First you need to make both bases the same:
Lets remove the ^p and ^4
To make the base of 42 equal to 41, you would have 41^x = 41
X - ln(42) / ln(41) = 1.00648904
Now you have 41^1.00648904(p) = 41^4
Now the bases are equal so we need to set the exponents to equal:
1.00648904(p) = 4
Divide both sides by 1.00648904 to solve for P
P = 4 / 1.00648904
P = 3.97421114
missing letter is 2
missing letter is 3
missing letter is 1
Hope it is helpful to you ☺️
Let the three apartments be A, B & C
The rent of A is $x
The rent of B is $y
The rent of C is $z
So x + y + z = 1600 .......(1)
Now
Maintenance of A is 20% of x = 0.20x
Maintenance of B is 20% of y = 0.20y
Maintenance of C is 25% of z = 0.25z
0.20x + 0.20y + 0.25z = 345
Multiplying by 100 we get
20x + 20y + 25 z = 34500
Dividing by 5 we get
4x + 4y + 5z = 6900 .......(2)
Monthly fee of A is 10% of x = 0.10x
Monthly fee of B is 20% of y = 0.20 y
Monthly Fee of C is 10% of z = 0.10z
Now
0.10x + 0.20y + 0.10 z= 1820 - 1600
0.10x + 0.20y + 0.10z = 220
Multiplying by 100 we get
10x + 20y + 10z = 22000
Dividing by 10
x + 2y + z = 2200 ....(3)
Making a Matrix of equation (1), (2) & (3)
![\left[\begin{array}{ccc}1&1&1\\4&4&5\\1&2&1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}1600\\6900\\2200\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%261%5C%5C4%264%265%5C%5C1%262%261%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1600%5C%5C6900%5C%5C2200%5Cend%7Barray%7D%5Cright%5D%20%20%20)
is the required matrix
Answer:
The population is 4 boxes with each having 30 cables.
Meanwhile the sample size is 1 box and 6 cables.