The area of a circle is 9π if and only if, its radius is 3. true or false
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Answer:
The student who weighted the rock 5 times has a 95% confidence interval of (25.2, 29.1) which is guaranteed to be more wider (less precise) than the other student who weighted the rock 20 times.
Step-by-step explanation:
What is Confidence Interval?
The confidence interval represents an interval that we can guarantee that the target variable will be within this interval for a given confidence level.
The confidence interval is given by
Where is the mean weight
is the standard deviation
is the critical value from t-table and n is the sample size.
The term is known as margin of error.
As the sample size is decreased the corresponding margin of error increases which results in wider confidence interval which means smaller precision.
The student who weighted the rock 5 times has a 95% confidence interval of (25.2, 29.1) which is guaranteed to be more wider (less precise) than the other student who weighted the rock 20 times.
We can say with 95% confidence that the true mean weight of the rock is within the interval of (25.2, 29.1).
For a two column proof, we want to start with the given information. From there, we will use various definitions, postulates, and theorems to fill in the rest.
Our two sets of given information are that Plane <em>M </em>bisects Line <em>AB </em>and that Line <em>PA</em> is congruent to Line <em>PB</em>.
We know from the definition of a bisector that it splits a line in two equal parts. Therefore, Line <em>AO</em> must be congruent to Line <em>BO</em>.
Now, we have two sides of a triangle that we have proved to be congruent to each other. From the image given in the original problem, we see that both triangles share Line <em>OP. </em>Line <em>OP</em> is congruent to Line <em>OP</em> through the reflexive property.
We now have proven that all three sides of the one triangle are congruent to the corresponding sides on the other triangle. Therefore, the triangles are congruent through the SSS theorem.
Our two sets of given information are that Plane <em>M </em>bisects Line <em>AB </em>and that Line <em>PA</em> is congruent to Line <em>PB</em>.
We know from the definition of a bisector that it splits a line in two equal parts. Therefore, Line <em>AO</em> must be congruent to Line <em>BO</em>.
Now, we have two sides of a triangle that we have proved to be congruent to each other. From the image given in the original problem, we see that both triangles share Line <em>OP. </em>Line <em>OP</em> is congruent to Line <em>OP</em> through the reflexive property.
We now have proven that all three sides of the one triangle are congruent to the corresponding sides on the other triangle. Therefore, the triangles are congruent through the SSS theorem.