Answer:
y=6
Step-by-step explanation:
7y+6=18-5y
-5y, -6
2y=12
y=6
Answer:
A. 49
Step-by-step explanation:
The average rate of change for the interval ranging from x = 3 to x = 5 for the given function represented in the table above can be calculated using:

x2 = 5
x1 = 3
f(x2) = f(5) = 125
f(x1) = f(3) = 27
Thus,


Average rate of change = 49
Average rate of change of the given table values representing an exponential function is A. 49.
Answer:
The mean is also increased by the constant k.
Step-by-step explanation:
Suppose that we have the set of N elements
{x₁, x₂, x₃, ..., xₙ}
The mean of this set is:
M = (x₁ + x₂ + x₃ + ... + xₙ)/N
Now if we increase each element of our set by a constant K, then our new set is:
{ (x₁ + k), (x₂ + k), ..., (xₙ + k)}
The mean of this set is:
M' = ( (x₁ + k) + (x₂ + k) + ... + (xₙ + k))/N
M' = (x₁ + x₂ + ... + xₙ + N*k)/N
We can rewrite this as:
M' = (x₁ + x₂ + ... + xₙ)/N + (k*N)/N
and (x₁ + x₂ + ... + xₙ)/N was the original mean, then:
M' = M + (k*N)/N
M' = M + k
Then if we increase all the elements by a constant k, the mean is also increased by the same constant k.
Answer:
Height of the cliff = 13.66 m
Step-by-step explanation:
Let the height of the cliff is 'x' m and distance between the base of the cliff and the boat is 'y' m.
From right triangle AOC,
tan 30° = 

y =
------(1)
From right angle triangle BOC,
tan 45° = 

x = y - 10
y = x + 10 -------(2)
From equations (1) and (2),



x = 13.66 m
Therefore, height of the cliff is 13.66 m.