Answer:
0.1333 = 13.33% probability that bridge B was used.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is

In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Arrives home by 6 pm
Event B: Bridge B used.
Probability of arriving home by 6 pm:
75% of 1/3(Bridge A)
60% of 1/6(Bridge B)
80% of 1/2(Bridge C)
So

Probability of arriving home by 6 pm using Bridge B:
60% of 1/6. So

Find the probability that bridge B was used.

0.1333 = 13.33% probability that bridge B was used.
<u>Answer:</u>
Liam will use 3.5 gallons of paint to paint his living room
<u>Solution:</u>
Given that Liam has
gallons of paint.
He uses
of paint to paint his living room
We need to find how many gallons of paint will Liam use
The gallons of paint Liam used can be found as follows:
Amount of paint Liam has =
gallons
Converting mixed fraction
to decimal we get 8.75
Amount of paint used = 2/5th of available amount

Hence Liam will use 3.5 gallons of paint to paint his living room
The angle is sin inverse 0.3535 which is around 21 degrees
Answer: x = 15, ∠K = 45.7°, ∠L = 45.7°, ∠M = 88.6°
<u>Step-by-step explanation:</u>
Since ∠K ≅ ∠L, then ΔKLM is an isoceles triangle with base KL
KM ≅ LM
3x + 23 = 7x - 37
23 = 4x - 37
60 = 4x
15 = x
KM = LM = 3x + 23
= 3(15) + 23
= 45 + 23
= 68
KL = 9x - 40
= 9(15) - 40
= 135 - 40
= 95
Next, draw a perpendicular bisector KN from K to KL. Thus, N is the midpoint of KL and ΔMNL is a right triangle.
- Since N is the midpoint of KL and KL = 95, then NL = 47.5
- Since ∠N is 90°, then NL is adjacent to ∠l and ML is the hypotenuse
Use trig to solve for ∠L (which equals ∠K):
cos ∠L = 
cos ∠L = 
∠L = cos⁻¹ 
∠L = 45.7
Triangle sum Theorem:
∠K + ∠L + ∠M = 180°
45.7 + 45.7 + ∠M = 180
91.4 + ∠M = 180
∠M = 88.6