Answer:
If you go to fill up your car, the amount of gasoline in your tank influences how much you pay. The amount is a volume calculation, regardless of whether you fill up with gallons or liters of gasoline or other fuels. On a lesser scale, when filling a gas can to transfer to another vehicle or utilize the gas to power another device, volume is used to calculate the amount needed.
Hope this helps!
Answer:
x = 
y = 
Step-by-step explanation:
![2x-3y=5\\5x=4y=14\\\\\left[\begin{array}{cc}2&-3\\5&-4\\\end{array}\right] \left[\begin{array}{c}x\\y\\\end{array}\right] =\left[\begin{array}{c}5\\14\\\end{array}\right]](https://tex.z-dn.net/?f=2x-3y%3D5%5C%5C5x%3D4y%3D14%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26-3%5C%5C5%26-4%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D5%5C%5C14%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Let A = ![\\\left[\begin{array}{cc}2&-3\\5&-4\\\end{array}\right]](https://tex.z-dn.net/?f=%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26-3%5C%5C5%26-4%5C%5C%5Cend%7Barray%7D%5Cright%5D)
The inverse of A multiplied by A = the identity matrix ![\left[\begin{array}{cc}1&0\\0&1\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Inverse of A = 
![\left[\begin{array}{ccc}-4&3\\-5&2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%263%5C%5C-5%262%5C%5C%5Cend%7Barray%7D%5Cright%5D)
detA = ad - bc = 
Inverse of A = ![\left[\begin{array}{cc}\frac{-4}{7} &\frac{3}{7} \\\frac{-5}{7} &\frac{2}{7}\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%7B-4%7D%7B7%7D%20%26%5Cfrac%7B3%7D%7B7%7D%20%5C%5C%5Cfrac%7B-5%7D%7B7%7D%20%26%5Cfrac%7B2%7D%7B7%7D%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{cc}\frac{-4}{7} &\frac{3}{7} \\\frac{-5}{7} &\frac{2}{7}\\\end{array}\right] \left[\begin{array}{ccc}5\\14\\\end{array}\right] = \left[\begin{array}{ccc}\frac{22}{7} \\\frac{3}{7} \\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%7B-4%7D%7B7%7D%20%26%5Cfrac%7B3%7D%7B7%7D%20%5C%5C%5Cfrac%7B-5%7D%7B7%7D%20%26%5Cfrac%7B2%7D%7B7%7D%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%5C%5C14%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B22%7D%7B7%7D%20%5C%5C%5Cfrac%7B3%7D%7B7%7D%20%5C%5C%5Cend%7Barray%7D%5Cright%5D)
<u>The correct answers are:</u>
$47.50;
$24.25;
$5.75;
$123.03;
$18;
$59;
Home by $7.50; and
separate rentals.
Explanation:
<u><em>For the first question:</em></u>
Your family purchases 2 adult tickets at $8 each; 2*8=16. You then purchase 1 10-18 ticket for $7.25 and 1 under 10 ticket for $4.25. You then purchase $20 in soda and popcorn. This gives us a total of:
16+7.25+4.25+20=47.50.
<u><em>For the second question:</em></u>
You purchase your ticket for 7.25 and a ticket for each of your siblings at 4.25, which is 2*4.25=8.50. You then purchase $10 in soda and popcorn. This gives us a total of:
7.25+8.50+10=25.75.
The change will be:
50-25.75=24.25.
<u><em>For the third question:</em></u>
5 tickets at $16.85 each would be 5*16.85=84.25.
This gives us
90-84.25=5.75 in change.
<u><em>For the fourth question:</em></u>
7 tickets at $13.79 each will cost 7*13.79=96.53.
The handling for all 7 tickets, at $2.50 each, will be 7*2.50=17.50
These together with the shipping charge will be
96.53+17.50+9=$123.03.
<u><em>For the fifth question:</em></u>
The book of 8 tickets, which cost $5.25 each, will be 8*5.25=$42.
This will give us
60-42=$18 in change.
<u><em>For the sixth question:</em></u>
He has buy one get one free tickets; this means he will buy 3 tickets and get 3 free for the first 6 tickets. He will then need to buy the 7th ticket; this means he will pay for 4 tickets:
4*10.25=$41.
Out of $100, he will have
100-41=$59 in change.
<u><em>For the seventh question:</em></u>
The tickets at Theatre Y cost 8.25*2=16.50. Two drink/popcorn combos at the theatre will cost 4.50*2=9. Together, this is 16.50+9=25.50.
The cost of the dvd rental (4.50), soda (1.50) and popcorn (2.00) at home is 4.50+1.50+2=8. This makes staying at home the cheaper option; it is
25.50-8=$17.50 cheaper.
<u><em>For the eighth question:</em></u>
4 separate rentals will cost 4*3.99=$15.96. This is cheaper than $20.
For question 1: To find the median, order both data values from least to greatest. Then find the middle value.
If there is an even number of values, find the two middle values, add them and divide by 2 to find the median.
