You want to determine the effect of soap on bacterial colonies. In order to make sure that the environment does not affect your experiment, you divide 12 different petri dishes in half - one side is exposed to soap, the other is a control. You measure the number of colonies that grow in each petri dish and come up with the following results:

petri dish 1 2 3 4 5 6 7 8 9 10 11 12
soap 10 5 7 10 19 11 13 17 19 8 11 10
control 20 17 11 17 26 18 21 25 24 17 17 1

Perform a complete hypothesis test to see if there is a difference in bacterial colonies between the soap and control dishes.

see explaination

Step-by-step explanation:

A colony can be defined as a visible mass of microorganisms all originating from a single mother cell, therefore a colony constitutes a clone of bacteria all genetically alike. In the identification of bacteria and fungi much weight is placed on how the organism grows in or on media.

See attachment for the step by step solution of the given problem.

Step-by-step explanation:

If we look, "y" can be factored out of the entire expression because it goes into them all. This gives y(2x^3 - 4x^2 + 8x - 16)

Since everything inside the brackets is a multiple of 2 we can factor it out.

2y (x^3 - 2x^2 + 8x - 16)

Here to factor (x^3 - 2x^2 + 8x - 16) we could either use a calculator, or notice that when we subsitute 2 into the equation, it equals 0. Therefore (x - 2) must be a factor. The other factor must be (x^2 + 8) because:

(x - 2) (      )

We need to have 1 x^3 so we know the first part of the factor must be x^2

The also need to have -16 when we multiply this out, -2 * something equals -16. Meaning we must have 8 inside of the brackets.

This gives :

(x - 2) (x^2 + 8).

When we expand this out we get (x^3 - 2x^2 + 8x - 16)

Therefore in total we have

2y (x - 2)(x^2 + 8)

There are other methods of factorising (x^3 - 2x^2 + 8x - 16), so use the method which you have been taught in class or the one I used.