Answer:
<em>6 days</em>
<em></em>
Step-by-step explanation:
Let the time taken by Carpenter working alone =
days
Then time taken by apprentice alone = Twice as that of taken by Carpenter = 2
days
Time taken working together = 2 days
Work done in one day working together = 
Work done in one day by Carpenter working alone = 
Work done in one day by apprentice working alone = 
Work done in one day by Carpenter working alone + Work done in one day by Carpenter working alone =
+
= Work done in one day working together = 

Time taken by Carpenter alone to complete the work = 3 days
Time taken by Apprentice alone to complete the work = 3
2= <em>6 days</em>
Answer:
The value is 
Step-by-step explanation:
From the question we are told that
The area of the rectangular pen is 
The cost of material used to make one side is 
The cost of material used to make the other sides is 
Now , the fence to be build around the rectangular pen has four sides, the first opposite sides are equal, let assume each of the to be x yard and the other opposite sides are also equal as well let assume of the to be y yard
So the cost is mathematically represented as

=> 
=> 
Now the area of the fence is mathematically represented as

=> 
=> ![C = 9x + 6[\frac{24}{x} ]](https://tex.z-dn.net/?f=C%20%3D%20%20%209x%20%20%2B%20%206%5B%5Cfrac%7B24%7D%7Bx%7D%20%5D)
=> ![C = 9x + [\frac{144}{x} ]](https://tex.z-dn.net/?f=C%20%3D%20%20%209x%20%20%2B%20%20%5B%5Cfrac%7B144%7D%7Bx%7D%20%5D)
Now differentiating


At minimum 
So




Now substituting for x in the equation above to obtain minimum cost
![C = 9(5.66) + [\frac{144}{5.66} ]](https://tex.z-dn.net/?f=C%20%3D%20%20%209%285.66%29%20%20%2B%20%20%5B%5Cfrac%7B144%7D%7B5.66%7D%20%5D)

Answer: A. $4.12
Step-by-step explanation:
Y=a(1+r/n)^nt is the equation we use to solve this.
a= $0.43
t=37 - take 1980 and subtract it from 2017
r= .063 - the 6.3% goes into a decimal
n = 1
Y= ?
Y= 0.43( 1+ .063/1) ^1*37
Y= 0.43 (1.063) ^37
Y= 4.12
Answer:
<k = 20
Step-by-step explanation:
Inscribed Angle = 1/2Intercepted Arc
<K = 1/2 (40)
<k = 20