Answer:
35
Step-by-step explanation:
175/5
Answer:
The median of Group A is greater than the median of Group B.
Step-by-step explanation:
Given
![\begin{array}{cccccccccc}{Group\ A} & 4.5 & 4.8 & 4.6 & 5.0 & 4.8 & 4.4 & 4.7 & 5.2 & 3.9 \ \\ {Group\ B} & 5.5 & 4.9 & 4.0 & 4.2 & 4.8 & 4.1 & 3.5 & 4.6 & 4.3 \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bcccccccccc%7D%7BGroup%5C%20A%7D%20%26%204.5%20%26%204.8%20%26%204.6%20%26%205.0%20%26%204.8%20%26%204.4%20%26%204.7%20%26%205.2%20%26%203.9%20%5C%20%5C%5C%20%7BGroup%5C%20B%7D%20%26%205.5%20%26%204.9%20%26%204.0%20%26%204.2%20%26%204.8%20%26%204.1%20%26%203.5%20%26%204.6%20%26%204.3%20%5C%20%5Cend%7Barray%7D)
Required
Which of the options is true
(a) Group A complete in less time
To do this, we calculate the average of both using:
![\bar x = \frac{\sum x}{n}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B%5Csum%20x%7D%7Bn%7D)
Where
![n = 9](https://tex.z-dn.net/?f=n%20%3D%209)
So, we have:
![\bar x_A = \frac{4.5 + 4.8 + 4.6 + 5.0 + 4.8 + 4.4 + 4.7 + 5.2 + 3.9}{9}](https://tex.z-dn.net/?f=%5Cbar%20x_A%20%3D%20%5Cfrac%7B4.5%20%2B%204.8%20%2B%204.6%20%2B%205.0%20%2B%204.8%20%2B%204.4%20%2B%204.7%20%2B%205.2%20%2B%203.9%7D%7B9%7D)
![\bar x_A = \frac{41.9}{9}](https://tex.z-dn.net/?f=%5Cbar%20x_A%20%3D%20%5Cfrac%7B41.9%7D%7B9%7D)
![\bar x_A = 4.66](https://tex.z-dn.net/?f=%5Cbar%20x_A%20%3D%204.66)
![\bar x_B =\frac{5.5 + 4.9 + 4.0 + 4.2 + 4.8 + 4.1 + 3.5 + 4.6 + 4.3}{9}](https://tex.z-dn.net/?f=%5Cbar%20x_B%20%3D%5Cfrac%7B5.5%20%2B%204.9%20%2B%204.0%20%2B%204.2%20%2B%204.8%20%2B%204.1%20%2B%203.5%20%2B%204.6%20%2B%204.3%7D%7B9%7D)
![\bar x_B =\frac{39.9}{9}](https://tex.z-dn.net/?f=%5Cbar%20x_B%20%3D%5Cfrac%7B39.9%7D%7B9%7D)
![\bar x_B =4.43](https://tex.z-dn.net/?f=%5Cbar%20x_B%20%3D4.43)
<em>The average time of Group A is higher than that of B, this means that Group A spend more time, on average.</em>
<em></em>
(b) Group A has a greater median
First, we sort the given data in ascending order
![\begin{array}{cccccccccc}{Group\ A} & 3.9 & 4.4 & 4.5 & 4.6 & 4.7 & 4.8 & 4.8 & 5.0 & 5.2 \ \\ {Group\ B} & 3.5 & 4.0 & 4.1 & 4.2 & 4.3 & 4.6 & 4.8 & 4.9 & 5.5 \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bcccccccccc%7D%7BGroup%5C%20A%7D%20%26%203.9%20%26%204.4%20%26%204.5%20%26%204.6%20%26%204.7%20%26%204.8%20%26%204.8%20%26%205.0%20%26%205.2%20%5C%20%5C%5C%20%7BGroup%5C%20B%7D%20%26%203.5%20%26%204.0%20%26%204.1%20%26%204.2%20%26%204.3%20%26%204.6%20%26%204.8%20%26%204.9%20%26%205.5%20%5C%20%5Cend%7Barray%7D)
The median is then calculated using:
![Median = \frac{n + 1}{2}th](https://tex.z-dn.net/?f=Median%20%3D%20%5Cfrac%7Bn%20%2B%201%7D%7B2%7Dth)
This gives:
![Median = \frac{9 + 1}{2}th](https://tex.z-dn.net/?f=Median%20%3D%20%5Cfrac%7B9%20%2B%201%7D%7B2%7Dth)
![Median = \frac{10}{2}th](https://tex.z-dn.net/?f=Median%20%3D%20%5Cfrac%7B10%7D%7B2%7Dth)
![Median = 5th](https://tex.z-dn.net/?f=Median%20%3D%205th)
The median is the fifth item for both groups.
