1 box = 2 recorders
3 boxes = 6 recorders
5+6 = 11 recorders
Modulo - The result of multiplying the original number by three and the result of multiplying the digits by three must be the same.
What is modulo?
In mathematics, the phrase modulo, which literally means "with respect to a modulus of," is frequently used to claim that two different mathematical objects can be regarded as comparable if their difference is explained by a third component.
Using the Fermat's little theorem:

when x=10. You may easily establish the identity by multiplying it term by word. All terms cancel, excluding the first and last ones. Therefore, any power of ten minus one is divisible by nine, and consequently, by three
Now consider a multi-digit natural number, 43617 for example.


Other than the sum of the digits, every term on the right is divisible by 3. The result of multiplying the original number by three and the result of multiplying the digits by three must be the same.
to learn more about exponents and power visit:
brainly.com/question/19120853
#SPJ4
Answer:

Step-by-step explanation:
I will work with radians.
![$\frac {\cos^2 \left(\frac{\pi}{2}-x \right)+\sin(-x)-\sin^2 \left(\frac{\pi}{2}-x \right)+\cos \left(\frac{\pi}{2}-x \right)} {[\sin(\pi -x)+\cos(-x)] \cdot [\sin(2\pi +x)\cos(2\pi-x)]}$](https://tex.z-dn.net/?f=%24%5Cfrac%20%7B%5Ccos%5E2%20%5Cleft%28%5Cfrac%7B%5Cpi%7D%7B2%7D-x%20%5Cright%29%2B%5Csin%28-x%29-%5Csin%5E2%20%5Cleft%28%5Cfrac%7B%5Cpi%7D%7B2%7D-x%20%5Cright%29%2B%5Ccos%20%5Cleft%28%5Cfrac%7B%5Cpi%7D%7B2%7D-x%20%5Cright%29%7D%20%7B%5B%5Csin%28%5Cpi%20-x%29%2B%5Ccos%28-x%29%5D%20%5Ccdot%20%5B%5Csin%282%5Cpi%20%2Bx%29%5Ccos%282%5Cpi-x%29%5D%7D%24)
First, I will deal with the numerator

Consider the following trigonometric identities:




Therefore, the numerator will be

Once



Now let's deal with the numerator
![[\sin(\pi -x)+\cos(-x)] \cdot [\sin(2\pi +x)\cos(2\pi-x)]](https://tex.z-dn.net/?f=%5B%5Csin%28%5Cpi%20-x%29%2B%5Ccos%28-x%29%5D%20%5Ccdot%20%5B%5Csin%282%5Cpi%20%2Bx%29%5Ccos%282%5Cpi-x%29%5D)
Using the sum and difference identities:





Therefore,
![[\sin(\pi -x)+\cos(-x)] \cdot [\sin(2\pi +x)\cos(2\pi-x)] \implies [\sin(x)+\cos(x)] \cdot [\sin(x)\cos(x)]](https://tex.z-dn.net/?f=%5B%5Csin%28%5Cpi%20-x%29%2B%5Ccos%28-x%29%5D%20%5Ccdot%20%5B%5Csin%282%5Cpi%20%2Bx%29%5Ccos%282%5Cpi-x%29%5D%20%5Cimplies%20%5B%5Csin%28x%29%2B%5Ccos%28x%29%5D%20%5Ccdot%20%5B%5Csin%28x%29%5Ccos%28x%29%5D)
![\implies [p+4] \cdot [p \cdot 4]=4p^2+16p](https://tex.z-dn.net/?f=%5Cimplies%20%5Bp%2B4%5D%20%5Ccdot%20%5Bp%20%5Ccdot%204%5D%3D4p%5E2%2B16p)
The final expression will be

The five number summary data for the data-set is:
<h3>What is the five number summary of a data-set?</h3>
The five number summary of a data-set is composed by:
- The smallest and the greatest value.
- The first quartile, which is the median of the bottom 50%.
- The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.
- The third quartile, which is the median of the upper 50%.
For this problem, we have that:
- The smallest value is of 0.
- The greatest value is of 11.
The data-set has 10 elements, which is an even cardinality, hence the median is the <u>mean of the 5th and the 6th elements</u>, hence:
Me = (5 + 5)/2 = 5.
The first half of the data-set is:
0, 2, 2, 4.
Hence the first quartile is:
Q1 = (2 + 2)/2 = 2.
The second half of the data-set is:
5,5,7,11.
Hence the third quartile is:
Q3 = (5 + 7)/2 = 6.
More can be learned about the five number summary data of a data-set at brainly.com/question/17110151
#SPJ1
I think the answer was 0.18 but I'm not sure so...yeah