We need to find out how many adults must the brand manager survey in order to be 90% confident that his estimate is within five percentage points of the true population percentage.
From the given data we know that our confidence level is 90%. From Standard Normal Table we know that the critical level at 90% confidence level is 1.645. In other words,
.
We also know that E=5% or E=0.05
Also, since,
is not given, we will assume that
=0.5. This is because, the formula that we use will have
in the expression and that will be maximum only when
=0.5. (For any other value of
, we will get a value less than 0.25. For example if,
is 0.4, then
and thus,
.).
We will now use the formula

We will now substitute all the data that we have and we will get



which can approximated to n=271.
So, the brand manager needs a sample size of 271
Since 25% is 1/4 of 100%, then you do 8/4 and you get 2 and then you do 2 + 8 = 10.
Answer:
a. 
Step-by-step explanation:
The given equation is;

To solve by the x-intercept method we need to graph the corresponding function using a graphing calculator or software.
The corresponding function is

The solution to
is where the graph touches the x-axis.
We can see from the graph that; the x-intercepts are;
(-1,0),(3,0) and (6,0).
Therefore the real solutions are:
