D)
![z = -0.877](https://tex.z-dn.net/?f=z%20%3D%20-0.877)
The value of the test statistic is z = -0.877.
Answer:
\csc N = \frac{\text{hypotenuse}}{\text{opposite}}=\mathbf{\frac{25}{24}}
cscN= opposite
hypotenuse = 24/25
Step-by-step explanation: