Answer:
1) The range is found by subtracting the minimum data entry from the maximum data entry.
2) It is easy to compute.
3) It uses only two entries from the data set.
Step-by-step explanation:
We are given the following information in the question:
1) Range is difference between the highest value and the lowest value of the data.
- To find the range we first arrange the data in the increasing order and then select the highest and the lowest value of the data, Then the lowest value is subtracted from the highest value to find the range.
Option A) The range is found by subtracting the minimum data entry from the maximum data entry.
2) Advantage of range as a measure of variation.
- Since the method to calculate range of a data set is very easy, it is one of the advantages to use range as a method of variation.
Option B) It is easy to compute.
3) Disadvantage of range to use as a method of variation.
- The disadvantage of using range is that it does not measure the spread of the data set
- It only measures the spread between highest and lowest data points in data set.
Option C) It uses only two entries from the data set.
80,000 per year....there are 12 months in a year
80,000 / 12 = 6666.67 per month
Divide -38 by -5
The negatives cancel out since a negative divided by a negative is a positive.
7.6
Proof by induction
Base case:
n=1: 1*2*3=6 is obviously divisible by six.
Assumption: For every n>1 n(n+1)(n+2) is divisible by 6.
For n+1:
(n+1)(n+2)(n+3)=
(n(n+1)(n+2)+3(n+1)(n+2))
We have assumed that n(n+1)(n+2) is divisble by 6.
We now only need to prove that 3(n+1)(n+2) is divisible by 6.
If 3(n+1)(n+2) is divisible by 6, then (n+1)(n+2) must be divisible by 2.
The "cool" part about this proof.
Since n is a natural number greater than 1 we can say the following:
If n is an odd number, then n+1 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
If n is an even number" then n+2 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
Therefore by using the method of mathematical induction we proved that for every natural number n, n(n+1)(n+2) is divisible by 6. QED.
