You multiply odd numbers in the following manner

• 1 x 3 = 3

• 1 x 3 x 5 = 15

• 1 x 3 x 5 x 7 = 105

• etc.

The number 12 is exactly divisible by six numbers (i.e. 1, 2, 3, 4, 6, and 12). The number 243 is also exactly divisible by six numbers (i.e. 1, 3, 9, 27, 81 and 243).

There are 16 numbers in the range of 1-100 that are exactly divisible by six numbers (i.e. 12, 18, 20, 28, 32, 44, 45, 50, 52, 63, 68, 75, 76, 92, 98 and 99). How many numbers in the range of 1-20000 are exactly divisible by six numbers?

Given the following set of linear equations:

x₁ + 2x₂ - x₃ = 3

3x₁ - x₂ + 2x₃ = 9

2x₁ + x₃ = 7

What is the value of x₃?

In your workspace, you have 3 corresponding vectors:

• country = a list of countries (e.g. ["Australia", "Malaysia", "Vietnam", "Malaysia", "China", "Australia"....]) in which country names can be repeated, and are not arranged in any order. 
• year = a list of years (e.g. [1901, 1975, 1990, 2001, 1995, 1975, ....]), in which each combination of country and year appears only once.
• population = a list of populations for the corresponding country in the corresponding year (i.e. for the given examples, the first entry of this vector would give Australia's population in 1901)

Write a line of code that will create a variable called "answer", and assign it the population of France in 1972

In order to fit an exponential model, y = Ae^Bx, to a set of data, the points in the dataset first need to be transformed. A linear relationship should be seen when you plot:

Apply a single application of Simpson’s 3/8 rule to evaluate the following integral. What is the output?

What is the approximate value of the following integral using a single application of Simpson’s 1/3 rule?

What is the approximate value of the following integral using two applications of the composite trapezoidal method?