Answer:
7.21 units
Step-by-step explanation:
The shortest length needed to connect the house to the existing pipeline is the perpendicular distance between the location of the house (2,9) and the line y = 2/3x - 1.
The perpendicular distance (d) between a point () and the line Ax + By + C = 0 is given as:
The line is given by y = 2/3 x - 1; 2/3x - y - 1 = 0. The point = (2, 9)
hence A = 2/3, B = -1, C = -1, . Therefore:
Using the Fundamental Counting Theorem, it is found that for each case, the total number of outcomes is:
a) 60,466,176.
b) 5,961,600.
<h3>What is the Fundamental Counting Theorem?</h3>It is a theorem that states that if there are n things, each with ways to be done, each thing independent of the other, the number of ways they can be done is:
Item a:
No restrictions, hence for each of the five characters, there are 36 outcomes, hence .
Then, the possible number of passwords is:
Item b:
The letters and the digits have to be alternated, hence:
Then, the possible number of passwords is:
To learn more about the Fundamental Counting Theorem, you can take a look at brainly.com/question/24314866