33 1/3% is the same thing as 0.3 repeated or typically 0.33, and as a fraction it is equivalent to 1/3.
Calculate the average (arithmetic mean) for the data set (rounded to the nearest tenth
1 answer:
The right answer is 19.9
Step-by-step explanation:
Given data set is;
(18, 23, 17, 25, 15, 18, 18, 16, 27, 25, 18, 19)
Sum of terms = 18+23+17+25+15+18+18+16+27+25+18+19 = 239
Number of terms in data set = 12
Average =
Average =
Average = 19.91
The average of data set is 19.91
The right answer is 19.9
Keywords: average, addition
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Part 1
Focus on triangle ABC.
Since AB is a diameter of the circle, this means angle ACB is 90 degrees. Refer to Thale's Theorem. Or you could use the inscribed angle theorem. Thale's theorem is a special case of the inscribed angle theorem.
Minor arc CB is 48 degrees. Use the inscribed angle theorem to see that angle CAB is 48/2 = 24 degrees.
Therefore, angle CBA = 90 - (angle CAB) = 90 - 24 = 66 degrees
<h3>Answer: 66</h3>========================================================
Part 2
Inscribed angle CBA was found to be 66 degrees back in part 1.
This doubles to 132 degrees to represent minor arc AC.
Or you could note that:
minor arc AC = 180 - (minor arc CB) = 180 - 48 = 132
Inscribed angle BCD is 48 degrees. This doubles to 96 degrees when using the inscribed angle theorem, and this is the measure of minor arc CBD.
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Here's what we know about the arc measures of the circle
- minor arc AC = 132 degrees
- minor arc CB = 48 degrees
- minor arc BD = 96 degrees
These three arcs, along with minor arc AD, will add up to get a full 360 degree circle. Check out the diagram below.
Adding those 3 pieces gets us 132+48+96 = 276
This means minor arc AD has to be 360 - 276 = 84 degrees
Then use the inscribed angle theorem one more time to divide the minor arc AD in half to get the inscribed angle ACD
84/2 = 42
<h3>Answer: 42</h3>