So, we have:
![A =4.7](https://tex.z-dn.net/?f=A%20%3D4.7)
![B =4.3](https://tex.z-dn.net/?f=B%20%3D4.3)
4.7 is greater than 4.3
Hence, (b) is true
<em>Since (b) is true and only one option is correct, then (c) and (d) are incorrect</em>
Answer:
![x=5](https://tex.z-dn.net/?f=x%3D5)
Step-by-step explanation:
We have the equation:
![34\cdot 3^{x-2}-2\cdot 3^{x-3}=0.8\cdot 10^{x-2}+10^{x-3}](https://tex.z-dn.net/?f=34%5Ccdot%203%5E%7Bx-2%7D-2%5Ccdot%203%5E%7Bx-3%7D%3D0.8%5Ccdot%2010%5E%7Bx-2%7D%2B10%5E%7Bx-3%7D)
Let's simplify this a bit. Let
. Then
. We can substitute the exponents:
![34\cdot3^u-2\cdot 3^{u-1}=0.8\cdot 10^u+10^{u-1}](https://tex.z-dn.net/?f=34%5Ccdot3%5Eu-2%5Ccdot%203%5E%7Bu-1%7D%3D0.8%5Ccdot%2010%5Eu%2B10%5E%7Bu-1%7D)
Use the properties of exponents, we can write
. We can do the same thing on the right. So:
![34\cdot3^u-2\cdot \frac{3^u}{3}=0.8\cdot 10^u+\frac{10^u}{10}](https://tex.z-dn.net/?f=34%5Ccdot3%5Eu-2%5Ccdot%20%5Cfrac%7B3%5Eu%7D%7B3%7D%3D0.8%5Ccdot%2010%5Eu%2B%5Cfrac%7B10%5Eu%7D%7B10%7D)
We can now factor out a
from the left and a
on the right. This yields:
![3^u(34-2\cdot\frac{1}{3})=10^u(0.8+ \frac{1}{10})](https://tex.z-dn.net/?f=3%5Eu%2834-2%5Ccdot%5Cfrac%7B1%7D%7B3%7D%29%3D10%5Eu%280.8%2B%20%5Cfrac%7B1%7D%7B10%7D%29)
Evaluate the expressions within the parentheses:
![3^u(34-\frac{2}{3})=10^u(\frac{9}{10})](https://tex.z-dn.net/?f=3%5Eu%2834-%5Cfrac%7B2%7D%7B3%7D%29%3D10%5Eu%28%5Cfrac%7B9%7D%7B10%7D%29)
Evaluate:
![3^u(\frac{100}{3})=10^u(\frac{9}{10})](https://tex.z-dn.net/?f=3%5Eu%28%5Cfrac%7B100%7D%7B3%7D%29%3D10%5Eu%28%5Cfrac%7B9%7D%7B10%7D%29)
Now, let's multiply both sides by
. So:
![3^u=10^u(\frac{9}{10})(\frac{3}{100})](https://tex.z-dn.net/?f=3%5Eu%3D10%5Eu%28%5Cfrac%7B9%7D%7B10%7D%29%28%5Cfrac%7B3%7D%7B100%7D%29)
Also, let's divide both sides by
. Multiply on the right:
![\frac{3^u}{10^u}=\frac{27}{1000}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5Eu%7D%7B10%5Eu%7D%3D%5Cfrac%7B27%7D%7B1000%7D)
Therefore:
![3^u=27\text{ and } 10^u=1000](https://tex.z-dn.net/?f=3%5Eu%3D27%5Ctext%7B%20and%20%7D%2010%5Eu%3D1000)
We can now substitute back u. Notice that 27 is the same as 3 cubed and 1000 is the same as 10 cubed. So:
![3^{x-2}=3^3\text{ and } 10^{x-2}=10^3](https://tex.z-dn.net/?f=3%5E%7Bx-2%7D%3D3%5E3%5Ctext%7B%20and%20%7D%2010%5E%7Bx-2%7D%3D10%5E3)
Since they have the same base, their exponents must be equal. Therefore:
![x-2=3](https://tex.z-dn.net/?f=x-2%3D3)
Add 2 to both sides:
![x=5](https://tex.z-dn.net/?f=x%3D5)
So, the value of x is 5.
And we're done!
As long as the equation has a solution of 26, it is fine. Let the solution = 26, and let solution = s
You will have to make a equation, in which when you plug in 26 for solution, it is the answer.
let x = a number
For example:
x - 10 = s
s = 26
x -10 (+10) = 26 (+10)
x = 36
x - 10 = 26, in which x = 36
hope this helps
Answer:
9.055
Step-by-step explanation:
12.7 - 4.705 = 7.995
7.995 + 1.06 = 9.055