what is the equation of a line that passes through the point (1,3) and is parallel to a line with a slope of -2?
1 answer:
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Answer:
X = 45°
Y = 72°
Step-by-step explanation:
There is a supplementary angle (an pair of angles that create a straight line is equal to 180°) and there is the rule that all three angles in a triangle equal 180° as well.
Answer:
So then the minimum sample to ensure the condition given is n= 38
Step-by-step explanation:
Notation
represent the sample mean for the sample
population mean (variable of interest)
represent the population standard deviation
n represent the sample size
ME = 4 the margin of error desired
Solution to the problem
When we create a confidence interval for the mean the margin of error is given by this formula:
(a)
And on this case we have that ME =4 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
The critical value for 96% of confidence interval now can be founded using the normal distribution. The significance is . And in excel we can use this formula to find it:"=-NORM.INV(0.02;0;1)", and we got
, replacing into formula (b) we got:
So then the minimum sample to ensure the condition given is n= 38
Two main facts are needed here:
1. The logarithm , regardless of the base of the logarithm, exists for
.
2. The square root exists for
.
(in both cases we're assuming real-valued functions only)
By (2) we know that exists if
, or
.
By (1), we know that exists if
, or
. But as long as the square root exists, it will always be positive, so this condition will always be met.
Ultimately, then, we only require , so the function has domain
.
To determine the range, we need to know that, in their respective domains, and
increase monotonically without bound. We also know that
at minimum, at which point the square root term vanishes, so the least value the function takes on is
. Then its range would be
.