the following data give the hours spent studying per week by nine students. 12, 16, 7, 22, 11, 18, 7, 25, 16. (a) find the mean,
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The Angle HCA is equal to 52°. This is arrived at using the knowledge of the Total value of Angles in a Triangle and the Total Value of Angles in a Polygon.
<h3>What other principles were used to arrive at the answer?</h3>
The other principles of mathematics that were used to arrive at the above answer are:
- Total Angles on a straight line;
- Total Angles on a point; and
- Line segments.
Step 1 - Recall that we have been given Angles AHB and BAH to be 128° and 28° respectively.
We also know that:
- The sum of angles in a triangle is 180°;...................A
- The sum of angles on a straight line is 180°;.........B
- The sum of angles in a polygon is 360°; while.....C
- The total sum of angles at a point is 360°.............D
Since A...therefore:
When ∠AHB (128°) and ∠BAH are taken from 180° we have DBA = ∠28°.
By observation, we can deduce that ∠BDE, ∠CDH, ∠CEH and ∠AEH are all right-angled triangles.
Using the above, we are able to repeat this process of solving for each angle until we have ∠HCA.
To verify that our answer is correct, recall that sum of angles in a polygon is 360°
That means:
∠BDA + ∠DHE + ∠CEH + ∠HCA = 360°
That is, 90+ 128 + 90 + 52 = 360°
See attached images and;
Learn more about Angles in a Triangle at:
brainly.com/question/25215131
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If the pressure, volume, and temperature are 202650 Pa, 0.004 cubic meters, and 400.15 K. Then the number of the mole is 0.24 mol.
<h3>What is thermodynamics?</h3>It is a branch of science that deals with heat and work transfer.
We know that the Ideal gas equation is given as
PV = nRT
Where
P = Pressure (Pa)
V = Volume (in m³)
n = Number of moles (mol)
R = universal gas constant (8.314 J⋅K⁻¹⋅mol⁻¹)
T = temperature (in K)
We have
P = 2 atm = 202.65 × 10³ Pa
V = 4 liters = 0.004 m³
T = 127 °C = 400.15 K
Then we have
Then the number of the mole will be
More about the thermodynamics link is given below.
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