Answer:

Step-by-step explanation:
Given
Length of string = x inches
Required
Determine the length in yards
Represent the equivalent length with y
Such that

Divide x by 36 to get equivalent in yards


Hence, the equivalent in yards is 
Answer:

Step-by-step explanation:
So we have the two functions:

And we want to find f(g(1)).
So, let's find g(1) first:

Substitute 1 for x:

Simplify:

Add:

So:

Now, substitute 2 for x in f(x):

Multiply:

Add:

So:

Answer:

Step-by-step explanation:
Notice that all three sides of the given triangle has one tick mark.
This means that all three sides are congruent, meaning that we have an equilateral triangle.
And for equilateral triangles, all three angles are also congruent.
So:

Also, recall that the interior angles of a triangle is always 180. Thus:

Substitute:

Combine like terms:

Substitute:

Multiply:

Thus:

And we are done!
Answer:
The probability is
≅ 
Step-by-step explanation:
Let's analyze the question.
There are 15 students in the 8th grade.
The students are randomly placed into three different algebra classes of 5 students each.
We are looking for the probability that Trevor, Terry and Evan will be in the same algebra class.
One possible way to solve this question is to think about the product probability rule.
We can use it because we are in an equiprobable space. (And also the events are independent).
Let's set for example a class for Evan.
The probability that Evan will be in a class is 
Then for Terry there are
places out of
that puts Terry in the Evan's class.
We write 
Finally for Trevor there are
places out of the remaining
that puts Trevor in the same class with Evan and Terry.
Using the product rule we write :

The probability of the event is
≅ 
Answer:
95% Confidence interval: (39.43, 61.58)
Step-by-step explanation:
We are given the following in the question:
Sample mean,
= $50.50
Sample size, n = 15
Alpha, α = 0.05
Sample standard deviation = 20
95% Confidence interval:
Putting the values, we get,
95% Confidence interval: (39.43, 61.58)