The period, phase shift, and vertical shift are; Period is 2π/3, Shift is 4 units to the left and vertical shift is 6 units up.
<h3>How to find waveform properties?</h3>
We are given the waveform equation as;
csc[3(x + 4)] + 6.
Expanding this gives us;
csc[3x + 12] + 6.
Period = 2π/b
From the given waveform, b = 3. Thus;
Period = 2π/3
Phase shift = -c/b
where c from the given waveform is 12. Thus;
Phase shift = -12/3 = -4
Thus, phase shift is 4 units to the left while vertical shift is 6 units upawrds.
Read more about waveform at; brainly.com/question/25699025
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Using the probability concept, it is found that:
P(board-certified or teacher) = 0.8462.
<h3>What is a probability?</h3>
A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>.
Researching the problem on the internet, it is found that:
- There is a total of 10 + 6 + 5 + 18 = 39 professionals.
- Of those, 15 are board-certified, plus 18 that are non-board certified teachers, hence the number of desired outcomes is 33.
Then:
Hence:
P(board-certified or teacher) = 0.8462.
You can learn more about the probability concept at brainly.com/question/15536019
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