Solve the following system of equations: 3x − 2y = 6 6x − 4y = 12 (0, 0) (6, 12) Infinitely many solutions No solutions
2 answers:
<u>Answer:</u>
The correct answer option is: infinitely many solutions.
<u>Step-by-step explanation:</u>
We are given the following system of equations:
--- (1)
--- (2)
Dividing equation (2) by 2 to get:
--- (3)
As the equation (3) is same as the equation (1), therefore the system will have infinitely many solutions.
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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