Answer:
Amount of material for chain link = 30 feet
Amount of material for rope = 50 feet
Step-by-step explanation:
Let the amount of chain link = X
The amount of rope be represented by Y
He bought a total of 80 feet of materials
Hence we have:
X + Y = 80 ....... Equation 1
Y = 80 - X
The chain-link cost two dollars per foot and the rope cost 1.50 per foot he spent a total of $135
X × $2 + Y × $1.50 = $135
2X + 1.5Y = 135 ......Equation 2
Substitute 80 - X for Y in Equation 2
2X + 1.5(80 - X) = 135
2X + 120 - 1.5X = 135
Collect like terms
2X - 1.5X = 135 - 120
0.5X = 15
X = 15/0.5
X = 30 feet
Substitute 30 feet for X in Equation 1
X + Y = 80 ....... Equation 1
30 + Y = 80
Y = 80 - 30
Y = 50 feet
Hence the amount of material he used for the chain link = 30 feet and the amount of material he used for the rope was = 50 feet
Answer:
Step-by-step explanation:
We will prove by mathematical induction that, for every natural n,
We will prove our base case (when n=1) to be true:
Base case:
As stated in the qustion, 
Inductive hypothesis:
Given a natural n,
Now, we will assume the inductive hypothesis and then use this assumption, involving n, to prove the statement for n + 1.
Inductive step:
Let´s analyze the problem with n+1 stones. In order to move the n+1 stones from A to C we have to:
- Move the first n stones from A to C (
moves). - Move the biggest stone from A to B (1 move).
- Move the first n stones from C to A ( moves).
- Move the biggest stone from B to C (1 move).
- Move the first n stones from A to C ( moves).
Then,
.
Therefore, using the inductive hypothesis,
With this we have proved our statement to be true for n+1.
In conlusion, for every natural n,
Answer:
A
Step-by-step explanation:
Multiply 6 by 2/3 =4... Less than 6
Hello Nitagomez,
To start the numbers 1 through 6 are on a number cube.
Half of them are even, 2, 4, and 6.
So it makes sense that when you roll the cube 60 times, you should have 30 even numbers. The theoretical probability is 30.
A predication of 20 is 10 less than the expected value of 30.
10 out of 30 is 33%.
The predication is off by 33%, I would argue that it is not a very good prediction.
I hope this helps, Good luck!
MrEquation
Answer:
Yes
Step-by-step explanation:
It passes the vertical line test.
if you draw vertical lines, it should hit the function only once, if it hits coordinates with the same x value (for example, (1,2) and (1,3)), it is not a function.
In the graph, each x value is only hit once.
