If the alternative hypothesis of an experiment is "The true mean height of children is less than 60 inches," what is the null hy
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Since S is a point on the segment QR, then:
Use the diagram and trigonometric relationships to find the value of QS and QR. Then, use the above equation to solve for SR.
In the right triangle PQS, the side QS is opposite to the angle of 32º, and the side PQ is adjacent to the angle of 32º. Then, use the tangent trigonometric function to relate PQ to QS:
Isolate QS and replace PQ=14:
On the other hand, notice that the side QR in the right triangle PQR is opposite to the angle QPR, which has a measure of 32º+24º=56º.
Then, by a similar reasoning, we can use again the tangent function to find QR:
We have found expressions for QS and QR in terms of trigonometric relationships. Then, we can find an expression for SR:
Replace the expressions for QR and QS:
Use a calculator to find decimal expressions for tan(56º) and tan(32º). Then, find SR:
Therefore, to the nearest tenth, the length of the side SR (or RS, which is the same) is 12.0.
Conditional statement is a statement with a hypotesis and a conclusion:
or mathematically .
Converse statement of is statement
.
If you negate (that means stick a "not" in front of) both the hypothesis and conclusion, you get the inverse:
.
Finally, if you negate everything and flip p and q (taking the inverse of the converse) then you get the contrapositive:
.
Example:
1. Conditional statement: If I am sleeping, then I have closed eyes. (true)
2. Converse statement: If I have closed eyes, then I'm sleeping. (not necessarily true)
3. Inverse statement: If I'm not sleeping, then I haven't closed eyes. (not necessarily true)
4. Contrapositive statement: If I haven't closed eyes, then I'm not sleeping. (true)