Find the value of x. #9,10,11,&12
1 answer:
Answer:
Step-by-step explanation:
9). It's given in the triangle → Two angles are equal in measure
Therefore, by the definition of an isosceles triangle, opposite sides of the equal angles are equal in measure.
x = 12
10). Two sides of the given triangles are equal in length.
By the definition of an isosceles triangle, opposite angles of the equal sides of the triangle will be equal in measure.
Therefore, y = 55°
By the triangle sum theorem,
x° + y° + 55° = 180°
x° + 55° + 55° = 180°
x = 180 - 110
x = 70°
11). By the definition of an isosceles triangle, opposite sides of the equal angles will be equal in measure.
x + 3 = 12
x = 9
12). By the definition of an isosceles triangle, opposite angles of the equal sides of the triangle will be equal in measure.
m∠2 = 53°
x + 65 = 53
x = 53 - 65
x = -12
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The standard deviation of the frequency distribution is 5.54
<h3>How to determine standard deviation?</h3>The table of values is given as:
x f(x)
0-3 13
4-7 13
8-11 10
12-15 11
16-19 0
20-23 3
Rewrite the table by calculating the class midpoints:
x f(x)
1.5 13
5.5 13
9.5 10
13.5 11
17.5 0
21.5 3
Start by calculating the mean using:
This gives
Evaluate
The standard deviation is then calculated as:
So, we have:
Evaluate
Solve
Hence, the standard deviation is 5.54
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