The length of a rectangular garden is 5m greater than its width. The area of the garden is at least 45m^2. What are the possible
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Answer:
A sample size of 79 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
For this problem, we have that:
The margin of error is:
95% confidence level
So , z is the value of Z that has a pvalue of
, so
.
What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.09?
A sample size of n is needed.
n is found when M = 0.09. So
Rounding up to the nearest whole number.
A sample size of 79 is needed.
Use the definition of absolute value,
If x - 1 ≥ 0, then |x - 1| = x - 1, and so
|x - 1| = 5x + 2
x - 1 = 5x + 2
4x = -3
x = -3/4
Otherwise, if x - 1 < 0, then |x - 1| = -(x - 1), which means
|x - 1| = 5x + 2
-x + 1 = 5x + 2
6x = -1
x = -1/6