What transformation is represented by the rule (x, y)→(−y, x)?
1 answer:
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Answer:
1.) .399
2.) {.369, .429}
Step-by-step explanation:
The proportion of criminals in this sample that were caught was =.39944, .399 rounded to three decimal places.
To construct the confidence interval, you need three pieces of information: the statistic, the critical value, and the standard error.
The statistic is given in the first part of the problem with the proportion of criminals in the sample that were caught was .399.
The critical value, we are told, is the z equivalent of 90%, or 1.645. You can find this value using a z table or with the inverse normal function on a calculator.
Finally, we need the standard error. The formula for standard error for a proportion with a single population is so in this situation it would be
=.0183.
The confidence interval would be .399±.018×1.645 or .399±.030 {.369, .429}
Answer:
The intersection is .
The Problem:
What is the intersection point of and
?
Step-by-step explanation:
To find the intersection of and
, we will need to find when they have a common point; when their
and
are the same.
Let's start with setting the 's equal to find those
's for which the
's are the same.
By power rule:
Since implies
:
Squaring both sides to get rid of the fraction exponent:
This is a quadratic equation.
Subtract on both sides:
Comparing this to we see the following:
Let's plug them into the quadratic formula:
So we have the solutions to the quadratic equation are:
or
.
The second solution definitely gives at least one of the logarithm equation problems.
Example: has problems when
and so the second solution is a problem.
So the where the equations intersect is at
.
Let's find the -coordinate.
You may use either equation.
I choose .
The intersection is .