the employee earned $1813 from Nachos
Explanation:
The theater's popcorn sales is inversely proportional to nacho sales
Let theater's popcorn = P
nacho sales = N
![P\text{ }\alpha\text{ }\frac{1}{N}](https://tex.z-dn.net/?f=P%5Ctext%7B%20%7D%5Calpha%5Ctext%7B%20%7D%5Cfrac%7B1%7D%7BN%7D)
Equating the relationship:
![\begin{gathered} P\text{ = k(}\frac{1}{N}) \\ P\text{ = }\frac{k}{N} \\ \text{where k = constant of proportionality} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20P%5Ctext%7B%20%3D%20k%28%7D%5Cfrac%7B1%7D%7BN%7D%29%20%5C%5C%20P%5Ctext%7B%20%3D%20%7D%5Cfrac%7Bk%7D%7BN%7D%20%5C%5C%20%5Ctext%7Bwhere%20k%20%3D%20constant%20of%20proportionality%7D%20%5Cend%7Bgathered%7D)
when theater sales = $2,254
Nacho sales = $1,628
![\begin{gathered} 2254\text{ =}\frac{k}{1628} \\ k\text{ = 2254(1628)} \\ k\text{ = 3}669512 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%202254%5Ctext%7B%20%3D%7D%5Cfrac%7Bk%7D%7B1628%7D%20%5C%5C%20k%5Ctext%7B%20%3D%202254%281628%29%7D%20%5C%5C%20k%5Ctext%7B%20%3D%203%7D669512%20%5Cend%7Bgathered%7D)
The relationship becomes:
![P\text{ = }\frac{3669512}{N}](https://tex.z-dn.net/?f=P%5Ctext%7B%20%3D%20%7D%5Cfrac%7B3669512%7D%7BN%7D)
When cost of the theater popcorn = $2,024
The cost from nachos = ?
We would use the relationship to get the above:
![\begin{gathered} 2024\text{ = }\frac{3669512}{N} \\ 2024N\text{ = 3669512}18 \\ N\text{ = }\frac{\text{3669512}}{2024} \\ N\text{ = }1813 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%202024%5Ctext%7B%20%3D%20%7D%5Cfrac%7B3669512%7D%7BN%7D%20%5C%5C%202024N%5Ctext%7B%20%3D%203669512%7D18%20%5C%5C%20N%5Ctext%7B%20%3D%20%7D%5Cfrac%7B%5Ctext%7B3669512%7D%7D%7B2024%7D%20%5C%5C%20N%5Ctext%7B%20%3D%20%7D1813%20%5Cend%7Bgathered%7D)
Hence, the employee earned $1813 from Nachos
Answer:
x = 8, and y = 12
Step-by-step explanation:
There are 2 variables, so you need 2 equations to form a system of equations in two variables.
The upper left triangle has all angle measures given: 100, 2x + y, 5x + y. We know that the sum of the measures of the angles of a triangle is 180.
First equation:
100 + 2x + y + 5x + y = 180
Simplify:
7x + 2y = 80 (First equation)
Now we see that the upper and lower sides are parallel, so alternate interior angles are congruent. The angles measuring 2x + y and 5x - y are alternate interior angles and are congruent.
Second equation:
2x + y = 5x - y
Simplify:
3x - 2y = 0 (Second equation)
Now we use the first equation and the second equation as a system of simultaneous equations to solve for x and y.
7x + 2y = 80
3x - 2y = 0
Solve the second equation for 2x.
3x = 2y
Now replace 2y in the first equation with 3x.
7x + 3x = 80
10x = 80
x = 8
Replace x with 8 in the second equation.
3(8) - 2x = 0
24 = 2x
x = 12
Answer: x = 8, and y = 12
Answer:
(MAD) mean absolute deviation: 114.2
Step-by-step explanation:
Mean: 62 + 71 + 83 + 110 + 501 + 94 + 227 = 1,148/7 = 164
164 - 62 = 102
164 - 71 = 93
164 - 83 = 81
164 - 110 = 54
164 - 501 = 337
164 - 94 = 70
164 - 227 = 63
Mean Absolute Deviation: 102 + 93 + 81 + 54 + 337 + 70 + 63 = 800/7 = 114.2
The answer is 43 because when you multiply 6x6 you get 36 and if you add 6 more you get 42 which is one less that 43
Answer:
2,541 minutes
Step-by-step explanation:
i hope this helps