The triangle Sum Theorem says that the sum of all the angles in a triangle has to equal 180 degrees. Since all three sides (and, consequently, angles) in an equilateral triangle are the same, you can divide 180 by 3 to find the measure of any angle of an equilateral triangle (60 degrees).
Answer:
Step-by-step explanation:
we know that
The value of sine of an angle in a right triangle is equal to the opposite side of the angle divided by the hypotenuse
so
Find the mean ( average):
105 + 104 + 110 + 112 + 114 + 106 + 108 +109 = 868
Mean = 868 / 8 = 108.5
Standard deviation:
108.5 - 105 = 3.5, 3.5^2 = 12.25
108.5 - 104 = 4, 4^2 = 16
110 - 108.5 = 1.5, 1.5^2 = 2.25
112 - 108.5 = 3.5, 3.5^2 = 12.25
114 - 108.5 = 5.5, 5.5^2 = 30.25
108.5 - 106 = 2.5, 2.5^2 = 6.25
108.5 - 108 = 0.5, 0.5^2 = 0.25
109 - 108.5 = 0.5, 0.5^2 = 0.25
12.25 + 16 +2.25 + 12.25 + 30.25 +6.25+0.25+0.25 = 79.75
79.75/8 = 9.96875, SQRT(9.96875) = 3.1573
Standard Deviation = 3.1573
108.8 +/- 1.96 *(3.1573/sqrt(8) = 110.687 and 106.312
110.687 - 108.5 = 2.19
108.5 - 106.312 = 2.19
Margin of error = +/- 2.19
A dozen people is 12. 5 people get off.
12 - 5 = 7
