Answer:
the probability is 0.311 (31.1%)
Step-by-step explanation:
defining the event L= being late to work :Then knowing that each mode of transportation is equally likely (since we do not know its travel habits) :
P(L)= probability of taking the bicycle * probability of being late if he takes the bicycle + probability of taking the car* probability of being late if he takes the car  + probability of taking the bus* probability of being late if he takes the bus +probability of taking the train* probability of being late if he takes the train = 1/4  * 0.75 +   1/4 * 0.43 + 1/4  * 0.15  + 1/4 * 0.05 = 0.345
then we can use the theorem of Bayes for conditional probability. Thus defining the event C= Bob takes the car , we have
P(C/L)=  P(C∩L)/P(L) = 1/4 * 0.43 /0.345 = 0.311 (31.1%)
where
P(C∩L)= probability of taking the car and being late
P(C/L)= probability that Bob had taken the car given that he is late
 
        
             
        
        
        
Answer:

Step-by-step explanation:
All right triangles must follow the Pythagorean Theorem  where
 where  is the hypotenuse of the triangle.
 is the hypotenuse of the triangle.
Verify:

 
        
                    
             
        
        
        
It would be 157 that would be the one that makes sense
        
             
        
        
        
Answer:
Step-by-step explanation:
- x( x² - 12x + 21 ) 
 
        
             
        
        
        
Answer: x = -44 
Step-by-step explanation:
1/2(x - 10) =  (x+8)    Apply the distributive property
 (x+8)    Apply the distributive property 
1/2x  - 5 = 3/4x + 6       Add 5 to both sides 
          +5              +5 
   1/2x = 3/4x + 11    Subtract 3/4x  from both sides 
-3/4x       -3/4x 
     -1/4x = 11       Divide both sides by -1/4 
      x =   -44