Answer:
12.57
Step-by-step explanation:
<h3>Answer:
122 degrees</h3>
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Explanation:
Angle BAC can be shortened to "angle A" since the letter A is in the middle.
Angle BCA can be shortened to "angle C" for similar reasoning.
We're told that angles A and C are base angles. For any isosceles triangle, the base angles are congruent
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Let's use this fact to solve for x.
angle A = angle C
7x+1 = 5x+9
7x-5x = 9-1
2x = 8
x = 8/2
x = 4
Once we know what x is, we can find each base angle
- angle A = 7x+1 = 7*4+1 = 28+1 = 29
- angle C = 5x+9 = 5*4+9 = 20+9 = 29
Both angles A and C are 29 degrees each, so this confirms we have the correct x value.
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The last step is to use the fact that all three angles of a triangle add to 180 degrees. This will help us find angle B, which is the vertex angle.
A+B+C = 180
29+B+29 = 180
B+58 = 180
B = 180-58
B = 122
The vertex angle is 122 degrees.
So we can say either angle B = 122, or we could say angle ABC = 122
"angle ABC" is the same as "angle CBA".
Answer:
No, the events "brown hair" and "brown eyes" are not independent.
Step-by-step explanation:
The table that represents the hair and eye colors of thirty students of the fifth grade are given in table as:
Brown hair Blonde hair Total
Green eyes 9 6 15
Brown eyes 10 5 15
Total 19 11 30
No, the events "brown hair" and "brown eyes" are not independent.
Since, two events A and B are said to be independent if:
P(A∩B)=P(A)×P(B)
where P denotes the probability of an event.
Here we have:
A= students having brown hair.
B= students having brown eyes.
A∩B= students having both brown hair and brown eyes.
Now,
P(A)=19/30 (ratio of addition of first column to the total entries)
P(B)=15/30 ( ratio of addition of second row to the total entries)
Also,
P(A∩B)=10/30
Now as:
P(A∩B) ≠ P(A)×P(B)
Hence, the two events are not independent.
