The answer is 45
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Answer:


Step-by-step explanation:
First we define two generic vectors in our
space:


By definition we know that Euclidean norm on an 2-dimensional Euclidean space
is:

Also we know that the inner product in
space is defined as:

So as first condition we have that both two vectors have Euclidian Norm 1, that is:

and

As second condition we have that:


Which is the same:

Replacing the second condition on the first condition we have:

Since
we have two posible solutions,
or
. If we choose
, we can choose next the other solution for
.
Remembering,

The two vectors we are looking for are:

Step-by-step explanation:
Let n be the number of nickels that Casey has.
We are told that Megan has 4 times as many nickels as Casey has, therefore, the number of nickels that Megan has will be 4*n.
Now we will add the amounts of nickels that Casey and Megan have to find the total amount of nickels.

Therefore, the expression
will represent the total number of nickels that Casey and Megan have .
Upon combining like terms we will get,


Therefore, Casey and Megan have 5n nickels.
Answer:
So Sara can fill 24 pint bottles completly with 3 gallons of juice.
Step-by-step explanation:
This question can be solved using a rule of three.
Each pint has 0.125 gallons. How many pints are 3 gallons?
1 pint - 0.125 gallons
x pints - 3 gallons



So Sara can fill 24 pint bottles completly with 3 gallons of juice.
The formula would be I=(37)(.04)(6) which would give you $8.88