Consider the following functions. f={(−4,−1),(1,1),(−3,−2),(−5,2)} and g={(1,1),(2,−3),(3,−1)}: Find (f−g)(1).
fenix001 [56]
Answer:
0
Step-by-step explanation:
Subtraction of functions has the property:
f={(−4,−1),(1,1),(−3,−2),(−5,2)} has (1,1) means that f maps 1 to 1, therefore f(1) = 1
g={(1,1),(2,−3),(3,−1)} has (1,1), means that g maps 1 to 1, therefore g(1)=1
As a Result, since (f−g)(1) = f(1) - g(1), we have (f−g)(1) = 1-1=0
Answer:
The solution is 
Step-by-step explanation:
We need to write everything as a power of 3.
We know that:
So
And
This following property is also important:
To solve, the first step is putting everything with the variable x on one side and everything without the variable x on the other side
This means that:
The mean is the average of a set of numbers.
To find the mean of this data, form a number set by gathering all the numbers.
We need to find the average weekly allowance. To do this, each number in the number set should be the different allowances, and their quantity is the number of students who earned that allowance.
In this case, there would be seven 0s, five 3s, seven 5s, three 6s, and two 8s.
The numbers are:
0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 8, 8
To find the mean of these numbers, add then together then divide by the total amount of numbers.
This means doing:
(0 + 0 + 0 + 0 + 0 + 0 + 0 + 3 + 3 + 3 + 3 + 3 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 6 + 6 + 6 + 8 + 8) / 7 + 5 + 7 + 3 + 2
An easier formula could be used by using multiplication.
This would be [7(0) + 5(3) + 7(5) + 3(6) + 2(8)] / 24
This is a lot easier to read!
Now to solve it.
7 • 0 = 0
5 • 3 = 15
7 • 5 = 35
3 • 6 = 18
2 • 8 = 16
0 + 15 + 35 + 18 + 16 = 84
84 / 24 = 3.5
The mean is 3.5, or $3.50
This means that the average weekly allowance amongst these students is $3.50.
Hope this helps!
