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The statement first, and the statement second are correct because the number of dimes is 34, and the number of quarters is 66
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
0.1x + 0.25y = 19.9 and
x + y = 100
Let x = number of dimes
y = number of quarters
After solving the above system of equations by substitution method.
y = 66
x = 34
Thus, the statement first, and the statement second are correct because the number of dimes is 34, and the number of quarters is 66
Learn more about the linear equation here:
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Using the z-distribution, as we are working with a proportion, it is found that samples of 937 should be taken.
<h3>What is a confidence interval of proportions?</h3>A confidence interval of proportions is given by:
In which:
is the sample proportion.
- z is the critical value.
- n is the sample size.
The margin of error is given by:
In this problem, we have that:
- The estimate is of
.
- The margin of error is of M = 0.03.
- 95% confidence level, hence
, z is the value of Z that has a p-value of
, so
.
Then, we solve for n to find the minimum sample size.
Rounding up, it is found that samples of 937 should be taken.
More can be learned about the z-distribution at brainly.com/question/25890103