<u>Answer:</u>
$6.00
<u>Step-by-step explanation:</u>
To solve this problem, we have to construct two separate equations for each family, and then use any of the methods for solving simultaneous equations.
Let's consider <em>h </em>to represent the cost of 1 hot dog, and <em>w </em>to mean the cost of 1 water bottle.
• For the first family:
We can rearrange the equation to make <em>w</em> the subject:
⇒ 
⇒ 
• For the second family:
Since we have previously obtained an expression for <em>w</em> in terms of <em>h</em>, we can substitute that expression for <em>w</em> in the above equation, and then solve for <em>h</em>:
⇒ 
⇒ 
⇒ 
[Multiplying both sides of the equation by 3]
⇒ 
⇒ 
⇒ 
∴ The price of one hot dog is $6.00.
Answer:
17 times
Step-by-step explanation:
Answer:
4 games played = 1/56
5 games played = 5/56
6 games played = 15/56
7 games played = 35/56
Step-by-step explanation:
The probability of each time winning is 0.5
So there are a couple of ways the series could go.
- Team A could win all first 4 matches. We can depict this as A-A-A-A
- Team A could win 4, while having lost 1. Lets depict this a A-B-A-A-A
- Team A could win 4, while having lost 2. A-B-B-A-A-A
- Team A could win 4, while having lost 3. A-B-B-B-A-A-A
These 4 possibilities could be repeated with B winning as well. It should be noted that these are the only ways for the series to end. We find the number of permutations of each possibility above to find their probability.
I advise you to study 'how to permute identical objects' for this.
These permutations are stated below:
1. 4!/4! = 1
2. 
= 5
3 
= 15
4 
= 35
These are they ways A or B could win. The total is 1+5+15+35 = 56. The answer given thus reflects the possibilities.
