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dmitriy555 [2]
3 years ago
15

Katherine is a waitress at a restaurant. Each day she works, Katherine will make a guaranteed wage of $20, however the additiona

l amount that Katherine earns from tips depends on the number of tables she waits on that day. From past experience, Katherine noticed that she will get about $7 in tips for each table she waits on. How much would Katherine expect to earn in a day on which she waits on 11 tables? How much would Katherine expect to make in a day when waiting on tt tables?
Mathematics
1 answer:
Norma-Jean [14]3 years ago
5 0
$97.


If Katherine’s wage is $20 the whole day and if she averages about $7 from each table and waits 11, she would get $97. 11 x 7 = 77 + 20 = 97.
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Help please!!!!!!!!!
In-s [12.5K]

ANSWER

24


EXPLANATION

For a matrix A of order n×n, the cofactor C_{ij} of element a_{ij} is defined to be


   C_{ij} = (-1)^{i+j} M_{ij}


M_{ij} is the minor of element a_{ij} equal to the determinant of the matrix we get by taking matrix A and deleting row i and column j.


Here, we have


   C_{11} = (-1)^{1+1} M_{11} = M_{11}


M₁₁ is the determinant of the matrix that is matrix A with row 1 and column 1 removed. The bold entries are the row and the column we delete.


   \begin{aligned} A=\begin{bmatrix} \bf 1 & \bf -6 & \bf -4\\ \bf 7 & 0 & -3 \\ \bf -9 & 8 & -8 \end{bmatrix} \implies M_{11} &= \text{det}\left(\begin{bmatrix} 0&-3 \\ 8&-8 \end{bmatrix} \right)  \end{aligned}


Since the determinant of a 2×2 matrix is


   \det\left(  \begin{bmatrix} a & b \\ c& d  \end{bmatrix} \right) = ad-bc


it follows that


   \begin{aligned} A=\begin{bmatrix} \bf 1 & \bf -6 & \bf -4\\ \bf 7 & 0 & -3 \\ \bf -9 & 8 & -8 \end{bmatrix} \implies M_{11} &= \text{det}\left(\begin{bmatrix} 0&-3 \\ 8&-8 \end{bmatrix} \right) \\ &= (0)(-8) - (-3)(8) \\ &= -(-24) \\ &= 24 \end{aligned}


so C_{11} = M_{11} = 24

4 0
3 years ago
If there are 400 ounces in 25 pounds, how many ounces are in 8 pounds
ladessa [460]
The answer is:  " 128 oz. " . 
_________________________________________________________
There are:  " 128 oz. " (in " 8 lbs." ) .
_________________________________________________________
Explanation:
________________________________________________________
Set up a proportion;  as a fraction; as follows:
________________________________________________________

 400/ 25  = x / 8 ; 

in which:  "x" = the number of "ounces [oz.] there are in "8 lbs." ;
________________________________________________________
We shall solve for "x" , the answer to the problem:

Cross-factor multiply:

25x = (400) * 8 ; 

→ 25x = 3200 ; 

Divide each side of the equation by "25" ; to isolate "x" on one side of the equation; & to solve for "x" ; 

→ 25x / 25 = 3200 / 25 ; 

→  x = 128 .
_________________________________________________________
Answer:  " 128 oz. " . 
_________________________________________________________
There are:  " 128 oz. " (in " 8 lbs." ) .
_________________________________________________________

Note of interest:  " 16 oz. =  1 lb. " (exact conversion). 

So;  "8 lbs.  <span>=  ?</span>  oz. " ; 

→  " 8 lbs. * (16 oz/ 1 lb)  =   ( 8 * 16) oz.  =  128 oz. ;  →  which is our answer!
_________________________________________________________
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It is 1 and one half.
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