Answer:
See each problem below.
Step-by-step explanation:
1. The 3 streets, North, Center, and South are parallel.
Avenue A is perpendicular to North Street.
That means the angles formed by North Street and Avenue A are right angles. Because of corresponding angles and parallel lines, the angles formed by Avenue A with Center Street and also the angles formed by Avenue A and South Street are also all right angles. That makes those corresponding angles congruent. That makes Avenue A and South Street perpendicular.
2. One angle is corresponding to the 70° angle and also measures 70°. The adjacent angle to the 70° angle is supplementary to it and measures 110°.
70°, 100°
3. Angles ACB and ACD form a linear pair and are supplementary. That means that the sum of their measures is 180°.
m<ACB + m<ACD = 180°
5x + m<ACD = 180
m<ACD = 180 - 5x
4. Angles BCF and CFE are same side interior angles of parallel lines cut by a transversal, so they are supplementary.
m<BCF + m<CFE = 180°
4x + 11x = 180
15x = 180
x = 12
m<BCF = 4x = 4(12) = 48
m<CFE = 11x = 11(12) = 132
m<BCF = 48°
m<CFE = 132°
5.
Angles CFG and DCF are same side interior angles of parallel lines cut by a transversal, so they are supplementary.
m<BCF + m<CFE = 180°
(3x) + (7x + 40) = 180
10x = 140
x = 14
m<CFG = 3x = 3(14) = 42
m<DCF = 7x + 40 = 7(14) + 40 = 138
m<CFG = 42°
m<DCF = 138°
6. See picture below.
7. <AGE, <BEG, <CHG, <DHF
8. If m<AGE = 85°, what is m<CHG?
Answer: Angles AGE and CHG are corresponding angles, so they are congruent.
m<CHG = 85°
A and B are dependent events. This means that the outcome of B affects the outcome of A.
We have that "the probability that A occurs given that B occurs" is symbolized by
P(A|B)
This is what we want to find.
We have that:
P(A): probability that event A occurs.
P(A) = 1/4
P(B): probability that event B occurs.
P(B) = 8/9
P(A&B): probability that both events A and B occurs.
P(A&B) = 1/5
We have that:
Replacing in the equation:
Since,
Then