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cluponka [151]
3 years ago
9

Find the measure of angles 1–12 in the complex figure. Explain how you found each angle measure.

Mathematics
1 answer:
soldier1979 [14.2K]3 years ago
8 0
I'll start with the triangle figure. 
Interior angles of a triangle is equal to 180°. The given triangle is an Isosceles triangle. It has 2 equal sides and 2 equal angles.

#7 is 69° because its vertical angle is 69°. Vertical angles are equal.
#8 is 111°. As I said, isosceles triangle has 2 equal angles. The angle that is beside #8 is 69°, equal to #7. So, 180° - 69° = 111°
Interior angles are already given except for #4. So, 180° - 69° - 69° = 42°
#3 is computed by 180° - 42° - 69° = 69°

#9 = 116° ; alternate interior angles are equal.
#10 = 180° - 116° = 64°

The last triangle looks like an equilateral triangle. It means that its sides and angles are equal.

360° / 6 = 60°
#1, #2, #5, and #6 = 60° each
#11 = 60° - equilateral triangle, all interior angles are equal.
#12 = 30°; 180° - 90° - 60° =  30°

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A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 6%
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Answer:

a

\% E =  0.9 \%

b

\%E_1 = 10.1 \%

Step-by-step explanation:

From the question we are told that

The probability that an employees suffered lost-time accidents last year is P(e) =  0.06

The probability that an employees suffered lost-time accident during the current year is

P(c) =  0.05

The probability that an employee will suffer lost time during the current year given that the employee suffered lost time last year is

P(c | e) =  0.15

Generally the probability that an employee will experience lost time in both year is mathematically represented as

P(c \ n \ e) =  P(e) *  P(c \ |\ e)

=> P(c \ n \ e) =  0.06*   0.15

=> P(c \ n \ e) = 0.009

Generally the percentage of employees that will experience lost time in both year is mathematically represented as

\% E =  P(e \ n \ c ) * 100

=> \% E =  0.009 * 100

=> \% E =  0.9 \%

Generally the probability that an employee will experience at least one lost time accident over the two-year period is mathematically represented as

P(e \ u \ c) =  P(e) + P(c) - P(e \ n \  c)

=> P(e \ u \ c) =  0.06 + 0.05 - 0.009

=> P(e \ u \ c) =  0.101

Generally the percentage of the employees who will suffer at least one lost-time accident over the two-year period is mathematically represented as

\%E_1 = P(e \ u \ c) *  100

=> \%E_1 = 0.101*  100

=> \%E_1 = 10.1 \%

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