If a book about animals has a sale price of $3.50 after a 70% discount is taken, what was the original price?
2 answers:
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Using equivalent angles, the solutions are given as follows:
a) .
b) .
c)
Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.
For item a, we have to find the equivalent angle on the 2nd quadrant, where the sine is also positive.
Hence:
Hence .
For item b, if two angles are complementary, the sine of one is the cosine of the other.
Complementary angles add to 90º = 0.5pi, hence:
The equivalent angle on the second quadrant is:
Hence the solutions are:
For item c, the angles are also complementary, hence:
The tangent is also positive on the third quadrant, hence the equivalent angle is:
Hence the solutions are:
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Answer:
A sample of 1032 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 .
The margin of error is:
A sample of 300 components showed that 20 were defective.
This means that
99% confidence level
So , z is the value of Z that has a pvalue of
, so
.
How large a sample is needed to estimate the true proportion of defective components to within 2.5 percentage points with 99% confidence?
A sample of n is needed.
n is found when M = 0.025. So
Rounding up
A sample of 1032 is needed.