If <em>f(x)</em> is a density function, then its integral over the entire real line should be 1:

so yes, <em>f(x)</em> is indeed a density function.
Answer: m = 32
Step-by-step explanation:
32 divided by 8 = 4
Answer:


Step-by-step explanation:
Given

Solving (a): Expand
To do this, we make use of pascal triangle
When the exponent is 6, the factors are: 1, 6, 15, 20, 15, 6 and 1
As a rule, the exponent of 1 will start from 0 and then increase by 1 in each term while the exponent of 3x will start from 6 and then decrease by 1 in each term.
So, we have:

Expand



Solving (b): (0.97)^6
Rewrite as:

Express -0.03 as 3 * -0.01

So, by comparing:
and 

Recall that:

This gives:

Using a calculator


--- approximated
The 13th term of the geometric sequence is:

<h3>What is a geometric sequence?</h3>
A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:

In which
is the first term.
As a <u>function of the mth term</u>, the nth term can also be given as follows:

In this problem, we have that:

Hence the 17th term is:



More can be learned about geometric sequences at brainly.com/question/11847927
#SPJ1
So in order to get the small rectangle big we need a whole number bigger that 1 or an improper fraction so let's cross out the answer choices that don't meet the above requirements!!
A and C are not improper fractions and are less than 1 so they're wrong!!
We can solve by making an equation,

So 80 × what will give us 500.
We can do this two ways and I'll show you both!!

We can divide both sides by 80 and get,

Which is answer choice B which makes sense since answer choice D is too small.
Or, we can plug in our two answer choices and see if it checks out to be 500!!

The above statement is true!!

The above statement is false since 80 × 5/2 = 200, not 500, the number we need!!