You sold 96 adult tickets, 48 child tickets, and 15 senior tickets.
Since you are manning the ticket box for the community theater, and you have sold a total of 201 tickets, and adult tickets to the show cost $ 18, senior tickets cost $ 15, and a child's ticket costs $ 8, and the total amount you have. collected is $ 2967, you also know you have sold twice as many adult tickets as children's tickets, to determine how many of each type of ticket have you sold the following calculation must be performed:
- 100 x 18 + 50 x 8 + 51 x 15 = 2965
- 102 x 18 + 51 x 8 + 48 x 15 = 2964
- 96 x 18 + 48 x 8 + 57 x 15 = 2967
Therefore, you sold 96 adult tickets, 48 child tickets, and 15 senior tickets.
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Since QP and QB are equal the triangle PQB the angles:
![\begin{gathered} \measuredangle QPB=\measuredangle QBP \\ \measuredangle QPB=x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cmeasuredangle%20QPB%3D%5Cmeasuredangle%20QBP%20%5C%5C%20%5Cmeasuredangle%20QPB%3Dx%20%5Cend%7Bgathered%7D)
The last angle can be found by adding all the internal angles and making it equal to 180 degrees.
![\begin{gathered} \measuredangle QPB+\measuredangle QBP+\measuredangle BQP=180 \\ x+x+\measuredangle BQP=180 \\ \measuredangle BQP=180-2x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cmeasuredangle%20QPB%2B%5Cmeasuredangle%20QBP%2B%5Cmeasuredangle%20BQP%3D180%20%5C%5C%20x%2Bx%2B%5Cmeasuredangle%20BQP%3D180%20%5C%5C%20%5Cmeasuredangle%20BQP%3D180-2x%20%5Cend%7Bgathered%7D)
The angle BQP and the angle AQP are suplementary, this means that their sum is equal to 180 degrees. So we have:
![\begin{gathered} \measuredangle AQP+\measuredangle BQP=180 \\ \measuredangle AQP+180-2x=180 \\ \measuredangle AQP=180-180+2x \\ \measuredangle AQP=2x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cmeasuredangle%20AQP%2B%5Cmeasuredangle%20BQP%3D180%20%5C%5C%20%5Cmeasuredangle%20AQP%2B180-2x%3D180%20%5C%5C%20%5Cmeasuredangle%20AQP%3D180-180%2B2x%20%5C%5C%20%5Cmeasuredangle%20AQP%3D2x%20%5Cend%7Bgathered%7D)
Since the sides AP and PQ are equal, then the angle PAQ is equal to AQP.
![\begin{gathered} \measuredangle PAQ=\measuredangle AQP \\ \measuredangle PAQ=2x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cmeasuredangle%20PAQ%3D%5Cmeasuredangle%20AQP%20%5C%5C%20%5Cmeasuredangle%20PAQ%3D2x%20%5Cend%7Bgathered%7D)
To find the last angle on that triangle we can add all the internal angles and make it to 180 degrees.
![\begin{gathered} \measuredangle PAQ+\measuredangle AQP+\measuredangle APQ=180 \\ 2x+2x+\measuredangle APQ=180 \\ \measuredangle APQ=180-4x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cmeasuredangle%20PAQ%2B%5Cmeasuredangle%20AQP%2B%5Cmeasuredangle%20APQ%3D180%20%5C%5C%202x%2B2x%2B%5Cmeasuredangle%20APQ%3D180%20%5C%5C%20%5Cmeasuredangle%20APQ%3D180-4x%20%5Cend%7Bgathered%7D)
The angle APC is suplementary with the sum of the angles APQ and BPQ. So we have:
![\begin{gathered} \measuredangle APC+\measuredangle APQ+\measuredangle BPQ=180 \\ \measuredangle APC+180-4x+x=180 \\ \measuredangle APC=3x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cmeasuredangle%20APC%2B%5Cmeasuredangle%20APQ%2B%5Cmeasuredangle%20BPQ%3D180%20%5C%5C%20%5Cmeasuredangle%20APC%2B180-4x%2Bx%3D180%20%5C%5C%20%5Cmeasuredangle%20APC%3D3x%20%5Cend%7Bgathered%7D)
The sides AP and AC are equal, therefore the angles APC and ACP are also equal.
![\begin{gathered} \measuredangle ACP=\measuredangle APC \\ \measuredangle ACP=3x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cmeasuredangle%20ACP%3D%5Cmeasuredangle%20APC%20%5C%5C%20%5Cmeasuredangle%20ACP%3D3x%20%5Cend%7Bgathered%7D)
Then we can find the last angle on that triangle.
![\begin{gathered} \measuredangle CAP+\measuredangle ACP+\measuredangle APC=180 \\ \measuredangle CAP+3x+3x=180 \\ \measuredangle CAP=180-6x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cmeasuredangle%20CAP%2B%5Cmeasuredangle%20ACP%2B%5Cmeasuredangle%20APC%3D180%20%5C%5C%20%5Cmeasuredangle%20CAP%2B3x%2B3x%3D180%20%5C%5C%20%5Cmeasuredangle%20CAP%3D180-6x%20%5Cend%7Bgathered%7D)
The angle CAB is equal to the sum of CAP and PAQ. So we have:
![\begin{gathered} \measuredangle CAB=\measuredangle CAP+\measuredangle PAQ \\ \measuredangle CAB=180-6x+2x \\ \measuredangle CAB=180-4x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cmeasuredangle%20CAB%3D%5Cmeasuredangle%20CAP%2B%5Cmeasuredangle%20PAQ%20%5C%5C%20%5Cmeasuredangle%20CAB%3D180-6x%2B2x%20%5C%5C%20%5Cmeasuredangle%20CAB%3D180-4x%20%5Cend%7Bgathered%7D)
Since the sides AB and BC are equal, then the angles ACB and CAB must also be equal. We can find the value of x with this.
![\begin{gathered} \measuredangle BAC=\measuredangle ACB \\ 180-4x=3x \\ 7x=180 \\ x=\frac{180}{7} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cmeasuredangle%20BAC%3D%5Cmeasuredangle%20ACB%20%5C%5C%20180-4x%3D3x%20%5C%5C%207x%3D180%20%5C%5C%20x%3D%5Cfrac%7B180%7D%7B7%7D%20%5Cend%7Bgathered%7D)
The value of x is 180/7
Yes you are doing it right because 7*5=35 and 8*3=24.
Answer:
Data warehouse
Step-by-step explanation:
Data warehouse is a technology that combines data from one or more sources so it can be compared for making business decisions.
Moreover, Data warehouse can be explained as a technology that combines from one or more sources so it can be prepared for making business decisions. A data warehouse is constructed by Integrating data from multiple heterogeneous sources that support analytical reporting, and decision making.
Answer:
1
Step-by-step explanation:
note that i =
, thus
i² = (
)² = - 1
= i² × i² = - 1 × - 1 = 1