Based on their observations and the data they collected, the Grants concluded that evolution by natural selection had occurred in the medium ground finch population. The increase in the average beak size of the offspring was a direct result of the change in the food supply during the drought. In order to have reached this conclusion, the Grants must have either assumed or proven that several other facts about the finch population were true. Which statements represent information that must be true in order for the Grants conclusion to be correct?

the correct answer is - d. china has a large and growing population.

the fact that china has a large (the biggest) population, and it is still growing, doesn't hinder the agriculture production in the country. in fact, it can for increased production in the agriculture, since there's more labor force, as well the sheer mass of people produces lots of scientists that come up with new inventions as to how to improve this sector. nice example is the inner mongolia region in china, in general dominated by the gobi desert, but few scientist came up with a nice idea as to how to make the region productive by using plants that are very resistant to droughts, so lots of people have been employed, and the region is becoming greener and greener each year, and the production of food in this region is also increasing.

c. establishing proper sleep hygiene

answer-

the statement that f(x) = |x+a| + b has exactly one x-intercept is sometimes correct.

solution-

it solely depends on b, whether the function will have one or two or zero x intercept.

this plot of the given function, f(x) = |x+a| + b will be the basic absolute value graph i.e v shape, with vertex translated to (-a, b), instead of origin.

1-   if b is zero, the graph will have exactly one x-intercept, at x= -a

2- if b is positive, the whole graph will be above the x-axis, hence it will have no x-intercepts.

3- if b is negative, the graph will be below the x-axis, hence it will have two x-intercepts.

∴ the statement is sometimes true.