# Tutor profile: Constantinos C.

## Questions

### Subject: Biology

A new hummingbird species is discovered in the Peruvian Amazon in an area known for its avian biodiversity. It is observed to feed only from the flowers of a specific plant species, even if there are dozens of other flowers available. Explain how the species could have evolved to only feed from one type of plant.

This hummingbird species has a specific niche due to natural selection. With many other bird species around, there is a lot of competition for food. Therefore, hummingbirds that are better at feeding from this plant would have an advantage over others of the same species, and would be more likely to reproduce. This means that over time the hummingbird species would be able to create a specific niche and be more successful. By specialising to feed from a specific plant, it has an advantage over other species since it can feed from that type of flower more effectively.

### Subject: Statistics

Andrew complains to Consumer Protection Bureau that he receives much lower internet speeds than promised by a telecommunications company. The company claims the wiring at Andrew's house is to blame. The Bureau wants to test Andrew's claims by checking the internet speed at Andrew's location and three others. State what the hypothesis and the dependent and independent variables are for this scenario. Explain your reasoning and what results you are expecting if Andrew is right.

1) Hypothesis: What we think the results will show. In this case, the hypothesis would be that the internet speed measured is different than the one advertised by the company at all 4 locations, meaning Andrew's specific location is not the reason for the difference in internet speeds. 2) Dependent variable: This is the variable we are testing, which is the internet speed at each location. 3) Independent variable: This is the variable we are manipulating: the location of each test. The speed is measured at 4 different locations to see if the wiring at Andrew's house is responsible. 4) Results: The results we are expecting are 4 speed measurements that are similar between them but lower than what the company claimed. The measurement at Andrew's house should not be significanlty different than the average of the other three.

### Subject: Algebra

If: $$x^{2} - y = 14 $$, and $$2y -4 = 12x$$ What are the values of x and y?

If $$2y -4 = 12x$$, then $$2y = 12x+4$$. We then divide by 2 and we end up with $$y = 6x +2$$. We replace y in the other equation, and instead of $$x^{2} - y = 14 $$ we can write it as $$x^{2} -(6x+2) = 14 $$. We then expand the brackets and move 14 to the left side to equate the equation to 0: $$x^{2} -(6x+2) = 14 $$ -> $$x^{2} -6x-2 = 14 $$ -> $$x^{2} -6x-2 -14 = 0 $$ -> $$x^{2} -6x-16 = 0 $$ If these two sets of brackets equal 0, then that means that one of the two brackets must equal 0. Therefore, x has two possible values, $$x =8$$ and $$x=-2$$. We then substitute these two values of x into the other equation: If $$x=8$$: $$2y = 12x+4$$ -> $$2y = 12(8)+4$$ -> $$2y = 96 +4$$ -> $$2y = 100$$ -> $$y = 50$$ If $$x=-2$$: $$2y = 12x+4$$ -> $$2y = 12(-2)+4$$ -> $$2y = -24+4$$ -> $$2y = -20$$ -> $$y = -10$$ Therefore, the two possible sets of values for x and y are: $$x=8$$, $$y=50$$, and $$x=-2$$, $$y =-10$$

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