(The answer is 12.082.) Juan used 12.082 meters of rope.
        
             
        
        
        
Answer: Kim can mow the greens alone in 6 hours.
Step-by-step explanation:
Let K be the rate Kim mows the greens, and S the rate for Shayla.  The rates K and S will be in greens/hour.
We know they can mow 1 green in 4 hours.  We can state this as a sum of their rates times the 4 hours equals one green:
(4 hours)*(K + S) = 1 green
We are told that K = 2S [Kim is twice as fast as Shayla]
Subsititute:
(4 hours)*(K + S) = 1 green
(4 hours)*(2S + S) = 1 green
4*(2S + S) = 1 green
12S = 1 green
Shalya's rate is 1 green/12 hours
Kim is twice as fast:  K = 2S
Kim's rate is 1 green/6 hours.
 
        
             
        
        
        
Answer:
The probability that no more than 70% would prefer to start their own business is 0.1423.
Step-by-step explanation:
We are given that a Gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than work for someone else.
Let  = <u><em>sample proportion of people who prefer to start their own business</em></u>
 = <u><em>sample proportion of people who prefer to start their own business</em></u>
The z-score probability distribution for the sample proportion is given by;
                                Z  =   ~ N(0,1)
  ~ N(0,1)
where, p = population proportion who would prefer to start their own business = 72%
             n = sample of 18-29 year-olds = 600
Now, the probability that no more than 70% would prefer to start their own business is given by = P(  
  70%)
 70%) 
        P(  
  70%) = P(
 70%) = P(  
  
  ) = P(Z
 ) = P(Z  -1.07) = 1 - P(Z < 1.07)
 -1.07) = 1 - P(Z < 1.07)
                                                                        = 1 - 0.8577 = <u>0.1423</u>
The above probability is calculated by looking at the value of x = 1.07 in the z table which has an area of 0.8577.
 
        
             
        
        
        
Answer:
 (-3,-20)
Step-by-step explanation:
4 +8x = y ...... equation (1)
6x - y = 2 ........equation(2)
from equation 2
6x - y = 2
6x -(4+8x) =2
6x - 4 + 8x = 2
     +4              +4
6x - 8x = 6
-2x=6
divide by -2
x= -3
put x in equation (1) to solve for y
4 + 8x = y
4+8(-3)=y
4-24=y
-20=y 
y= -20
solution = (-3,-20)